Datasets:

vgoldberg

/

longform_article_summarization

like 9

recent discoveries of exoplanets with earth - like mass and radius @xcite have intensified debate on how such planets compare to earth in other respects . due to observational bias , many of the discovered exoplanets inhabit short - period , close - in orbits and have effective temperatures exceeding many hundreds of kelvin . for such planets , a likely outcome of dynamical evolution is tidal locking to their parent stars and , most probably , capture into a 1:1 spin - orbit resonance @xcite . synchronous rotation causes asymmetric insolation and , in the absence of a substantial atmosphere , a strong ( 100 s to 1000 s k ) temperature contrast between these planets permanent day and night sides , as has been estimated for corot-7b @xcite and is plausible for kepler-10b @xcite . characterization of exoplanet surfaces is challenging and numerical simulations can help determine possible scenarios . subsolidus convection is likely within the silicate mantles of rocky exoplanets but its vigor and surface expression depend on mantle temperature , composition , and rheology . within the solar system , earth is the only planet that currently exhibits plate tectonics which , on a geologic time scale , regulates volatile species in earth s atmosphere via volcanic outgassing , silicate weathering , and subduction of precipitated carbon @xcite . venus is thought to experience infrequent global - scale resurfacing events , possibly the result of mantle - wide episodic overturn and associated with the formation of a dense greenhouse atmosphere , e.g. , @xcite . mars has experienced recent substantial volcanism although there is no evidence for recent crustal mobility , suggesting a stagnant lid regime with convective activity in the mantle interior below a static single - plate lithosphere , e.g. @xcite . elevated surface temperatures can affect a planet s interior dynamics @xcite and its surface properties , as exemplified by insolation - driven variations of mercury s lithospheric strength @xcite . although there are no examples in our solar system , a hemispheric contrast in surface temperature may influence the interior dynamics and surface expression of exoplanets . here , we investigate the effect of elevated surface temperature and strong surface temperature contrasts for earth - mass planets on ( i ) patterns of mantle convection , ( ii ) tectonic regimes , and ( iii ) the rate and distribution of partial melting ( volcanism ) . for this purpose , we conducted numerical simulations of mantle convection with imposed surface temperatures . we investigated planetary mantle convection through numerical simulations of an incompressible fluid at infinite prandtl number using the classical boussinesq formulation . the associated conservation equations for mass , momentum , and energy are solved numerically using the finite element package citcoms-3.1.1 @xcite . we investigated effective rayleigh numbers @xmath1 in the range @xmath210@xmath3 , where @xmath4 , @xmath5 , @xmath6 , and @xmath7 are the respective reference values for density , gravitational acceleration , thermal expansivity , and thermal diffusivity , @xmath8 is the time - averaged mantle viscosity , @xmath9 is the temperature contrast across the mantle , and @xmath10 is the mantle thickness . bottom and internal heating both contribute to the heat budget . internal radiogenic heat production is uniformly distributed across the mantle domain and constant in time in our models . the non - dimensional internal heat generation rate , defined as @xmath11 @xcite , is set to 11 ; this corresponds to a dimensional heating rate of @xmath12 w kg@xmath13 , close to the present - day chondritic heating rate @xcite . our calculations ignore dissipation of tidal forces that can contribute to mantle heating and thermal runaway , depending on orbital eccentricity and type of resonance @xcite . however , without external perturbations , tidal dissipation renders orbital eccentricity insignificant on myr gyr time scales and tidal effects can be neglected . for the mantle domain , we employ an annulus ( bi - section of a 3-d spherical domain ) that is aligned with the ecliptic plane . all domain boundaries are free - slip and two side boundaries are imposed at the antistellar point . we adopt earth s outer radius ( @xmath14 = 6371 km ) and mantle thickness ( @xmath10 = 2891 km ) , and allocate 257 x 65 nodal points in the lateral and radial directions , respectively , with gradual mesh refinement towards the top and bottom boundaries where temperature variations are generally greatest . to permit plate - like behavior of the surface boundary layer , we adopt a composite viscous / pseudo - plastic rheology in our models , following @xcite . temperature - dependent viscosity @xmath15 is described by an arrhenius - type law : @xmath16,\ ] ] where the reference viscosity is @xmath17 pa s , and @xmath18 is the dimensionless mantle potential temperature that relates to the dimensional temperature , @xmath19 , as @xmath20 , with @xmath9 = 2400 k the potential temperature contrast across the mantle and @xmath21 the surface potential temperature . viscosity changes by 5 orders of magnitude over the considered temperature range ( @xmath22 $ ] ) and generates a lithosphere over a weaker mantle . pseudo - plastic yielding concentrates strain and allows for lithospheric break - up in confined regions that mimic subduction zones and spreading centers @xcite . in regions where the model stress exceeds an assigned yield stress , @xmath23 , a yield viscosity is calculated as @xmath24 , where @xmath25 is the second invariant of the strain rate tensor . the composite rheology is described as @xmath26 . we did not consider strain- or strain - rate - weakening @xcite , or time - dependent damage rheology @xcite , which could further enhance plate - like behavior but would significantly complicate our analysis . we assign distinct temperature conditions for 3 contrasting cases . in a first set ( `` cold '' or c - models ) we apply a uniform , time - constant surface temperature @xmath21 = 273 k , comparable to earth . a second set ( `` hot '' or h - models ) mimics close - in planets ( i.e. , orbital distance of @xmath27 = 0.13 au around a solar mass star ) with efficient heat redistribution and a uniform surface temperature of @xmath21 = 759 k. a third set ( `` asymmetric '' or a - models ) considers planets on a similar close - in orbit that lack heat redistribution . for these models , a high substellar temperature of @xmath28 = 1073 k decreases sinusoidally to the terminus and is kept constant on the night side at @xmath21 = 273 k. for all models , the core - mantle boundary ( cmb ) potential temperature is uniform and constant at @xmath29 = 2673 k. each simulation is run for several billion years ( gyr ) of model time and we exclude the first 1 gyr of initial transients to focus on statistically steady - state behavior . to quantify tectonic regimes , we make use of two previously - defined diagnostics @xcite . first , to quantify the localization of surface strain rates , we define `` plateness '' as @xmath30 , where @xmath31 is the area fraction that encompasses 80% of the total surface strain rate . @xmath32 corresponds to strain localization for isoviscous convection . second , lid mobility @xmath33 is defined as the ratio of the root - mean - square ( rms ) surface flow velocity relative to the rms velocity of the entire mantle domain , @xmath34 . models with plate - like behavior are characterized by @xmath35 and for stagnant lid convection @xmath36 . to allow faster calculations , we made use of the symmetry of the problem and determined tectonic regimes ( section [ sct - res1 ] ) for models of 180@xmath37 opening angle , with side boundaries at the sub - stellar and anti - stellar points . for 4 representative models the time - averaged @xmath38 and @xmath33 values differ by only @xmath39% and @xmath40% , respectively , when comparing models of 180@xmath37 and 360@xmath37 . pressure - release partial melting is calculated following @xcite . we only consider melting in regions where convective flow is upward and where real ( potential + adiabatic ) temperatures exceed the mantle solidus temperature ( @xmath41 ) . for @xmath42 we use a parameterization for dry mantle peridotite with a 1 bar value of @xmath43 k and @xmath44 k km@xmath13 , in rough agreement with experimental measurements ( e.g. , hirschmann 2000 ) . in melting regions , the local melting rate , @xmath45 , is calculated as @xmath46 , where @xmath47 is the degree of melting and @xmath48 is the upward convective flow velocity . we use a constant value @xmath49 km@xmath13 for the adiabatic melt production per kilometer of upwelling @xcite . the local melting rate , @xmath45 , is subsequently integrated over each melt column to give the surficial melt distribution . we limit melt production to a maximum depth of 50 km , which results in a time - averaged melt production for a nominal earth model ( c150 ) consistent with earth s present - day melt production of @xmath50 km@xmath51yr@xmath13 @xcite . our choice of maximum depth affects the total melt production but has a small influence on the comparison between models or on surficial distributions of melt . because side boundaries promote vertical flow and unphysical concentration of melt at the substellar point , we calculate melting from models with a 360@xmath37 opening angle . c - models show a variety of convection regimes for a progressive increase of the yield stress values @xmath23 . at @xmath52 mpa , continuous yielding prevents the formation of stiff surface plates . instead , a mobile lid style of convection , characterized by diffuse surface deformation , occurs ( figure [ fig - convect]a , red curve ) . at @xmath53 mpa , surface deformation is approximately plate - like with stiff surface plates separated by narrow regions of concentrated deformation . surface plates exhibit approximately piecewise constant velocities ( figure [ fig - convect]a , green curve ) and converge toward subduction - like downwellings while diverging at localized spreading centers ( figure [ fig - convect]d ) . a further increase of the yield stress produces a more time - dependent solution with alternating periods of surface mobility and stagnation . for sufficiently high yield stress ( 800 mpa ) , surface mobility diminishes and stagnant lid convection persists ( figure [ fig - convect]a , blue curve ) . to further demonstrate tectonic regimes , we show plateness @xmath38 and mobility @xmath33 in figure [ fig - domainplot ] . for the c - models ( figure [ fig - domainplot]a ) , plateness increases to @xmath54 with increasing yield stress at high mobility ( @xmath55 ) until the lid mobility rapidly decreases ( @xmath36 ) around @xmath56 mpa ( and plateness becomes irrelevant ) . for the h - models , coherent lithospheric plates do not develop because low viscosities near the warm ( @xmath21 = 759 k ) surface promote viscous deformation and suppress pseudo - plastic yielding , consistent with the predictions of @xcite . surface velocities are greater and have a more diffuse distribution than in the c - models ( figure [ fig - convect]b ) . due to increased lithospheric mobility ( e.g. model h150 , figure [ fig - convect]e ) plateness is consistently lower for the h - models ( @xmath57 , figure [ fig - domainplot]b ) compared to the c - models ( @xmath54 , [ fig - domainplot]a ) . as @xmath23 increases , stagnant lid prevails but plate - like behavior is not observed ( figure [ fig - domainplot]b ) . [ h ] @xmath58{f1a } & \includegraphics[width=4.9cm , angle=0]{f1b } & \includegraphics[width=4.9cm , angle=0]{f1c}\\ \includegraphics[width=4.9cm , angle=0]{f1dd } & \includegraphics[width=4.9cm , angle=0]{f1ee } & \includegraphics[width=4.9cm , angle=0]{f1ff}\\ \includegraphics[width=4.9cm , angle=0]{f1gg } & \includegraphics[width=4.9cm , angle=0]{f1hh } & \includegraphics[width=4.9cm , angle=0]{f1ii}\\ & \includegraphics[width=4.9cm , angle=0]{f1j } & \\ \end{array}$ ] 2 for the a - models , a marked ( @xmath59 = 800 k ) temperature contrast causes global - scale asymmetries in tectonic regime . near the substellar point , high surface temperatures induce convective upwelling and diffuse surface velocities ( figure [ fig - convect]c and [ fig - convect]f ) . away from the substellar point , plate - like behavior occurs and surface plates preferentially move toward the antistellar point ( figure [ fig - convect]f ) . a global scale dichotomy is reflected in the tectonic regimes diagnosed separately for the day and night sides ( figure [ fig - domainplot]c ) . the hot day side is consistently characterized by mobile lid convection with diffuse deformation , similar to the h - models , while the cold night side exhibits plate - like behavior for a large parameter space , similar to the c - models ( figure [ fig - domainplot]a ) . [ h ] @xmath60{./f2}\\ \end{array}$ ] flow patterns in the a - models are characterized by convective upwelling near the hot sub - stellar point , near - surface flow from the hot day side to the cold night side where most downwellings occur , and a deep mantle return flow toward the day side ( figure [ fig - convect]f ) . an asymmetric degree 1 pattern of mantle flow persists , with convection cells that occupy the entire half - mantle domain ( figure [ fig - convect]i ) . for the c- and h - models with uniform surface temperature , convective downwellings are more randomly distributed across the domain and this results in less persistent convective flow ( figure [ fig - convect]g and [ fig - convect]h ) . as a diagnostic for persistent mantle flow , we use the rms value of the time - averaged flow velocity normalized by the time average of the rms flow velocities , or @xmath61 , where overlines indicate time - averaged values . the persistent flow in model a150 is reflected by relatively high time - averaged convective flow velocities ( @xmath62 = 0.53 ) , compared to models with a uniform surface temperature , c150 ( @xmath62 = 0.41 ) and h150 ( @xmath62 = 0.43 ) . to estimate the surface temperature contrast @xmath59 that is required for maintaining asymmetric mantle flow , we compare power spectra of time - integrated lateral convective flow velocities for models with different @xmath59 ( figure [ fig - spectra ] ) . for surface temperature contrasts @xmath0400 k , a dominant degree 1 signal reflects persistent convection cells with upwelling at the substellar point and downwelling at the antistellar point . a systematic degree 1 signal is not discernible for models with @xmath59@xmath63400 k and this reflects more randomly oriented convection cells with a richer variety of length scales . [ h ] @xmath64{./f3}\\ \end{array}$ ] for surface temperature contrasts @xmath65400 k , melt rates show an uneven distribution without a coherent global pattern ( figure [ fig - melt]a , green and orange curves ) , and a total melt production similar to the present - day earth value of @xmath220 km@xmath66 yr@xmath13 @xcite ( figure [ fig - melt]b ) . above @xmath67400 k , melt occurs preferentially within upwellings near the hot substellar point ( figure [ fig - melt]a , red and purple curves ) . due to more persistent day side melting , the total melt production rises above the present day earth value by a factor of @xmath25 for @xmath59 = 800 k and @xmath230 for @xmath59 = 1200 k ( figure [ fig - melt]b , red and purple circles , respectively ) . [ h ] @xmath68{./f4}\\ \end{array}$ ] for planets at the same orbital distance , more than double the amount of melt is produced in the model with uniform surface temperature h150 ( figure [ fig - melt]b , blue circle ) than in the asymmetric model a150 ( figure [ fig - melt]b , red circle ) . melting is more vigorous for model h150 because diffuse surface deformation occurs globally , and is less vigorous for model a150 because deformation occurs diffusely only near the substellar point . many recently - discovered exoplanets inhabit close - in orbits and this results in high ( 100 s to 1000 s k ) effective temperatures ( figure [ fig - eptemps ] ) . planets closer than 0.5 au are likely tidally locked ( figure [ fig - eptemps ] , black dotted line ) @xcite and synchronously rotating around their parent stars . at distances of @xmath630.1 au , earth - mass planets are unlikely to retain an atmosphere , due to atmospheric loss either by extreme ultraviolet ( euv ) heating @xcite or stellar wind erosion @xcite ( figure [ fig - eptemps ] , purple dashed curves ) . these boundaries move outward for smaller planets that orbit around larger stars . absence of a substantial atmosphere results in high substellar temperatures , approximated as @xmath69 , and the night side remains cold . thus , hot a - model behavior is expected for close - in orbits , and our results demonstrate that a persistent hemispheric surface temperature contrast @xmath0400 k can maintain a degree 1 pattern of mantle convection in which the planetary surface moves preferentially toward subduction zones on the cold night side . these planets should exhibit an inhospitable day side with vigorous volcanism and a cold night side that allows for more earth - like tectonics and plate - like behavior . melt production increases with increasing surface temperature contrast , and at 0.13 au the calculated total melting rate is @xmath25 times higher than for a cool planet at 1 au where plate tectonic behavior occurs globally ( c - models ) . at intermediate distances ( @xmath20.1 au ) , an atmosphere is more likely to persist and atmospheric redistribution of heat is expected to produce a uniform hot surface . for such planets , our h - model results demonstrate that mobility of the lithosphere prevents the formation of coherent plates and the emergence of earth - like plate tectonics . compared to an asymmetric model at the same orbital distance , melt production is enhanced by a factor @xmath702 , and occurs globally across a surface that is characterized by diffuse deformation . our results suggest the possbility of different feedback mechanisms.volcanic outgassing is responsible for the formation of secondary planetary atmospheres . therefore , asymmetric conditions can only be sustained if the atmosphere is continuously eroded . if , instead , an atmosphere is retained , heat redistribution promotes mobile lid convection with diffuse deformation and further increases global volcanic outgassing . this suggests a positive feedback in favor of a thick atmosphere , unless another mechanism modifies the atmospheric balance . for example , no melt production is calculated for one - plate model planets , a possibility for potential close - in equivalents of present - day venus . atmospheres would be unprotected against solar wind erosion if a magnetodynamo is deactivated due to a transformation from plate tectonics to a regime that is less efficient at cooling the mantle and core @xcite . substantial atmospheric loss would allow for a negative feedback and such planets could fluctuate between symmetric and asymmetric end- member scenarios or reach an intermediate equilibrium , depending on the timescale of atmospheric loss relative to mantle thermal evolution . the dependence of tectonic regimes on @xmath23 for our nominal earth models is consistent with previous studies performed using 2-d cartesian , 3-d cartesian , and 3-d spherical geometries @xcite . as in the above - mentioned studies plate - like behavior occurs at yield stresses lower than classical estimates for dry oceanic lithospheric strength by up to @xmath21000 mpa @xcite , but weak fault zone fabric may account for this discrepancy @xcite . the weak dependence of tectonic regimes on @xmath71 shown in figure [ fig - domainplot]a is in agreement with numerical results of @xcite and scaling laws of plate tectonic convection by @xcite . because a higher @xmath71 is expected for more massive planets , this low sensitivity to @xmath71 suggests that our results can be applied to planets of various sizes . convection in massive `` super - earth '' mantles may be influenced by their more extreme pressure and temperature conditions . for example , mineral physics calculations suggest a viscosity decrease of 2 to 3 orders of magnitude for the deep mantles of super - earths @xcite , in favor of vigorous convective overturn . high mantle pressure allows for mineral phase transformations that do not occur in earth s mantle @xcite but which can strongly influence the dynamics of super - earth mantles @xcite . although important questions remain , our simulations demonstrate the strong influence that surface temperature contrasts exert on mantle convection , surface tectonics , and volcanism for close - in rocky exoplanets . distinct scenarios are likely associated with variations in albedo , volcanism , and atmospheric content that may become astronomically detectable in the future . 1 batalha , n. m. et al . 2011 , apj , 729 , 1 bercovici , d. 1996 , epsl , 144 , 41 borucki , w .- j . 2011 , arxiv , 1102.0541v2 buffett , b. a. 2002 , grl , 29 , 1555 b@xmath72hounkova , m. tobie , g. , choblet , g. & @xmath73adek , o. 2011 , apj , 728 , 89 christensen , u. 1984 , epsl , 64 , 153 christensen u. r. & tilgner , a. 2004 , nature , 429 , 168 correia , a. c. m. & laskar , j. 2010 , in exoplanets , ed . s. seager ( tuscon , az : univ . arizona press ) , 526 escartin , j. , andreani , m. , hirth , g. & evans , b. 2008 , epsl , 268 , 463 foley , b. j. & becker , t. w. 2009 , g3 , 10 , q08001 gaidos , e. , conrad , c. p. , manga , m. & hernlund , j. 2010 , apj , 718 , 596 glatzmaier , g. a. 1988 , gafd , 43 , 223 hirschmann , m. m. 2000 , g3 , 1 , 2000gc000070 howard , a. w. et al . 2010 , science , 330 , 653 karato , s .- i . 2011 , icarus , 212 , 14 kasting , j. f. , whitmire , d. p. , reynolds , r. t. , 1993 , icarus , 101 , 108 kohlstedt , d. l. , evans , b. & mackwell , s. j. 1995 , jgr , 100 , 15587 korenaga , j. 2010a , jgr , 115 , b11405 korenaga , j. 2010b , apj , 725 , l43 lammer , h. , kasting , j. f. , chassefi@xmath74re , e. , johnson , r. e. , kulikov , y. n. & tian , f. 2008 , ssr , 139 , 399 . l@xmath75ger , a. et al . 2009 , a&a , 11933 , 1 lenardic , a. , jellinek , a. m. & moresi , l .- n . 2008 , epsl , 271 , 34 mayor , m. et al . 2009 , a&a , 507 , 487 mckenzie , d. & bickle , m. j. 1988 , j. petrol . , 29 , 625 moore , d. e. & rymer , m. j. 2007 , nature , 448 , 7155 moresi , l. & solomatov , v. 1998 , gji , 133 , 669 phipps morgan , j. 2001 , g3 , 2 , 2000gc00049 raddick , m. j. , parmentier , e. m. & schreier , d. s. 2002 , jgr , 107 , doi:10.1029/2001jb000617 richards , m. a. , yang , w .- s . , baumgardner , j. r. & bunge , h .- p . 2001 , g3 , 2 , 2000gc000115 solomon , s. c. , bullock , m. a. & grinspoon , d. h. 1999 , science , 286 , 87 spohn , t. et al . 2001 , ssr , 96 , 231 tackley , p. j. 2000a , g3 , 1 , 2000gc000036 tackley , p. j. 2000b , g3 , 1 , 2000gc000043 tian , f. 2009 , apj , 703 , 905 turcotte , d. l. & schubert , g. 2002 , geodynamics , 2nd ed . ; cambridge university press umemoto , k. , wentzcovitch , r. m. & allen , p. b. 2006 , science , 311 , 983 van den berg , a. p. , yuen , d. a. , beebe , g. l. , christiansen , m. d. 2010 , pepi , 178 , 136 van heck , h. j. & tackley , p. j. 2008 , grl , 35 , l19312 walker , j. c. g. , hays , p. b. & kasting , j. f. 1981 , jgr , 86 , 9776 williams , j .- p . , ruiz , j. , rosenburg , m. a. , aharonson , o. & philips , r. j. 2011 , jgr , 116 , e01008 zhong , s. , zuber , m. t. , moresi , l.n . & gurnis , m. 2000 , jgr , 105 , 11063

recently discovered exoplanets on close - in orbits should have surface temperatures of 100 s to 1000 s of k. they are likely tidally locked and synchronously rotating around their parent stars and , if an atmosphere is absent , have surface temperature contrasts of many 100 s to 1000 s k between permanent day and night sides . we investigated the effect of elevated surface temperature and strong surface temperature contrasts for earth - mass planets on the ( i ) pattern of mantle convection , ( ii ) tectonic regime , and ( iii ) rate and distribution of partial melting , using numerical simulations of mantle convection with a composite viscous / pseudo - plastic rheology . our simulations indicate that , if a close - in rocky exoplanet lacks an atmosphere to redistribute heat , a @xmath0 400 k surface temperature contrast can maintain an asymmetric degree 1 pattern of mantle convection in which the surface of the planet moves preferentially toward subduction zones on the cold night side . the planetary surface features a hemispheric dichotomy , with plate - like tectonics on the night side and a continuously evolving mobile lid day side with diffuse surface deformation and vigorous volcanism . if volcanic outgassing establishes an atmosphere and redistributes heat , plate tectonics is globally replaced by diffuse surface deformation and volcanism accelerates and becomes distributed more uniformly across the planetary surface . 2[. ]

perinatal stroke leads to congenital hemiparesis [ 16 ] ; however , these children may also have neurocognitive deficits , language impairment , behavioral disorders , and epilepsy [ 24 , 714 ] . previous outcome studies of perinatal stroke have been mainly focused on an isolated clinical function : either motor function [ 1 , 2 , 4 , 7 , 9 , 15 ] or cognitive function [ 3 , 5 , 8 , 1316 ] . perinatal ischemic stroke is a group of heterogeneous conditions in which there is a focal disruption of the cerebral blood flow secondary to arterial or venous thrombosis or embolization during the perinatal period . based on clinical - radiographical findings , there are two main subtypes of perinatal stroke : arterial ischemic stroke ( ais ) and periventricular venous infarction ( pvi ) [ 3 , 4 , 9 , 18 ] . the ais involves arterial occlusion mostly in the middle cerebral artery ( mca ) territory [ 3 , 4 , 9 , 18 ] , comprising large areas in the parietal , temporal , and frontal cortex and/or in the basal ganglia including the corticospinal tract . the pvi , in contrast , comprises purely subcortical areas , predominantly the periventricular white matter , but also other parts of the descending corticospinal tract [ 3 , 9 ] . in both types of vascular injury , damage of the corticospinal tract leads to hemiparesis [ 1 , 2 , 6 ] . previous data about long - term cognitive development mostly apply to children with perinatal ais [ 710 , 13 , 14 , 16 ] ; however , results vary to a great extent . cognitive deficit in children with presumed pvi has received less attention and these children are usually investigated together with children with presumed ais [ 4 , 7 , 14 ] . task - based functional magnetic resonance imaging ( fmri ) is used to investigate separate functions like motor and language [ 20 , 21 ] functions in stroke children . the fmri has revealed the functional plasticity of the brain in the case of focal brain damage in perinatal stroke patients [ 19 , 21 ] . however , task - based studies present several challenges for stroke patients , including motor task - related motion artifacts , inconsistent performance , mirror movements , or individual ability to perform the task altogether . furthermore , although structural damage from stroke is focal , remote dysfunction can occur in regions connected to the area of lesion . resting - state fmri ( rs - fmri ) is acquired in the absence of a task , which allows exploring the global functional organization of the brain and how it is altered in brain damage . it is now well established that many resting - state networks ( rsn ) are robust , that is , consistent across subjects , and involve the sensory ( visual , auditory , and somatosensory ) and motor regions of the brain , as well as a number of associative control networks ( default , dorsal stream , frontoparietal , and ventral stream ) [ 24 , 25 ] . a framework based on connectivity and neural communication across the brain regions provides us with a view of the brain as organized in an ensemble of functional networks in adults [ 25 , 26 ] and in children [ 27 , 28 ] . however , there exist differences in functional connectivity in global rsn between infants and young children , on one hand , and adults , on the other , which are due to brain developmental progression in regional and network specialization [ 28 , 29 ] . during childhood , changes occur in the hierarchical and regional organization of brain connectivity , and functional connections between distant regions become stronger with advancing maturation . the process of network maturation appears to be parallel with the progress of behavioral maturation and sensorimotor development precedes the development of the systems underlying higher cognition . furthermore , certain networks , such as the default mode network ( dmn ) , are only slightly functionally connected in childhood but increase in connection strength over time until they are fully developed by adulthood . thus , an early childhood stroke that affects immature connections might have a stronger impact on functional reorganization compared to a stroke that affects more mature networks . the relationship between functional connectivity , sensory deficits , and structural abnormality remains poorly understood . however , to our knowledge , rs - fmri data for children with stroke are limited and refer only to the somatosensory system . have investigated rs - fmri in perinatal stroke patients with cortical and periventricular lesions and demonstrated a relationship between functional connectivity and somatosensory impairment . children who had lesions in the mca territory displayed significantly less functional connectivity in the somatosensory cortex than children with periventricular lesions . recently , a small group of children with spastic cerebral palsy and another group of hemiplegic cerebral palsy after cortical and subcortical damage were investigated with rs - fmri without data about the vascular origin of the damage . saunders found differences in the motor network in patients with perinatal ais and pvi compared to controls and suggested that in these children extensive plasticity in the brain occurs after experiencing a stroke , which consequently has an effect on the functional connections between the areas of the brain at rest . there were also significant differences in plasticity between the ais and pvi groups , suggesting that the functional reorganization of the motor function is different in each of these groups . the aim of the study was to identify differences in resting - state networks and cognitive development in children with perinatal ais and pvi and to compare the obtained data with the corresponding data for healthy controls . the estonian pediatric stroke database contains data for 80 children with perinatal stroke , initially collected for an epidemiological study ( 19942003 ) and prospectively updated through 2015 . all radiological images in estonia are archived in a single all - estonian picture archiving system . of the 80 children with perinatal stroke , those with neonatal sinovenous thrombosis ( n = 4 ) , neonatal hemorrhagic stroke ( n = 7 ) , or inadequate magnetic resonance imaging ( n = 2 ) were excluded . ischemic stroke was classified as ais or pvi using the criteria based on a previous study by kirton and coworkers and modified by ilves and coworkers [ 3 , 21 ] . patients were only considered eligible for our preliminary study when ( a ) they had documented unilateral left - hemisphere ais or pvi ( for the sake of homogeneity in the study as perinatal stoke affects more often the left side according to previous studies ) but also in our database ( 68% ) ; ( b ) they were aged 717 ; and ( c ) they were able to remain still for about 45 minutes without sedation and to follow instructions during the mri investigation . of the 67 patients with perinatal ischemic stroke , 22 had unilateral left - side pvi and 24 had unilateral left - side ais . the parents were contacted by phone and were asked to participate in the outcome study . also , the parents were enquired about the child 's ability to undergo the mri investigation without sedation ; otherwise only studies of cognitive and motor outcome were applied . eleven children with pvi , 10 children with ais , and 25 ages and sex matched healthy voluntary controls without contraindications for mri agreed to participate in the rs - fmri investigation . the control children were recruited from among children of the hospital staff members and their acquaintances and from among their classmates and friends attending regular school without learning difficulties . written informed consent was obtained from the parents and from the children aged seven years or older for participation in the study in accordance with the declaration of helsinki . the study was approved by the ethics review committee on human research , university of tartu ( protocol no . one child ( 1/11 ) with pvi , three with ais ( 3/10 ) , and six controls ( 6/25 ) were excluded from the analysis due to artifacts in the acquired mri sequences or due to a shorter than planned investigation time . the final rs - fmri analysis included 36 children , among them 10 with pvi ( age range 7.615.9 years , 3 boys ) , 7 with ais ( age range 10.417.4 years , 5 boys ) , and 19 age and sex matched controls ( age range 8.117.9 years , 9 boys ) without significant differences in age or sex between the groups . the individual demographic and neuroimaging data of the children with pvi and ais are presented in table 1 . all children with pvi had been symptom - free after birth and had received the diagnosis of presumed perinatal stroke after 28 days of life . four children with ais were diagnosed after birth and three were diagnosed beyond the neonatal period ( presumed ais ) . clinical evaluation of stroke patients was made by pediatric neurologists ( r l , s l ) according to pediatric stroke outcome measurement ( psom ) . the psom is a disease - specific outcome measure for children with stroke and comprises 115 test items . it yields a deficit severity score ranging from 0 to 2 ( 0 : no deficit , 0.5 : mild deficit , normal function , 1 : moderate deficit , impaired function , and 2 : severe deficit , missing function ) for five subscales : right sensorimotor , left sensorimotor , language production , language comprehension , and cognitive / behavioral performance . hemiparesis was diagnosed in children who had abnormal tone and reflexes associated with moderate or severe sensorimotor impairment ( impaired or missing function ) , that is , hemiplegic cerebral palsy and congenital hemiparesis . cognitive performance was evaluated by a clinical psychologist ( m. m. ) who was blinded to the data for the stroke vascular subgroup or any rs - fmri data , using the kaufman assessment battery for children , second edition ( k - abc ii ) . the battery comprises ( a ) fluid - crystallized index , a general measure of cognitive ability that includes acquired knowledge ; ( b ) mental - processing index , a measure of mental processing ability that excludes measures of acquired knowledge ; and ( c ) nonverbal index , a general measure of nonverbal abilities . in addition , standard scores for five subscales ( sequential and simultaneous processing , learning , planning , and knowledge ) are provided . the range of possible scores is from 40 to 160 ( mean 100 , sd 15 ) . ischemic lesions were classified by the location and extent as described earlier [ 3 , 22 ] . among the children with pvi , five had small periventricular white matter damage in one lobe ( patients ( 1 ) to ( 5 ) ) , one child had unilateral ventricular enlargement ( patient ( 6 ) ) , and four had large left - side periventricular porencephalic damage involving the periventricular area in several lobes ( patients ( 7 ) to ( 10 ) ) ( figure 1 ) . among the children with ais , there were two with a cortical stroke involving one lobe only ( patients ( 11 ) and ( 12 ) ) and five with a large cortical stroke involving several lobes and/or basal ganglia ( patients ( 13 ) to ( 17 ) ) ( figure 2 ) . all arterial strokes were located in the mca region : two in the proximal mca territory , two in the distal mca territory , and two in the posterior trunk of mca and one in the anterior trunk of mca ( table 1 ) . there were no differences in the size of stroke ( defined by involvement of one or several lobes ) between the pvi and the ais children ( p = 0.33 ) ( table 1 ) . the mri data were acquired with the philips 3-t achieva mr scanner using the 8-channel sense head coil 3.0t/8ch ( philips medical systems , best , the netherlands ) . the scans were performed without sedation or medication ; the participants were asked to stay awake and keep their eyes open . the scans were acquired using a fixed imaging protocol after the acquisition of an anatomical scan . the t1 weighted slices of the whole head were obtained using a 3d fast field echo sequence ( tr = 8.2 ms , te = 3.8 ms ) , with a field of view of 256 256 mm and an isotropic voxel size of 1 mm . to describe resting - state activity in the brain , 120 volumes of 50 axial t2-weighted slices of the whole head were acquired using a fast field echo single shot epi - bold sequence ( tr = 3000 ms , te = 35 ms ) , with a field of view of 230 230 mm and a voxel size of 3 mm isotropic . the rs - fmri data were visually inspected for motion and other imaging artifacts ; entire scans were excluded from further analysis or , when possible , the scan was rescheduled . during motion correction , the maximum calculated absolute mean displacement was 0.78 mm and the maximum relative mean displacement was 0.29 mm . the analysis of rs - fmri was made by a single investigator ( n. i. ) who was blinded to any clinical information or to the results of the cognitive tests , using the multivariate exploratory linear decomposition into independent components ( melodic ) tool , version 3.14 employing fsl from the fmrib software library ( https://www.fmrib.ox.ac.uk/fsl/ ) . the following preprocessing workflow consisted of the following steps : ( a ) discarding of the first 2 volumes from each subject for signal stabilization ; ( b ) motion correction using mcflirt ; ( c ) brain extraction of bold images ; ( d ) spatial smoothing with fwhm 6 mm ; ( e ) high - pass temporal filtering for 150 seconds . blood - oxygen level dependent ( bold ) volumes were registered to the t1 weighted structural volumes with 6 degrees of freedom using a boundary - based registration algorithm . subsequently , the structural images were registered to the mni-152 standard space with 12 degrees of freedom ( t1 standard brain averaged over 152 subjects ; montreal neurological institute , montreal , qc , canada ) [ 41 , 42 ] . the data of the resting - state functions for both the study and control groups were temporarily concatenated and analyzed using probabilistic independent component analysis ( pica ) . the components were visually evaluated and compared to previous literature data [ 24 , 25 , 27 , 4345 ] and 13 out of the 30 components were identified as anatomically and functionally relevant separate resting - state networks . the other 17 components reflected artifacts . the criteria for inclusion were signal within a low frequency range of 0.10.01 hz [ 46 , 47 ] , location of connectivity patterns mainly in gray matter , and presence of coherent voxel clusters . the subject - specific statistical maps of all rsn were created using a dual - regression tool from the fmrib software library [ 24 , 49 ] to test for differences in the identified components between the ais , pvi , and control groups . subsequently , groupwise comparison of rsn was carried out using a randomized , permutation - testing tool version 2.9 from fsl . for each resting - state network , threshold - free cluster enhancement ( tfce ) was performed . the resulting statistical maps were thresholded at p 0.05 and at p 0.01 ( tfce corrected for familywise errors ) for revealing group main effects . inference was only carried out on the subject specific z - maps of 13 relevant rsns . between - group effects were thresholded controlling for local false discovery rate ( fdr ) at q 0.1 to reduce susceptibility to type 1 errors when testing multiple resting - state networks . statistical evaluation was performed with the statistical package sas version 9.1 ( sas institute inc , cary , nc ) . prior to further analysis , normality of the data was evaluated using the kolmogorov - smirnov criterion . to compare the proportions , the chi - square test and fisher 's exact test ( when the expected values were < 5 ) were used . the nonparametric mann - whitney u - test was employed to compare the groups of ais and pvi . values are presented as means with the 95% confidence interval . the alpha level used to determine significance is p < 0.05 . the clinical findings and the data of cognitive functions for the children with pvi and ais are presented in tables 1 and 2 and the radiological findings are presented in figures 1 and 2 . the children with ais had significantly higher total psom scores compared to the children with pvi ( p = 0.0486 ) . all children had mild to severe sensorimotor deficit . however , 4/7 ( 57% ) of the children with ais and 8/10 ( 80% ) of the children with pvi had moderate to severe hemiparesis ; the difference between the pvi and ais groups was not statistically significant ( p = 0.59 ) . most children with ais ( 5/7 , 71% ) and only one child ( 1/10 , 10% ) with pvi had cognitive deficit according to psom ( p = 0.035 ) . according to the kaufman assessment battery for children , the children with ais received significantly lower scores ( figure 3 ) in all three general ability indexes than the children of the pvi group : fci ( mean 79.7 versus 99.2 , p = 0.013 ) , mpi ( mean 81.1 versus 97.7 , p = 0.017 ) , and nvi ( mean 84.4 versus 105.3 , p = 0.022 ) . the pvi group outperformed the ais group also in the subscale scores , while the results were significantly better for the children with pvi in simultaneous information processing ( mean 102.3 versus 78.6 ; p = 0.015 ) and in planning ability ( mean 110.2 versus 85.7 ; p = 0.017 ) . the children with ais performed significantly lower than the controls in all general ability and subscale indexes , except for learning . the overall cognitive development of the children with pvi in our study remained roughly within a normal range . however , children with pvi got lower results , compared to the control group in one general ability score ( fci ) , and in two subscales ( simultaneous and sequential information processing ) ( figure 3 ) . none of the 10 pvi children had epilepsy ; however , 5/7 children in the ais group had epilepsy and received antiepileptic medication ( p = 0.0034 ) . such networks have been described in previous studies using a similar methodology for adults [ 2426 , 51 ] and for children according to the present study , the networks were stable across the participants of the ais , pvi , and control groups . all of these 13 networks were found with independent pica analysis for each of the pvi , ais , and control groups . testing of the main effects of the group on the subject specific z - maps of these networks ( all p 0.05 and also p 0.01 tfce corrected for familywise errors ) showed significantly increased functional connectivity in the posterior and anterior components of dmn and in the task positive and medial temporal networks in the patients with ais ( p < 0.01 ) , compared to the controls . these networks , except for the anterior component of dmn ( p < 0.05 ) , were even increased in ais compared to pvi ( p < 0.01 ) , corrected for familywise errors . however , after fdr correction ( local fdr - corrected at q 0.1 ) , significantly increased functional connectivity was only found in the dmn posterior component in the left periventricular area of the ais patients versus the controls ( figure 5 ) . the control group showed increased functional connectivity in the primary visual , salience , task positive , cerebellum , and sensorimotor networks compared to the ais group ( p < 0.01 ) ; however , after fdr corrected analysis at q 0.1 , the difference was not significant . the pvi group showed increased functional connectivity in the medial visual , auditory , salience , ventral stream , and cerebellum networks compared to the patients with ais ( p < 0.01 ) ; however , after fdr corrected analysis at q 0.1 level , the difference was not significant . there were no statistical differences between the children of the pvi and control groups in rsn . we report differences in the rs - fmri networks and cognitive functions in children with left - hemisphere perinatal stroke of different vascular origin . more severe dysfunctions in the rs - fmri rsn networks and cognitive functions occurred in the ais compared to the pvi children . these results provide a preliminary insight into large - scale brain network dysfunction that may be the underlying cause of the various motor , cognitive , and behavioral problems in patients with perinatal stroke . the children with ais had significantly higher psom scores compared to the pvi children . depending on vascular origin , different pathogenetic mechanisms behind ais and pvi are responsible for the location of brain damage and outcome [ 3 , 4 ] . in ais , cortical - subcortical involvement is the most prominent location of damage ; in pvi , the main location of damage is the periventricular white matter while the cortical areas are spared . however , the corticospinal tract is often damaged , although in different locations , in the case of both types : 2460% of cases in ais [ 1 , 2 ] and up to 80% of cases in pvi . we found that although motor outcome was similar in children from both the ais and pvi groups , the measures of cognitive ability based on k - abc - ii scores were lower in ais compared to pvi . an earlier study by westmacott and coworkers also suggested that motor function was not linearly related to cognitive outcome and psom motor scores were not correlated with iq measures . some studies suggest , however , that overall cognitive development in perinatal stroke falls roughly within a normal range [ 10 , 1315 ] , although children with pvi and ais are often studied in one group . ricci and coworkers have found that only one - third of children show cognitive deficit after perinatal stroke . in some other studies , children with neonatal ais have significantly lower scores for working memory and processing speed compared to the normative population . this is also the case with the measures of general cognitive ability , verbal functioning , inhibitory control and working memory , or the measures affecting complex cognitive skills as abstract reasoning . our data confirmed that , according to k - abc - ii , the children of the ais group had significantly lower scores for general ability than the children of the pvi group . in addition , the former were less successful in the tasks that required higher cognitive abilities such as planning or simultaneous visual processing . cognitive problems in the children with pvi , all with presumed stroke , were less pronounced and only 1 of the 10 children in the study group had some mild cognitive problems . in an earlier study investigating both presumed stroke with ais and pvi , the proportion of children with presumed perinatal stroke who had cognitive or behavioral deficits was 29% . as in our study , the children with pvi had less behavioral and visual deficits than the children with a large proximal mca stroke but they had more spasticity than the children with stroke in the anterior trunk of mca . however , adverse cognitive and behavioral outcomes were more strongly correlated with cortical involvement compared to periventricular involvement in presumed perinatal stroke . we found significant global derangements in the cognitive networks at rs - fmri and in the cognitive function tests in the children with ais compared to the pvi and control groups . global neural network dysfunction can serve as a possible basis for derangements of complex cognitive functions and behavior as has also been reported in earlier stroke outcome studies [ 4 , 10 , 14 ] . the rsn of the children with pvi was not different from the corresponding measures for the control group . large - scale networks were identified in which the patients with ais showed significantly increased functional connectivity , compared to the controls and the children with pvi , in the posterior precuneus part and the anterior frontal part of dmn , in the medial temporal component of dmn , and in the task positive network ( p < 0.01 ) . these networks were even increased in ais compared to pvi ( p < 0.05 ) . however , after fdr correction , significantly increased functional connectivity was only found in posterior precuneus part of dmn in the ais children compared to the controls . the dmn is deactivated during demanding cognitive tasks and is involved in episodic memory processes and self - referential mental representations . earlier studies have found that most networks in children , in particular those supporting the basic motor function and sensory related processing , had a robust functional organization similar to mature adult patterns [ 27 , 28 , 43 ] . in contrast , dmn and the other rsn involved in the higher - order cognitive functions had immature characteristics , revealing incomplete and fragmented patterns , which indicates less developed functional connectivity , in infants aged 5 to 8 years and even at the age of 1013 years . a major difference between adults and children is the decomposition of dmn into several independent subsystems in children , composed of the bilateral posterior cingulate , the precuneus , the inferior parietal cortex , and the ventromedial prefrontal cortex , which are associated with the medial temporal regions [ 27 , 29 ] . at the same time , the posterior precuneus region of the dmn network serves as the main hub within dmn . the dmn has been found to be only weakly functionally connected in childhood but increases in connection strength over time . therefore , an early childhood stroke that affects immature connections might have a stronger impact on functional reorganization than a stroke that affects more mature networks . however , there exists also the hypothesis that damaged areas continue to support the performance of tasks involving them and the typical functional connections of these regions play an important role in preservation of normalcy after early perinatal stroke . in our study significant changes in dmn and especially in the posterior precuneus part of dmn , which is the main hub within dmn , were found in the children with ais who had also serious cognitive problems . also , were found in the ais and control children some derangements of the task positive network , which is part of the attention control networks . have generally immature characteristics in young age groups . cortical involvement of damage in ais compared to pvi with mainly periventricular damage can explain differences in network dysfunction . increased connectivity of the networks outside the region of primary damage ( dmn ) can be a compensatory effect occurring after cortical brain damage in children with ais due to brain 's plasticity ; in this case areas outside the lost tissue take over its functions . a similar finding the prefrontal regions , both ipsi- and contralateral to the lesion , were activated in patients but not in controls after language and visual search tasks , which may compensate for lost functions according to task - based fmri . such contralateral activation of the language function is seen more often in younger stroke patients before the age of 2 years . it is unknown whether the frontal task - based networks are activated due to alternative or compensational strategies . the small number of rs - fmri examinations of perinatal stroke could limit the statistical power and generalizability of the study results . still , our preliminary data were available for 10 children with pvi , which is close to the 12 cases of presumed pvi reported in a previous clinical - radiological study by kirton and coworkers . although significant differences both in cognitive function and in the global networks were found in the children with ais versus pvi , more clinical and rs - fmri data , especially for right hemisphere strokes , would be needed to evaluate the predictive value of rs - fmri results for establishment of cognitive deficit in these children . on our stroke database and in the cohort of this study , the children with ais had significantly more often epilepsy compared to the children with pvi . epilepsy per se and/or antiepileptic treatment may have had an impact on the cognitive ability of the former . earlier studies have also found that seizures are more frequent in children with cortical damage compared to periventricular damage in presumed perinatal stroke . cognitive impairments with lower performance in the intellectual and language measures have been found in children with perinatal stroke associated with seizures [ 4 , 10 , 11 , 13 , 15 ] . although there were no gender differences in our stroke group compared to the controls , there were more boys in the ais group , which could also influence the cognitive outcome . males with perinatal stroke performed tests significantly more poorly than a matched group of females in overall intellectual ability and in reading and processing speed [ 7 , 14 ] . it should be noted that as about 60% of the children with pvi in the estonian perinatal stroke database are female , it was difficult to recruit male subjects with pvi to the study . also , we had to exclude from the study the most severe cases when the mother thought that the child would not be able to follow instructions and stay still during mri without sedation . this could have diminished the statistical power of the rs - fmri data for the ais children . however , most of such cases were encountered in the ais group with bilateral asymmetrical involvement . our findings demonstrate differences in the cognitive function and in the neural network profile of children with hemiparesis with left - side ais compared to children with left - side pvi and controls matched for age and sex . the study shows that as the location of damage is different in children with ais and pvi , also the resting - state networks and cognitive outcome are different in these groups and children with ais and pvi should not be analyzed together in outcome studies . changes in the resting - state networks found in children with ais could possibly serve as an underlying dysfunction of cognitive brain functions in perinatal stroke patients . in order to better understand the value of derangements in the brain networks in perinatal stroke patients with cognitive and behavioral problems , it is important to promote early diagnosis , treatment , and rehabilitation of these children , to improve their quality of life , as well as the quality of life of their families .

perinatal stroke is a leading cause of congenital hemiparesis and neurocognitive deficits in children . dysfunctions in the large - scale resting - state functional networks may underlie cognitive and behavioral disability in these children . we studied resting - state functional connectivity in patients with perinatal stroke collected from the estonian pediatric stroke database . neurodevelopment of children was assessed by the pediatric stroke outcome measurement and the kaufman assessment battery . the study included 36 children ( age range 7.617.9 years ) : 10 with periventricular venous infarction ( pvi ) , 7 with arterial ischemic stroke ( ais ) , and 19 controls . there were no differences in severity of hemiparesis between the pvi and ais groups . a significant increase in default mode network connectivity ( fdr 0.1 ) and lower cognitive functions ( p < 0.05 ) were found in children with ais compared to the controls and the pvi group . the children with pvi had no significant differences in the resting - state networks compared to the controls and their cognitive functions were normal . our findings demonstrate impairment in cognitive functions and neural network profile in hemiparetic children with ais compared to children with pvi and controls . changes in the resting - state networks found in children with ais could possibly serve as the underlying derangements of cognitive brain functions in these children .

SECTION 1. CONVEYANCE OF LAND COMPRISING SUBTROPICAL HORTICULTURE RESEARCH STATION. (a) Definitions.--In this section: (1) County.--The term ``County'' means Miami-Dade County in the State of Florida. (2) Property.--The term ``Property'' means approximately 2 acres, more or less, of the federally owned land comprising the Subtropical Horticulture Research Station in the County, which-- (A) has been mutually delineated by the Secretary and the authorized representative of the County; and (B) fronts on SW 67th Avenue in Palmetto Bay, Florida. (3) Secretary.--The term ``Secretary'' means the Secretary of Agriculture. (b) Property Conveyance.-- (1) In general.--Not later than 120 days after the date on which the County deposits the consideration under paragraph (2) and cost reimbursement provided in this section with the Department of Agriculture, the Secretary shall convey and quitclaim to the County, all rights, title, and interests of the United States in the Property, subject to easements and rights of record and such other reservations, terms, and conditions as the Secretary may prescribe. (2) Consideration.-- (A) In general.--As consideration for the conveyance of the Property, the County shall pay to the Secretary an amount in cash equal to the market value of the property. (B) Appraisal.--To determine the market value of the Property, the Secretary shall have the Property appraised for the highest and best use of the Property in conformity with the Uniform Appraisal Standards for Federal Land Acquisitions developed by the Interagency Land Acquisition Conference. The approved appraisal shall at all times be the property of the United States. (3) Corrections.--With the agreement of the County, the Secretary may make minor corrections or modifications to the legal description of the Property. (4) Costs.-- (A) Transaction costs.--Except as provided in subparagraph (C), the County shall, at closing for the conveyance of the Property under this section, pay or reimburse the Secretary, as appropriate, for the reasonable transaction and administrative personnel costs associated with the conveyance authorized by this section, including the transaction costs of appraisal, title, hazardous substances examination, and closing costs. (B) Administrative costs.--In addition to transaction costs under subparagraph (A), the County shall pay administrative costs in the liquidated amount of $50,000. (C) Attorneys' fees.--The County and the Secretary shall each bear their own attorneys' fees. (5) Survey.--The County shall, at its cost, survey the exterior boundaries of the Subtropical Horticulture Research Station and the Property in accordance with Federal survey standards and to the satisfaction of the Secretary, and shall provide to the Secretary certified originals with signature and raised seal. (6) Release.--The County, by a recordable instrument that the Secretary determines is satisfactory, shall release the Department of Agriculture from the instrument dated September 8, 2006, titled ``Unity of Title''. (7) Security fencing.--On or before closing for the conveyance of the Property under this section, the County shall, at its cost, contract for the construction of a security fence located on the boundary between the Property and the adjacent land administered by the Secretary. The fence shall be of materials and standards approved in advance by the Secretary. The Secretary may approve temporary security structures for use during construction phases of the fence. (8) Other terms.--The Secretary and the County may otherwise effect the purpose of this section on such additional terms as are mutually acceptable and which are not inconsistent with the provisions of this section. (c) Receipts.-- (1) In general.--The Secretary shall deposit all funds received from the conveyance authorized under this section, including the market value consideration and the reimbursement for costs, into the Treasury of the United States to be credited to the appropriation for the Agricultural Research Service. (2) Use of funds.--Notwithstanding any limitation in applicable appropriation Acts for the Department of Agriculture or the Agricultural Research Service, all funds deposited into the Treasury pursuant to subsection (b) shall be available to the Secretary until expended, without further appropriation, for the operation, upkeep, and maintenance of the Subtropical Horticulture Research Station.

Directs the Secretary of Agriculture (USDA) to convey to Miami-Dade County, Florida, federally owned land comprising the Subtropical Horticulture Research Station in Miami-Dade County, Florida. Directs the County to pay specified costs.

mass transfer between components of close binaries is a common evolutionary phase for many astrophysically interesting binary systems . indeed , mass ejection and/or accretion is responsible for many of the most recognizable phenomena associated with close binaries , such as persistent or transient x - ray emission , neutron star spin - up , and orbital contraction or expansion . theoretical considerations of these and other associated phenomena in the literature probe these systems quite effectively , yet they often do not consider the effects of any eccentricity associated with the binary orbit . this can be of particular importance for binaries containing a neutron star or a black hole , where mass loss and natal kicks occurring during compact object formation may induce a significant eccentricity to the binary ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? after the formation of the compact object , tides tend to circularize the orbit on a timescale which strongly depends on the ratio of the radius of the compact object s companion to the orbital semi - major axis . because of this , orbits are usually assumed to circularize instantaneously when a binary approaches or begins a mass transfer phase . despite our generally well developed understanding of tidal interactions in close binaries , quantitative uncertainties in tidal dissipation mechanisms propagate into the determination of circularization timescales . for example , @xcite have shown that current theories of tidal circularization can not explain observed degrees of circularization of solar - type binaries in open clusters . circularization of high - mass binaries , on the other hand , is currently thought to be driven predominantly by resonances between dynamic tides and free oscillation modes , but initial conditions play an important role and an extensive computational survey of relevant parts of the initial parameter space has yet to be undertaken @xcite . furthermore , assumptions of instantaneous circularization immediately before or at the onset of mass transfer are in clear contrast with observations of eccentric mass transferring systems . in the most recent catalog of eccentric binaries with known apsidal - motion rates compiled by @xcite , 26 out of the 128 listed systems are semi - detached or contact binaries . among these mass - transferring systems , @xmath1 have measured eccentricities greater than @xmath2 . in addition , many high - mass x - ray binaries are known to have considerable orbital eccentricities @xcite . while mass transfer in these systems is generally thought to be driven by the stellar wind of a massive o- or b - star , it has been suggested that some of them may also be subjected to atmospheric roche - lobe overflow at each periastron passage of the massive donor ( e.g. * ? ? ? @xcite , @xcite , and @xcite were the first to study the effects of mass transfer on the orbital elements of eccentric binaries . however , their treatment was restricted to perturbations of the orbital motion caused by the variable component masses . @xcite extended these early pioneering studies to include the effects of linear momentum transport from one star to the other , as well as any other possible perturbations caused by the mass transfer stream in the system . however , these authors derived the equations governing the motion of the binary components with respect to a reference frame with origin at the mass center of the binary , which is not an inertial frame . their equations therefore do not account for the accelerations of the binary mass center caused by the mass transfer ( see [ sec - appb ] ) . more recent work on mass transfer in eccentric binaries has mainly focused on smoothed particle hydrodynamics calculations of the mass transfer stream over the course of a few orbits , without any consideration of the long - term evolution of the binary @xcite . hence , there is ample observational and theoretical motivation to revisit the study of eccentric mass - transferring binaries . in this paper , our aim is to derive the equations governing the evolution of the orbital semi - major axis and eccentricity in eccentric mass - transferring binaries , assuming conservation of total system mass and orbital angular momentum . in a subsequent paper , we will incorporate the effects of mass and orbital angular momentum losses from the system . our analysis is based on the seminal work of @xcite who was the first to derive the equations of motion of the components of eccentric mass - transferring binaries while properly accounting for the effects of the variable component masses on the stars mutual gravitational attraction , the transport of linear momentum from one star to the other , the accelerations of the binary mass center due to the redistribution of mass in the system , and the perturbations of the orbital motion caused by the mass - transfer stream . while the equations of motion derived by @xcite are valid for orbits of arbitrary eccentricity , the author restricted the derivation of the equations governing the evolution of the semi - major axis and eccentricity to orbits with small initial eccentricities . the paper is organized as follows . in 2 and 3 we present the basic assumptions relevant to the investigation and derive the equations governing the motion of the components of an eccentric mass - transferring binary under the assumption of conservative mass transfer . the associated equations governing the rates of change of the semi - major axis and the orbital eccentricity are derived in 4 , while numerical results for the timescales of orbital evolution due to mass transfer as a function of the initial binary mass ratio and orbital eccentricity are presented in 5 . for comparison , timescales of orbital evolution due to dissipative tidal interactions between the binary components are presented in 6 . 7 is devoted to a summary of our main results and a discussion of future work . in the appendices , lastly , we derive an equation for the position of the inner lagrangian point in eccentric binaries with non - synchronously rotating component stars ( appendix [ sec - appa ] ) , and present an alternative derivation for the equations governing the secular evolution of the orbital semi - major axis and eccentricity assuming instantaneous mass transfer between two point masses ( appendix [ sec - appc ] ) . we consider a binary system consisting of two stars in an eccentric orbit with period @xmath3 , semi - major axis @xmath4 , and eccentricity @xmath5 . we let the component stars rotate with angular velocities @xmath6 and @xmath7 parallel to the orbital angular velocity @xmath8 , and assume the rotation rates to be uniform throughout the stars . we also note that the magnitude of @xmath8 varies periodically in time for eccentric binaries , but its direction remains fixed in space . because of this , the stars can not be synchronized with the orbital motion at all times . at some time @xmath9 , one of the stars is assumed to fill its roche lobe and begins transferring mass to its companion through the inner lagrangian point @xmath10 . we assume this point to lie on the line connecting the mass centers of the stars , even though non - synchronous rotation may cause it to oscillate in the direction perpendicular to the orbital plane with an amplitude proportional to the degree of asynchronism @xcite . since the donor s rotation axis is assumed to be parallel to the orbital angular velocity , we can safely assume that the transferred mass remains confined to the orbital plane . we furthermore assume that all mass lost from the donor is accreted by its companion , and that any orbital angular momentum transported by the transferred mass is immediately returned to the orbit . the mass transfer thus conserves both the total system mass and the orbital angular momentum . we also neglect any perturbations to the orbital motion other than those due to mass transfer . at the lowest order of approximation , these additional perturbations ( e.g. , due to tides , magnetic breaking , or gravitational radiation ) are decoupled from those due to mass transfer , and can thus simply be added to obtain the total rates of secular change of the orbital elements . following @xcite , we derive the equations of motion of the components of an eccentric mass - transferring binary with respect to a right handed inertial frame of reference @xmath11 which has an arbitrary position and orientation in space ( see fig . [ fig - coords ] ) . we let @xmath12 be the mass of star @xmath13 at some time @xmath9 at which mass is transferred from the donor to the accretor , and @xmath14 the mass of the same star at some time @xmath15 , where @xmath16 is a small time interval . with these notations , @xmath17 corresponds to mass loss , and @xmath18 to mass accretion . we furthermore denote the point on the stellar surface at which mass is lost or accreted by @xmath19 . for the donor star , @xmath19 corresponds to the inner lagrangian point @xmath10 , while for the accretor , @xmath19 can be any point on the star s equator . for the remainder of the paper , we let @xmath20 correspond to the donor and @xmath21 to the accretor . because of the mass loss / gain , the center of mass of star @xmath13 at time @xmath22 is shifted from where it would have been had no mass transfer taken place . to describe this perturbation , we introduce an additional right - handed coordinate frame @xmath23 with a spatial velocity such that its origin follows the unperturbed orbit of star @xmath13 , i.e. , the origin of @xmath24 follows the path the center of mass of star @xmath13 would have taken had no mass transfer occurred . thus , at time @xmath9 , the center of mass of star @xmath13 lies at the origin of @xmath25 , while at time @xmath15 it has a non - zero position vector with respect to @xmath25 . we furthermore let the @xmath26-axis of the @xmath23 frame point in the direction of the orbital angular momentum vector , and let the frame rotate synchronously with the unperturbed orbital angular velocity of the binary in the absence of mass transfer . the direction and orientation of the @xmath27-axes are then chosen such that at time @xmath9 the @xmath27-axis points along the direction from the mass center of star @xmath13 to the mass center of its companion . to describe the shift in the mass center of star @xmath13 due to the mass loss / gain , we denote the position vector of @xmath25 at times @xmath9 and @xmath28 with respect to the inertial frame by @xmath29 and @xmath30 , respectively . the position vector of the center of mass of star @xmath13 at times @xmath9 and @xmath22 is then given by @xmath31 and @xmath32 , where @xmath33 is the position vector of the center of mass of star @xmath13 at time @xmath15 with respect to @xmath25 . moreover , we denote by @xmath34 and @xmath35 the vectors from @xmath25 to the position where the point @xmath19 on the stellar surface would be at times @xmath9 and @xmath22 , respectively , had no mass been lost / accreted . the various position vectors at time @xmath22 are related by @xmath36 which , at the lowest order of approximation in @xmath37 and @xmath33 , yields @xmath38 as expected , the displacement of the center of mass of star @xmath13 due to the mass loss / gain is directed along the line connecting the center of mass of the star and the mass ejection / accretion point . we furthermore denote with @xmath39 the vector from the center of mass of star @xmath13 at time @xmath15 to the position where the point @xmath19 would be at time @xmath15 , had no mass been transferred between the binary components , and with @xmath40 the perturbation of this vector caused by the mass transfer . it then follows that @xmath41 and thus , by definition , @xmath42 . at the lowest order of approximation in @xmath37 and @xmath43 , equation ( [ eq - delr ] ) therefore also yields @xmath44 the definitions of and the relations between these various position vectors are illustrated schematically in fig . [ fig - coords ] . next , we denote the absolute velocity of the center of mass of star @xmath13 with respect to the inertial frame of reference at times @xmath9 and @xmath22 by @xmath45 and @xmath46 , respectively , and the absolute velocity of the ejected / accreted mass element by @xmath47 . the linear momentum @xmath48 of star @xmath49 at time @xmath9 is then given by @xmath50 and the total linear momentum @xmath51 of star 1 and the ejected mass element at time @xmath52 by @xmath53 similarly , the total linear momentum @xmath54 of star 2 and the mass element to be accreted at time @xmath9 is given by @xmath55 and the linear momentum @xmath56 of star 2 at time @xmath57 by @xmath58 at time @xmath15 the velocity of the center of mass of star @xmath13 can be written as @xmath59 where @xmath60 is the absolute velocity of the origin of @xmath23 at time @xmath22 , @xmath61 is the orbital angular velocity of the binary at time @xmath15 in the absence of mass transfer , and @xmath62 is the perturbation of the orbital angular velocity at time @xmath22 due to the mass loss / gain of the binary components . in the limit of small @xmath63 , taking the difference between the linear momenta @xmath64 and @xmath65 , dividing the resulting equation by @xmath63 , and noting that the absolute velocity @xmath66 of the origin of @xmath23 at time @xmath9 is equal to @xmath45 , yields @xmath67 here , @xmath68 is the sum of all external forces acting on star @xmath13 , @xmath69 is the mass loss / accretion rate of star @xmath13 , and @xmath70 is the relative velocity of the ejected / accreted mass element with respect to the ejection / accretion point @xmath19 . in the derivation of equation ( [ eq - ui ] ) , we have made use of equations ( [ eq - delr ] ) and ( [ eq - vtdt ] ) and restricted ourselves to first - order terms in the small quantities @xmath37 and @xmath71 . the absolute acceleration of the center of mass of star @xmath13 with respect to the inertial frame @xmath11 is given by @xmath72 where @xmath73 is the acceleration of the origin of @xmath23 with respect to @xmath11 , @xmath74 is the relative acceleration of the center of mass of star @xmath13 with respect to @xmath25 , and @xmath75 is the coriolis acceleration of the center of mass of star @xmath13 with respect to @xmath25 which vanishes for small @xmath63 . ] . the expressions for @xmath76 and @xmath77 follow from the observation that @xmath78 , which one obtains by dividing equation ( [ eq - delrho ] ) by @xmath63 in the limiting case of small @xmath63 . the equation of motion for the mass center of star @xmath13 with respect to the inertial frame @xmath11 then becomes @xmath79 we can now obtain the equation describing the relative motion of the accretor ( star 2 ) with respect to the donor ( star 1 ) by taking the difference of the equations of motion of the stars with respect to the inertial frame of reference . for convenience , we first decompose the sum of the external forces acting on each star as @xmath80 where @xmath81 is the newtonian constant of gravitation , and @xmath82 the total gravitational force exerted on star @xmath13 by the particles in the mass - transfer stream . it follows that @xmath83 where @xmath84 is the position vector of the accretor with respect to the donor , and @xmath85 is the velocity of the ejected / accreted mass element with respect to the mass center of the mass losing / gaining star . equation ( [ eq - r21 ] ) can be written in the form of a perturbed two - body problem as @xmath86 where @xmath87 is a unit vector in the direction of @xmath88 , @xmath89 is a unit vector in the orbital plane perpendicular to @xmath88 in the direction of the orbital motion , and @xmath90 is a unit vector perpendicular to the orbital plane parallel to and in the same direction as @xmath8 . the functions @xmath91 , @xmath92 , and @xmath93 are found by taking the dot product of the perturbing force arising from the mass transfer between the binary components and the unit vector in the @xmath87 , @xmath89 , and @xmath90 directions , respectively . these vector components are @xmath94 where @xmath95 is the angle between @xmath87 and the vector from the center of mass of the accretor to the mass accretion point @xmath96 , and the subscripts @xmath97 , @xmath98 , and @xmath99 denote vector components in the @xmath87 , @xmath89 , and @xmath90 directions , respectively . in working out the vector products @xmath100 , we assumed that @xmath96 is located on the equator of the accreting star as lying on the stellar surface . though , in practice , it can lie at any point near the star where the transferred mass can be considered to be part of the accretor . for instance , if an accretion disk has formed around the accretor , it would be equally valid to write @xmath96 as the point where the transferred mass impacts the outer edge of the accretion disk . ] . the terms contributing to the perturbed orbital motion can be categorized as follows : ( i ) term proportional to @xmath82 represent gravitational perturbation on the binary components caused by mass elements in the mass - transfer stream ; ( ii ) terms proportional to @xmath101 represent linear momentum exchange between the mass donor and accretor ; and ( iii ) terms proportional to @xmath102 represent shifts in the position of the mass centers of the mass donor and accretor due to the non - spherical symmetry of the mass loss or gain . in the limiting case where both stars are treated as point masses ( @xmath103 and @xmath104 ) , the only non - zero terms in the perturbed equations of motion are those due to gravitational perturbations of the mass transfer stream and the transport of linear momentum . the most recent study on the orbital evolution of eccentric mass - transferring binaries has been presented by ( * ? ? ? * ; * ? ? ? * hereafter mw83 and mw84 , respectively ) . these authors extended the work of @xcite , @xcite , and @xcite by accounting for the effects of linear momentum transport between the binary components , as well as possible perturbations to the orbital motion caused by the mass transfer stream . however , they also derived the equations describing the motion of the binary components with respect to a frame of reference with origin at the mass center of the binary , which , for mass transferring systems , is not an inertial frame of reference . the equations therefore do not account for the accelerations of the binary mass center caused by the mass transfer . here , we demonstrate that if the procedure adopted by matese & whitmire is developed with respect to an inertial frame of reference that is not connected to the binary , the resulting equations are in agreement with those derived in [ relmot ] . the core of matese & whitmire s derivation is presented in section ii of mw83 . while the authors choose to adopt a reference frame with origin at the binary mass center early on in the investigation , the choice of the frame does not affect the derivation of the equations of motion up to and including their equation ( 24 ) . in particular , equation ( 13 ) in mw83 , which , in our notation , reads @xmath105 is valid with respect to any inertial frame of reference with arbitrary position and orientation in space . the same applies to equation ( 1 ) in mw84 : @xmath106 in these equations , @xmath107 is the linear momentum of star @xmath13 , and @xmath108 is the amount of linear momentum transported by the transferred mass per unit time ( see equation ( 3 ) of mw84 ) . substitution of equation ( [ eq - apb - p ] ) into equation ( [ eq - apb - pdot ] ) then yields @xmath109 and thus @xmath110 where @xmath84 . setting @xmath111 , this equation is in perfect agreement with equation ( [ eq - r21 ] ) derived in [ relmot ] . in mw83 and mw84 , the authors incorrectly set @xmath112 and @xmath113 in equation ( [ eq - apb - mrddot ] ) , which is valid only when the origin of the frame of reference coincide with the mass center of the binary . for a mass - transferring binary , such a frame is , however , not an inertial frame and can therefore not be used for the derivation of the equations of motion of the binary components . instead of equation ( [ eq - apb - eqm ] ) , matese & whitmire therefore find equations ( 7)(8 ) in mw84 , which lack the terms associated with the acceleration of the binary mass center due to the mass transfer . in the classical framework of the theory of osculating elements , the equations governing the rate of change of the orbital semi - major axis @xmath4 and eccentricity @xmath5 due to mass transfer are obtained from the perturbing functions @xmath91 and @xmath92 as ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) @xmath114 , \label{eq - dadt}\ ] ] @xmath115 \right\ } , \label{eq - dedt}\end{aligned}\ ] ] where @xmath116 is the mean motion and @xmath117 the true anomaly . these equations are independent of the perturbing function @xmath93 which solely appears in the equations governing the rates of change of the orbital inclination , the longitude of the ascending node , and the longitude of the periastron . after substitution of equations ( [ eq - s ] ) and ( [ eq - t ] ) for @xmath91 and @xmath92 into equations ( [ eq - dadt ] ) and ( [ eq - dedt ] ) , the equations governing the rates of change of the semi - major axis and eccentricity contain periodic as well as secular terms . here we are mainly interested in the long - term secular evolution of the orbit , and so we remove the periodic terms by averaging the equations over one orbital period : @xmath118 @xmath119 the integrals in these definitions are most conveniently computed in terms of the true anomaly , @xmath117 . we therefore make a change of variables using @xmath120 for binaries with eccentric orbits , the resulting integrals can be calculated analytically only for very specific functional prescriptions of the mass - transfer rate @xmath121 ( e.g. , when @xmath121 is approximated by a dirac delta function centered on the periastron , see [ sec - delta ] ) . in general , the integrals must be computed numerically . since the perturbing functions @xmath91 and @xmath92 depend on the properties of the mass transfer stream , calculation of the rates of secular change of the orbital semi - major axis and eccentricity , in principle , requires the calculation of the trajectories of the particles in the stream ( cf . as long as no mass is lost from the system , such a calculation automatically incorporates the conservation of total angular momentum in the system . special cases of angular momentum conservation can , however , be used to bypass the calculation of detailed particle trajectories . here , we adopt such a special case and assume that any orbital angular momentum carried by the particles in the mass - transfer stream is always immediately returned to the orbit , so that the orbital angular momentum of the binary is conserved . the orbital angular momentum of a binary with a semi - major axis @xmath4 and eccentricity @xmath5 is given by @xmath122^{1/2 } , \label{eq - j}\ ] ] so that @xmath123 where a dot indicates the time derivative . in the case of eccentric orbits , substitution of equations ( [ eq - dadt ] ) and ( [ eq - dedt ] ) into equation ( [ eq - jdot ] ) leads to @xmath124 as we shall see in the next section , by setting @xmath125 and @xmath126 and substituting equation ( [ eq - t ] ) for @xmath92 , equation ( [ eq - jt ] ) allows us to calculate the @xmath89-component of the final velocities of the accreting particles as a function of their initial velocities without resorting to the computation of the ballistic trajectories of the mass transfer stream . in the limiting case of a circular orbit , equation ( [ eq - jdot ] ) is usually used to derive the rate of change of the semi - major axis of circular binaries under the assumption of conservation of both total mass ( @xmath127 ) and orbital angular momentum ( @xmath128 ) : @xmath129 the assumption of orbital angular momentum conservation over secular timescales ( @xmath126 ) is a standard assumption in nearly all investigations of conservative mass transfer in binary systems ( e.g. , * ? ? ? * ; * ? ? ? * ) , which is valid over long timescales provided there is no significant storage of angular momentum in the spins of the components stars , the accretion flow , and/or the accretion disk . in future work , we will investigate the consequences of both mass and orbital angular momentum losses from the binary on the evolution of the orbital elements . in order to assess the timescales of orbital evolution due to mass transfer in eccentric binaries , we observe that , for eccentric binaries , mass transfer is expected to occur first at the periastron of the relative orbit , where the component stars are closest to each other . we therefore explore the order of magnitude of the timescales assuming a delta function mass transfer profile centered at the periastron of the binary orbit @xmath130 where @xmath131 is the instantaneous mass transfer rate , and @xmath132 is the dirac delta function . we calculate the rates of secular change of the orbital semi - major axis and eccentricity from equations ( [ eq - dadt])([eq - dnudt ] ) , and neglect any gravitational attractions exerted by the particles in the mass - transfer stream on the component stars . hence , we set @xmath133 [ sec - delta ] substituting equations ( [ eq - t ] ) , ( [ eq - dnudt ] ) , and ( [ eq - del ] ) ( [ eq - f12y ] ) into equation ( [ eq - jt ] ) for @xmath134 then yields a relationship between the initial and final @xmath89-component of the velocities of the transferred mass and the initial and final positions of the transferred mass given by @xmath135 where the subscript @xmath136 indicates quantities evaluated at the periastron of the binary orbit , @xmath137 is the binary mass ration , and we have used the relation @xmath138 . assuming the transferred mass elements are ejected by star 1 at the @xmath10 point with a velocity @xmath139 equal to the star s rotational velocity at @xmath10 , we write @xmath140 moreover , under the assumption that each periastron passage of the binary components give rise to an extremum of @xmath141 , the derivative @xmath142 is equal to zero in equation ( [ eq - vr ] ) , so that @xmath143 . \label{eq - vrel}\ ] ] for a binary with orbital period @xmath144 , eccentricity @xmath145 , and component masses @xmath146 and @xmath147 , with @xmath148 the distance from star 1 to @xmath10 ( see appendix a ) , and @xmath149 ( the circularization radius around a compact object for these binary parameters ; see @xcite ) , the accreting matter has a @xmath89-velocity component of the order of @xmath150 . after substitution of equation ( [ eq - dnudt ] ) and equations ( [ eq - f12x])([eq - vr ] ) , the integrals in equations ( [ eq - dadtsec ] ) and ( [ eq - dedtsec ] ) for the rates of secular change of the orbital semi - major axis and eccentricity can be solved analytically to obtain @xmath151 , \label{eq - deltaa } \end{aligned}\ ] ] @xmath152 . \label{eq - deltae}\end{aligned}\ ] ] we note that for a delta - function mass transfer rate given by equation ( [ eq - del ] ) the @xmath87-component of the velocities @xmath139 and @xmath153 does not enter into the derivation of theses equations due to the @xmath154 term in equations ( [ eq - dadt ] ) and ( [ eq - dedt ] ) . furthermore , in the limiting case of a circular orbit , equation ( [ eq - deltaa ] ) reduces to equation ( [ circ - da ] ) , provided that @xmath155 in that equation is interpreted as the secular mean mass transfer rate @xmath156 . in appendix b , we present an alternative derivations to equations ( [ eq - deltaa ] ) and ( [ eq - deltae ] ) in the limiting case where the stars are treated as point masses . the rates of secular change of the semi - major axis and orbital eccentricity are thus linearly proportional to the magnitude of the mass transfer rate at periastron . besides the obvious dependencies on @xmath4 , @xmath5 , @xmath157 , and @xmath158 , the rates also depend on the ratio of the donor s rotational angular velocity @xmath159 to the orbital angular velocity @xmath160 at periastron through the position of the @xmath10 point , @xmath161 . a fitting formula for the position of the @xmath10 point accurate to better than @xmath162 over a wide range of @xmath157 , @xmath5 , and @xmath163 is given by equation ( [ xl1fit ] ) in appendix [ sec - appa ] . while the fitting formula can be used to obtain fully analytical rates of secular change of the semi - major axis and eccentricity , we here use the exact solutions for the position of @xmath10 obtained by numerically solving equation ( [ xl ] ) in appendix [ sec - appa ] . for a detailed discussion of the properties of the @xmath10 point in eccentric binaries , we refer the interested reader to @xcite . to explore the effects of mass transfer on the orbital elements of eccentric binaries , we calculate the rates of secular change of the semi - major axis and eccentricity and determine the characteristic timescales @xmath164 and @xmath165 . while the actual timescales are given by the absolute values of @xmath166 and @xmath167 , we here allow the timescales to be negative as well as positive in order to distinguish negative from positive rates of secular change of the orbital elements . we also note that since @xmath168 ( see appendix a ) , the timescales do not explicitly depend on the orbital semi - major axis @xmath4 except through the ratio @xmath169 of the radius of the accretor to the semi - major axis . for convenience , we therefore assume the accretor to be a compact object with radius @xmath170 . the timescales are found to be insensitive to terms containing @xmath169 in equation ( [ eq - deltaa ] ) and ( [ eq - deltae ] ) . varying @xmath171 from @xmath172 to @xmath173 changes the timescales by less that 10% . in what follows , we therefore set @xmath174 . an implicit dependence on @xmath4 may then still occur through the amplitude @xmath175 of the mass transfer rate at periastron . since incorporating such a dependence in the analysis requires detailed modeling of the evolution of the donor star , which is beyond the scope of this investigation , we here restrict ourselves to exploring the timescales of orbital evolution for a constant @xmath175 . the linear dependence of @xmath176 and @xmath177 on @xmath175 in any case allows for any easy rescaling of our results to different mass transfer rates . in fig . [ delta1 ] , we show the variations of @xmath166 and @xmath167 as functions of @xmath157 for @xmath178 and @xmath179 . in all cases , the donor is assumed to rotate synchronously with the orbital angular velocity at the periastron , and the accretor is assumed to be a neutron star of mass @xmath180 . the timescales of the secular evolution of the semi - major axis show a strong dependence on @xmath157 , and a milder dependence on @xmath5 , unless @xmath181 . the timescales for the secular evolution of the orbital eccentricity always depend strongly on both @xmath157 and @xmath5 . these timescales can furthermore be positive as well as negative , so that the semi - major axis and eccentricity can increase as well as decrease under the influence of mass transfer at the periastron of the binary orbit . from fig . [ delta1 ] , as well as equations ( [ eq - deltaa ] ) and ( [ eq - deltae ] ) , it can be seen that , for a given ratio of the donor s rotational angular velocity to the orbital angular velocity at periastron , the line dividing positive from negative rates of secular change of the orbital elements is a function of @xmath157 and @xmath5 . this is illustrated further in fig . [ contours ] where the timescales of orbital evolution are displayed as contour plots in the @xmath182-plane . the thick black line near the center of the plots marks the transition values of @xmath157 and @xmath5 where the rates of secular change of @xmath4 and @xmath5 transition from being positive ( to the left of the thick black line ) to negative ( to the right of the thick black line ) . varying @xmath163 between @xmath183 and @xmath184 changes the position of the transition line by less than @xmath185 in comparison to the @xmath186 case displayed in figures [ delta1 ] and [ contours ] . in the limiting case of a circular orbit , the orbit expands when @xmath187 and shrinks when @xmath188 , in agreement with the classical result obtained from equation ( [ circ - da ] ) . for non - zero eccentricities , the critical mass ratio separating positive from negative values of @xmath189 decreases with increasing orbital eccentricities . this behavior can be understood by substituting the fitting formula for the position of the @xmath10 point given by equation ( [ xl1fit ] ) in appendix [ appl1 ] into equation ( [ eq - deltaa ] ) and setting @xmath190 . however , we can fit the critical mass ratio separating expanding from shrinking orbits with a simpler formula given by @xmath191 the critical mass ratio separating positive from negative values of @xmath192 is largely independent of @xmath5 . proceeding in a similar fashion as for the derivation of equation ( [ eq - dadttran ] ) , we derive the critical mass ratio separating increasing from decreasing eccentricities to be approximately given by @xmath193 last , we note that a more quantitative numerical comparison between the above approximation formulae for @xmath194 and the exact numerical solutions shows that equations ( [ eq - dadttran ] ) and ( [ eq - dedttran ] ) are accurate to better than 1% . a crucial question for assessing the relevance of the work presented here is how the derived orbital evolution timescales compare to the corresponding timescales associated with other orbital evolution mechanisms such as tides . in fig . [ fig - tid - lin ] , we show the secular evolution timescales of the semi - major axis and orbital eccentricity of a mass - transferring binary due to tidal dissipation in the donor star as a function of @xmath157 , for different values of the eccentricity , @xmath5 . the timescales are strong functions of @xmath195 and are determined as in @xcite for stars with radiative envelopes is ( j. hurley , private communication ) @xmath196 ] ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? the radius @xmath197 is determined by assuming the donor is on the zero - age main sequence and that the orbital separation is then obtained by equating the radius of the donor ( given by * ? ? ? * ) to the volume - equivalent radius of its roche lobe at the periastron of the binary orbit ( see * ? ? ? * ) . as before , we assume the donor rotates synchronously with the orbital motion at periastron and that the accretor is a @xmath198 neutron star . the timescales of orbital evolution due to tides range from a few myr to more than a hubble time , depending on the binary mass ratio and the orbital eccentricity . the discontinuity in the timescales at @xmath199 corresponds to the transition from donor stars with convective envelopes ( @xmath200 ) to donor stars with radiative envelopes ( @xmath201 ) which are subject to different tidal dissipation mechanisms . it follows that tides do not necessarily lead to rapid circularization during the early stages of mass transfer , especially for orbital eccentricities @xmath202 . furthermore , for the adopted system parameters , the orbital eccentricity always decreases , while the orbital semi - major axis can either increase or decrease . hence , in some regions of the parameter space , the effects of tides and mass transfer are additive , while in other regions they are competitive . this is illustrated in more detail in figure [ fig - tot_timescale ] where we show the orbital evolution timescales due to the combined effect of tides and mass transfer . in the calculations of the timescales , we have assumed that , at the lowest order of approximation , the effects of tides and mass transfer are decoupled . the total rate of change of the orbital elements is then given by the sum of the rate of change of the orbital elements due to tides and mass transfer . when @xmath203 and @xmath204 , the effects of tides and mass transfer on the orbital semi - major axis are always opposed , with the orbital expansion due to mass transfer dominating the orbital shrinkage due to tides . in the case of the orbital eccentricity , the increase of the eccentricity due to mass transfer dominates the decrease due to tides for mass ratios smaller than some critical mass ratio which depends strongly on the orbital eccentricity . since the timescales of orbital evolution due to mass transfer are inversely proportional to the magnitude @xmath175 of the mass - transfer rate at periastron , the parameter space where and the extent to which mass transfer dominates increases with the rate of mass transfer at periastron . in figure [ fig - tot_contour ] , we show the total orbital evolution timescale due to the sum of tidal and mass transfer effects as a contour plot in the @xmath182-plane . the thick black lines indicate the transitions from positive ( left of the thick black line ) to negative ( right of the thick black line ) rates of change of the semi - major axis and eccentricity . the white dividing line near @xmath205 corresponds to the transition between tidal dissipation mechanisms in stars with convective envelopes ( @xmath206 ) and stars with radiative envelopes ( @xmath207 ) . it follows that there are large regions of parameter space where the combined effects of mass transfer and tidal evolution do not rapidly circularize the orbit . in particular , for @xmath208 and @xmath209 orbital circularization always takes longer than 10gyr , while for @xmath157 to the left of the thick black line the orbital eccentricity grows rather than shrinks . for a given @xmath157 left of the thick black line , the timescales for eccentricity growth increase with increasing @xmath5 though , so that there is no runaway eccentricity growth . hence , for small @xmath157 , mass transfer at the periastron of eccentric orbits may provide a means for inducing non - negligible eccentricities in low - mass binary or planetary systems . the orbital semi - major axis , on the other hand , always increases when @xmath210 , but can increase as well as decrease when @xmath211 , depending on the binary mass ratio @xmath157 . we recall that both the tidal and mass transfer orbital evolution time scales depend on the ratio of the donor s rotational angular velocity @xmath159 to the orbital angular velocity @xmath160 and that we have set @xmath186 in all figures shown . we developed a formalism to calculate the evolution of the semi - major axis and orbital eccentricity due to mass transfer in eccentric binaries , assuming conservation of total system mass and orbital angular momentum . adopting a delta - function mass - transfer profile centered at the periastron of the binary orbit yields rates of secular change of the orbital elements that are linearly proportional to the magnitude @xmath175 of the mass - transfer rate at the periastron . for @xmath212 , this yields timescales of orbital evolution ranging from a few myr to a hubble time or longer . depending on the initial binary mass ratio and orbital eccentricity , the rates of secular change of the orbital semi - major axis and eccentricity can be positive as well as negative , so these orbital elements can increase as well as decrease with time . comparison of the timescales of orbital evolution due to mass transfer with the timescales of orbital evolution due to tidal dissipation shows that the effects can either be additive or competitive , depending on the binary mass ratio , the orbital eccentricity , and the magnitude of the mass - transfer rate at the periastron . contrary to what is often assumed in even the most state - of - the - art binary evolution and population synthesis codes , tides do not always lead to rapid circularization during the early stages of mass transfer . thus , phases of episodic mass transfer may occur at successive periastron passages and may persist for long periods of time . as a first approximation , the evolution of the orbital semi - major axis and eccentricity due to mass transfer in eccentric binaries can be incorporated into binary evolution and population synthesis codes by means of equations ( [ eq - deltaa ] ) and ( [ eq - deltae ] ) in which the mass - transfer rate is approximated by a delta - function of amplitude @xmath175 centered at the periastron of the binary orbit . in future papers , we will relax the assumption of conservation of total system mass and orbital angular momentum , and examine the effects of non - conservative mass transfer on the orbital elements of eccentric binaries . we also intend to study the onset of mass transfer in eccentric binaries in more detail , adopting realistic mass - transfer rates appropriate for atmospheric roche - lobe overflow in interacting binaries as discussed by @xcite . we will consider individual binary systems that are known to be eccentric and transferring mass during periastron passage , as well as populations of eccentric mass - transferring binaries and their descendants . [ appl1 ] a crucial element in the description of mass transfer in any binary system is the location of the inner lagrangian point ( @xmath10 ) through which matter flows from the donor to the accretor . while a solution for the location of @xmath10 is not analytic , the case of circular orbits with synchronized components can be approximated by the formula @xmath213 where @xmath214 is the distance of the @xmath10 point from the mass center of the donor star in units of the distance between the stars , and @xmath137 is the mass ratio of the binary defined as the ratio of the donor mass @xmath158 to the accretor mass @xmath215 . for mass ratios in the range @xmath216 , this formula is valid to an accuracy of better than 2% ( e.g. * ? ? ? the above formula has been generalized by @xcite to include the effect of a non - synchronously rotating donor star : @xmath217 \left ( 1 + \frac{4}{9}\log{q } \right ) . \label{ps}\ ] ] here , @xmath159 is the rotational angular velocity of the donor , and @xmath218 the orbital angular velocity of the binary . for @xmath219 and @xmath220 , the formula is valid to an accuracy of better than 3% . it is to be noted though that @xcite derived the position of the @xmath10 point under the assumption that the orbital and rotational periods of the binary and its component stars are much longer than the dynamical timescale of the donor . despite the better than 3% accuracy of the fit given by equation ( [ ps ] ) , the formula may therefore still break down because the underlying formalism is no longer valid . in this paper , it is necessary to generalize the formula for the position of the @xmath10 point even further to account for a non - zero eccentricity as well as non - synchronous rotation . for this purpose , we determine the equipotential surfaces describing the shape of the components of a non - synchronous , eccentric binary . our procedure is a generalization of the steps outlined by @xcite for the derivation of the equipotentials of a non - synchronous , circular binary . here , we consider an eccentric binary system where the stars are considered to be centrally condensed and spherically symmetric , and thus can be well described by roche models of masses @xmath158 and @xmath215 . their orbit is assumed to be keplerian with semi - major axis @xmath4 and eccentricity @xmath5 . star 1 is furthermore assumed to rotate uniformly with a constant angular velocity @xmath6 parallel to the orbital angular velocity @xmath8 . we note that for an unperturbed keplerian orbit , the magnitude of @xmath8 is a function of time , while the direction and orientation remain fixed in space . as is customary , we determine the equipotential surfaces with respect to a cartesian coordinate frame @xmath11 with origin @xmath221 at the mass center of star 1 , and with the @xmath222-axis pointing along @xmath6 . the @xmath223- and @xmath224-axes are co - rotating with the star at angular velocity @xmath159 . since non - synchronously rotating binary components are inevitably subjected to time - dependent tides invoked by their companion , the mass elements will oscillate with frequencies determined by the difference between the rotational and orbital frequencies . here , we neglect these tidally induced oscillations as well as any other type of bulk motion of matter due to , e.g. , convection . this approximation is valid as long as the characteristic timescale associated with the motion of the mass elements is sufficiently long compared to the star s dynamical timescale ( more extended discussions on the validity of the approximation can be found in @xcite , @xcite , and @xcite ) . star 1 is then completely stationary with respect to the co - rotating frame of reference . with respect to the @xmath11 frame , the equation of motion of a mass element at the surface of star 1 is given by @xmath225 where @xmath226 and @xmath227 are the position vectors of the mass element with respect to the mass center of the binary and star 1 , respectively , and @xmath228 is the position vector of the center of mass of star 1 with respect to the center of mass of the binary , and @xmath229 and @xmath230 are the centrifugal and coriolis acceleration with respect to the rotating coordinate frame . under the assumption that , in an inertial frame of reference , the only forces acting on the considered mass element are those resulting from the pressure gradients in star 1 and the gravitational attractions of star 1 and its companion , the acceleration of the mass element with respect to the binary s center of mass is given by @xmath231 where @xmath81 is the newtonian constant of gravitation , @xmath232 the mass density , @xmath136 the pressure , and @xmath233 the position vector of the mass element with respect to the mass center of star 2 . the gradient in equation ( [ eq - r0 ] ) and subsequent equations in this appendix are taken with respect to @xmath223 , @xmath224 , and @xmath222 . the acceleration of the center of mass of star 1 with respect to the binary mass center , on the other hand , is given by @xmath234 where @xmath235 ( simplified to @xmath236 in what follows ) is the time - dependent distance between star 1 and star 2 . substituting equations ( [ eq - r0 ] ) and ( [ eq - r ] ) into equation ( [ eq - r1 ] ) , we obtain @xmath237 when the @xmath223-axis coincides with the line connecting the mass centers of the two stars , the third and fourth term in the right - hand member of equation ( [ eq - r1.2 ] ) can be written as the gradient of a potential function as @xmath238 @xmath239,\ ] ] where @xmath223 and @xmath224 are the cartesian coordinates of the mass element under consideration . with these transformations , equation ( [ eq - r1.2 ] ) becomes @xmath240 where @xmath241 since star 1 is assumed to be static in the rotating frame , @xmath242 , so that equation ( [ a8 ] ) reduces to @xmath243 this equation governs the instantaneous shape of the equipotential surfaces at the instant when the @xmath223-axis coincides with the line connecting the mass centers of the two stars . however , since this instant is entirely arbitrary , the equation is generally valid and can be used to determine the shape of the star at any phase of the orbit , with appropriate re - definition of the @xmath223-axis at every instant . a similar equation was derived by @xcite and @xcite . next , we look for the critical equipotential surface for which matter starts to flow from star 1 to star 2 through the inner lagrangian point @xmath10 . for circular binaries with synchronously rotating component stars , the @xmath10 point is always located on the line connecting the mass centers of the two stars . @xcite have shown that non - synchronous rotation combined with a misalignment between the spin axis of star 1 and the orbital plane may cause the @xmath10 point to oscillate in the @xmath222-direction . as a first approximation , we here neglect these oscillations and assume the @xmath10 point to be located on the line connecting the mass centers of the two stars . the position of the @xmath10 point is then obtained by setting @xmath244 . the resulting equation for the position of @xmath10 is @xmath245 which can be rewritten in dimensionless form as @xmath246 here , @xmath247 is the position of the @xmath10 point on the @xmath223-axis in units of the distance between the two stars , @xmath137 is the binary mass ratio , @xmath248 is the ratio of the star 1 s rotational angular velocity to the orbital angular velocity at periastron , and @xmath249 . in the latter expression , @xmath250 is the distance between the stars at periastron . note that in the particular case of a circular orbit , equation ( [ xl ] ) reduces to the equation for the position of the @xmath10 point derived by @xcite and @xcite . equation ( [ xl ] ) must be solved numerically for the location of @xmath10 . since we have made no explicit assumptions about the relative location of the two star in the orbit , and we have let the distance between the stars @xmath251 , with @xmath117 the true anomaly , be an explicit function of time , this equation characterizes the position of the @xmath10 point at any position in the orbit . figure [ fig - l1 ] shows the relative change @xmath252 in the position of the @xmath10 point as a function of the true anomaly for @xmath253 , @xmath254 , and a variety of eccentricities . the position of the @xmath10 point over the course of a single orbit varies by less than 15% when @xmath255 , and by 3040% when @xmath256 . at apastron , @xmath257 increases with increasing eccentricity when @xmath258 , and decreases with increasing eccentricity when @xmath259 . this turn - around at @xmath260 is caused by the increasing deviations from synchronous rotation at apastron with increasing orbital eccentricity . we have also derived a fitting formula for the position of the @xmath10 point at the periastron of the binary orbit as a function of @xmath157 , @xmath5 , and @xmath261 : @xmath262 this fitting formula is accurate to better than @xmath162 for mass ratios @xmath263 , eccentricities @xmath264 , and ratios of stellar rotational angular velocities to orbital angular velocities at periastron @xmath265 . in the limiting case of a circular , synchronized binary , equation ( [ xl1fit ] ) reduces to equation ( [ eq - xl1cs ] ) , while for a circular , non - synchronized binary , equation ( [ xl1fit ] ) reduces to equation ( [ ps ] ) . a detailed discussion of the properties of all five lagrangian points and the volume of the critical roche lobe in eccentric binaries is presented in @xcite [ sec - appc ] when the components of a mass - transferring binary are treated as point masses and mass transfer is assumed to be instantaneous , an alternative derivation of the equations governing the secular change of the orbital semi - major axis and eccentricity may be obtained from the equations for the specific orbital energy and angular momentum . this method is commonly used to relate the post- to pre - supernova orbital parameters of binaries in which one of the components undergoes an instantaneous supernova explosion ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? as in section [ orbevtim ] , we assume conservation of total system mass and describe the mass transfer by a delta function mass - transfer rate centered at the periastron of the binary orbit [ see equation ( [ eq - del ] ) ] . the relative orbital velocity , @xmath266 , of two stars with masses @xmath158 ( the donor star ) and @xmath215 ( the accreting star ) in a binary with orbital semi - major axis @xmath4 and eccentricity @xmath5 is given by @xmath267 where @xmath81 is the newtonian constant of gravitation , and @xmath88 is the relative position vector of the accretor with respect to the donor . under the assumption that mass elements are transferred instantaneously between the two stars , the distance @xmath268 is the same right before and right after mass transfer , so that the rate of change of the orbital semi - major axis due to instantaneous mass transfer is given by @xmath269 next , the specific orbital angular momentum of the binary written in terms of the binary component masses and orbital elements is given by @xmath270 noting that @xmath271 at periastron , and proceeding in a similar way as for the derivation of equation ( [ eq - c - dadt ] ) , we derive the rate of change of the orbital eccentricity due to instantaneous mass transfer to be @xmath272 finally , we eliminate @xmath266 from equations ( [ eq - c - dadt ] ) and ( [ eq - c - dedt ] ) to obtain equations for the rates of changes of the orbital semi - major axis and eccentricity in terms of the binary orbital elements and component masses . for this purpose , we use the conservation of linear momentum to write the rate of change of the relative orbital velocity due to mass - transfer as @xmath273 where @xmath139 and @xmath153 are the relative velocities of the transferred mass elements with respect to the mass center of the donor and accretor , respectively . to obtain an equation for the change in the magnitude of @xmath274 , we write the vector components of @xmath274 , @xmath139 , and @xmath153 with respect to the @xmath87 , @xmath89 , and @xmath90 unit vectors introduced in section [ relmot ] , and take the dot product of equation ( [ eq - c - vrelvec ] ) with @xmath274 . since , @xmath275 at the periastron of the binary orbit , it follows that @xmath276 assuming conservation of orbital angular momentum it then follows from equations ( [ eq - jdot ] ) and ( [ eq - c - dadt])([eq - c - vrel ] ) that @xmath277 where we have used kepler s 3rd law and that @xmath278 at the periastron of the binary orbit . this equation is identical to equation ( [ eq - vr ] ) in the limiting case where @xmath103 and @xmath279 . substituting equations ( eq - c - vdm2 ) and ( eq - c - vrel ) into equations ( [ eq - c - dadt ] ) and ( [ eq - c - dedt ] ) and averaging over the orbital period , we find @xmath280 @xmath281 these equations are identical to equations ( [ eq - dadtsec ] ) and([eq - dedtsec ] ) in the limiting case where @xmath282 and @xmath283 . we are grateful to an anonymous referee for insightful comments which helped to improve the paper , as well as to ronald taam for useful discussions , and to richard oshaughnessy for discussions regarding methods used to fit the position of the @xmath10 point in eccentric , non - synchronous binaries . this work is partially supported by a nasa graduate fellowship ( nng04gp04h / s1 ) to j.s . , and a nsf career award ( ast-0449558 ) , a packard fellowship in science and engineering , and a nasa atp award ( nag5 - 13236 ) to v.k .

we investigate the secular evolution of the orbital semi - major axis and eccentricity due to mass transfer in eccentric binaries , assuming conservation of total system mass and orbital angular momentum . assuming a delta function mass transfer rate centered at periastron , we find rates of secular change of the orbital semi - major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron . the rates can be positive as well as negative , so that the semi - major axis and eccentricity can increase as well as decrease in time . adopting a delta - function mass - transfer rate of @xmath0 at periastron yields orbital evolution timescales ranging from a few myr to a hubble time or more , depending on the binary mass ratio and orbital eccentricity . comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides can not , in all cases , circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer . the formalism presented can be incorporated in binary evolution and population synthesis codes to create a self - consistent treatment of mass transfer in eccentric binaries .

House Oversight and Government Reform Committee Chairman Darrell Issa (R-Calif.) faces off with ranking member Elijah Cummings (D-Md.) after former Internal Revenue Service official Lois Lerner once again refused to answer questions at a congressional hearing. (The Washington Post) House Oversight and Government Reform Committee Chairman Darrell Issa (R-Calif.) faces off with ranking member Elijah Cummings (D-Md.) after former Internal Revenue Service official Lois Lerner once again refused to answer questions at a congressional hearing. (The Washington Post) The war between Democrats and Rep. Darrell Issa (R-Calif.), the controversial chairman of the House Oversight and Government Reform Committee, took on a new intensity Thursday when some Democratic lawmakers called for Issa to be stripped of his committee chairmanship. “Mr. Issa is a disgrace and should not be allowed to continue in a leadership role,” Rep. Marcia L. Fudge (D-Ohio), who leads the Congressional Black Caucus, wrote in a strongly worded letter to House Speaker John A. Boehner (R-Ohio). The uproar followed the latest clash between Issa and the committee’s top Democrat, Rep. Elijah E. Cummings (Md.), on Wednesday, when Issa abruptly ended a committee hearing without allowing Democrats to speak and cut off Cummings’s microphone while he was speaking. In the letter to Boehner, Democrats described the behavior as “outrageous” and “disrespectful.” But on Thursday, the House Republican leadership stood by Issa. “Darrell Issa is the chairman, he’s done an effective job as chairman, and I support him,” Boehner told reporters during his weekly media address. The clash came Wednesday morning as the committee met for a hearing as part of the investigation into the Internal Revenue Service’s targeting controversy. After peppering former IRS official Lois Lerner, who invoked her Fifth Amendment right against self-incrimination, with questions, Issa adjourned the meeting without giving Democrats an opportunity to speak. Cummings asked that the hearing be continued, but Issa refused and had Cummings’s microphone turned off. Republicans on the panel, led by Issa, then walked out of the room while the enraged Maryland congressman continued to speak. House Democrats also introduced a resolution Thursday reprimanding Issa, but the chamber voted along party lines to table it. Cummings told reporters Thursday that several Republican members of the committee have since apologized to him for Issa’s conduct. Later Thursday, Issa told U-T San Diego that he had reached out to Cummings and apologized. “I could have offered to reopen the hearing and allowed him to make a second statement,” Issa told the newspaper. “As chairman, I should have been much more sensitive to the mood of what was going on, and I take responsibility.” Cummings responded to the apology in a statement, saying: “My sincere hope is that as we move forward, we will respect the opinions of all members of the committee.” In a press briefing earlier in the day, Cummings had said: “Chairman Issa wanted to hold a hearing, and then shut it down before the Democrats could utter one syllable. It is un-American.” Friction between Issa and Cummings, neither of whom has established a reputation for diplomacy, stands in contrast to other committee leaders who have found ways to collaborate on controversial issues. Republicans and Democrats both expressed outrage over the IRS’s targeting efforts after the actions became known last May, but the flare-up Wednesday serves as the latest sign of the partisanship and dysfunction that have dominated the oversight committee in recent years. The IRS hearings appeared to be unfolding in a fashion similar to 2011, when the House voted to hold Attorney General Eric H. Holder Jr. in contempt of Congress for refusing to share information regarding a Justice Department gun-tracking program known as “Fast and Furious.” In that case, Holder and Justice officials declined to grant several requests for information from Issa’s committee, citing executive privilege. After months of disputes — including several heated exchanges between Holder and GOP members of the committee — the panel voted to hold Holder in contempt, against strong objections from Democrats. Days later, a House vote made Holder the first sitting attorney general to be held in contempt of Congress. The issue became a cause among conservative voters ahead of the 2012 presidential election, and both parties attempted to exploit the episode for political gain. Now, House Democrats allege, Republicans are attempting to revive the IRS scandal as a political football and put it back in play for the upcoming midterm elections. “What happened was so outrageous, so demeaning, so unjudicial, so awful in every respect,” said Rep. Louise M. Slaughter (N.Y.), senior Democrat on the House Rules Committee, who added that “we just absolutely have reached a boiling point.” As Issa has pressed forward with the IRS investigation — periodically leaking snippets of evidence to support his theory that the IRS actions were attempts by the Obama administration to silence conservative critics — Cummings has cited information and findings to the contrary, declaring in a June interview with CNN that “the case is solved, and if it were me, I would wrap this case up and move on.” Conservatives have griped that the clash between Issa and Cummings has overshadowed the hearing itself — during which Lerner did not answer questions about the investigation into whether the IRS targeted political groups for disproportionate scrutiny. On Thursday, Cummings hit back. He said that, had he been allowed to speak, he would have asked about the potential to have Lerner’s attorney address the committee, which he said could have helped provide answers to Issa’s questions. On Thursday, several House Democrats alleged that, instead of truly seeking answers, Issa and other Republicans are using the hearings as a way to keep voters talking about the IRS investigation as the midterm elections approach. “The Republicans are determined to keep this issue of the IRS alive,” said Rep. Sander M. Levin (Mich.), the ranking Democrat on the House Ways and Means Committee. “What happened yesterday was the political strategy of the Republicans: going berserk.” Those criticism were echoed by House Minority Leader Nancy Pelosi (D-Calif.), who told reporters at her weekly news briefing that Issa’s behavior toward Cummings was disrespectful. She also said she was surprised that Boehner is standing by the California congressman. “I can’t see how Republicans wouldn’t be running . . . to disassociate themselves from such behavior,” she said. “You would think they would be heading to the hills.” Ed O’Keefe contributed to this report. ||||| A chastened Rep. Darrell Issa says he has apologized to a fellow senior lawmaker for abruptly cutting off his microphone during a hearing Wednesday before the House Oversight and Government Reform Committee. Issa, R-Vista, said he made a personal apology on Thursday to the man he silenced, Rep. Elijah Cummings, D-Md. “Mr. Cummings is a member of Congress who works very hard for his constituents,” he said. Issa’s remarks came during a telephonic conversation with U-T San Diego after a House condemnation resolution pressed by Democrats earlier in the day failed to pass. The resolution called for sanctioning Issa for “the offensive and disrespectful manner” in which he conducted the hearing on Capitol Hill. The resolution failed on a vote of 211-186 as House Republicans refused to back it. A video of Issa-Cummings dispute during a hearing on whether the Internal Revenue Service has targeted tea party type groups went viral in political circles Wednesday. Cummings exploded when Issa refused to let him make a statement and ask a question. Issa had moments earlier brought the hearing to an end after IRS official Lois Lerner refused to testify about an issue House Democrats say is nothing more than a political witch hunt. Cummings is the ranking Democrat on the panel, and he and Issa have jousted before. But cutting Cummings off drew the ire of the Congressional Black Caucus, which petitioned Speaker John Boehner to strip Issa of the chairmanship he has held for the last three years. Issa called what happened “an unfortunate incident.” When Lerner refused to testify, Issa ended the hearing and signaled committee staffers to turn off lawmaker microphones. As those were being shut down, Cummins pleaded for more time to ask another question. Instead of asking a question immediately, Cumming accused Issa of leading a “one-sided” probe. Nonetheless, Issa said he should have taken another tack. “I could have offered to reopen the hearing and allowed him to make a second statement,” he said. “As chairman, I should have been much more sensitive to the mood of what was going on, and I take responsibility.” While no House or committee rules were broken, Issa said it’s his responsibility when a committee member is upset. When they spoke, Issa said he and Cummings talked about how each could “do a better job going forward.” Their discussion also included whistle blower legislation from Cummings that Issa has agreed to co-sponsor. In a meeting with reporters in Washington before they spoke, Cummings said he “didn’t want to get caught up in the disrespect” but said Issa had been “undemocratic and unfair.” “A number of Republican members on our committee have come up and said to me, ‘Don’t tell him, but I apologize. You shouldn’t have been treated that way,’” Cummings said.

– The normally unrepentant Darrell Issa has personally apologized to a fellow congressman over a high-profile snub on the House floor, reports the San Diego Union-Tribune. The chairman of the House Oversight panel offered his mea culpa to Democrat Elijah Cummings after a testy exchange amid this week's grilling of former IRS official Lois Lerner. When Issa peppered Lerner with questions, she took the Fifth, and he abruptly adjourned the hearing. When Cummings, the ranking Democrat, tried to speak, Issa cut off his microphone (complete with finger-dragging motion across the throat) and left with other Republicans on the panel. "I am a member of the Congress of the United States of America," Cummings declared as Issa tried to get him to stop. Yesterday, the Congressional Black Caucus sent a letter to John Boehner calling Issa a "disgrace" and demanding he be stripped of his committee leadership, reports the Washington Post. Boehner stood by Issa, who later said: “I could have offered to reopen the hearing and allowed him to make a second statement. As chairman, I should have been much more sensitive to the mood of what was going on, and I take responsibility.” A New York Times analysis agrees and sees a pattern: Issa has made a big deal out of his various White House investigations, but he "has proved to be his own worst enemy, stepping on his own message with his antics and clouding whatever political impact his investigations might be having." A Democratic bid to censure him failed along party lines.

the model of a classical one - component plasma has - due to its simplicity - been widely investigated both theoretically and with various numerical and simulation methods , see e.g. @xcite and @xcite , respectively . since the pioneering numerical work of brush , sahlin , teller @xcite , the thermodynamic and dynamic characteristics of the classical ocp have been studied in detail . in particular , the dependence of the properties on the coupling parameter @xmath2 , where @xmath3 is the mean interparticle distance and @xmath4 the density , have been investigated up to very large values of @xmath0 @xcite . among the most important thermodynamic results is the prediction of crystallization at values of @xmath0 of the order of 172 - 180 @xcite . furthermore , investigations of the dynamic properties of strongly correlated classical plasmas have indicated that the wave number dependent plasmon dispersion changes from monotonic growth , common for weakly coupled plasmas , to a decreasing dispersion around @xmath5 3 @xcite . on the other hand , there is growing interest in the dynamic properties of dense _ quantum _ plasmas , in particular in astrophysics , laser plasmas and condensed matter . while the case of strong degeneracy ( strong quantum limit ) and weak coupling at very high densities is well described by the random phase approximation ( rpa , see e.g. @xcite ) , the properties at _ intermediate coupling and degeneracy _ remain poorly explored . especially , one is interested in the dynamic plasma behavior in cases where the average kinetic energy is of the same order as the mean potential energy , i.e. @xmath6 , where collisionless theories such as the rpa fail , e.g. @xcite . for these situations , quantum molecular dynamics ( qmd ) simulations @xcite are the appropriate numerical approach which , however , is yet lacking the required efficiency . for weakly degenerate plasmas , with @xmath7 , where @xmath8 is the debroglie wave length ( see below ) , it is expected that one can perform much simpler classical md simulations using effective quantum pair potentials , e.g. @xcite . these potentials can be derived from the 2-particle slater sum using morita s method . it is the aim of this paper to explore this md approach in detail , especially for the analysis of the optical ( langmuir ) plasmon dispersion . it is natural to start this analysis with ocp simulations because they have the advantage of the absence of a collapse of oppositely charged particles at small distances . on the other hand , the existence of a homogeneous background of oppositely charged particles leads to some additional technical difficulties compared to 2-component systems , due to restricted carrier rearrangement causing less effective screening of the coulomb interaction . one major problem of md simulations of dynamical properties is that the behavior at small wave numbers is difficult to investigate . the reason is that large box - sizes are required which , for the analysis of high density plasmas , translates into large particle numbers . the current increase of available computer power gives one the possibility to investigate size - dependent properties like the density - density correlations @xmath9 for smaller k - vectors than before . in this paper , we are able to present accurate results for the dynamical properties of the ocp , such as the dynamical structure factor and the wave vector dispersion of langmuir oscillations . our simulations for intermediate values of the coupling parameter , @xmath10 , show an interesting dispersion : the frequency increases up to a maximum and , for large wave numbers , decreases again . further , we investigate the role of quantum effects by comparing simulations with the coulomb potential and an effective quantum pair potential ( kelbg potential @xcite ) for the region of small and intermediate coupling . we found that quantum diffraction effects have noticable influence on the behavior of the optical dispersion curves . increase of the degeneracy leads to a softenig of the dispersion @xmath11 , especially at intermediate wave vectors . a central quantity to determine the dynamic properties of charged many - particle systems is the frequency - dependent dielectric function @xmath12 which , for the ocp , is given by @xmath13 here @xmath14 is the spatial fourier transform of the coulomb potential , @xmath15 , and @xmath16 is the longitudinal polarization function . thus , many - body effects enter the dielectric function via @xmath17 . there exist many approximations for the latter function , the simplest one being mean - field theories which neglect short - range correlation effects , i.e. collisions between the particles . for the classical ocp , the mean - field result is the vlasov polarization : @xmath18 here @xmath19 , indicating the retarded ( causal ) character of the polarization and the dielectric function . further , @xmath20 is the distribution function . the vlasov polarization applies only to classical plasmas , where the wave character of the particles can be neglected . quantum effects are important if the interparticle distance or the debye radius become comparable to the debroglie wave length @xmath21 . therefore , quantum diffraction effects should show up in the dielectric properties at large wave numbers . the quantum generalization of the vlasov polarization is the rpa polarization function given by @xmath22 in this paper we consider only plasmas in equilibrium , so @xmath20 and @xmath23 are the maxwell and fermi function , respectively . one readily confirms that , in the limit of long wavelengths , @xmath24 , indeed the rpa result ( [ p_rpa ] ) goes over to the vlasov polarization function ( [ p_vlasov ] ) . an important quantity which follows from dielectric function ( [ df ] ) via the fluctuation - dissipation theorem is the dynamical structure factor @xmath25 @xmath26 which shows the frequency spectrum of density fluctuations for a given value of @xmath27 . as mentioned above , the mean field expressions ( [ p_vlasov ] ) and ( [ p_rpa ] ) neglect short - range correlations and are , therefore , valid only for weakly coupled plasmas , @xmath28 . there exist many theoretical concepts to go beyond the rpa which are based on quantum kinetic theory , density functional theory and other approaches . this is beyond the scope of this paper , see e.g. ref . @xcite and references therein . here , we consider the alternative approach to the ocp at finite coupling which is based on molecular dynamics simulations . the dielectric and dynamical properties of an interacting many - particle system are easily accessible from the density - density correlation function which is defined as @xmath29 where @xmath30 is the number of particles . @xmath31 is the fourier component of the density , @xmath32 which is computed from the trajectories @xmath33 of all particles . the dynamical structure factor is just the fourier transform of the density - density correlation function ( [ dcf ] ) @xmath34 equation ( [ s_md ] ) can be directly compared to formula ( [ s_mf ] ) and , thus , allows for a comparison of the simulation results with the statistical theories . furthermore , eq . ( [ s_md ] ) allows to investigate the influence of quantum effects on the dynamical properties and plasmon dispersion of the ocp . variations of the interaction potential ( see below ) directly affect the particle trajectories and , via eqs . ( [ dcf])([s_md ] ) , the dynamical structure factor . the simulations have been performed in a cube of length @xmath35 containing @xmath30 interacting electrons on a uniform positive background . for this system , we solved newton s equations of motion containing all pair interactions which are derived from a total potential @xmath36 , see below . as an algorithm of motion we used a second - order scheme in form of the swope algorithm @xcite . since our simulations are performed in the microcanocial ensemble , the mean kinetic energy may change . therefore , to maintain the chosen value of temperature and @xmath0 , we applied scaling ( renormalization ) of all velocities at every second step . a central goal of our simulations was to study the influence of quantum effects . we , therefore , performed several simulations which used either a coulomb potential or an effective quantum pair potential ( see below ) . to permit flexibility in the use of the potential , @xmath37 was divided into a short - range and a long - range part , @xmath38 , where quantum effects influence only @xmath39 , whereas the behavior at large distances , @xmath40 , is dominated by the long - range coulomb interaction . let us first describe the treatment of the long - range term . the long - range interaction was computed in standard way using periodic boundary conditions and the ewald summation procedure @xcite . as a result , the long - range potential is given by the coulomb interaction in the main box and all image cells : @xmath41}{|\vec{r}+ \vec{n } l| } + \sum^{n_x , n_y , n_z \le 5 , n^2 \le 27}_{\vec{n}\neq 0 } \frac{{\rm exp}(-\pi n^2 ) \cos(2 \pi \vec{n } \vec{r } /l)}{\pi l } - \frac { 1}{l } , \label{ewald}\end{aligned}\ ] ] where erfc is the complementary error function , @xmath35 - the side length of the simulation cell and @xmath42 - a vector of integer numbers which labels the periodic images of the simulation box . in this expression , the first term corresponds to a potential of particles with gaussian broadened charge distribution around the electrons with a width of @xmath43 , the second one - the compensating gaussian distributions , and the last one accounts for the influence of the homogeneous background . it turns out that the second term in ( [ ulong ] ) can be reduced to 2 loops ( one over the particles and one over the vectors @xmath42 in the reciprocal space ) and is not very time consuming . the more complicated part is the first term which contains three loops . in case of a two - component plasma , a proper choice of the width of the gaussian distribution and use of periodic boundary conditions greatly simplifies this term due to cancellations . in contrast , for an ocp , the background cancels the interactions only partially , `` statically '' . as a result , convergence of the sum is worse , and one needs to take into account all first neighboring image cells ( total of 26 ) at every time step . the contribution of all neighboring cells except for the main one ( @xmath44 ) was computed , before the start of the simulations and stored in 3-dimensional tables for the potential and forces . during the simulations , we used 3d - bilinear interpolation at every step to obtain the values of the potential and forces for intermediate distances . we found that 100 grid points in every direction are adequate , so the total size of the table was @xmath45 elements . the particle interactions inside the main ( @xmath46 ) cell were evaluated directly at every time step without minimum image convention . let us now discuss the short - range potential . as has been shown by kelbg and co - workers @xcite , quantum effects can be treated efficiently by an effective pair potential , the kelbg potential : @xmath47 where @xmath48 . as a consequence of quantum effects , this potential differs from the coulomb potential at small distances @xmath49 and is finite at @xmath50 . further , it is temperature - dependent via the thermal debroglie wavelength . the kelbg potential can be regarded as the proper quantum pair potential following from the two - particle slater sum @xmath51 without exchange effects : @xmath52 it treats quantum diffraction effects exactly , up first order in @xmath0 . frequently other quantum pair potentials have been used , including the deutsch potential @xcite , which has the same value at @xmath50 but differs from the kelbg potential at intermediate distances . as was mentioned by hansen @xcite , symmetry effects do not have a big influence on the dynamical properties ( although they give a major contribution to the static properties , especially for the light mass components ) . using the kelbg potential ( [ kelbg ] ) , we can immediately separate the short - range part of the interaction , @xmath53 which has been calculated together with the first sum of eq . ( [ ewald ] ) using the interpolation table . the kelbg potential contains just the lowest order quantum corrections ( lowest order in @xmath54 ) and is , thus , accurate at small coupling , @xmath55 . nevertheless , we expect that it correctly reproduces the influence of quantum effects also at intermediate coupling , @xmath56 . further improvements are straightforward , e.g. by including exchange effects or by evaluating the full two - particle slater sum . we note that the described numerical procedure applies to such improved quantum pair potentials as well , even if they are not given analytically . solving newton s equations with forces derived from the total potential @xmath57 , we computed thermodynamic and static quantities , such as total energy and pair distribution function in usual manner . the results will be presented in the next section . here we discuss some details on computation of the dynamical properties , as they require much more effort and computation time in order to achieve sufficient accuracy . to obtain useful results for the dynamical structure factor , requires simulation results in a sufficiently broad range of wave numbers and frequencies . natural units of the wave number and frequency are @xmath58 and the plasma frequency @xmath59 , respectively , which will be used in the following . the minimum wave number @xmath60 depends on the size @xmath35 of the simulation box and thus , for a given density or coupling parameter , on the number of particles @xmath30 . one readily verifies that @xmath61 or , using dimensionless wave numbers , @xmath62 . clearly , to reduce @xmath60 requires an essential increase of the number of particles in the simulation . the simulation accuracy can be further increased by taking advantage of the isotropy of the plasma in wave vector space . indeed , in equilibrium , the density - density correlation function and dynamical structure factor should only depend on the absolute value of the wave vector . on the other hand , the simulations yield slightly different results for different directions of the wave vector . averaging over all results corresponding to the same absolute value of @xmath63 allows to reduce the statistical error . for example , the minimum wave number @xmath60 corresponds to directions of @xmath63 along either the x- , y- or z - axis , cf . ( [ rho_k ] ) , so we can use the average of the three . the next larger value is @xmath64 , corresponding to the diagonals in the x - y , x - z and y - z planes . the third value , @xmath65 , corresponds to the space diagonal and is not degenerate ; consequently it carries the largest statistical error . this is the main reason for the fluctuations of the numerical results for the wave vector dispersion , see for example fig . 5 . finally , to resolve the collective plasma oscillations , the duration of the simulations has to be much larger than the plasma period . also , increased simulation times leads to a reduction of the noise . we found that times of the order of 250 plasma periods are adequate . we have performed a series of simulations for varying values of @xmath0 and @xmath66 , using the coulomb and kelbg potential . also , time step and particle number have been varied until a satisfactory compromise between accuracy and simulation efficiency has been achieved . the parameters of the runs chosen for the figures below are summarized in table i. we mention that kinetic energy conservation in all runs ( if velocity scaling was turned off ) did not exceed @xmath67 . also , the results for the total energy ( not shown ) , in case of the coulomb potential , agree very well with data from the literature . we first consider the pair distribution function @xmath68 for varying interaction potentials and parameter values . 1 shows @xmath68 for three values of the coupling parameter , @xmath69 . as expected , the coulomb pair distribution function is close to the debye - hckel limit for small coupling , with increasing @xmath0 , the deviations , especially around @xmath70 , grow systematically . the kelbg pair distributions practically coincide with the coulomb functions for @xmath71 but deviate from the latter at small distances of the order of the thermal debroigle wave length @xmath8 where quantum effects are important . clearly , with increasing degeneracy , the ratio @xmath72 increases , and the deviations extend to larger distances and grow in magnitude . with increasing @xmath0 , the deviations become smaller since coulomb effects dominate the behavior at small distances . let us now turn to the dynamical properties . in case of an ocp , charge and mass fluctuations are identical because of the rigid opposite charge background . in our simulations , we have calculated the density - density correlation function ( [ dcf ] ) and , by numerical fourier transformation , obtained the dynamical structure factor @xmath73 for several ( from 6 to 10 , depending on the simulation ) wave numbers , the values of which are determined by the size of the simulation box l ( see above ) . the value of the smallest wave number is given in table i. the frequency dependence of @xmath73 for several wave vectors is presented in figs . 2 - 4 for the coulomb and kelbg potentials . also , the results of the mean - field models are shown . the peak of the structure factor is related to the optical plasmon ( langmuir mode ) of the electrons , its position shows the plasmon frequency @xmath74 , its width - the damping of the mode . in the limit @xmath75 , @xmath76 for all models . for increasing wave numbers , the width of the peak grows steadily , and it merges with the continuum of single - particle excitations , e.g. @xcite , therefore , no results for larger wave numbers are shown . consider now the results for the plasmon dispersion more in detail , cf . first , we discuss the mean field results ( [ s_mf ] ) which are calculated using the vlasov and rpa polarizations , eqs . ( [ p_vlasov ] ) and ( [ p_rpa ] ) , respectively . the vlasov result was computed using the formulas given in the review of kugler @xcite , and for the rpa , a code was developed which accurately evaluates the pole integration in eq . ( [ p_rpa ] ) . both approximations show the same general trend for small and intermediate wave numbers : with increasing wave number , the plasmon frequency and the damping increase . at large @xmath77 , the dispersion exhibits a maximum and decreases again . in all situations , the rpa yields a slightly smaller frequency than the vlasov result , whereas the damping values are very close to each other . let us now turn to the simulation results . the coulomb and kelbg simulations have been performed for exactly the same parameters , except for n and run time ( cf . table i ) . ( notice that , in contrast to the kelbg case , the coulomb simulations depend only on @xmath0 which can be achieved by various combinations of density and temperature ) . comparison of the two simulations shows , cf . fig . 2 , that the results for the structure factors are very similar in case of small @xmath0 . peak positions and widths as well as the low and high frequency tails are very close to each other . the reason is obvious : since the potentials ( and pair distributions , cf . fig . 1 ) differ only at a small interparticle distances of the order of @xmath8 , differences in the structure factor would show up only at @xmath78 , which is about an order of magnitude larger than the wave numbers shown in fig . , the plasmon peak has already a width of the order of the frequency and no longer describes a well - defined collective excitation . it is now interesting to compare the simulation results to the theoretical approximations . the first observation is that the simulation peaks are significantly broader , cf . this is obvious since the simulations fully include interparticle correlations missing in the mean - field results . consequently , the plasmon damping contains collisional damping in addition to the landau damping ( which is the only damping mechanism in the mean - field models ) . correspondingly , the plasmon peaks in the simulations are shifted to smaller frequencies . this effect grows with increasing wave number as well as with increasing coupling ( see also fig . 5 ) . we note that , in our simulations , this shift is observed for all wave numbers , which is in contrast to the result of hansen [ see fig . @xcite for @xmath79 . in other words , the plasmon dispersion curves from the md simulations are lower than the mean - field result for all wave vectors @xmath63 , which is seen more clearly in fig . as expected the md curves for the structure factor are much closer to the rpa than to the vlasov result . in fig . 5 we plot the optical plasmon dispersion curves for three values of the coupling parameter for the vlasov and rpa dispersions together with the simulation results . we further show the well - known analytical approximation to the langmuir dispersion , @xmath80 clearly , this predicts a monotonically increasing dispersion . however , this approximation is valid only for @xmath81 and for @xmath55 . let us now consider the simulation results which do not have this limitation . in fig . 5 we show the md results for a coulomb potential and for the kelbg potential for three values of the degeneracy parameter , @xmath82 one clearly sees that , for these parameters , the dispersion is positive , @xmath83 , up to wave numbers of the order of one over the mean interparticle distance . for larger @xmath77 , the dispersion changes sign . this general trend is observed for the coulomb and the kelbg potential . on the other hand , with increasing quantum effects , @xmath66 , the deviations between the two potentials are growing , which becomes more pronounced as @xmath0 increases , cf . the curves for @xmath84 and @xmath85 : the dispersion in case of the kelbg potential shows a softer increase with increasing wave number and reaches a lower maximum approximately at the same wave number as in the coulomb case . we mention that this sign change of the dispersion has not been reported by hansen @xcite . comparing the simulations with the mean - field results , we again see that the md dispersions proceed lower than the mean field results , and this effect grows with increasing @xmath0 and increasing wave number . once more , we confirm that the rpa dispersion is much closer to the md result than the vlasov dispersion , at least for @xmath86 . [ as mentioned above , the simulation results for the dispersion show certain statistical fluctuations due to the varying accuracy of the results for the different wave numbers ] . let us now consider the plasmon damping more in detail . fig . 6 , shows the damping ( full width at half maximum of the plasmon peak of the structure factor ) as a function of wave number . it is interesting to compare with the familiar analytical expression from the vlasov theory , e.g. @xcite , @xmath87 where @xmath88 is the dimensionless wave number in units of the inverse the debye radius @xmath89 given in table i. formula ( [ vlasov_damp ] ) is derived under the condition that the damping is much smaller then the frequency [ @xmath90 , and is limited to small wave numbers @xmath91 . as expected , the damping given by formula ( [ vlasov_damp ] ) which is only landau damping , is much smaller than the damping found in the simulations , as the latter contain the full collisional damping also . obviously , for small coupling and small @xmath77 , eq . ( [ vlasov_damp ] ) shows the correct trend . however , deviations increase rapidly with growing coupling parameter . furthermore , the simulations which are not limited to small wave numbers , show a qualitatively different behavior at large @xmath77 : a monotonic increase of the damping . interesingly , with increasing @xmath0 the damping is reduced , cf . 6a , b . finally , we try to extend the analytical result for the plasmon dispersion , eq . ( [ vlasov_lim ] ) , to larger @xmath0 and to include quantum effects . to this end , we used the md data with the kelbg potential to construct an improved fit of the form @xmath92 . the result is shown in fig . 7 for @xmath84 and @xmath85 . due to the large fluctuations in the dispersion data and the increasing damping for large wave numbers , we used a weighted fit where the smallest @xmath93values had the largest weight and the statistical errors of the individual points have been taken into account . table ii contains the resulting fit parameters . according to this data both parameters @xmath94 and @xmath95 depend on @xmath0 and @xmath66 . the parameter @xmath94 is close to @xmath96 in agreement with eq . ( [ vlasov_lim ] ) , but with increasing @xmath0 , deviations are growing , compare table ii . we see no systematic influence of quantum effects on the parameter @xmath94 for @xmath84 . noticeable effects show up for @xmath85 , where increased degeneracy leads to a reduction of the coefficient @xmath94 . the second fit parameter allows to qualitatively reproduce the change of the sign of the dispersion . the overall agreement is satisfactory for wave numbers up to the inverse mean interparticle distance up to which the plasmons are comparatively weakly damped . we have presented classical molecular dynamics simulations of the dielectric properties of a one - component plasma at intermediate coupling and degeneracy , @xmath97 and @xmath98 . while classical md simulations can be extended to very large values of @xmath0 , they have limited applicablility to quantum plasmas . we used , as an effective quantum pair potential , the kelbg potential which correctly describes quantum diffraction effects for small @xmath0 . in general , we found that the simulation results for the dielectric properties and the plasmon dispersion with the coulomb and the kelbg potential are rather close , but start to deviate from each other as @xmath0 increases . nevertheless , the use of the kelbg potential is preferable . it correctly treats close collisions , i.e. the two - particle interaction at distances smaller than the debroglie wavelength . this is of even higher importance in the case of two - component plasmas where the kelbg potential allows to avoid the collapse of oppositely charged particles . therefore , the present investigation should be important for future work on two - component plasmas . finally , we mention that the kelbg potential is only the first term of a @xmath0 expansion . therefore , for @xmath99 the account of higher order corrections to the quantum diffraction effects is necessary . work on this subject is in progress . 999 j.p . hansen , phys . rev . a * 8 * , 3096 ( 1973 ) j.m . caillol , d. levesque , j.j . weis , and j.p . hansen , j. stat . phys * 28 * , 325 ( 1982 ) j. ortner , f. schautz , and w. ebeling , phys . e * 56 * , 1 ( 1997 ) r.k . moudgil , p.k . ahluwalia , and k. tankeshwar , phys . b * 54 * , 8809 ( 1996 ) w. schlke , k. hppner , and a. kaprolat , phys . rev . b * 54 * , 17464 ( 1996 ) s.g . brush , h.l . sahlin , and e. teller , j. chem . * 45 * , 2102 ( 1966 ) w.l . slattery , e.d . dollen , and h.e.dewitt , phys . a * 26 * , 2255 ( 1982 ) s. ogata , s. ichimaru , phys . a * 36 * , 5451 ( 1987 ) r.t . farouki , and s. hamaguchi , phys . e * 47 * , 4330 ( 1993 ) s. ichimaru , `` statistical plasma physics '' vol.*ii * , addison - wesley publishing company , 1994 ; g.s . stringfellow , h.e . dewitt , and w.l . slattery , phys . a * 41 * , 1105 ( 1990 ) d. pines , and ph . nozieres , `` the theory of quantum liquids '' , benjamin , new york 1966 g.d . mahan , `` many - particles physics '' , plenum press , new york/ london 1990 w.d . kraeft , d. kremp , w. ebeling , and g. rpke , `` quantum statistics of charged particle systems '' ( plenum , london , new york , 1986 ) m. bonitz , `` quantum kinetic theory '' , b.g . teubner , stuttgart / leipzig 1998 n. kwong , and m. bonitz , phys . rev 84 * , 1768 ( 2000 ) see e.g. d. klakow , c. toepffer , and p .- reinhard , phys . a * 192 * , 55 ( 1994 ) ; v.s . filinov , j. mol . phys . * 88 * , 1517 , 1529 ( 1996 ) g. kelbg , ann . physik ( leipzig ) * 12 * , 219 ( 1963 ) ; * 13 * , 354 ( 1964 ) ; * 14 * , 394 ( 1964 ) w.c . swope , h.c . andersen , p.h . berens , and k.r . wilson , j. chem . * 76 * , 637 , ( 1982 ) w. ebeling , h.j . hoffmann , and g. kelbg , contr . plasma phys . * 7 * , 233 ( 1967 ) b.r.a . nijboer , and f.w . de wette , physica * xxiii * , 309 ( 1957 ) m.j.l . sangster , and m. dixon , advances in physics * 25 * , 247 ( 1976 ) c. deutsch , phys . a * 60 * , 317 ( 1977 ) j.p . hansen , i.r . mcdonald , and e.l . pollock , phys . a * 11 * , 1025 ( 1975 ) a.a . kugler , j. stat . * 8 * , 107 ( 1973 ) g. zwicknagel , phd thesis , university of erlangen 1994 a.f . aleksandrov , l.s . bogdankievich , a.a . rukhadze , principles of plasma electrodynamics , springer , 1984

classical molecular dynamics ( md ) simulations for a one - component plasma ( ocp ) are presented . quantum effects are included in the form of the kelbg potential . results for the dynamical structure factor are compared with the vlasov and rpa ( random phase approximation ) theories . the influence of the coupling parameter @xmath0 , degeneracy parameter @xmath1 and the form of the pair interaction on the optical plasmon dispersion is investigated . an improved analytical approximation for the dispersion of langmuir waves is presented .

FILE - In this Dec. 17, 2014 file photo, people eat at a McDonald's restaurant in Tokyo. McDonald's Corp. officials in Japan bowed deeply Wednesday, Jan. 7, 2015 to apologize for a human tooth, plastic... (Associated Press) TOKYO (AP) — McDonald's Corp. officials in Japan bowed deeply Wednesday to apologize for a human tooth, plastic pieces and other objects found in the burger chain's food, highlighting how consumers here are both loving and hating the fast-food eatery. The hubbub over objects turning up in the food comes on the heels of a different kind of problem at the popular chain — a lack of fries, stemming from a shortage set off by labor disruptions on the U.S. West Coast. Last year, McDonald's in China and Japan along with other fast-food brands were hit by a scandal over expired meat from a Chinese supplier. In the recent cases, a child's mouth was injured by a piece of plastic in an ice cream sundae in December. The fragment had fallen into the dispenser while being assembled, according to McDonald's. In another case, a customer who bought a Big Mac set in August last year found a tooth in the fries. McDonald's said none of its employees at the outlet or its suppliers had lost a tooth, and there were no signs the tooth had been fried. It was still investigating how the tooth and plastic got in the food. "To make such cases zero is our goal," said Takehiko Aoki, a senior executive. "We are doing our utmost to tackle them, one by one." Aoki denied such cases highlighted an overall quality-control problem and called them "isolated" cases. He acknowledged there were other cases, including metal in a pancake and plastic in a McMuffin, but declined to give a tally of the incidents. He said it was possible that outsiders had planted the tooth and other items. In two other cases, pieces of plastic were found in the Chicken McNuggets, delivered from a plant in Thailand. One was blue, and so it could have fallen in during production, but the other was clear, a type not used at McDonald's, officials said. "I will eat McNuggets. I will feed McNuggets to my children. I have no doubts," said Aoki. McDonald's is popular in Japan, running more than 3,000 restaurants. Over the years, it has survived "mad cow" scares and more general health worries about high calories. Orders for fries were limited last year to small servings because of a potato shortage. Large fries came back Monday. ___ Follow Yuri Kageyama on Twitter at https://twitter.com/yurikageyama ||||| The McDonald's sign is reflected in a puddle in Tokyo January 7, 2015. TOKYO McDonald's Japan (2702.T) has apologized to customers and vowed to ensure product safety after objects including a tooth and plastic were found in its food, the latest trouble for a fast-food chain hit by sliding sales and a shortage of french fries. The chain, 49.9 percent-owned by McDonald's Corp (MCD.N), has been grappling with falling sales that began long before a food safety scandal last summer hit confidence in its products. Convenience stores in particular have drawn away customers with broader ranges of ready-made meals and low-priced coffee. McDonald's Japan brought in Chief Executive Sarah Casanova last March to reverse the trend, but the company is still on track to record its sixth straight year of sales declines and its first annual loss in 11 years. Wednesday's apology came after a diner found a roughly 4 cm (1 1/2 inch) strip of vinyl in a Chicken McNugget at the weekend. That prompted the chain to halt sales of nuggets made on the same day as the contaminated item at a plant in Thailand. The company is still investigating the cause. Among other incidents, a human tooth was found in a customer's french fry in August, while a child in December cut his mouth on a piece of plastic that was in a chocolate sundae. At a packed news conference, executives sought to reassure the public of the safety of McDonald's food. "I am confident that my family can eat McDonald's products," said Takehiko Aoki, senior vice president at McDonald's Holding Co (Japan) Ltd. "I think our response has been appropriate," he said when questioned on whether the company had been slow to announce its findings, explaining that the handling of each case is different. McDonald's Japan only started sourcing nuggets from three Thai plants less than six months ago. The change was aimed at boosting confidence in product quality after Chinese supplier Shanghai Husi Food Co Ltd was accused of selling expired meat. The Thai plant that produced the nugget found to contain vinyl is located in Saraburi, owned by Cargill, McDonald's Japan said. Cargill Thailand was not immediately available for comment. On Monday, just days after the latest discovery, McDonald's Japan resumed sales of all sizes of french fries for the first time in three weeks. A labor dispute at U.S. West Coast ports had delayed imports, forcing the company to ration portions. McDonald's Japan shares closed down 0.9 percent on Wednesday versus a 0.3 percent rise in the Jasdaq index .JSD. (Additional reporting by Chris Meyers in TOKYO and Khettiya Jittapong in BANGKOK; Editing by Christopher Cushing and Elaine Hardcastle) ||||| TOKYO—The operator of the McDonald’s chain in Japan on Wednesday disclosed four cases of contaminated food throughout the country, fueling already-heightened food-safety concerns after its Chinese supplier was reported to have sold expired chicken nuggets. McDonald’s Holdings Co. (Japan) Ltd. said a human tooth was found inside a pack of french fries sold in Osaka in August. In Fukushima prefecture, a child was also slightly injured...

– Things you don't expect to hear from McDonald's: There is no indication that a human tooth found in an order of fries was fried. That from the fast-food giant's Japan unit, which has been digging into the discovery of the tooth, which turned up in an order placed in August in Osaka. McDonald’s Holdings Co. (Japan) Ltd. further says it doesn't yet know how it ended up there: Workers at the plant that produces the fries don face masks, and none of the employees of the location in question reported an absent tooth. As the AP puts it, McDonald's Japan officials "bowed deeply" today in apology over the tooth, as well as plastic pieces that were recently found in its food. The Wall Street Journal reports that three plastic incidents were discussed. A child eating a sundae last month was lightly injured by a plastic piece determined to have come from a machine involved in assembling the dessert. The other two incidents involved plastic in chicken nuggets: One was blue, and so it could have fallen in during production (its Thai suppliers use colored materials to make it easier to sight instances of contamination), but the other was clear, a type not used at McDonald's, officials say. Reuters notes that McDonald's Japan has been obtaining its nuggets from Thai producers for less than six months, following a scandal involving a Chinese supplier that allegedly used expired meat. The company's problems stretch back further: McDonald's Japan is expected to report a sixth consecutive year of declining sales and its first loss in 11 years.

the investigation of the double beta ( @xmath6 ) decay is considered now as one of the most sensitive probe of physics beyond the standard model of particles and interactions @xcite . the observation of the neutrinoless ( @xmath25 ) mode of @xmath6 decay could establish an absolute scale of the neutrino mass and the neutrino mass hierarchy , clarify the nature of the neutrino ( dirac or majorana particle ) and check the conservation of the lepton number . the process also depends on possible existence of light nambu - goldstone bosons ( majorons ) and hypothetical admixture of right - handed currents in weak interaction . at present the two neutrino ( 2@xmath26 ) 2@xmath27 decay , process of nuclear transformation @xmath28 , was observed in 10 isotopes with the half - lives in the range of @xmath29 yr , while only limits on @xmath30 decays up to @xmath31 yr were set in numerous experiments @xcite . the sensitivity of experiments to search for @xmath6 processes , which transform @xmath32 nucleus to @xmath33 : double electron capture ( @xmath8 ) , electron capture with emission of positron ( @xmath34 ) , and double positron ( @xmath35 ) decay , are on the level of @xmath36 yr @xcite ; even allowed in the standard model the two neutrino mode is still not observed decay of @xmath37ba was obtained in @xcite by geochemical method . however , this result has to be confirmed by direct counting experiments . ] . at the same time , the investigation of neutrinoless @xmath8 and @xmath34 processes could give an important information about possible contribution of the right - handed currents to the neutrinoless double @xmath38 decay rate @xcite . therefore developments of experimental methods to search for `` double beta plus '' processes are required . the @xmath1pt is one of the twenty two potentially @xmath7 active nuclei @xcite . the energy of the double beta decay is @xmath39 kev @xcite . the decay scheme of the @xmath1pt is presented in fig . 1 . it is also worth noting that in the capture of two electrons from external atomic shells , the energy release is close to the energy of the excited level of @xmath1os with @xmath40 kev @xcite . such a coincidence could give a resonant enhancement of the neutrinoless double electron capture in result of energy degeneracy . the possibility of the resonant neutrinoless double electron capture was discussed in refs . @xcite , where an enhancement of the rate by some orders of magnitude was predicted for the case of coincidence between the released energy and the energy of an excited state . according to @xcite , high @xmath41 atoms are strongly favored to search for resonant @xmath8 decay . it should be noted that @xmath1pt has the greatest @xmath41 value among the nuclei for which a resonant double electron capture is possible . unfortunately the natural abundance of @xmath1pt is very low : @xmath42 @xcite . perhaps this fact , together with the rather high cost of platinum , explains the absence of experimental results ( after the only one old study @xcite ) to search for @xmath6 decay of this nuclide . a modest limit on @xmath7 decay of @xmath1pt on the level of @xmath43 yr was calculated in @xcite on the basis of the early experiment @xcite with corrections on the decay energy , experimental efficiency and the natural isotopic abundance . another platinum isotope @xmath2pt is potentially @xmath44 active , with the energy of decay @xmath45 kev @xcite . the isotopic abundance of @xmath2pt is @xmath46 @xcite . the decay scheme of @xmath2pt is presented in fig . as one can see , the @xmath11 decay of @xmath2pt to the first excited @xmath47 level of @xmath2hg can be searched for by using an external @xmath4 detector . the aim of this study was the search for double @xmath0 processes in @xmath1pt and @xmath2pt with the help of ultra - low background hp ge @xmath4 spectrometry . two platinum cups and one lid designed for chemistry purposes with the total mass of 42.53 g were used in the experiment . taking into account the isotopic composition of the platinum , the sample contains @xmath48 nuclei of @xmath1pt and @xmath49 nuclei of @xmath2pt . the search for double @xmath0 decay of platinum was realized at the laboratori nazionali del gran sasso of the infn ( average overburden of @xmath50 meters of water equivalent ) @xcite with a p - type hp ge detector ( gecris , 468 @xmath3 of volume ) . the energy resolution of the spectrometer is fwhm = 2.0 kev for the 1333 kev @xmath4 line of @xmath51co . the data with the sample were accumulated over 1815.4 h , while the background spectrum was taken over 1045.6 h. the spectra normalized on the time of measurements are presented in fig . there is a certain difference between the pt and the background spectra , mainly due to the contamination of the platinum by @xmath52ir ( @xmath53 d @xcite ) . the activity of @xmath52ir is equal to ( @xmath54 ) mbq / kg . the radioactive iridium could appear in platinum due to the cosmogenic activation of pt by cosmic rays at the earth surface . in addition , iridium usually accompanies platinum in ores . therefore @xmath52ir can be created in result of neutron capture by @xmath55ir which is one of two naturally occurring iridium isotopes ( @xmath56 , the cross section for thermal neutrons is @xmath57 b @xcite ) . however , the half - life of the ground state of @xmath52ir is @xmath58 d @xcite , and the exponential decrease in time of the @xmath52ir activity should be observed during our 75.6 d measurements . in fact , the behaviour of the counting rate in the f.e . 468.1 kev @xmath4 peak of @xmath52ir can not be explained by this assumption ( see fig . 4 ) . a fit of the data by the exponential function corresponding to the decay of @xmath52ir gives too large value of @xmath59/n.d.f.@xmath60 . at the same time the data is very well described ( @xmath59/n.d.f.@xmath61 ) by exponential decay with the half - life 241 y ( decay of @xmath62ir , see fig . , the @xmath52ir activity should be ascribed not to the ground state , but to the isomeric @xmath62ir level with @xmath63 kev and @xmath64 yr @xcite . this isomeric state decays to the ground state of @xmath52ir emitting 155.1 kev and 13.0 kev @xmath4 s which are however strongly converted to electrons ( coefficients of conversion are equal to @xmath65 and @xmath66 @xcite ) . this explains the absence of the 155.1 kev peak in our data . a peak at the energy 137 kev is caused by the @xmath67 decay of @xmath1pt to the lowest excited 137.2 kev level of @xmath68os ( the first evidence is reported in @xcite ) . we have also observed some excess of events in the 662 kev peak of @xmath69cs . the response functions of the detector to decays of @xmath70k , @xmath51co , @xmath69cs , @xmath52ir , u / th daughters in the platinum sample were simulated by egs4 code @xcite with initial kinematics given by the decay0 event generator @xcite . the activity of @xmath69cs and @xmath52ir , as well as upper limits on contamination by @xmath70k , @xmath51co and u / th daughters are presented in table 1 . the investigation of radioactive contaminants in platinum samples is important also e.g. when selecting the materials to build platinum crucibles to be used for growing radiopure inorganic crystal scintillators . .radioactive contamination of the platinum sample measured with hp ge detector . gamma emitters and energies of @xmath4 lines used to determine the activity of the isotopes are specified in the 3rd column . the upper limits are given at 90% c.l . , and the uncertainties of the measured activities are estimated at 68% c.l . [ cols= " < , < , < , < " , ] we do not observe any peaks in the spectrum accumulated with the platinum sample which could indicate double @xmath0 activity of @xmath1pt or @xmath2pt . therefore only lower half - life limits ( @xmath71 ) can be set according to the formula : @xmath72 , where @xmath73 is the number of potentially @xmath6 unstable nuclei , @xmath74 is the detection efficiency , @xmath75 is the measuring time , and @xmath76 is the number of events of the effect searched for which can be excluded at given confidence level ( c.l . , all the limits obtained in the present study are given at 90% c.l . ) . the efficiencies of the detector to the double @xmath0 processes in the platinum isotopes were also calculated with the egs4 code @xcite and decay0 event generator @xcite . one positron can be emitted in the @xmath7 decay of @xmath1pt with energy up to ( @xmath77 ) kev . the annihilation of the positron will give two 511 kev @xmath4 s leading to extra rate in the annihilation peak . part of the spectrum in the energy interval @xmath78 kev is shown in fig . 5 . there are annihilation peaks in both the spectra accumulated with the platinum sample ( @xmath79 ) counts and in the background spectrum ( @xmath80 ) counts . the decays of @xmath69cs and @xmath52ir , present in the used platinum sample , provide no contribution to the peak . the difference in the areas of the annihilation peak ( @xmath81 ) counts , which can be attributed to electron capture with positron emission in @xmath1pt , gives no indication on the effect . in accordance with the feldman - cousins procedure @xcite we should take @xmath82 counts which can be excluded at 90% c.l . taking into account the detection efficiency ( @xmath83 ) , we have estimated a limit on the half - life of @xmath1pt relatively to two neutrino @xmath7 decay as : @[email protected].@xmath86 yr . the detection efficiency in a case of neutrinoless @xmath34 decay is slightly lower ( 13.9% ) , which leads to the limit : @[email protected].@xmath88 yr . in the @xmath89 decay the first excited level of @xmath1os could also be populated with emission of @xmath4 quanta with the energy 186.7 kev . there is a peak at the energy of ( @xmath90 ) kev with the area ( @xmath91 ) counts in the spectrum accumulated with the platinum sample ( see fig . most likely this peak can be explained by @xmath67 decay of @xmath92u to the excited levels of @xmath93th . some part of the peak can be due to @xmath67 decay of @xmath94ra to the excited level 186.2 kev of @xmath95rn . at the same time we can not surely estimate a contribution to this peak neither from the decay of @xmath92u nor from the decay of @xmath94ra . for @xmath92u we set only the limit on activity of @xmath92u in the platinum ( @xmath96 mbq / kg ) . even much stronger limit ( @xmath97 mbq / kg ) was obtained on the activity of @xmath94ra by analysis of @xmath98pb and @xmath98bi peaks . thus , we ascribe very conservately 120 counts to the @xmath7 decay of @xmath1pt to the first excited level of @xmath1os , which leads to the following limit on the process : @xmath84g.s.@xmath99kev@xmath100 yr . however , a better limit can be set by using the estimation of the annihilation peak area ( the detection efficiency for the process is @xmath101 ) : @xmath84g.s.@xmath99kev@xmath102 yr . the same limit was set for the neutrinoless @xmath7 decay of @xmath1pt to the excited 186.7 kev level of @xmath1os . the @xmath103 capture in @xmath1pt to the ground state of @xmath1os will give cascade of x rays and auger electrons with the individual energies up to 73.8 kev @xcite . the most intensive x ray lines should have the energies 61.5 ( 27.4% ) , 63.0 ( 46.7% ) , 71.1 ( 5.5% ) , 71.4 ( 10.6% ) and 73.4 kev ( 3.7% ) . contributions to the spectrum in this energy region ( see fig . 6 , a ) are expected from the decay of @xmath52ir , the excitation of pt by the decays of @xmath69cs , and also from the decays of u / th daughters contained in the materials of the detector . to set a limit on the process searched for , the energy spectrum was fitted by the model consisting of the sum of five gaussians ( to describe the expected 61.5 , 63.0 , 71.1 , 71.4 and 73.4 kev peaks in @xmath1os ) , two gaussians ( 65.1 and 66.8 kev x ray lines due to excitation of pt ) , and a polynomial function of the first degree ( background ) . a fit in the energy interval ( @xmath104 ) kev gives the area of the @xmath103 effect as ( @xmath105 ) counts . according to the feldman - cousins procedure we should take @xmath106 counts at 90% c.l . therefore taking into account the efficiency to detect the expected effect ( 1.9% ) we set the following limit on the @xmath103 capture in @xmath1pt : @[email protected].@xmath108 yr . the distribution of the excluded effect of the @xmath103 decay in @xmath1pt is shown at fig . 6 , a. the @xmath109 energy of @xmath1pt allows also the population of several excited levels of @xmath1os . in a subsequent de - excitation process , one or few cascade @xmath4 quanta ( together with conversion electrons and @xmath110 pairs ) will be emitted . to estimate limits on two neutrino double electron capture in @xmath1pt , the energy spectrum accumulated with the platinum sample was analyzed in different energy intervals . the results of the estimations are presented in table 2 , where the energies of the @xmath4 peaks , used to derive the limits , are also specified . in the neutrinoless double electron capture to the ground state of the daughter nuclei , in addition to the x rays , some other particle(s ) should be emitted to take away the rest of the energy . usually one bremsstrahlung @xmath4 quantum is assumed . the energy of the @xmath4 quantum is expected to be equal to @xmath111 , where @xmath112 and @xmath113 are the binding energies of the first and of the second captured electrons on the atomic shell . the binding energies on the @xmath114 , @xmath115 and @xmath116 shells in os are equal to @xmath117 kev , @xmath118 kev , @xmath119 kev and @xmath120 kev @xcite , respectively . therefore , the expected energies of the @xmath4 quanta for the @xmath121 capture in @xmath1pt to the ground state of @xmath1os are in the intervals : i)@xmath122 kev for the @xmath123 ; ii ) @xmath124 kev for the @xmath125 ; iii ) @xmath126 kev for the @xmath127 process . there is only one peak at the energy of 1238 kev with the area ( @xmath128 ) counts in the spectrum accumulated with the platinum sample in the energy interval of interest ( @xmath129 ) kev ( see fig . 6 , b ) . more likely this is the @xmath4 peak 1238.1 kev from the decays of @xmath98bi ( daughter of @xmath94ra from @xmath130u family ) . it is rather difficult to estimate a contribution of the @xmath98bi @xmath4 quanta to the peak area because we do not know exactly location of the @xmath94ra contamination in the materials of the set - up . conservatively we assume that all the peak area is due to the neutrinoless @xmath131 decay of @xmath1pt . taking into account the calculated efficiency to detect @xmath4 quanta with the energy ( @xmath129 ) kev ( @xmath132 ) , it gives the following limit on the process searched for : @[email protected].@xmath134 yr . there are no clear peaks in the energy intervals ( @xmath135 ) kev and ( @xmath136 ) kev expected for the @xmath125 and the @xmath127 processes in @xmath1pt . taking into account the calculated detection efficiencies for @xmath4 quanta with the energies in these intervals ( 4.6% ) and limits on the numbers of events of the effects ( @xmath137 and @xmath138 counts , respectively ) we have obtained the following limits on the @xmath25 double electron captures in @xmath1pt to the ground state of @xmath1os : @[email protected].@xmath140 yr , @[email protected].@xmath142 yr . limits on the @xmath121 decay of @xmath1pt to the excited levels of @xmath1os were obtained in the similar way as for the @xmath143 mode by analysis of the experimental data in the energy intervals where intensive @xmath4 peaks from the processes are expected . the limits on double electron capture in @xmath1pt to the ground and excited levels of @xmath1os are presented in table 2 . the atomic mass difference between @xmath1pt and @xmath1os atoms is very close to the energy of the excited level 1382.4 kev in @xmath1os . a resonance transition could be fulfilled if two external electrons will be captured . there is no peak in the energy spectrum accumulated with the platinum sample with the energy 1195.7 kev expected from de - excitation of the 1382.4 kev level of @xmath1os ( see fig . 1 ) . taking into account the detection efficiency for 1195.7 kev @xmath4 quanta ( 4.5% ) we set the following limit on the decay : @xmath144g.s.@xmath145 kev@xmath146 yr . to set a limit on the double @xmath27 transition of @xmath2pt to the @xmath147 excited level of @xmath2hg with the energy of 411.8 kev , the energy spectrum ( see fig . 6 , c ) was fitted in the energy interval ( @xmath148 ) kev by a straight line ( which represents the background model ) and the expected peak at 411.8 kev . the fit gives the area of the peak ( @xmath149 ) counts , which allows to exclude 29 counts at 90% c.l . taking into account the detection efficiency ( @xmath150 ) we have obtained the following limit on the process searched for : @xmath151g.s.@xmath152 kev@xmath153 the measurements performed over 1815 h with a 42.5 g sample of platinum with the help of an ultra - low background hp ge @xmath4 spectrometer ( 468 @xmath3 ) were used to set limits on double @xmath0 processes in @xmath1pt in the range of @xmath154 yr , which is @xmath155 orders of magnitude higher than the limit on @xmath156 ( g.s . @xmath157 g.s . ) decay obtained in @xcite by a re - analysis of the early experiment @xcite . the search for the possible resonant @xmath121 capture to the 1382.4 kev level was realized for the first time . for future applications , taking into account the strong dependence of the resonant process on the difference in atomic masses of @xmath1pt and @xmath1os , precise measurements of the atomic masses are required . moreover , it would also be useful to precisely study the characteristics of the 1382.4 kev level of @xmath1os ( spin , parity , decay scheme ) . search for @xmath6 transition of @xmath2pt to the 411.8 kev excited level of @xmath2hg was carried out at the first time giving the limit @xmath158 yr . the measurements allowed us to estimate the radioactive contamination of the used platinum sample . in particular , we have detected 7 mbq / kg of @xmath69cs and 40 mbq / kg of @xmath52ir in this platinum sample . the contamination of @xmath51co , @xmath94ra , @xmath159ra and @xmath159th does not exceed the level of a few mbq / kg , while the activities of @xmath70k , @xmath92u , @xmath130u are less than a few tens mbq / kg ( we assume a broken equilibrium in u / th chains ) . to improve the sensitivity of the experiment we are going to increase the mass of the platinum by one order of magnitude . further improvements can be achieved by increasing the detection efficiency and the exposition , and obviously by using enriched @xmath1pt isotope . specially developed multi - crystal hp ge detectors could also be applied to reach a sensitivity to double @xmath0 processes in @xmath1pt on the level of @xmath160 yr . this would be particularly interesting also because of the possibility of a resonant double electron capture in @xmath1pt having such isotope the largest @xmath41 value ( the nuclear parameter which greatly favors the process ) among the nuclei where a resonant double electron capture could occur . the group from the institute for nuclear research ( kyiv , ukraine ) was supported in part through the project `` kosmomikrofizyka-2 '' ( astroparticle physics ) of the national academy of sciences of ukraine . zdesenko , rev . 74 ( 2002 ) 663 ; + s.r . elliot , p. vogel , ann . nucl . part . 52 ( 2002 ) 115 ; + j.d . vergados , phys . ( 2002 ) 1 ; + s.r . elliot , j.engel , j. phys . g 30 ( 2004 ) r183 ; + f.t . avignone iii , g.s . king , yu.g . zdesenko , new j. phys . 7 ( 2005 ) 6 ; + h. ejiri , j. phys . japan 74 ( 2005 ) 2101 ; + h.v . klapdor - kleingrothaus , int . e 17 ( 2008 ) 505 ; + f.t . avignone iii , s.r . elliott , j. engel , rev . 80 ( 2008 ) 481 . barabash , phys . c 81 ( 2010 ) 035501 . tretyak , yu.g . zdesenko , at . data nucl . data tables 61 ( 1995 ) 43 ; 80 ( 2002 ) 83 . gavriljuk et al . , phys . at . 69 ( 2006 ) 2124 . barabash et al . , j. phys . g 34 ( 2007 ) 1721 . kim et al . , nucl . phys . a 793 ( 2007 ) barabash et al . a 807 ( 2008 ) 269 . j. dawson et al . , nucl . phys . a 799 ( 2008 ) 167 . p. belli et al . b 658 ( 2008 ) 193 . p. belli et al . phys . j. a 36 ( 2008 ) 167 . barabash et al . , phys . c 80 ( 2009 ) 035501 . p. belli et al . j. a 42 ( 2009 ) 171 . p. belli et al . phys . a 824 ( 2009 ) 101 . p. belli et al . phys . a 826 ( 2009 ) 256 . n.i . rukhadze et al . , ( 2010 ) 012072 . p. belli et al . , j. phys . g 38 ( 2011 ) 015103 . meshik et al . , phys . c 64 ( 2001 ) 035205 . m. hirsch , k. muto , t. oda , h.v . klapdor - kleingrothaus , z. phys . a 347 ( 1994 ) 151 . g. audi , a.h . wapstra , c. thibault , nucl . a 729 ( 2003 ) 337 . b. singh , nucl . data sheets 99 ( 2003 ) 275 . winter , phys . 100 ( 1955 ) 142 . voloshin , g.v . mitselmakher , r.a . eramzhyan , jetp lett . 35 ( 1982 ) 656 . j. bernabeu , a. de rujula , c. jarlskog , nucl . b 223 ( 1983 ) 15 . z. sujkowski , s. wycech , phys . c 70 ( 2004 ) 052501 . bohlke et al . , j. phys . data 34 ( 2005 ) 57 . fremlin , m.c . walters , proc . soc . a 65 ( 1952 ) 911 . zhou chunmei , nucl . data sheets 95 ( 2002 ) 59 . c. arpesella et al . , astropart . ( 2002 ) 1 . m. laubenstein et al . , appl . isotopes 61 ( 2004 ) 167 . r.b . firestone et al . , _ table of isotopes _ , john wiley & sons , new york , 8th edition ( 1996 ) and cd update ( 1998 ) . baglin , nucl . data sheets 84 ( 1998 ) 717 . p. belli et al . , first observation of alpha decay of @xmath1pt to the first excited level of @xmath68os , rom2f/2010/22 accepted for publication on phys . nelson et al . , slac - report-265 , stanford , 1985 . ponkratenko et al . , phys . at . 63 ( 2000 ) 1282 ; v.i . tretyak , to be published . feldman , r.d . cousins , phys . d 57 ( 1998 ) 3873 .

a search for double @xmath0 processes in @xmath1pt and @xmath2pt was realized with the help of ultra - low background hp ge 468 @xmath3 @xmath4 spectrometer in the underground gran sasso national laboratories of the infn ( italy ) . after 1815 h of data taking with 42.5 g platinum sample , @xmath5 limits on @xmath6 processes in @xmath1pt ( @xmath7 and @xmath8 ) have been established on the level of @xmath9 yr , 3 to 4 orders of magnitude higher than those known previously . in particular , a possible resonant double electron capture in @xmath1pt was restricted on the level of @xmath10 yr at 90% c.l . in addition , @xmath5 limit on @xmath11 decay of @xmath2pt ( @xmath12 ) to the 2@xmath13 excited level of @xmath2hg has been set at the first time : @xmath14 yr . the radiopurity level of the used platinum sample is reported . * first search for double @xmath0 decay of platinum by ultra - low background hp ge @xmath4 spectrometry * 1.0 cm * p. belli@xmath15 , r. bernabei@xmath16 f. cappella@xmath17 , r. cerulli@xmath18 , f.a . danevich@xmath19 , a. di marco@xmath15 , a. incicchitti@xmath17 , m. laubenstein@xmath18 , s.s . nagorny@xmath19 , s. nisi@xmath18 , o.g . polischuk@xmath19 , v.i . tretyak@xmath19 * 0.3 cm @xmath15_infn sezione roma `` tor vergata '' , i-00133 rome , italy _ @xmath20_dipartimento di fisica , universit di roma `` tor vergata '' , i-00133 , rome , italy _ @xmath21_infn sezione roma , i-00185 rome , italy _ @xmath22_dipartimento di fisica , universit di roma `` la sapienza '' , i-00185 , rome , italy _ @xmath23_infn , laboratori nazionali del gran sasso , i-67010 assergi ( aq ) , italy _ @xmath24_institute for nuclear research , msp 03680 kyiv , ukraine _ 0.5 cm 0.4 cm _ pacs _ : 23.40.-s , 27.80.+w 0.4 cm _ keywords _ : double @xmath0 decay , @xmath1pt , @xmath2pt

in recent decades , many insights into photospheric processes were retrieved from spectropolarimetric observations , mainly in the visible and near - infrared spectral range . progress in this field was not only reached by the availability of ever larger telescopes ( with an improved spatial resolution ) or by going above the earth s disturbing atmosphere , but also by advancements in the analysis techniques . while in the early years of spectropolarimetric observations the physical parameters of the solar atmosphere ( temperature , magnetic field vector , line - of - sight ( los ) velocity , pressure , density and their height dependence ) were directly derived from the stokes profiles ( classical estimates , see , e.g. , * ? ? ? * for an overview ) , during the last approximately 25 years the usage of stokes inversion techniques has become established . initially the milne - eddington approach ( involving height - independent atmospheric parameters ; see , e.g , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) was most widely used , but with time ( and increasing computing power ) inversion codes that numerically solve the full radiative transfer equations became increasingly important . prominent examples of such codes are the sir code ( * * s**tokes * * i**nversion based on * * r**esponse functions ; * ? ? ? * ) and the spinor code ( * * s**tokes-**p**rofiles-**in**version-*o*-**r**outines ; * ? ? ? * ; * ? ? ? * ) , which assume local thermodynamic equilibrium ( lte ) , or the nicole code ( * * n**on - lte * * i**nversion * * co**de using the * * l**orien * * e**ngine ; * ? ? ? * ; * ? ? ? * ) , which also considers non - lte conditions . a stokes inversion is an iterative process that needs a first guess of the atmospheric parameters , which can be obtained from model calculations , from older results retrieved from similar targets , or in case of the magnetic field vector it can also be simply constant with height or random . the unno - rachkovsky equations for polarized radiative transfer @xcite are numerically solved for the initial atmosphere , which provides the first guess of the synthetic stokes profiles . these synthetic stokes profiles are then compared with observed stokes profiles . differences between the two sets of profiles are used to systematically change the initial atmosphere . this fitting process is iteratively repeated until a good match between the synthetic and observed stokes profiles is reached . finally , after multiple iterative steps , the atmosphere that leads to the best fit is considered as the best representation of the real sun ( within the limitations of the model ) and is output as the result of the stokes inversion . before the observed stokes profiles can be compared with the synthetic profiles , the latter need to be degraded with all the instrumental effects that were present during the observation . a convolution of the synthetic stokes profiles with the spectral transmission profile of the used instrument ( or its approximation by fitting the macroturbulent velocity ) is standard in nearly all inversion codes . such a transmission profile can be obtained , e.g. , by a laboratory measurement as part of the instrument calibration , or by a comparison of measured spectra with spectrally highly resolved spectra unaffected by spectral stray light ( e.g. , spectra recorded with the fourier transform spectrometer , cf . * ? ? ? * ; * ? ? ? a further improvement in the quality of the inversion results could be reached by considering the spatial degradation , which introduces a spatial coupling between the pixels of a data set . such spatial degradations can be described by the spatial point - spread function ( psf ) of the instrument that can either be measured , e.g. , via the phase - diversity ( pd ) technique @xcite , or it can be modeled from the telescope geometry ( e.g. , * ? ? ? * ) , or determined from an eclipse or a transit of mercury or venus ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the stokes images can then be deconvolved with the spatial psf prior to inversions ( e.g. , * ? ? ? * ; * ? ? ? * ) , which regularly lowers the signal - to - noise ratio ( e.g. , in case of the sunrise / imax data by a factor of three , see * ? ? ? * ) . in recent years methods were developed to avoid the increase in noise by considering the spatial psf not prior to , but during the inversion process . @xcite extended the stokes inversion code spinor by convolving the synthetic stokes images with a given spatial psf before the comparison with the observations ( see panel a of fig . [ fig1 ] ) . since this approach strictly avoids any deconvolution , the increase of noise can be avoided to a large extent . data recorded with the spectropolarimeter ( sp ) onboard the hinode satellite @xcite were then successfully used to apply the spatially coupled spinor code ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite introduced another approach that decomposes the stokes profiles into their principal components , which was later applied to quiet - sun data recorded with hinode / sp @xcite . it begs the question what further improvements of the stokes inversion technique appear possible . since the dynamics and evolution of the sun are of particular interest , often observation data sets do not only consist of individual snapshots at isolated points in time but of time series . the temporal evolution of the plasma in the solar photosphere can be well described by the equations of mhd , so that two consecutive observations of a time series ( separated by a sufficiently small interval of time , @xmath1 ) are not statistically independent of each other , but are coupled by the mhd equations ( including the equation of energy transfer ) . we expect that an inclusion of the mhd equations in the stokes inversion of a time series will significantly improve the results , because a model that combines the radiative transfer equations with the mhd equations contains more physics and hence has higher chances of approaching the real sun . panel b of fig . [ fig1 ] demonstrates how the mhd equations can be connected with a stokes inversion . the process starts with the determination of an initial guess of the atmospheric parameters for an observation recorded at time @xmath2 . in contrast to a traditional stokes inversion , the initial guess comprises additional quantities ( horizontal velocities , plasma density and total energy ) and has to be given on a geometrical height ( @xmath3 ) scale , since this is the natural scale of the mhd equations ( instead of an optical depth ( @xmath4 ) scale ) . the extended set of atmospheric parameters allows the calculation of the temporal evolution of the plasma via an mhd code till @xmath5 , which is the observation time of the next frame of the time series . after a conversion from the geometrical height into optical depth , a subset of the atmospheric parameters is used to calculate synthetic stokes profiles , which then can be spectrally and spatially degraded . the left branch of the flow chart in panel b of fig . [ fig1 ] illustrates this for the observation recorded at time @xmath2 , while the right branch does it for the next frame recorded at time @xmath5 . a systematic change of the atmospheric parameters tries to minimize the deviation of the synthetic stokes profiles from the observed ones ( for both time steps , @xmath2 and @xmath5 ) in an iterative fitting process . the extension of the atmospheric parameters from five to nine quantities together with the change to a geometrical height scale ( of typically hundreds of grid points instead of just a few optical depth nodes ) , as well as the need for the relatively slow mhd simulations make the computational effort of a complete integration of the mhd equations into the stokes inversion orders of magnitude higher than present computational capabilities . an implementation of the algorithm as shown in panel b of fig . [ fig1 ] is hence not yet possible . this work describes the very first approach towards the full spatially and temporally coupled inversion of spectropolarimetric observations of the solar photosphere , using mhd simulations and the psf to link the temporal and spatial information . [ observation ] explains the used observations , sect . [ simulation ] the employed mhd simulations . the method itself is outlined in sect . [ method ] , while in sect . [ summary ] we summarize and discuss the results we have achieved so far . the observations used in this study where recorded in june 2013 during the second stratospheric flight of the balloon - borne solar observatory sunrise . we refer to @xcite for technical details of the telescope and the gondola . @xcite give an overview of the updates applied to the second flight . image stabilization , correlation tracking , and real - time sensing of the lower wavefront aberrations were realized by a shack - hartmann wavefront sensor that also controlled the telescope s focus mechanism @xcite . two science instruments were operated in parallel onboard sunrise : the sunrise filter imager ( sufi ; * ? ? ? * ) to record broadband filtergrams in the violet and near - ultraviolet spectral range ( 214397 ) nm and the imaging magnetograph experiment ( imax ; * ? ? ? * ) for spectropolarimetric observations in the fei 525.02 nm line . this spectral line has a land factor @xmath6 and is one of the most zeeman - sensitive lines in the visible spectrum . an overview of the recorded data is given by @xcite . in this study we refer to an observation recorded by the imax instrument on 2013 june 12 , 23:39 ut . the telescope pointed to the active region ar 11768 close to disk center ( with cosine of the heliocentric angle @xmath7 ) . imax was operated in the v8 - 4 mode , i.e. , the full stokes vector was measured at eight wavelength positions ( 7 within the spectral line at @xmath8 pm and one in the continuum at @xmath9 pm offset from the line core ) where four images of 250 ms exposure time were accumulated at a time . the plate scale of imax was 0@xmath100545 per pixel . in the post - processing of the imax data , corrections for dark current and flat - field effects where applied . a pre - flight polarimetric calibration provided a mller matrix for each pixel of the field of view ( fov ) that allowed a removal of the instrumental polarization @xcite . because the primary mirror could not be included in the polarimetric calibrations and because the thermal environment was different during the observations than during calibration , the elements of the mller matrices slightly changed , which we took into account by applying an ad - hoc cross - talk removal of the order of 1% . the thus reduced data are named level-1 ( or non - reconstructed data ) . a pd measurement was achieved about two hours before the observation by inserting a pd plate into the optical path of one of the two imax cameras . this allowed the retrieval of a psf used to correct the data for low - order wavefront aberrations @xcite . the pd reconstructed data are named level-2 . more details are reported by @xcite . see also @xcite for additional details concerning data reduction steps specific to imax during the second sunrise flight . we accomplished realistic simulations of the radiative and magneto - hydrodynamical processes in the solar photosphere and upper convection zone with the muram ( * m*ax planck institute for solar system research / * u*niversity of chicago * ra*diation * m*agneto - hydrodynamics ) code , a three - dimensional , non - ideal , compressible mhd code that includes non - gray radiative transfer calculations in the energy equation under the assumption of local thermal equilibrium @xcite . the simulation box is 24 mm @xmath11 24 mm in its horizontal dimensions and has a depth of 6.1 mm . the cell size of the simulation box is 41.7 km in the two horizontal directions and 16 km in the vertical direction . we used a statistically relaxed purely hydrodynamical simulation as initial condition . a homogeneous unipolar vertical magnetic field of @xmath12 g was then introduced into the hydrodynamical simulation and the simulation run was continued for another three hours of solar time to reach again a statistically relaxed state . after the relaxation a single snapshot covering several pores with field strengths up to 3500 g ( at @xmath13 ) is used for this study , see the left panel of fig . the boundary conditions where periodic in the horizontal directions , closed at the top boundary of the box , while a free in- and outflow of plasma was allowed at the bottom boundary under the constraint of total mass conservation . the @xmath14 surface for the continuum at 500 nm was on average reached about 700 km below the upper boundary . the forward calculation mode of the spinor inversion code @xcite was used to compute synthetic stokes spectra of the fei 525.02 nm line used by imax . we synthesized the strongest 20 spectral lines in the range ( 524.72525.32 ) nm whose atomic parameters are listed in @xcite . the radiative transfer was calculated for a heliocentric angle of @xmath7 . in this section we present an alternative method to obtain the atmospheric parameters from observed stokes profiles , i.e. , an alternative to the traditional stokes inversion technique purely based on radiative transfer calculations and the computation of a model atmosphere assuming hydrostatic equilibrium ( usually restricted to the vertical direction ) . the idea is to use an mhd simulation of a target similar to the observations ( in our case pores and granulation ) for a stokes synthesis of the observed spectral range . the synthetic stokes data then have to be adapted to the pixel size of the observation and degraded with all the instrumental effects that influenced the observational data . to gain a comprehensive knowledge about these instrumental effects is possibly the largest difficulty of the method . we now consider the degraded mhd data set as a pool of stokes profiles that can be directly compared with the observed stokes profiles . in a first iteration , a pixel in the degraded data set is assigned to a particular observed pixel , namely the one that shows the least deviation between observed and synthetic stokes profiles . the assigned mhd pixels embody the inversion result of the first iteration . our inversion result ( a pixel in the degraded mhd data set ) is not only connected to the temperature , magnetic field vector , and los velocity in the photosphere as is the case for results of traditional stokes inversion techniques , but also the full set of undegraded mhd data is available , including horizontal velocities and also including information on the layers immediately below the solar surface , which are not directly accessible via spectral lines . because the layers below the solar surface drive the features at the solar surface , the inversion of a time series of stokes data has the potential to constrain the sub - surface dynamics . the stratifications of the atmospheric parameters obtained by our inversion method are available on a geometrical height scale , while traditional stokes inversions usually provide an optical depth scale , whose conversion into geometrical heights is influenced by the underlying assumptions ( see , e.g. , * ? ? ? * ) . while the method up to this point has already been considered by other authors in a more or less similar way @xcite , we go a step further and re - sort the mhd data set according to the best - fit results ( see sect . [ masi ] ) and use the re - sorted data as initial condition of a new muram simulation ( see sect . [ muramcontinuation ] ) . the re - sorting takes a physically consistent simulation box and produces a physically inconsistent one out of it , e.g. the horizontal flow pattern and the magnetic field lines are destroyed by the rearranging . during a relatively short relaxation process the muram code removes the physical inconsistencies ( in the same way when the 400 g were artificially introduced , see sec . [ simulation ] ) and we obtain mhd data that are very similar to the observation . while we only required from the original mhd simulation that it contains granulation and pores of any size and shape , the new simulation shows pores having sizes , shapes and positions within the fov that are similar to the observation . the better an mhd simulation matches the observation the better the fitting of stokes profiles can work , so that a significant improvement of the results can be reached by repeating the method iteratively , i.e. the new mhd simulation is used as input for a second iteration of spectral synthesis , degradation , stokes profile fitting , and mhd simulation . we name the new technique mhd - assisted stokes inversion ( masi ) . as mentioned in sect . [ observation ] , we have the choice between non - reconstructed and reconstructed observations . the reconstruction is done with a spatial psf determined by in - flight pd measurements which provide the low - order aberrations of the telescope ( defocus , coma , astigmatism , etc . ) , i.e. , aberrations that determine the inner core of the psf . the pd measurements do not ( or hardly ) provide information on high - order aberrations which determine the wings of the psf , e.g. , the stray - light behavior of the system . only if the degradation of the synthetic data reflects the real situation in the observed data to a high degree a physically meaningful comparison between them is possible . from the higher quality of the reconstructed data it is clear that a comparison with the non - reconstructed data requires a stronger degradation than a comparison with reconstructed data . because deconvolution of the data with the pd psf is not a straightforward procedure , we demonstrate our new inversion technique with non - reconstructed data this is to strictly avoid any deconvolution of the observations . in the following we depict all steps needed to degrade the synthetic data to the level of the non - reconstructed observations ( level-1 ) . the spectral psf of imax was measured in the laboratory before the launch of sunrise ( see the bottom panel of fig . 1 in * ? ? ? * ) and considers not only the transmission behavior of the etalon but also the used pre - filter . in addition to the 6.5 pm wide primary peak , the spectral psf also shows secondary peaks at around @xmath15 pm offset from the position of the transmision maximum . in order to include a possible influence of the secondary peaks we synthesize all the 20 spectral lines we could identify in the @xmath16 pm range around 525.02 nm . the synthetic stokes profiles are convolved with the spectral psf in order to reproduce the spectral resolution of imax . finally , stokes images are created for the spectral range @xmath17 pm to @xmath18 pm in spectral steps of @xmath19 pm , because such two - dimensional stokes images are needed for a convolution with a spatial psf such as the one we apply in the following degradation step . the chosen spectral sampling of @xmath19 pm is a reasonable compromise between the amount of data and the spectral resolution . the chosen spectral range is a bit wider than the scanning range of imax in its v8 - 4 mode ( @xmath20 pm to @xmath9 pm ) because of the blueshift effect inherent in imax , which will be explained in section [ masi ] . as mentioned above , the diffraction at the telescope 1-m aperture and the low order wavefront aberrations were measured by imax during the flight via the phase - diversity technique . consequently , the synthetic stokes images are convolved with the spatial psf retrieved from the pd data to take these effects into account . besides the 1-m aperture of the telescope at the considered wavelength , the spatial resolution of sunrise was limited by the stability of the image . the pointing system stabilized the gondola to an accuracy of a few arcseconds , while the correlating wave - front sensor ( cws ) controlled a tip / tilt mirror so that the reflected beam was further stabilized down to an rms value of only 0@xmath10025 ( measured during the flight by the cws ) . applying an artificial jitter of that strength to mhd images led to significantly less image smearing than seen in the imax observations . a possible , but speculative , explanation could be a differential motion between the cws camera and the imax cameras . all cameras are located within the post - focus - instrumentation ( pfi ) structure , that is made of carbon fiber and was designed for high stiffness . nonetheless , with an f/121 beam inside the image stabilization and light distribution system ( islid ; * ? ? ? * ) even a minute bending ( due to vibrations ) would suffice to explain the imax image quality . in order to take the actual image smearing into account we decided to apply a combination of two butterworth lowpass filters ( one with a low cut - off frequency , the other with a much higher one ; * ? ? ? * ) because it degraded the mhd data slightly more realistically than a convolution with a two - dimensional gaussian ( as we applied to data from the first sunrise flight in * ? ? ? * ) , in particular with respect to the power spectrum . a reliable determination of the stray - light properties of sunrise is a challenge since they strongly influence the data ( in particular the rms intensity contrast ) but are difficult to measure . @xcite assessed the stray - light contamination of the first flight imax data from analyzing observations of the solar limb . unfortunately , during the second flight the limb was only observed in the late phase of the mission when imax had problems with the electronics stabilizing the etalon temperature . the limb data contain clear evidence for a non - local stray - light contamination , i.e. , that the stray - light psf has extended wings . additionally , we can distinguish between two stray - light sources : the light level seen at the image border not exposed to sunlight ( the border is caused by the field stop at the entrance of the imax instrument ) can only be caused by imax internal stray light , while the somewhat higher total stray - light level in the off - limb region of the images indicates a second , albeit smaller contribution coming most probably from outside imax . unfortunately , we can not use the limb data for a more quantitative assessment of the stray - light properties because of the floating etalon temperature and also because the correlation tracker had problems to stabilize the image in the direction parallel to the solar limb , making these images less sharp than those on disk . during the sunrise calibration on ground , a fibre bundle was placed in the secondary focal plane , f2 . the fibre bundle is an extended light source with a diameter of about 8@xmath105 centered in the @xmath21 imax fov making this a nearly ideal target to determine the stray - light properties of imax . an illumination with sunlight was not possible for technical reasons so that an artifical light source ( 75 w xenon lamp ) had to be used . all frames of the fibre - bundle calibration campaign were summed up . the summed image was then deconvolved with the ideal ( i.e. stray - light and aberration free ) fibre - bundle image approximated by a binary mask image retrieved by applying an intensity threshold to each fibre of the summed fibre - bundle image . the deconvolution was done via the lucy - richardson algorithm @xcite which is an iterative method that uses only convolutions . compared to the sun , the light level of the used artifical light source was extremely low leading to a low signal - to - noise ratio in the outer parts of the fibre - bundle images . hence the stray - light related far wings of the psf could not be retrieved with the needed accuracy . even if these attempts in measuring the stray - light psf did not yield a result that could be directly used , they helped to considerably narrow down the shape of the azimuthally averaged psf . from this we could determine that the stray light seen by imax has neither a purely local nor a purely global character , but that an influence of the stray light on every spatial scale is present . since the stray - light psf could not be determined with adequate accuracy , only the utilization of a simplistic stray - light model remains . we contaminate the synthetic stokes @xmath22 images with 25% global stray light . stokes @xmath23 , @xmath24 , @xmath25 are not contaminated because most of the stray light was created internally inside imax and the internal stray light is largely unpolarized . the above strength of the global stray light was tested by a test - wise inversion of the imax data carried out with the traditional spinor code and in particular by evaluating the resulting magnetic field maps . a simple and hence robust atmospheric model was used : three @xmath26 nodes for the temperature ; everything else was assumed to be height - independent . without any stray - light correction the inversion provided kilogauss fields mainly along the edges of pores , and unrealistic weaker fields in the center of the pores . this effect can be explained by the broad wings of the stray - light psf . inside the pores the low temperatures together with the shallow temperature gradients lead to low intensities and extremely small line depths of the 525.02 nm spectral line , so that a contamination with light from the bright vicinity of the pores causes a significant underestimation of the field strength . a global stray - light correction of the data lowered this effect considerably . the best results could be reached for a stray - light strength of 25% . two other methods , which are independent of the field weakening in the pores , confirmed that a 25% of global stray - light together with the butterworth filtering is reasonable . firstly , the intensity of the darkest pixel in the synthetic pores in the mhd simulations increases from 8.6% to 38.8% of the mean quiet - sun intensity , @xmath27 when the various degradation steps described above are applied . this value agrees nicely with the minimum intensity of the non - reconstructed imax data , 38.4% . we note that the size of the largest pore in the mhd data is smaller than in the imax data , which possibly makes the comparison of the minimum intensities problematic , but later in this study we will see that the match also holds if the imax data are compared with simulations of nearly identical pore sizes . secondly , the rms contrast of the stokes @xmath22 continuum image of the non - reconstructed imax data , 6.8% , is similar to the constrast of the fully degraded mhd data , 7.7% ( pores were excluded when we determined these numbers ) . imax stokes @xmath23 , @xmath24 , and @xmath25 images at the continuum wavelength ( + 22.7 pm ) were used to calculate histograms of a quiet - sun region , which is generally free of polarization signals . the histograms showed a clear gaussian shape with a standard deviation of about @xmath28 ( level-1 data ) or @xmath29 ( level-2 data ) , respectively . @xmath27 is the mean continuum intensity of the selected quiet - sun region . we did not add any noise to the synthetic data to avoid complicating the comparison with the observations , but we used the standard deviation as the noise value for all four stokes parameters when calculating the @xmath0 values of the merit function we define in eqs . ( [ eq_merit1 ] ) and ( [ eq_merit2 ] ) . since our method relies on a direct comparison between degraded synthetic stokes profiles and observed stokes profiles ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , a realistic degradation is crucial . in this section we assess the quality of the degradation steps decribed in sect . [ degradation ] by comparing the two data sets . in our experience it is important that not just a single quantity ( e.g. the rms intensity contrast ) is compared but multiple ones . in practice , the measurement of instrumental effects might not be possible with the necessary accuracy , so those effects often need to be approximated by simplified models ( in our case stray light and jitter ) containing one or more adjustable parameters . [ fig2 ] exhibits the influence of the degradation on the synthetic stokes @xmath22 continuum image and compares the undegraded and degraded synthetic images with the corresponding imax observation . the degradation clearly lowers the contrast and the spatial resolution so that the image quality of the synthetic data is brought down to the level of the observation . in fig . [ fig3 ] we show the azimuthally averaged power spectra ( e.g. , * ? ? ? * ; * ? ? ? * ) and in fig . [ fig4 ] the intensity histograms both calculated from the images displayed in fig . [ fig2 ] . the same color coding is used for figs . [ fig3 ] to [ fig5 ] : the black line corresponds to the undegraded synthetic data , the red line to the degraded synthetic data , and the green line to the non - reconstructed imax observations . a comparison of the power spectra reveals that our degradation steps bring the spectrum down to roughly the level of the observed spectrum , but some mismatch remains . for wave numbers @xmath30 the synthetic power is not sufficiently suppressed by the degradation , while it is too low for higher wave numbers ( see fig . [ fig3 ] ) . continuum images versus the wave number , @xmath31 . the black line corresponds to the undegraded mhd simulation , the red line to the fully degraded data , and the green line displays the level-1 imax observation . ] the degradation of the synthetic data reduces the rms intensity contrast from 27.5% down to 10.7% which is 0.2% lower than the observational contrast of 10.9% ( see fig . [ fig4 ] ) . the histograms are calculated for the full fov , including pores . if we exclude the pores ( that fill different fractions of the fov in the two data sets ) then we find the rms contrast values given in sect . [ straylight ] . continuum intensity . the color coding is the same as in fig . rms contrasts are indicated in the text labels . the histograms cover the full fov , i.e. the pores are included . ] as mentioned above , the stray light can have a severe influence on the line depths , in particular in the pores . hence we also show histograms of the stokes @xmath22 line depth in fig . while the standard deviation matches well between the degraded simulation and the observation , the mean value of the synthetic data is slightly lower than the observed value ( see text labels ) . additionally , the synthetic line - depth histogram exhibits a bi - modal shape which is not the case for the observed histogram . , but for the stokes @xmath22 line depth . mean values and their standard deviations are indicated in the text labels . ] [ fig2 ] to [ fig5 ] illustrate the quality of our degradation . the remaining discrepancies can be caused by various effects , such as the uncertainties in the stray - light correction mentioned in sect . [ straylight ] . additionally , the lowpass filtering with a combination of two butterworth filters is only a very simple way of modelling the residual jitter . although the degradation of the mhd data might not perfectly mimic the behavior of imax we believe it successfully accounts for the most important contributions . after taking the various instrumental effects into account , we now have two data sets available that are directly comparable , except for two remaining discrepancies . the first discrepancy concerns the magnetic polarity , because our mhd simulation is a unipolar one , while both magnetic polarities are present in the imax observation . hence we create a second mhd data set by flipping the sign of the magnetic field vector , while all other quantities remain unchanged . the second mhd data set is degraded in the same manner as the original one , so that a bipolar data set can be produced by combining the two opposite polarity data sets . the second discrepancy concerns the blueshift that is the sum of the field - dependent etalon blueshift and the constant convective blueshift . the etalon blueshift is a wavelength shift across the fov due to the inclination of the off - axis rays as they reach the etalon in a collimated configuration . the map of the total blueshift is provided by the imax calibration process @xcite . for the traditional stokes inversion method the velocity map needs to be corrected for the blueshift just at the very end . in the masi case the blueshift has to be taken into account directly during the fitting of the observed stokes profiles . consider now a given pixel of the observation data . its position within the fov of imax determines its blueshift . this particular blueshift is subtracted from the nominal wavelengths of the v8 - 4 mode . every degraded synthetic profile ( which has high spectral sampling ) of all pixels in the mhd fov is then re - sampled at the corrected wavelengths , resulting in a blueshift - corrected mhd data set . we then browse through the corrected mhd data set in order to identify the pixel whose stokes profiles match the observed one best . we assess the similarity of stokes profiles by defining the following @xmath0 merit function : @xmath32 where @xmath33 is the pixel position within the observed fov composed of @xmath34 pixels , while @xmath35 is the position within the mhd fov consisting of @xmath36 pixels . @xmath37 runs over the eight wavelengths of the v8 - 4 mode and @xmath38 over the four stokes parameters , @xmath22 , @xmath23 , @xmath24 , @xmath25 , e.g. @xmath39 means the degraded synthetic stokes @xmath23 signal at the wavelength @xmath40 pm . @xmath41 is the noise level of the stokes parameter @xmath38 . this step of the masi algorithm searches for the mhd pixel whose degraded stokes profiles provide the smallest @xmath0 value for the given observed pixel . the position of the best - fit mhd pixel within the mhd fov is assigned to the observed pixel . repeating this procedure for all observed pixels needed 19 hours on a single intel(r ) core(tm ) i7 - 2760qm and results in two maps having the size of the observed fov and giving the x and y coordinates of the best - fit mhd pixels ( not shown ) . these coordinates are then used to create a new mhd data set by re - sorting the original one . the new mhd data set covers the fov of the observation and holds for each position within the fov the one mhd pixel that fits the observed one at this position best . we note that not all pixels of the simulation need to find their way into the re - sorted data set , whereas others may provide the best fit to multiple stokes profiles . [ fig6 ] demonstrates the re - sorting using the example of the degraded stokes @xmath22 continuum image . the archive of the stokes @xmath22 , @xmath23 , @xmath24 , and @xmath25 profiles calculated from the used mhd snapshot contains @xmath42 entries ( see the left panel of fig . [ fig6 ] ) . 19% of the entries in the archive provide best fits to the stokes parameters in the imax data set , i.e. this fraction is actually chosen by the code to build up the re - sorted data set ( right panel of fig . [ fig6 ] ) , whose comparison with the imax observation ( right panel of fig . [ fig2 ] ) shows a remarkable match . only the penumbra - like region around the position ( 15,14 ) looks less smooth than other regions , mainly because it is composed of just a few intensity levels . maps of the stokes @xmath25 signal at a wavelength offset by @xmath43 pm from the line core are compared between the imax observation and the masi result in fig . the bipolar structure of ar 11768 is well reproduced by masi as well as most of the magnetic fine structure . a mismatch is again found in the penumbra - like region around the position ( 15,14 ) and also in the flux - emergence region around ( 30,12 ) because our archive of synthetic stokes profiles does not contain profiles of such features with a nearly horizontal magnetic field . image in the red wing of the fei 525.02 nm line , normalized to the mean quiet - sun intensity . left panel : non - reconstructed data observed by imax . right panel : degraded mhd data re - sorted by the first masi iteration . ] another difference in the stokes @xmath25 images can be found for the interior of the pores . the peripheral region of the pores is well reproduced by the first masi iteration , while the weakening of the circular polarization in the central part of the pores differs slightly . we speculate that the discrepancy is caused by imperfections in the degradation of the data , in particular by our imperfect knowledge of the stray - light contribution to the psf . on top of that , the equal noise levels in the calculation of the merit function leads to a certain bias towards stokes @xmath22 because the stokes @xmath22 amplitude is larger then the stokes @xmath23 , @xmath24 , and @xmath25 amplitudes . panel a of fig . [ fig8 ] shows the undegraded stokes @xmath22 continuum image after the re - sorting . its rms quiet - sun intensity contrast of 22.5% is only slightly below the value of the undegraded mhd data before the re - sorting , 25.1% ( left panel of fig . [ fig2 ] ) but considerably larger than the contrast of the degraded image , 6.6% ( right panel of fig . [ fig6 ] ) . the undegraded masi result restores the rough topology of pores and granules quite well . however , the transition regions between granules and intergranular lanes are not very smooth but show lots of small - scale spatial discontinuities . the quality of the masi results relies not only on how well the mhd data are degraded but also on a good representation of the observed target types by the mhd data set . pores and granulation are contained in our mhd simulation and hence these features can be reproduced by the mhd pixels quite well . since the simulation does not contain any penumbra or similar features of more horizontal fields , one can not expect good fits for the observed penumbra - like region . a look at the @xmath0 map ( panel b of fig . [ fig8 ] ) reveals the same conclusion . the largest @xmath0 values can be found in the penumbral region . the mean @xmath0 value of the first masi iteration is 17.1 , while it is 27 for a traditional spinor inversion of the used non - reconstructed imax observation ( including a 25% global stray - light correction ) . a decomposition of the @xmath0 values into contributions from stokes @xmath22 ( panel c of fig . [ fig8 ] ) and stokes @xmath23 , @xmath24 , and @xmath25 together ( panel d of fig . [ fig8 ] ) reveals that even for the regions of more horizontal field around positions ( 15,14 ) and ( 30,12 ) the two contributions are of roughly the same magnitude . on average stokes @xmath22 contributes 63% to the total @xmath0 value , while the fraction of stokes @xmath23 , @xmath24 , and @xmath25 together is 37% . values at the end of the first iteration of stokes profile fitting ( panel b ) , contribution of stokes @xmath22 ( panel c ) and of stokes @xmath23 , @xmath24 , @xmath25 together ( panel d ) to the total @xmath0 . panels b - d are plotted on a logarithmic scale . ] more details of the re - sorted mhd data will be presented after the second masi iteration in sect . [ iterating ] . after the first step of the masi method has been introduced and applied to an imax observation and after we have presented some results , we now take the next step , which takes advantage of the availability of the entire set of mhd quantities because the re - sorting does not only process the degraded stokes images but all available data are re - sorted . we start a new muram simulation that uses the first step masi result as the initial condition . the boundary conditions of the new run are identical to the ones described in sect . [ simulation ] . the re - sorting of the mhd data increased the horizontal dimensions of the simulation box to the size of the imax observation , 33.8 mm @xmath11 33.8 mm , while the depth of the box is kept at 6.1 mm . [ fig9 ] displays maps of the bolometric intensity for snapshots taken at 10s , 1min , 3min , 10min , 56min , and 107min of solar time after the start of the muram continuation ( see text labels ) . the re - sorting of the mhd data by the masi technique destroys important physical properties of the system , e.g. the horizontal flow pattern is arbitrarily re - sorted , the horizontal pressure balance is disturbed , and also the magnetic field lines are changed by the re - sorting , so that maxwell s equation @xmath44 is violated . even if the granulation pattern observed by imax is given as the initial condition , immediately after the start of the muram continuation the imax granulation pattern gets destroyed , mainly caused by the unrealistic horizontal velocites . after about 3min of solar time a new granulation pattern has evolved that is statistically similar , but looks different in detail from the imax granulation . the newly developed granulation pattern indicates that after approximately 3min a new horizontal flow pattern has been established , at least in the upper layers of the convection zone . the muram code is also able to reestablish the physical consistency with respect to the magnetic field . each muram calculation can lead to tiny deviations from the @xmath44 constraint due to numerical rounding errors . hence the code includes a @xmath45 cleaning algorithm which is of great benefit for our muram continuation of a re - sorted mhd data set . an analysis of the temporal evolution of the @xmath45 field ( not shown ) reveals that after 34min the value has reached the normal value seen before the re - sorting . because on average pores live much longer than granules , their details also evolve within a few minutes but their rough shape remains unaffected for longer time . since for stray - light analyses it might be important to work with synthetic pores of the same size as in the observations , it is interesting to mention that smaller pores ( e.g. at the positions ( 24,29 ) , ( 28,30 ) , and ( 38,23 ) in the right panel of fig . [ fig2 ] ) can disappear after a while ( see snapshot @xmath46s of fig . [ fig9 ] ) , but because the magnetic flux is conserved , pores of similar sizes can reappear at similar locations ( see snapshot @xmath47s ) . an animation of the bolometric intensity as well as the vertical components of the velocity and magnetic field vector at optical depth unity is available in the online edition . our considerations in the previous sects . [ concept]-[muramcontinuation ] started with mhd data containing a solar scene that is similar to the observed scene only in the sense that it contains similar types of features . after the mhd data were degraded , they could be used for a stokes inversion of the observation via the described method . the first iteration masi result was a re - sorted mhd data set that was used as the initial condition of a new muram simulation . after about half an hour the new simulation reached a statistically relaxed state in which the horizontal flow pattern and the magnetic field lines were again in accordance with the mhd equations . that way we obtain mhd data containing a solar scene that is both , physically consistent ( at least in the visible layers of the sun ) , and much more similar to our imax observations than the mhd data we started with we now pursue the question whether an iteration of the outlined method is able to improve the correspondance of the simulated and the observed data . the reapplication of the method described in the following text is named the second masi iteration . we use the snapshot at @xmath48s ( bottom left panel of fig . [ fig9 ] ) as the mhd data set for the second iteration because we aim for a close resemblance to the imax observation . in particular we are interested in the smaller pores that are difficult to treat with the traditional stokes inversion technique . actually one should only use snapshots taken after the relaxation process is entirely completed ( @xmath49min ) , but because @xmath45 drops very rapidly during the first 10min after which it continues to slowly reach the value before the re - sorting after a further 24min , the selected snapshot at @xmath50min strikes a reasonable balance . ( we note that the smaller pores temporarily disappear for @xmath51min . ) the trick of doubling the mhd data set in order to make its magnetic field bipolar is no longer needed because the snapshot at @xmath48s is already bipolar . 30 hours of execution time were needed to run the muram code for 600s of solar time on a cluster of 160 intel(r ) xeon(r ) cores e5 - 2670 . a further change in the second iteration is that we this time invert reconstructed imax data ( level-2 ) via masi in order to demonstrate that the masi method leaves the user the choice , whether the observations are deconvolved with a psf or the mhd data are convolved . this can be an advantage , because a deconvolution of observational data with a psf leads regularly to a decrease in the signal - to - noise ratio , while it provides a higher spatial resolution ( compare panel a of fig . [ fig10 ] with the right panel of fig . [ fig2 ] ) . as a consequence , the convolution of the mhd data with the pd psf is skipped this time because the pd psf is already considered during the reconstruction of the imax data . all other degradation steps ( convolution with the spectral psf , butterworth lowpass filtering , and 25% global stray - light contamination ) have to be applied in the same way as for the first iteration . the rms quiet - sun intensity contrast of the degraded synthetic stokes @xmath22 continuum image , 13.67% , agrees very well with the contrast of the imax level-2 data , 13.25% , likewise the intensity of the darkest pixel ( @xmath52 for the synthetic data and @xmath53 for the imax data ) . the similarity between simulation and observation makes it possible to extend the merit function by a term that slightly reduces the demolition of the horizontal flow pattern and magnetic field lines by the re - sorting : @xmath54 where @xmath55 is a constant that determines the strength of the correction term and @xmath56 is the distance between the considered observed pixel and the synthetic one . the correction term , @xmath57 , gives a preference to synthetic pixels that are located close to the observed pixel . in our example we set @xmath58 , which is a relatively small value , in order to prefer neighbouring pixels only in the case that multiple synthetic pixels possess almost identical stokes profiles . with this selection , 19% of the @xmath34 entries in the archive of the second iteration provide the best - fit results used for the re - sorted data set . [ fig10 ] contrasts the stokes @xmath22 continuum and line - core image of the reconstructed imax observation with the degraded masi result of the second iteration . compared to the first iteration the agreement has slightly improved . even the penumbra - like region does not show any obvious artifacts . a comparison of the observed stokes profiles ( reconstructed and corrected for the etalon blueshift ) with the best - fit profiles resulted from the second masi iteration can be seen in fig . [ fig11 ] . we selected three pixels located at the positions ( 13@xmath1089,26@xmath1079 ) , ( 17@xmath1048,39@xmath1037 ) , and ( 6@xmath1043,18@xmath1035 ) in fig . [ fig10 ] and representing a bright point , an intergranular lane , and a pore . masi provides for the three pixels a magnetic field strength at @xmath13 of 1520 g , 205 g , and 2490 g , respectively . the kilogauss field in the pore and in the bright point broadens the spectral line . the low temperature gradient in the pore together with the temperature sensitivity of the fei 5250.2 line leads to a shallow stokes @xmath22 profile . since the magnetic field is weak for the intergranular - lane pixel , the corresponding polarization signals are also weak . the magnetic field of the pixel in the pore and the pixel in the bright point is strong and nearly vertical so that the stokes @xmath23 and @xmath24 signals are weak , while the stokes @xmath25 profiles reach values of a few percent . continuum ( panel a ) and line - core ( panel c ) image of the reconstructed imax observation and the degraded stokes @xmath22 continuum ( panel b ) and line - core ( panel d ) image from the @xmath59 iteration masi result . ] , @xmath23 , @xmath24 , and @xmath25 profiles from a position inside a bright point ( red ) , an intergranular lane ( blue ) , and a pore ( black ) . the squares display the reconstructed and blueshift - corrected imax observation , while the solid lines correspond to the @xmath59 masi iteration , i.e. the best - fit inversion results . all profiles are normalized to the spatially averaged quiet - sun intensity . ] a look at the undegraded stokes @xmath22 continuum image of the re - sorted mhd data set demonstrates the improvements of the second iteration even more distinctly . while the result of the first iteration showed a wealth of small - scale discontinuities ( see the left panel of fig . [ fig12 ] ) , this is rarely the case for the ouput of the second iteration ( right panel of fig . [ fig12 ] ) . the improvement of the inversion s quality can also be seen by a comparison of the @xmath0 maps . panels a and b of fig . [ fig13 ] show the total @xmath0 map of the second iteration decomposed into the distance term , @xmath57 , and the remaining stokes part , @xmath60 . the stokes part is further decomposed into the contribution of purely stokes @xmath22 ( @xmath61 , panel c of fig . [ fig13 ] ) and the remaining stokes parameters ( @xmath62 , panel d ) , which allows a direct comparison of the @xmath0 components of the first iteration ( panels b - d of fig . [ fig8 ] ) with the ones of the second iteration ( panels b - d of fig . [ fig13 ] ) . the maximum @xmath60 value of the second iteration is @xmath63 times lower than for the first iteration . the mean @xmath60 value decreased from @xmath64 to @xmath65 , the mean @xmath61 value from @xmath66 to @xmath67 , and the mean @xmath62 value from @xmath68 to @xmath69 . on average , the additional correction term , @xmath57 , contributes 34% to the total @xmath0 value , while 48% originate from stokes @xmath22 , and 18% from stokes @xmath23 , @xmath24 , and @xmath25 together . continuum image after the first ( left panel ) and second ( right panel ) masi iteration . only the bottom left @xmath70 part of the considered field of view is shown for a better visibility of details . ] values of the second iteration provided by the distance term in eq . [ eq_merit2 ] ( panel a ) , by the sum of all four stokes parameters ( panel b ) , by only stokes @xmath22 ( panel c ) , and by the sum of stokes @xmath23 , @xmath24 , @xmath25 ( panel d ) . all panels are plotted on a logarithmic scale . ] stokes @xmath25 maps in the red wing of the 525.02 nm line are displayed for the reconstructed imax observation and the degraded masi result in fig . [ fig14 ] . the reconstructed imax stokes @xmath25 image shows much more fine structure than the level-1 data ( see left panel in fig . [ fig7 ] ) . most of the fine structure is well reproduced by the second masi iteration , although some features are not well fitted , largely the ones with a nearly horizontal magnetic field . nonetheless , the discrepancy between observation and masi at the position of the penumbra - like feature and also of the flux - emergence region is lower than for the first masi iteration . image at @xmath43 pm offset from the line core . left panel : reconstructed imax data . right panel : degraded mhd data re - sorted by the second masi iteration . ] we consider some more undegraded quantities of the second masi iteration in figs . [ fig15 ] to [ fig16 ] . [ fig15 ] compares maps of the los velocity between imax and masi . since a 25% global stray - light contamination is part of the masi degradation , we applied a corresponding stray - light correction to the reconstructed imax data and fitted the stokes @xmath22 profiles with a gaussian . the central position of the gaussian ( corrected for the blueshift ) provides the los velocities in the left panel of fig . [ fig15 ] . the right panel displays the vertical component of the re - sorted mhd velocity vector at the optical depth @xmath13 , because this depth is roughly the formation height of the 525.02 nm line . the velocity scale was shifted to reach a zero mean value over the entire fov . for both panels of fig . [ fig15 ] the granulation outside the pores exhibits the typical upflows within granules and downflows for the intergranular lanes . the contrast of the masi result is larger than the one of the observation , possibly because the formation height of the 525.02 nm is somewhat higher than @xmath13 . for display reasons we limited the velocity range to @xmath71km / s because the gaussian fits of the observed profiles have significant difficulties at the edges and inside the pores ( see the black and yellow regions in the left panel of fig . [ fig15 ] ) . in the pores the temperatures are low and the temperature gradiants are small , both leading to shallow spectral lines . in combination with the photon noise the gaussian fits can lead to unreasonable results . gaussian fit ) . right panel : undegraded mhd data at @xmath13 re - sorted by the second masi iteration . negative velocities correspond to upflows . ] finally , we present the magnetic field of the second masi iteration . the left panel of fig . [ fig16 ] displays the field strength , while the right panel shows the field inclination , both at the optical depth of @xmath13 . in the pores we find field strengths up to 3400 g . we note that the masi results hardly show any field weakening in the pores , that we mentioned in sect . [ straylight ] , which further indicates that our simplistic stray - light model is not too far off from reality . , both taken from the undegraded second iteration masi result . ] we obtained atmospheric parameters such as temperature , magnetic field vector , and los velocity from a spectropolarimetric observation by finding the best matched stokes profiles from a snapshot of an mhd simulation , degraded as realistically as possible to the level of the observed data . because the mhd data set contains the full set of atmospheric parameters , we were able to re - sort the vertical columns of the original mhd data corresponding to the best - fits of observational stokes profiles and used the re - sorted data as the initial condition of a new mhd simulation . since the spatial relations of the columns are destroyed ( in the horizontal directions ) by the re - sorting , the initial condition is physically inconsistent . the inconsistencies include the re - arranged horizontal flow pattern both , above the solar surface and below it , and the loss of local horizontal pressure balance , which are closely related to the convection in the granulation cells , so that the observed granulation pattern gets destroyed immediately after the start of the muram continuation . the muram code is able to remove the physical inconsistencies , so that after about 3min a new granulation pattern has evolved and after about half an hour of solar time the divergence of the magnetic field vector is brought down to zero . further studies are needed to find ways to reduce the relaxation time , e.g. by carrying out more iterations or by advancing the applied merit function to preserve the horizontal flows of a granule in a statistical way ( as we tried by adding the very simplistic distance term in eq . [ eq_merit2 ] ) . after the relaxation we obtained physically consistent mhd simulations that show a solar scene quite similar to the observed one . we used a snapshot of the new simulations to apply a second iteration of the method . the higher similarity to the observation improved the match between observed and synthetic stokes profiles . in particular , the improvement can be seen if undegraded stokes images of the two iterations are compared and also by a significant decrease in the mean @xmath0 value and its contributions from stokes @xmath22 and from stokes @xmath23 , @xmath24 , @xmath25 , respectively . the high computational effort needed for the muram simulations hindered the realization of further iterations within this study , which are expected to lead to a stepwise convergence between observation and simulation , although it is clear that effects of an imperfect modelling of instrumental effects and imperfections of the mhd code ( e.g. , for penumbrae ) can not be lowered by more iterations . the masi technique can be understood as a first step towards an integration of the mhd equations into the stokes inversion of a time series . although we are still a long way away from this long - term goal , a few applications of the technique can already be considered : 1 . by means of the masi technique we are able to create mhd simulations that are very similar to an observation . this can be quite helpful in analyzing physical phenomena . for example , the mhd data allow for insights into all physical quantaties , even the ones that are not covered by the spectral lines ( horizontal velocities , densities , pressures , horizontal force balance ) . it can also be advantageous that the mhd data are free of noise and can have higher spectral , spatial , and temporal resolution . moreover , the availability of an mhd simulation similar to the observation can be also quite useful in analyzing instrumental effects ( e.g. , the stray - light behavior ) . 2 . the masi method allows the creation of new mhd simulations with interesting solar targets , e.g. , light bridges , complex sunspot or pore topologies , which was difficult in the past . 3 . the masi results after the first step can be used as a first - guess atmosphere for a traditional stokes inversion technique so that the traditional inversion can converge faster . although the technique presented here is promising , this paper is limited to first steps and much work remains to be done to test and improve it further . a first important test could be a comparison between the masi results and the results of traditional inversion techniques . ideally , this should be done with realistically degraded mhd data , because then the errors caused by the masi technique can be disentangled from the errors made by traditional inversions , which would not be easily possible if observational data are inverted . furthermore , it should be investigated if more iterations lead to further improvements and if so how many iterations are needed until the @xmath0 values converge to its final value . an application of the masi method to other observational data sets is also desirable , in particular to data with full line profiles ( i.e. better spectral sampling ) and a better knowledge of instrumental effects . additionally , the mhd archive should be expanded by features harboring more horizontal fields ( flux emergence , penumbrae ) and local - dynamo simulations . possibly , the performance of masi improves if the re - sorted mhd data are spatially smoothed ( similar to the smoothing applied as part of the spinor inversion of the imax data , see * ? ? ? * ) before being used as initial condition of an mhd simulation . it also appears advisable to introduce stokes - specific weighting factors in the merit function in order to reach a better balance between the contributions of the four stokes parameters . finally , an error estimate of the method should be derived , e.g. , by considering all vertical columns of the original mhd data set that lead to very similar @xmath0 values . the german contribution to sunrise and its reflight was funded by the max planck foundation , the strategic innovations fund of the president of the max planck society ( mpg ) , dlr , and private donations by supporting members of the max planck society , which is gratefully acknowledged . the spanish contribution was funded by the ministerio de economa y competitividad under projects esp2013 - 47349-c6 and esp2014 - 56169-c6 , partially using european feder funds . the national center for atmospheric research is sponsored by the national science foundation . the hao contribution was partly funded through nasa grant number nnx13ae95 g . the national solar observatory ( nso ) is operated by the association of universities for research in astronomy ( aura ) inc . under a cooperative agreement with the national science foundation . this work was partly supported by the bk21 plus program through the national research foundation ( nrf ) funded by the ministry of education of korea .

we present a new method of stokes inversion of spectropolarimetric data and evaluate it by taking the example of a sunrise / imax observation . an archive of synthetic stokes profiles is obtained by the spectral synthesis of state - of - the - art magnetohydrodynamics ( mhd ) simulations and a realistic degradation to the level of the observed data . the definition of a merit function allows the archive to be searched for the synthetic stokes profiles that match the observed profiles best . in contrast to traditional stokes inversion codes , which solve the unno - rachkovsky equations for the polarized radiative transfer numerically and fit the stokes profiles iteratively , the new technique provides the full set of atmospheric parameters . this gives us the ability to start an mhd simulation that takes the inversion result as initial condition . after a relaxation process of half an hour solar time we obtain physically consistent mhd data sets with a target similar to the observation . the new mhd simulation is used to repeat the method in a second iteration , which further improves the match between observation and simulation , resulting in a factor of 2.2 lower mean @xmath0 value . one advantage of the new technique is that it provides the physical parameters on a geometrical height scale . it constitutes a first step towards inversions giving results consistent with the mhd equations .

in a narrow sense , neuroimaging workflows involve neuroimaging image processing and analysis . in a more broader sense , the workflow in a neuroimaging study involves a number of other processes : gathering information , designing the experiment , brain scanning , interpretation of the study , relating it to other studies and communicating the study . data mining in neuroimaging may not only be applied as the standard neuroimaging analysis but also set to work on other components in workflow , and visualization of the data mining results may help the individual researcher in understanding his or her data as well as in communication with other researchers . a number of tools exists for visualizing neuroimaging data mining results when the result is a volumetric neuroimage . there are , however , also visualization tools for other aspects of the neuroimaging process , and one example is our brede toolbox ( nielsen and hansen , 2000a ) . starting out as a program for handling and visualization of data from the brainmap database of fox et al . ( 1994 ) the brede toolbox now includes its own database of results from neuroimaging the brede database ( nielsen , 2003 ) as well as analysis and visualization functions for a range of tasks . we have setup an automated workflow involving a few non - interactive batch scripts that construct practically the entire web presence of the brede database with static web pages and visualizations . furthermore , automated workflows using the ontologies of the brede database can perform mass meta - analysis across brain functions or brain regions ( nielsen , 2005 ; nielsen et al . the abundance of tools for visualization as well as for other aspects of the neuroimaging process has spawned an interest in generating overviews for these tools , and now there exist several web - based directories : neuroscience database gateway ( ndg ) ( gardner and shepherd , 2004 ) , neuroscience information framework ( nif ) ( gardner et al . , 2008 ) , neuroimaging informatics tools and resources clearinghouse ( nitrc ) ( buccigrossi et al . , 2008 ) , i do imaging and internet analysis tools registry ( iatr ) , see also ( dinov et al . , 2008 ) . some of these have an api so that html or xml for a specific tool can be requested . nitrc , iatr and i do imaging have web 2.0 components with user - provided tool ratings and nitrc has an associated wiki . since 2001 , i have updated the bibliography on neuroinformatics which also lists numerous tools . recently i began the brede wiki with structured information about neuroscience including neuroimaging visualization tools . anyone can micro - publish relevant information , and the structured content allows for off - wiki database queries ( nielsen , 2009 ) . many meta - analyses use so - called forest plots and funnel plots , where scatter plots with whiskers display effect sizes and estimators of their variations in two dimensions ( lewis and clark , 2001 ) , see figure 1 . these meta - analyses typically investigate a single variable continuous or dichotomous and its relation to another variable , e.g. , a personality trait and its association with a genetic polymorphism . in neuroimaging meta - analysis , we have a quite different situation : the neuroimage result contains not just one variable but many variables , i.e. , voxels . one would need thousands of standard meta - analysis plots to capture the result across studies . another much more fundamental problem stems from the fact that neuroimaging researchers typically only report the positive results , e.g. , areas with activation to a given task , not signal changes for brain regions that did not survive the statistical threshold selected . meta - analysts usually regard the discarding of negative results as a heresy , referring to it as the file drawer problem or with the term publication bias . all the standard statistical meta - analysis technique require that also negative results are reported , at least to some extent ( hedges and olkin , 1985 ) . so we may ask if it is at all possible to make appropriate analyses and visualizations across studies in neuroimaging ? components in the scalable vector graphics image file are hyperlinked and the content may be controlled interactively through a html form . recent work with image - based meta - analysis has shown the possibility of constructing sensible forest and funnel plots for functional neuroimaging data ( salimi - khorshidi et al . , 2009b ) . the program associated with the original brainmap database displayed coordinates in 2d tri - planar plot ( fox et al . , 1994 ) . this type of visualization is maintained in a newer version of the database with the program sleuth ( laird et al . webcaret may display coordinates in 3d as colored spheres together with an inflated cortical surface ( van essen and dierker , 2007 ) , see figure 2 . the brede toolbox can generate 3d visualizations in the corner cube style of rehm et al . plotting points in 3d is not straightforward , simple zero dimensional graphics do not give an important perception of depth , therefore we use 3d glyphs of different color and shape . to help the viewer in spatial localizing the coordinates we can add components in a configurable workflow such as ac / pc axes , stalks for the glyphs , glyph shadows on the tri - planar walls , contour and cerebral cortex outlines from the atlas of talairach and tournoux ( 1988 ) . figure 3 shows two visualizations of this kind with figure 3a displaying all coordinates in the brede database from papers authored by edward t. bullmore and figure 3b displaying cingulate coordinates colored according results from a text mining of the associated abstracts ( nielsen et al . , 2005 , 2006a ) . the batch script setup for the brede database will automatically generate a plot like figure 3a for each author mentioned in the author ontology . sometimes these simple plots reveal interesting features : the bullmore coordinates appear somewhat limited to the middle of the inferior - superior axis perhaps reflecting a restricted field of view selected for some of the studies . the elaborate and automated workflow for generating a plot like figure 3b involves : select a brain region and from the brede database brain region ontology get all naming variation of the brain region and its subareas . with these names extract coordinates from papers recorded in the database , model their spatial distribution and include extra non - matched coordinates that lies within the region.get abstracts from the brede database that for the brain region in question have one or more coordinates and perform text mining , which results in clusters of themes , such as pain and memory and documents belonging to these clusters.perform statistical tests on the spatial distribution of the coordinates grouped according to the text mining clusters to determine if the text mining has discovered functions that are segregated in the region . select a brain region and from the brede database brain region ontology get all naming variation of the brain region and its subareas . with these names extract coordinates from papers recorded in the database , model their spatial distribution and include extra non - matched coordinates that lies within the region . get abstracts from the brede database that for the brain region in question have one or more coordinates and perform text mining , which results in clusters of themes , such as pain and memory and documents belonging to these clusters . perform statistical tests on the spatial distribution of the coordinates grouped according to the text mining clusters to determine if the text mining has discovered functions that are segregated in the region . webcaret server - side display of returned coordinates from the surface management system database ( sumsdb ) with a query on middle frontal gyrus. the right window offers some control over the rendering and the buttons in the left window may rotate the cortical surface . sumsdb allows the query on a neuroanatomical label to be invoked from another program or web site by simple web linking , and the brede wiki automatically constructs such links . ( a ) coordinates from the five studies in the brede database authored by edward t. bullmore . the 3d glyphs have type and color according to paper : dark blue ( phillips et al . , 1997 ) , light blue ( phillips et al . , 1998 ) , light green boxes ( bullmore et al . , 1996 ) , orange spheres ( hunkin et al . , 2002 ) , red ( calvert et al . , 1999 ) . ( b ) cingulate coordinates colored according to the clustering results after a text mining of abstracts in the brede database . memory cluster while the light yellow are from the pain cluster . from nielsen et al . the procedure is done for all brain regions in the brede database brain region ontology and figure 3b shows one of the regions that listed high after sorting brain regions according to statistical significance in the spatial distribution test . data mining directly with the coordinates has been termed coordinate - based meta - analysis ( cbma ) and several methods exists ( wager et al . , 2009 ) , for the most part they involve a form of estimation of a conditional probability density p(v|c ) in stereotaxic space v. the conditioning , c , may be , e.g. , for a specific brain function or a specific anatomical label . once the probability density is estimated it can be converted to a volume by sampling the probability density in voxels and visualized in the same way as standard neuroimages , or the density can be used to color - code the cortical surfaces in a 3d visualization , see wager et al . ( 1997 ) introduced the method to model the probability density : a single confined area the primary motor area for the mouth were examined so only a model with mean and standard deviation was devised , i.e. , a simple gaussian model . as more complex brain functions are distributed in brain space , our first effort in modeling the probability density was by gaussian mixture models ( nielsen and hansen , 1999 ) : ( 1)p(v|c)=kkc p(v|k ) p(k|c ) , where each p(v|k ) estimates a 3d gaussian probability density . figure 4a shows the isosurfaces in a model of this type where the parameters have been fitted to data from the brainmap database . here , each ellipsoids corresponds to a single gaussian p(v|k ) and c corresponds to three different labels of behavioral domain from the brainmap database that are associated with each coordinate . although the gaussian mixture model may generalize , the ellipsoids do not look neuroanatomical plausible and call for yet more flexible models . figure 4b is generated with kernel density estimation using a gaussian kernel ( nielsen and hansen , 2000b ) . such models seems to generate probabilities that are somewhat more neuroanatomical plausible than the gaussian mixture model . vrml visualizations with coordinate - based meta - analysis of data from brainmap with isosurfaces in conditional probability densities . ( a ) gaussian mixture model of the three main behavioral domains in brainmap : perception ( red wireframe ) , cognition ( green surface ) and motion ( m-textured surface ) . from nielsen and hansen ( 1999 ) . ( b ) kernel density modeling of auditory ( red wireframe ) and vision ( green ) studies . from nielsen and hansen ( 2000b ) . the isosurfaces in the probability densities in both subplots of figure 4 has been set for display purpose . the methods for probability density estimation of coordinates are not limited to activations but may be applied to any kind of coordinates in stereotaxic space from deactivations , cortical stimulations , lesions or structural changes , e.g. , obtained with voxel - based morphometry . when a probability density estimate is constructed for a set of coordinates and it is converted to a voxel - volume , then the volumes across multiple sets of coordinates may be aggregated into a single data matrix x(sets voxels ) . this data matrix may then be decomposed with multivariate analysis in a number of ways , e.g. , with singular value decomposition for principal component analysis , ulv = x , where the left factorization matrix u(sets components ) contains loading over sets of coordinates for each principal component and the right factorization matrix v(vowel components ) contains loadings over voxels . other types of decomposition for this matrix are independent component analysis ( ms = x , with m the mixing matrix and s the source matrix ) , non - negative matrix factorization ( wh = x ) and k - means clustering ( ca = x , with c a centroid matrix and a an assignment matrix ) . the right decomposition matrices , v , s , h and a all contain vectors that each represents a volume . as part of the workflow for presenting the information in the brede database on the web the decompositions work on data matrices formed from sets of papers and sets of experiments , and corner cube visualizations figure 5 shows such a visualization for a component from non - negative matrix factorization , i.e. , a row in the h matrix . such visualizations may be useful for navigating among the studies in the database , and to a certain extent they reveal spatial distributions of the cognitive components of the brain . together with the visualization on the web page are listed the experiments that have high association with the component , i.e. , experiments associated with large elements in a column of the left matrix w. for the component in figure 5 they are experiments described as , e.g. , visual object decision , buildings visual objects , color perception during free viewing and passively viewed scenes. corner cube visualization on the web page of the brede database with results from a non - negative matrix factorization of experiments in the database . before putting too much trust in visualizations and analysis across studies one needs to remember that the study results may have arisen in quite different ways . in standard meta - analysis the only variations between studies that are usually modeled is the number of subjects and the standard deviation of the data in the individual studies . in neuroimaging meta - analysis and visualization these variables besides there are several other variables that neither are considered : the varying thresholds applied , e.g. , corrected and uncorrected p - values ( nielsen et al . , 2006b ) , the difference in field of view between studies , the reporting style of coordinates ( e.g. , extent threshold , number of maxima per cluster ) as well as the variation from the different pre - processing and analysis choices that have been made . ( 2009a ) compared different cbma models and their application of a threshold makes a blob appear and disappear depending on the type of cbma . quite a few tools exist for interactive neuroimaging visualization across the internet . often these tools are based on a client server model with the client implementing the visualization and graphical user interface in java . among these tools are jiv that renders multiple volume data by orthogonal slice views implemented as a java applet ( cocosco and evans , 2001 ) . iiv implements a similar functionality ( lee et al . , 2008 ) , and mindseer can also render in 3d remotely ( moore et al . , 2007 ) neuroterrain implements 3d visualization and has demonstrated its use in connection with a mouse atlas ( gustafson et al . , 2007 ) . the talairach applet renders a digital representation of the talairach atlas and combines it with neuroanatomical labeling of coordinates via the talairach daemon described by lancaster et al . also in connection with the brainmap database the java client - program sleuth plots 3d points in orthogonal 2d slices based on user query to the brainmap server ( laird et al . , the internet brain volume database ( ibvd ) records published values for brain region volumes across variables such as gender and diagnosis ( kennedy et al . , 2003 ) . since the neuroimaging data analysis arrives at one single value the brain volume in cubic centimeters the visualization of the data is relatively simple compared to other neuroinformatics visualizations : from web - based user queries ibvd generates on - the - fly png image - files with the brain volumes from the different studies plotted as a function of age with color - coding and the variability indicated . interactive visualization systems for neuroimages with server - side 3d rendering have been described by poliakov et al . ( 2005 ) and a public system is available with the webcaret web service , see figure 2 . with the brede toolbox we construct 3d visualizations browsable on the web by using the virtual reality modeling language ( vrml ) ( iso / iec , 1997 ; nielsen and hansen , 2000a ) , see the vrml examples in figure 4 . when defined in the middle of 1990s vrml held great promise to get wide - spread use for 3d interactive and hyperlinked visualizations , but since then it has had limited growth : vrml lacks good browser implementations and there has been erratic adoption of a scripting language . nevertheless , it is one of the few means for web distribution of 3d content in free standardized form . an alternative format is the universal 3d file format ( u3d ) that can be embedded in newer versions of the pdf format . ( 2007 ) implements vrml export . for the web presentation of the brede database , we generate 3d corner cube visualizations of the coordinates in the database with an offline matlab batch script , both as image files embedded on the web page as well as vrml files , see figure 6 . matlab is not well suited to work as a web script , and for the interactive web scripts associated with the brede database , there are presently no visualization implemented . the inc interactive talairach atlas renders 2d orthogonal slices from the talairach and the mni single subject atlases . this web service can merge a user - given coordinate with the visualization , and as such we use it for visualization of individual coordinates from the brede database and the brede wiki , see figure 7 for an example . screenshot of the web page for an experiment in brede database with a corner cube visualization of the coordinates in a experiment together with a wireframe indicating an isosurface of the kernel density estimate with the coordinates . an interactive rendering is provided with the link to a generated corner cube visualization in a vrml file . the web - based inc interactive talairach atlas queried with a coordinate from the brede wiki . besides java , vrml and standard image files such as png the scalable vector graphics ( svg ) format may prove useful for internet - based visualizations , see figure 1 for an example . data mining results from neuroimaging analysis are not the only type of information for visualization . information about the background , design , scanning , analysis procedure , and interpretation surrounds the data mining results of a typical neuroimaging study . in scientific articles context information , though sometimes authors also use tables to describe , e.g. , subject information . authors rarely apply visualizations for this kind of information except in situations with explanation of the experimental design and scanning . the experimental design has a natural temporal evolution and as such the visualization often displays the design as a function of time . users of the behavioral experiment software from psychology software tools is familiar with the graphical programming environment of e - prime which has this kind of visualization as an integral part of the development of the experiment . other parts of the neuroimaging study may be visualized with what is usually referred to as information visualization . in a demonstration visualization , we employed a torus topology for an entire neuroimaging study process constructing 3d icons for funding , the experimental design , authors , experimental subjects , etc . the usefulness of such a visualization depends on how effective it conveys information compared to standard text , and if the visualization format requires specialized and limited distributed programs for rendering and interaction the impact may be small . manual creation of these visualizations is infeasible , the visualization should be constructed automatically from description of the study , e.g. , the so - called some workflow management systems display the processing flow graphically ( dinov et al . , 2008 ) . screenshot of a vrml rendering seeking to convey parts of the information surrounding a neuroimaging study : 3d icons for funding , research organization , researchers , software , subjects , and scanner placed in a torus . when neuroimaging studies get reported in articles the relationships between the articles can be turned in to visualizations . many types of visualizations exist and many relationships may be revealed : between terms , concepts , citations to and from articles as well as between authors , cited authors and cited journals . the visualizations are of course not limited to articles only in neuroimaging , see , e.g. , card et al . ( 2007 ) use a spherical embedding algorithm to display a bipartite graph in 3d space with two spheres . one of their illustrations visualized the relationship between poster sessions in the society for neuroscience 2006 meeting together with words from the abstracts in the sessions . cluster bush , that describe the clusters in a hierarchical multivariate analysis ( nielsen et al . , 2005 ) : clusters are indicated with dots and thick lines indicate a large similarity between two clusters . given a set of abstracts the automated workflow for generating a plot like figure 9 involves the conversion of the texts to a bag - of - words matrix , the exclusion of a large number of words ( stop words ) , hierarchical non - negative matrix factorization and lastly the cluster bush visualization all implemented with the functions of the brede toolbox . cluster bush visualization of the text mining results of the abstracts in the brede database . coordinate - based meta - analysis and text mining can be combined to form visualizations , see figure 10 and nielsen et al . the workflow for constructing the visualization in the figure involves the setup of a matrix describing the words in the abstract of papers and the construction of another matrix from kernel density estimation with the coordinates in each paper . after non - negative matrix factorization each individual factor may be rendered in 3d and associated with words from the abstract , e.g. , the blue area in figure 10a in the occipital lobe is associated with words such as visual and functional atlas generated from a combined data mining of text and brain coordinates from the brede database . ( a ) corner cube visualization with labeled brain areas . ( b ) automatically generated legend with words from the text mining of abstracts . based on a corpus of articles published between 1997 and 2000 in the journal neuroimage we could plot cited authors and cited journals in 2d . the data mining with visualization would for example reveal a dichotomy between pet and fmri ( nielsen , 2002 ) , see figure 11 . here , the workflow involves specialized algorithms that extract citations and the use of matrix computations , particularly singular value decomposition , for multidimensional scaling - like projection of the data onto 2d . for the brede database , we automatically construct what we have termed authors near the center , such as friston and dolan , have high network degrees , which here corresponds to the number of authored articles ( nielsen , 2002 ) . visualization of data mining result of journal co - citation analysis with singular value decomposition on citation data from neuroimage . the concentric circles indicate the number of articles written by the author in the corpus . the brede toolbox automatically constructs similar , albeit smaller , bullseye visualizations for each author represented in the brede database author ontology . the well - tested and widely used graphviz package provides spatial graph layout for a given network ( gansner and north , 2000 ) . at one point the pubgene web service used graphviz in a large - scale application for displaying relations between genes based on literature in pubmed ( jenssen et al . , 2001 ) . these graphs display the brain function and brain region ontologies , e.g. , indicating that vision has perception as taxonomic parent or that the cingulate area is a parent for the posterior cingulate , see figure 13 . our workflow with the brede toolbox involves extraction of the ontology from brede database xml files , construction of a file with the graph that graphviz reads , invoking graphviz for generation of an image file , and then finally construction of the web page with the image file embedded . graphviz can construct html image maps so the nodes in the graph image are associated with clickable hyperlinks . on the final web page a reader may navigate the brain region and brain function ontologies by clicking on the nodes in the graph . the brede toolbox can also use graphviz for layout of other types of data that can be described as a network , e.g. , from structural equation modeling of regional neuroimaging data . a number of journal web sites use plots called citation map in the style of graphviz for visualizing in- and out - going citations of each article , see , e.g. , bmj and the journal of neuroscience web sites . for presenting the brede database brain region ontology on the web the workflow with the brede toolbox invokes the graphviz program which generates hyperlinked plots of the brain region hierarchy , here for the posterior cingulate gyrus. another type of graph visualization within neuroimaging is the interactive graph visualization with a hyperbolic browser that features in tools from the laboratory of neuro imaging ( loni ) : love and itools ( dinov et al . , 2006 , 2008 ) . isi web of knowledge provides a java applet to render their citation information with a similar topology . with the brede toolbox we are able to build a workflow with extraction of data from the brede database , automated data mining and visualizations . an advantage of the automated procedure is that little human intervention is required to update the visualizations as new data is added to the database . the visualizations can display not only spatial neuroimages , but for example also results from text mining , and visualization can take place across the internet with data originating on one server and displayed on another . the brede database represents just a small fragment of the results from the published literature ( derrfuss and mar , 2009 ) . databases such as neuronames , brainmap and sumsdb are much larger . however , no universal database exist for coordinates from functional neuroimaging . to gain a higher degree of coverage future work may attempt to aggregate data from different databases for combined visualizations . since typical meta - analytic data is anonymous and small ( compared to a typical neuroimaging study ) , it is easier to share such data and we may see collaborative internet - based analyses and visualizations . building a collaborative system for neuroimaging data requires more effort , and in the brede wiki only simple visualizations are presently available . science 2.0 where data , analyses and visualizations can be shared in web - based collaborative and user - friendly environments . the authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .

a few neuroinformatics databases now exist that record results from neuroimaging studies in the form of brain coordinates in stereotaxic space . the brede toolbox was originally developed to extract , analyze and visualize data from one of them the brainmap database . since then the brede toolbox has expanded and now includes its own database with coordinates along with ontologies for brain regions and functions : the brede database . with brede toolbox and database combined , we setup automated workflows for extraction of data , mass meta - analytic data mining and visualizations . most of the web presence of the brede database is established by a single script executing a workflow involving these steps together with a final generation of web pages with embedded visualizations and links to interactive three - dimensional models in the virtual reality modeling language . apart from the brede tools i briefly review alternate visualization tools and methods for internet - based visualization and information visualization as well as portals for visualization tools .

Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period. ||||| Breaking News Emails Get breaking news alerts and special reports. The news and stories that matter, delivered weekday mornings. / Updated By Alex Johnson California became the first state to ban schools from using the "Redskins" team name or mascot Sunday, a move the National Congress of American Indians said should be a "shining example" for the rest of the country. The law, which Gov. Jerry Brown signed Sunday morning, goes into effect Jan. 1, 2017. It's believed to affect only four public schools using the mascot, which many Indian groups and activists find offensive, but its impact is significant symbolically — California has the largest enrollment of public school students in the nation, according to the National Center for Education Statistics. The state Assembly overwhelmingly approved the California Racial Mascots Act in May, about a month before the Obama administration went on record telling the Washington Redskins that they would have to change their name before they would be allowed to move to a stadium in Washington, D.C., from their current home in suburban Maryland. Pro Football Talk: Obama Administration: Team Should Change Name Before Returning to D.C. In a joint statement with the nonprofit group Change the Mascot, the National Congress of American Indians praised California for "standing on the right side of history by bringing an end to the use of the demeaning and damaging R-word slur in the state's schools." "They have set a shining example for other states across the country, and for the next generation, by demonstrating a commitment to the American ideals of inclusion and mutual respect," it said. The U.S. Patent Office agreed last year that the nickname is "disparaging of Native Americans" and canceled the Washington pro football team's federal trademark protection. ||||| These crawls are part of an effort to archive pages as they are created and archive the pages that they refer to. That way, as the pages that are referenced are changed or taken from the web, a link to the version that was live when the page was written will be preserved.Then the Internet Archive hopes that references to these archived pages will be put in place of a link that would be otherwise be broken, or a companion link to allow people to see what was originally intended by a page's authors.The goal is to fix all broken links on the web . Crawls of supported "No More 404" sites.

– The "Redskins" at four California high schools have until Jan. 1, 2017 to find a new name. Gov. Jerry Brown has signed a bill that bans public schools in the state from using the term for sports team or their mascots, reports the Los Angeles Times. This is the first statewide ban of the term and the National Congress of American Indians praised the move as a "shining example" to other states that puts California on the "right side of history," reports NBC. The group, which describes the term as "demeaning and damaging," says it hopes the California law will put more pressure on the Washington Redskins to change their name. The move affects high schools in Madera County, Calaveras County, Tulare County, and Merced County, where opponents say the name has been used for generations and shouldn't be considered offensive, the Merced Sun-Star reports. The state will provide funds to help the schools buy things like new uniforms and signs, reports the San Francisco Chronicle. Brown approved the "Redskins" bill but vetoed a measure banning public parks and buildings from being named after Confederate figures, saying the issue is "quintessentially for local decision makers," reports the LA Times. (This California high school retired its controversial Arab mascot—and replaced it with another Arab mascot.)

we realized the four internal coin states @xmath33 with the linear polarization states , horizontal @xmath34 and vertical @xmath35 , and two spatial modes @xmath36 and @xmath37 , similar to the four spatial modes proposed in ( _ 27 _ ) . the spatial modes correspond to the two input ports of the first polarizing beam splitter ( fig . a.1 ) ) . we encoded the states by @xmath38 to implement our quantum operations in the four - dimensional hilbert space of the quantum coin we decomposed the @xmath39 unitary coin operation into products of multiple @xmath40 operations ( _ 31 _ ) . each @xmath40 transformation is implemented either by half - wave plates ( hwp ) or an electro - optic modulator ( eom ) . in the basis of the four coin states the transformations are given by @xmath41 with @xmath42 being the angle of @xmath43 , @xmath44 , relative to its optical axis and @xmath45 a tunable phase . depending on the position of the four hwps in the setup ( fig . a.1a ) they operate on different coin state pairs , due to the spatial switch via polarizing beam splitters ( pbs ) . the hadamard coin ( fig . 2b+e ) was obtained for the configurations @xmath46 , while the coin used in fig . 2d+e was given by @xmath47 , @xmath48 . to implement controlled - hadamard gates either @xmath49 or @xmath50 were aligned to their optical axis ( @xmath51 ) , while the remaining plates were set to @xmath52 ( fig . the transformation of the eom with @xmath53 corresponds to a controlled - z operation . additional static phase factors changing the relative phase between the four coin states can occur during the propagation through the setup . however , these phases do not influence the final propability distribution due to the property of the coin operators that can be implemented with the used optical elements . given precise phase control , two additional hwps and a pbs would allow the implementation of arbitrary @xmath39 coin operators . our experiment simulates a 2d quantum walk on a regular square lattice , which means that a walker can move in four possible directions from a given site . the direction of the movement is determined by the current coin state of the walker . to implement the quantum walk in a 2d topology we use the time - multiplexing technique ( _ 9 _ ) . this method maps each individual position of the 2d graph on the one - dimensional time line . in contrast to determining the direction of the following step in space , the coin state defines a fixed time delay in the time - multiplexed system . a.1 shows the first step of a quantum walk in our system and the corresponding mapping of the temporal spread on the 2d lattice . the propagation of the initial pulse representing the walker through the setup is split into five parts : 1 . we initialize the photonic input state in the coin state @xmath54 with the starting time corresponding to position @xmath55 . 2 . after launching the pulse into the setup we perform the coin operation @xmath56 , as defined in eq . a2 . 3 . split by a polarizing beam splitter ( pbs ) the pulse travels through two fibers of different lengths . the resulting time separation @xmath57 can be interpreted as a step in vertical ( @xmath23 ) direction . we hereby define the transformation @xmath58 for pulses passing the longer fiber , while the pulses in the shorter arm acquire the transformation @xmath59 . additional retardation plates hereby compensate for unwanted polarization effects in the fibers . 4 . subsequently @xmath60 and @xmath61 implement the coin operation @xmath62 ( eq . a2 ) , determining the coin state for the horizontal ( @xmath22 ) direction . the step operator in the horizontal ( @xmath22 ) direction is performed with a second pbs and a temporal shift @xmath63 , obtained by traveling in two free space paths of different lengths . as a result one step in our quantum walk setup combines both a shift in vertical and horizontal direction , restricting the translation on a 2d grid to the diagonal neighbors ( fig . starting in the origin , this leads to a spread over maximally @xmath64 positions after @xmath11 steps . after each step a time resolving measurement gives information about the location of the photon . the detection times for the first and second step of a hadamard walk are shown in fig . a.1b . at the first detection the photons can arrive at four different times , which is either the minimal time @xmath65 ( corresponding to position state @xmath66 ) , @xmath67 stating position @xmath68 , @xmath69 ( @xmath70 ) or @xmath71 ( @xmath72 ) . at the second step on the other hand , multiple pulses can arrive simultaneously at the detectors . independent of the coin state and , hence , spatial and polarization modes of the photons , all coinciding detections correspond to the same position state @xmath73 . in the following step wave packets in the same time bin and spatial mode interfere at @xmath74 ( @xmath75 ) , while wave packets in different spatial modes can interfere at @xmath76 ( @xmath77 ) . during the time evolution , the area of the grid covered by the quantum walker grows quadratically with the number of steps . the use of the time - multiplexing technique guarantees that the number of elements stays constant independent of the size of the simulated grid . in the experimental implementation it is only the lengths of the optical paths that needs to be adjusted to the maximum number of steps that are to be realized . in addition , the performance of our time - multiplexed setup is limited only by imperfections of the optical components resulting in errors , decoherence and losses . in the following we want to discuss each point individually . a sharp limitation for the maximal step number is given by the design of the experiment . if the minimal time for one round trip @xmath65 is shorter than the temporal expansion of all positions in a single step , temporal overlaps between different steps can occur . we choose our experimental parameters @xmath78 and @xmath79 without eom such that @xmath80 and @xmath81 to prevent temporal overlaps of different positions for the first 12 steps . an occurring additional delay induced by the modulator changed the conditions without inducing unwanted temporal overlaps . however , by simply changing the fiber lengths or the path differences the step number can easily be increased . the most significant source of systematic errors in the setup is the eom . due to the architecture of the modulator the applied phase is not only affecting the horizontal polarization component , as shown in eq . a2 , but also the vertical component with a factor 1/3.5 . this decreases the achievable similarities for quantum walks where controlled - z coin operations are used . additionally , the wave front of pulses passing the modulator are distorted differently for both polarizations , which influences the occurring interferences . both effects are included in the theory presented in fig . a replacement of the eom with an optimized modulator would improve the achievable similarity at higher number of steps . decoherence in the time - multiplexed setup can occur if mechanical vibrations of the optical elements influence the interference properties . typically mirrors vibrate with a frequency below 500hz , corresponding to a time scale of 2ms . the duration of twelve steps in the current setup is less than @xmath82 , a factor of 200 faster compared to mirror vibrations . this suggests that decoherence effects will not influence the time - multiplexed quantum walk up to at least 100 steps . at the present stage the main factor limiting the scalability is given by the losses per step . these are induced by the probabilistic detection method and losses at optical elements . to counter the effect of losses one can either start with an increased intensity or use optical amplifiers , as shown in ( _ 32 _ ) . while the first approach requires an active protection of the single - photon detectors , the second prohibits the use of the experiment with single - photon sources . a third method to reduce the losses is a change from probabilistic to a deterministic coupling mechanism with additional polarization modulators . this technique combined with a change - over to a low - loss wavelength regime ( 1550 nm ) , makes the setup interesting for single photon input states . using one of the described methods to circumvent the losses can increase the number of steps significantly . to quantify the two - particle entanglement simulated in the system we assumed that the quantum walk evolution results in a pure state @xmath83 after @xmath11 steps , with the complex parameters @xmath84 . the assumption is based on the fact that the system does not show signs of decoherence for any of the coin operators , confirmed by the high values of the measured similarities . the von neumann entropy @xmath24 , which quantifies the entanglement ( _ 33 _ ) is given by @xmath85 with the eigenvalues @xmath86 of the reduced density matrix @xmath87 , given by the trace over one subsystem . for details see ( _ 23 _ ) . by individually measuring the arrival probability in each coin and position state we obtain the absolute squared of the parameters @xmath88 , hence no direct extraction of the phase information is possible . however , we can obtain information about the relative phases between position and coin states from the final interference pattern . as a result we can reconstruct the phase distribution with the help of the theoretical model up to three undetermined relative phases between the four different coin states and a global phase factor . by choosing the phases inducing the minimal entropy , we are able to give a lower bound for the simulated entanglement in the experiment . d. aharonov , a. ambainis , j. kempe , u. vazirani , in _ proceedings of the thirty - third annual acm symposium on theory of computing _ , stoc 01 , hersonissos , greece , 6 to 8 july 2001 ( acm , new york , ny , usa , 2001 ) , pp . 5059 . a. ambainis , j. kempe , a. rivosh , in _ proceedings of the sixteenth acm - siam symposium on discrete algorithms _ , soda 05 , vancouver , canada , 23 to 25 january 2005 ( society for industrial and applied mathematics , philadelphia , 2005 ) , p. 1099 - 1108 .

multi - dimensional quantum walks can exhibit highly non - trivial topological structure , providing a powerful tool for simulating quantum information and transport systems . we present a flexible implementation of a 2d optical quantum walk on a lattice , demonstrating a scalable quantum walk on a non - trivial graph structure . we realized a coherent quantum walk over 12 steps and 169 positions using an optical fiber network . with our broad spectrum of quantum coins we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions . introducing dynamic control allowed for the investigation of effects such as strong non - linearities or two - particle scattering . our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems . quantum simulation constitutes a paradigm for developing our understanding of quantum mechanical systems . a current challenge is to find schemes , that can be readily implemented in the laboratory to provide insights into complex quantum phenomena . quantum walks @xcite serve as an ideal test - bed for studying the dynamics of such systems . examples include understanding the role of entanglement and interactions between quantum particles , the occurrence of localization effects @xcite , topological phases @xcite , energy transport in photosynthesis @xcite , and the mimicking of the formation of molecule states @xcite . while theoretical investigations already take advantage of complex graph structures in higher dimensions , experimental implementations are still limited by the required physical resources . all demonstrated quantum walks have so far been restricted to evolution in one dimension . they have been realized in a variety of architectures , including photonic @xcite and atomic @xcite systems . achieving increased dimensionality in a quantum walk @xcite is of practical interest as many physical phenomena can not be simulated with a single walker in a one - dimensional quantum walk , such as multi - particle entanglement and non - linear interactions . furthermore , in quantum computation based on quantum walks @xcite search algorithms exhibit a speed - up only in higher dimensional graphs @xcite . the first optical approaches to increasing the complexity of a linear quantum walk @xcite showed that the dimensionality of the system is effectively expanded by using two walkers , keeping the graph one - dimensional . while adding additional walkers to the system is promising , introducing conditioned interactions and in particular controlled non - linear interactions at the single photon level is technologically very challenging . interactions between walkers typically result in the appearance of entanglement , and have been shown to improve certain applications , such as the graph isomorphism problem @xcite . in the absence of such interactions , the two walkers remain effectively independent , which severely limits observable quantum features . we present a highly scalable implementation of an optical quantum walk on two spatial dimensions for quantum simulation , using frugal physical resources . one major advance of a two - dimensional system is the possibility to simulate a discrete evolution of two - particles including controlled interactions . in particular , one walker , in our case a coherent light pulse , on a 2d lattice is topologically equivalent to two - walkers acting on a one - dimensional graph . thus , despite using an entirely classical light source , our experiment is able to demonstrate several archetypal two - particle quantum features . for our simulations we exploit the similarity between coherent processes in quantum mechanics and classical optics @xcite , as it was used for example to demonstrate grover s quantum search algorithm @xcite . a quantum walk consists of a walker , such as a photon or an atom , which coherently propagates between discrete vertices on a graph . a walker is defined as a bipartite system consisting of position ( @xmath0 ) and a quantum coin ( @xmath1 ) . the position value indicates at which vertex in the graph the walker resides , while the coin is an ancillary quantum state determining the direction of the walker at the next step . in a two - dimensional quantum walk the basis states of a walker are of the form @xmath2 describing its position @xmath3 in spatial dimension 1 and 2 and the corresponding two - sided coin parameters with @xmath4 . the evolution takes place in discrete steps , each of which has two stages , defined by coin ( @xmath5 ) and step ( @xmath6 ) operators . the coin operator coherently manipulates the coin parameter , leaving the position unchanged , whereas the step operator updates the position according to the new coin value . explicitly , with a so - called hadamard coin @xmath7 , a single step in the evolution is defined by the operators , @xmath8 [ eq ] the evolution of the system proceeds by repeatedly applying coin and step operators on the initial state @xmath9 , resulting in @xmath10 after @xmath11 steps . the step operator @xmath6 hereby translates superpositions and entanglement between the coin parameters directly to the spatial domain , imprinting signatures of quantum effects in the final probability distribution . we performed 2d quantum walks with photons obtained from attenuated laser pulses . the two internal coin states are represented by two polarization modes ( horizontal and vertical ) in two different spatial modes [ app . 1 ] , similar to the proposal in @xcite . incident photons follow , depending on their polarization , four different paths in a fiber network ( fig . 1a ) . the four paths correspond to the four different directions a walker can take in one step on a 2d lattice . different path lengths in the circuit generate a temporally encoded state , where different position states are represented by discrete time - bins ( fig . 1b ) . each round trip in the setup implements a single step operation while the quantum coin operation is performed with linear optical elements ( half - wave plates , hwp ) [ app . 1 ] . in order to adjust the coin operator independently at each position we employed a fast - switching electro - optic modulator ( eom ) . a measurement with time - resolving single - photon counting modules allowed for the reconstruction of the output photo - statistics [ app . 2 ] . we have implemented two different kinds of quantum coins in our 2d quantum walks . first we investigated quantum walks driven only by separable coin operations , @xmath12 . here the separability can directly be observed in the spatial spread over the lattice , when initializing the walker in a separable state . as an example we measured a hadamard walk with photons initially localized at position @xmath13 . the probability distribution showing at which position the photons were detected after ten steps ( fig . 2a+b ) can be factorized into two independent distributions of one - dimensional quantum walks @xcite , stating no conceptual advantage of a 2d - quantum walk . however , two - dimensional quantum walks allow for much greater complexity using controlled operations . these operations condition the transformation of one coin state on the actual state of the other . due to the induced quantum correlations one obtains a non - trivial evolution resulting in an inseparable final state . the probability distribution for a hadamard walk with an additional controlling operation can be seen in fig . 2c+d . we compare the ideal theoretical distribution with the measured photo - statistics via the similarity , @xmath14 , quantifying the equality of two classical probability distributions ( @xmath15 for a completely orthogonal distributions and @xmath16 for identical distributions ) . for the hadamard walk ( fig . 2a+b ) we observe @xmath17 , and for the quantum walk with controlling gates ( fig . 2c+d ) @xmath18 ( after 10 steps , across 121 positions ) . increasing the number of walkers in a quantum walk effectively increases its dimensionality @xcite . specifically , for a given 1d quantum walk with @xmath19 positions and two walkers , there exists an isomorphic square lattice walk of size @xmath20 with one walker . by this topological analogy , a measured spatial distribution from a 2d lattice with positions ( @xmath21 ) can be interpreted as a coincidence measurement for two walkers at positions @xmath22 and @xmath23 propagating on the same linear graph . hereby each combined coin operation of both particles , including controlled operations , has an equivalent coin operation in a 2d quantum walk . this allows us to interpret the 2d walk in fig . 2c+d as a quantum walk with controlled two - particle operations , a system typically creating two - particle entanglement . the inseparability of the final probability distribution is then a direct signature of the simulated entanglement . in fig . 2e we show a lower bound for the simulated entanglement between the two particles during the stepwise evolution with four different coin operations . we quantified the simulated entanglement via the von neumann entropy @xmath24 , assuming pure final states after the quantum walk [ app . 4 ] . for this calculation the relative phases between the positions and coins were reconstructed from the obtained interference patterns , while phases between the four coin states were chosen to minimize the entanglement value . without conditioned operations the two particles evolve independently ( @xmath25 ) , whereas an evolution including controlled operations reveals a probability distribution characterized by bipartite entanglement . we found that the interactions presented in fig . 2c+d exhibit an entropy of at least @xmath26 after 12 steps , which is @xmath27 of the maximal entropy ( given by a maximally entangled state ) . the non - zero entropies obtained in the higher steps of the separable hadamard walk are attributed to the high sensitivity of the entropy measure to small errors in the distribution for @xmath28 . the investigated interactions can be interpreted as long - distance interactions with the interaction strength being independent of the spatial distance of the particles . this is a unique effect and highly non - trivial to demonstrate in actual two - particle quantum systems . contrary to the position independent interactions is the evolution of two - particle quantum walks with short - range interactions , that is interactions occurring only when both particles occupy the same position . these interactions can be interpreted as two - particle scattering or non - linear interactions . when utilizing a 2d quantum walk to simulate two walkers , all vertices on the diagonal of the 2d - lattice correspond to both walkers occupying the same position . hence , we can introduce non - linear interactions by modifying the coin operator on the diagonal positions while keeping all other positions unaffected . as an example of a two - particle quantum walk with non - linear interactions ( fig . 3 ) , the coin operator on the diagonal is in the form @xmath29 , where @xmath30 is a controlled phase operation implemented by a fast switching eom . the chosen operation simulates a quantum scenario of particular interest the creation of bound molecule states , predicted as a consequence of two - particle scattering @xcite . evidently , the quantum walk is to a large extent confined to the main diagonal ( @xmath31 as opposed to the hadamard walk @xmath32 ) , a signature of the presence of a bound molecule state . in general , using a coin invariant under particle exchange , bosonic or fermionic behavior can be simulated , depending on whether the initial states are chosen to be symmetric or anti - symmetric with respect to particle permutations . with our initial state being invariant under particle exchange we simulated an effective bose - hubbard type non - linearity for two bosons @xcite . we have demonstrated an efficient implementation of a two - dimensional quantum walk and proved the experimental feasibility to simulate a diversity of interesting multi - particle quantum effects . our experiment overcomes the technical challenges of two - particle experiments , while exhibiting very high similarity and scalability . combined with the flexibility in the choice of input state , controlling the coin at each position independently allows for simulations of a broad spectrum of dynamic quantum systems under different physical conditions . our experimental architecture can be generalized to more than two dimensions , with the addition of extra loops and orbital angular momentum modes as coin states @xcite . this opens a largely unexplored field of research , facilitating quantum simulation applications with multiple walkers , including bosonic and fermionic behavior , and non - linear interactions . it may be possible to study the effects of higher dimensional localization , graph percolations or utilize the network topology in conjunction with single- or two - photon states . additionally , a foreseeable future application for our system is the implementation of a quantum search algorithm . we demonstrated that , with a physical resource overhead , a classical experiment can simulate many genuine quantum features . while our experiment is important for simulation applications , it is equally interesting for understanding fundamental physics at the border between classical and quantum coherence theory . * acknowledgements : * we acknowledge financial support from the german israel foundation ( project no . 970/2007 ) . ag , m , vp , ch and ij acknowledge grant support from msm6840770039 and msmt lc06002 , sgs10/294/ohk4/3t/14 , ga r 202/08/h078 and otka t83858 . pr acknowledges support from the australian research council centre of excellence for engineered quantum systems ( project number ce110001013 ) .

we have seen remarkable progress in the understanding of pure dark matter structures over the last few years . this was triggered by numerical simulations which have observed general trends in the behaviour of the radial density profile of equilibrated dark matter structures from cosmological simulations , which roughly follow an nfw profile @xcite , ( see diemand et al 2004 for references ) . general trends in the radial dependence of the velocity anisotropy has also been suggested @xcite . recently , more complex relations have been identified , holding even for systems that do not follow the simplest radial power - law behaviour in density . these relations are first that the phase - space density , @xmath3 , is a power - law in radius @xcite , and second that there is a linear relationship between the density slope and the anisotropy ( hansen & moore 2005 , hereafter hm04 ) . a connection between the shape of the velocity distribution function and the density slope has also been suggested ( hansen et al 2005a , 2005b ) . using the jeans equation together with the fact that phase - space density is a power - law in radius allows one to find the density slope in the central region numerically @xcite , and even analytically for power - law densities @xcite . recently dehnen & mclaughlin ( 2005 , hereafter dm05 ) using both the phase - space density being a power - law in radius and also the @xmath0 relation , showed that one can solve the jeans equations analytically and extract the radial dependence of density , anisotropy , mass etc . the relationship between phase - space density and radius has been considered several times and seems to be well established , however , the other crucial ingredient in the analysis , namely the linear relationship between density slope and anisotropy has only been investigated qualitatively . we have performed a large set of simulations in order to quantify this relationship . we show that with present day simulations there does indeed appear to be a linear relation between density slope and anisotropy , which implies zero anisotropy near the density slope of approximately @xmath4 . we combine our findings with analytical results and find that the outer anisotropy is radial and close to @xmath5 . the @xmath0 relation was suggested based on a set of different numerical simulations , including spherical collapse simulations , collisions between initially isotropic nfw structures , merger between two disk galaxies , and finally structures formed in a @xmath6cdm cosmological simulation . the original relation had a large scatter , and there were several questions not fully answered , such as a possible dependence on shape or initial conditions . we have here performed controlled experiments to test exactly these points . the set of experiments are described in glorious detail in a coming publication , and we will not get into these aspects here . we will only mention , that for each simulation have we extracted all the relevant parameters in radial bins , logarithmically distributed from the softening length to beyond the region which is fully equilibrated . we calculate the radial derivative of the density ( the density slope ) @xmath7 and the velocity anisotropy @xmath8 in each radial bin , where the @xmath9 are the one dimensional velocity dispersions in the tangential and radial directions respectively . one of the test we performed was the head - on collision between two initially isotropic nfw structures . we then took the resulting structures and collided these headon again . the resulting structure is prolate when observed in density contours . one may fear that the resulting @xmath0 relation will depend strongly on the axis - ratios of such structures . in order to test this question , we extracted the resulting prolate structure after the first collision described above . we can now decide to collide this structure along different axes , either along the long , intermediate or short axes . we perform these 3 different collisions . we find that there is virtually no difference in the @xmath0 relation for these 3 different simulations . we conclude from this that whereas the definition of density slope does depend slightly on the shape of the density contours , then the @xmath0 relation is almost independent of the shape . to address the question of how strongly the @xmath0 relation from the head - on collisions described above depend on the initial conditions , we now perform collisions between structures with different initial degree of anisotropy . first we make a repeated head - on collision between two isotropic nfw structures . next we make repeated head - on collisions between two initially strongly radially anisotropic structures . and finally do we perform repeated head - on collisions between initially strongly tangentially anisotropic structures . we find that the resulting @xmath0 relation is virtually independent of initial conditions , and we conclude that the collisions were sufficiently violent to erase the initial conditions sufficiently to conform with the @xmath0 relation . in a recent paper , dehnen & mclaughlin ( 2005 ) showed , that under the two assumption that phase - space density is a power - law in radius , and that there is a linear @xmath0 relation , that the central slope of dark matter structures must be @xmath10 , where @xmath11 is the central anisotropy . we can now compare this result with our findings , and in figure [ fig : together2 ] we show the dm05 result for the _ central _ values as a thin ( blue ) straight line . we see that the two lines cross near @xmath12 and @xmath13 , showing that the central part of dark matter structures is isotropic , and that the central density slope is indeed @xmath14 . the outer density slope is about @xmath15 @xcite , which when compared with our findings result in @xmath16 . we have quantified the relationship between the density slope and the velocity anisotropy , the @xmath0 relation . we have performed a large set of simulations to investigate systematic effects related to shape and initial conditions , and we find that the @xmath0 relation is almost blind to both shape and initial conditions , as long as the system has been _ perturbed sufficiently _ and subsequently allowed to relax . when compared with analytical results we find that the central region is indeed isotropic with a density slope about @xmath17 , and that the outer asymptotic anisotropy is radial , with a magnitude of @xmath18 . austin , c. g. et al . 2005 , arxiv : astro - ph/0506571 . cole , s. , & lacey , c. 1996 , mrnas , 281 , 716 dehnen , w. , & mclaughlin , d. 2005 , arxiv : astro - ph/0506528 ( dm05 ) , j. , moore , b. , & stadel , j. 2004 , mnras , 353 , 624 hansen , s. h 2004 , mnras , 352 , l41 hansen , s. h. , & moore , b. 2004 , arxiv : astro - ph/0411473 ( hm04 )

one can solve the jeans equation analytically for equilibrated dark matter structures , once given two pieces of input from numerical simulations . these inputs are 1 ) a connection between phase - space density and radius , and 2 ) a connection between velocity anisotropy and density slope , the @xmath0 relation . the first ( phase - space density v.s . radius ) has been analysed through several different simulations , however the second ( @xmath0 relation ) has not been quantified yet . we perform a large set of numerical experiments in order to quantify the slope and zero - point of the @xmath0 relation . when combined with the assumption of phase - space being a power - law in radius this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy , central density slope of @xmath1 , and outer anisotropy of approximately @xmath2 .

a shock wave is termed nonradiative if the cooling time of the postshock gas exceeds the dynamical time scale . nonradiative shocks lack cooling zones , therefore the optical and ultraviolet line emission is excited close to the shock front . the emission line fluxes and line widths are sensitive to the shock velocity and the degree of postshock electron - ion / ion - ion equilibration . this property makes the optical and ultraviolet lines valuable tools for investigating collisionless heating in high mach number , low density shock waves . for an ion of mass @xmath4 , the jump conditions for a strong shock in an ideal gas medium ( @xmath5 ) give a postshock temperature @xmath6 in an unequilibrated shock , the electron and proton temperatures are in the ratio 1/2000:1 , while the temperatures of o ions and protons are in the ratio of 16:1 . in contrast , the temperatures of all three species are equal in an equilibrated shock . collisionless heating can produce equilibrations anywhere between these two extremes . in principle , the amount of collisionless heating from plasma waves , mhd turbulence and other processes is sensitive to such parameters as the magnetosonic mach number and angle between the magnetic field and shock front . understanding this relationship is of critical importance in the interpretation of x - ray , ultraviolet and optical data of high mach number collisionless shocks . a nonradiative shock in partially neutral gas emits a pure balmer line spectrum generated by collisional excitation . each balmer line consists of a narrow component produced by excitation of cold h i and a broad component produced by proton - h i charge exchange . the shock velocity and electron - ion equilibration can be gauged from the broad component line width and ratio of broad component to narrow component flux @xcite@xcite . the ion - ion equilibration can be gauged in turn by measuring the width of the o vi @xmath21032 , 1038 lines and the variation of o vi flux with position behind the shock . the target of our fuse observations was cygnus p7 , a nonradiative shock in the ne corner of the cygnus loop supernova remnant@xcite . we acquired ultraviolet spectra of cygnus p7 in june 2000 for a total of 64 ks ( all during orbital night ) and four slit positions behind the shock ( fig . the spectra presented here were acquired through the 4@xmath720@xmath8 medium resolution ( mdrs ) slit . slit position 1 was centered on the crisp balmer - dominated filament and placed parallel to it ( fig . 1 ) . to observe the intensity variation of o vi , we centered slits 2 , 3 and 4 at 5@xmath8 , 10@xmath8 and 15@xmath8 behind the shock , respectively . the one - dimensional spectra of positions 1 , 2 , 3 and 4 appear in fig . 2 . to minimize the background contribution , these spectra were extracted from the lif 1a channel ( one of four available with fuse ) , the detector yielding the highest effective area at @xmath91020 . the spectral resolution is 0.08 (25 ) , corresponding to filled slit emission . the 1-d spectra of cygnus p7 ( fig . 2 ) reveal three important features : ( 1 ) the o vi lines are considerably broader than the airglow lines , confirming the detection of o vi emission in the cygnus p7 shock . the velocity width of the o vi @xmath31032 line is @xmath0120 . combining this result with the shock velocity of 300@xmath1365 predicted from balmer line spectroscopy of cygnus p7 , we obtain @xmath100.7 . this is roughly consistent with the electron - proton equilibration @[email protected] predicted by the balmer line analysis ; in an earlier analysis@xcite of balmer line emission from cygnus p7 , we measured an h@xmath12 broad component width of 262 . this corresponds to a shock velocity of 265@xmath1365 for cases of no equilibration and full equilibration , respectively . ( 2 ) the o vi emission lines are strongly affected by absorption . the absorption features tend to shift blueward at slit positions farther and farther behind the shock . the variation of o vi flux with position is masked by the o vi absorption features ; ( 3 ) the shape of the @xmath31038 absorption profile differs from that of the @xmath31032 profile . this is mainly due to galactic h@xmath13 absorption at the position of the o vi @xmath31038 line . there are two possible explanations for the oberved o vi absorption : either the bulk of the absorption is produced by interstellar matter ( o vi , h@xmath13 , c ii@xmath14 , etc . ) along the line of sight , or the absorption is produced locally by o vi ions within the shock . there are three lines of evidence in favor of the latter interpretation : \(1 ) the velocity width of the o vi @xmath31032 absorption feature is @xmath090 , comparable to the width of the @xmath31032 emission line . the o vi column density and temperature required to produce the observed absorption are n@xmath152@xmath1610@xmath17 @xmath18 and t@xmath193@xmath1610@xmath20k . these values are @xmath2110 times larger than the o vi column density and temperature expected for the ism along the cygnus loop line of sight@xcite . ( 2 ) the progressively larger blueshift of the o vi absorption lines with distance behind the shock can not be explained by interstellar o vi absorption . ( 3 ) the line center ratio i@xmath22(v=0)/i@xmath23(v=0 ) varies significantly with slit position , from around 0.6 ( position 2 ) to 1.1 ( position 4 ) . these localized variations are consistent with o vi resonant scattering within the shock . the appearance of the o vi spectrum may be due to a combination of internal resonant scattering and a curved shock geometry . on the one hand , the o vi column density and temperature obtained from the fuse spectra are consistent with the range of shock velocities ( 300@xmath1365 from the balmer lines ) and preshock densities ( [email protected]@xmath10.3 @xmath25 from rosat x - ray observations ) estimated for cygnus p7 . on the other hand , a curved shock geometry could explain both the increasing value of i@xmath22(v=0)/i@xmath23(v=0 ) and the increasing absorption blue shift with position behind the shock . in a curved shock , o vi photons produced farther downstream could be absorbed by o vi ions on the near ( blue shifted ) side of the shock . in fuse observations of a nonradiative shock in the ne cygnus loop , we find o vi emission line widths consistent with moderate to high electron - ion equilibration . we also find strong o vi absorption near the centers of the o vi emission lines . a quantitative explanation of the interplay between the o vi emission and resonant scattering requires ( 1 ) a careful modeling of the shock geometry , and ( 2 ) a monte carlo simulation to adequately treat resonant scattering at moderate optical depths ( 0@xmath261 ) . we will address these issues in future work .

we present far ultraviolet spectra of a fast ( @xmath0300 ) nonradiative shock in the cygnus loop supernova remnant . our observations were performed with the far ultraviolet spectroscopic explorer ( fuse ) satellite , covering the wavelength range 905@xmath11187 . the purpose of these observations was to estimate the degree of electron - ion equilibration by ( 1 ) examining the variation of o vi @xmath21032 , 1038 intensity with position behind the shock , and ( 2 ) measuring the widths of the ovi lines . we find significant absorption near the center of the o vi @xmath31032 line , with less absorption in o vi @xmath31038 . the absorption equivalent widths imply an o vi column density greatly exceeding that of interstellar o vi along the cygnus loop line of sight . we suggest that the absorption may be due to resonant scattering by o vi ions within the shock itself . the widths of the o vi emission lines imply efficient ion - ion equilibration , in agreement with predictions from balmer - dominated spectra of this shock .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Medicaid Indian Health Act of 2005''. SEC. 2. APPLICATION OF 100 PERCENT FMAP FOR SERVICES FURNISHED TO AN INDIAN BY AN URBAN INDIAN HEALTH PROGRAM. (a) In General.--The third sentence of section 1905(b) of the Social Security Act (42 U.S.C. 1396d(b)), is amended by inserting before the period at the end the following: ``, or through an urban Indian health program receiving funds under title V of the Indian Health Care Improvement Act''. (b) Conforming Amendment.--Section 1911(c) of such Act (42 U.S.C. 1396j(c)), is amended by inserting ``, or through an urban Indian health program receiving funds under title V of the Indian Health Care Improvement Act'' after ``facilities''. SEC. 3. PROHIBITION ON IMPOSITION OF PREMIUMS, DEDUCTIBLES, COPAYMENTS, AND OTHER COST-SHARING ON INDIANS. Section 1916 of the Social Security Act (42 U.S.C. 1396o) is amended-- (1) in subsection (a)(3), by inserting ``(other than such individuals who are Indians (as defined in section 4 of the Indian Health Care Improvement Act)'' after ``other such individuals''; (2) in subsection (b), in the matter preceding paragraph (1), by inserting ``or who are Indians (as defined in section 4 of the Indian Health Care Improvement Act)'' after ``section 1902(a)(10)''; and (3) in subsection (c)(1), by inserting ``(other than such an individual who is an Indian (as defined in section 4 of the Indian Health Care Improvement Act))'' after ``section 1902(l)(1)''. SEC. 4. PROHIBITION ON RECOVERY AGAINST ESTATES OF INDIANS. Section 1917(b)(1) of the Social Security Act (42 U.S.C. 1396p(b)(1)) is amended, in the matter preceding subparagraph (A), by inserting `` who is not an Indian (as defined in section 4 of the Indian Health Care Improvement Act)'' after ``an individual'' the second place it appears. SEC. 5. REQUIREMENT FOR CONSULTATION WITH INDIAN TRIBES PRIOR TO APPROVAL OF SECTION 1115 WAIVERS. Section 1115 of the Social Security Act (42 U.S.C. 1315) is amended by adding at the end the following: ``(g) In the case of an application for a waiver of compliance with the requirements of section 1902 (or a renewal or extension of such a waiver) that is likely to affect members of an Indian tribe (as defined in section 4 of the Indian Health Care Improvement Act) or a tribal health program (whether operated by an Indian tribe or a tribal organization (as so defined) serving such members, the Secretary shall, prior to granting such a waiver under subsection (a) or renewing or extending such a waiver under subsection (e), consult with each such Indian tribe.''. SEC. 6. REQUIREMENT FOR FAIR PAYMENT BY MEDICAID MANAGED CARE ENTITIES TO INDIAN HEALTH PROGRAM PROVIDERS. Section 1903(m)(2)(A)(ii) of the Social Security Act (42 U.S.C. 1396b(m)(2)(A)(ii)) is amended to read as follows: ``(ii) such contract provides, in the case of entity that has entered into a contract for the provision of services with a facility or program of the Indian Health Service, whether operated by the Service or an Indian tribe or tribal organization (as defined in section 4 of the Indian Health Care Improvement Act) or an urban Indian health program receiving funds under title V of the Indian Health Care Improvement Act , that is not a Federally- qualified health center or a rural health clinic, that the entity shall provide payment that is not less than the highest level and amount of payment that the entity would make for the services if the services were furnished by a provider that is not a facility or program of the Indian Health Service;''. SEC. 7. TREATMENT OF MEDICAL EXPENSES PAID BY OR ON BEHALF OF AN INDIAN BY AN INDIAN HEALTH PROGRAM AS COSTS INCURRED FOR MEDICAL CARE FOR PURPOSES OF DETERMINING MEDICALLY NEEDY ELIGIBILITY. Section 1902(a)(17)(D) of the Social Security Act (42 U.S.C. 1396a(a)(17)(D)) is amended by inserting ``or by the Indian Health Service or an Indian tribe or tribal organization (as defined in section 4 of the Indian Health Care Improvement Act)'' after ``political subdivision thereof''. SEC. 8. STATE OPTION TO EXEMPT INDIANS FROM REDUCTIONS IN ELIGIBILITY OR BENEFITS. Section 1902 of the Social Security Act (42 U.S.C. 1396a)) is amended by inserting after subsection (j) the following: ``(k) The Secretary shall not disapprove a State plan amendment, or deny a State request for a waiver under section 1115 (or a renewal or extension of such a waiver), on the grounds that the amendment or waiver would exempt Indians (as defined in section 4 of the Indian Health Care Improvement Act) eligible for medical assistance from-- ``(1) any restriction on eligibility for medical assistance under this title that would otherwise apply under the amendment or waiver; ``(2) any imposition of premiums, deductibles, copayments, or other cost-sharing that would otherwise apply under the amendment or waiver; or ``(3) any reduction in covered services or supplies that would otherwise apply under the amendment or waiver.''. SEC. 9. EFFECTIVE DATE. (a) In General.--Except as provided in subsection (b), this Act and the amendments made by this Act apply to items or services furnished on or after January 1, 2006. (b) Extension of Effective Date for State Law Amendment.--In the case of a State plan under title XIX of the Social Security Act which the Secretary of Health and Human Services determines requires State legislation in order for the plan to meet the additional requirements imposed by the amendments made by a provision of this Act, the State plan shall not be regarded as failing to comply with the requirements of this Act solely on the basis of its failure to meet these additional requirements before the first day of the first calendar quarter beginning after the close of the first regular session of the State legislature that begins after the date of enactment of this Act. For purposes of the previous sentence, in the case of a State that has a 2- year legislative session, each year of the session shall be considered to be a separate regular session of the State legislature.

Medicaid Indian Health Act of 2005 - Amends title XIX (Medicaid) of the Social Security Act to: (1) apply 100% of the federal medical assistance percentage (FMAP) to services furnished to an Indian by an urban Indian health program; (2) prohibit the imposition of premiums, deductibles, copayments, and other cost-sharing on Indians; (3) prohibit recovery against estates of Indians; (4) require consultation with Indian tribes prior to approval of "Section 115" waivers; (5) provide for the treatment of medical expenses paid by or on behalf of an Indian by an Indian health program as medical care costs for purposes of determining medically needy eligibility; and (6) give states the option to exempt Indians from reductions in eligibility or benefits. Requires a Medicaid managed care organization contracting with an Indian Health Service (IHS) facility or program that is not a federally-qualified health center or a rural health clinic to provide payment at the highest level and amount that it would make for the services if they were furnished by a provider that is not an IHS facility or program.

solitary rectal ulcer syndrome ( srus ) is an uncommon disorder , with a reported prevalence of 1:100,000 adults . srus is characterized by symptoms such as hematochezia , rectal pain , rectal fullness and tenesmus . additionally , srus can be asymptomatic and found secondarily in patients undergoing surgery for defecatory disorders such as rectal intussusception and rectal prolapse . the diagnostic tools used include anorectal manometry , defecography and endoscopy with biopsies of the affected area . unfortunately , however , the diagnosis of srus is often significantly delayed , and in many studies the average time from onset of symptoms to diagnosis was between 4 and 8 years [ 2 , 3 , 4 ] . this delay is likely due to the fact that srus can mimic other gastrointestinal conditions such as neoplasm and inflammatory bowel disease ( ibd ) . we present a 24-year - old female with no prior gastrointestinal complaints who complained of 6 months of bloody diarrhea and weight loss . the patient had been given a diagnosis of ibd prior to presentation and had been receiving prednisone and a 5-asa medication for 2 months with no relief of her symptoms . unfortunately she continued to have difficulties with hematochezia and ultimately required surgical intervention which resolved her symptoms . a 24-year - old previously healthy female was seen in consultation for complaints of 6 months of bloody diarrhea . the stool was mixed with frank blood and clots and on occasions she would pass blood without stool . her family history was notable for lymphoma and the absence of ibd or other gastrointestinal conditions . also noted was a 15-pound weight loss since the onset of her symptoms accompanied by fatigue and malaise . prior to being seen in our clinic , she had undergone colonoscopy elsewhere that noted an ulcerated , apple - core lesion at 10 cm from the rectal verge . biopsies were interpreted as ulceration consistent with an inflammatory polyp ; no dysplasia was seen . she was then prescribed oral mesalamine as well as cortisone enemas as treatment for ibd . these therapies did not improve her symptoms and she was ultimately started on prednisone 20 mg p.o . she had been on steroids for approximately two months with no improvement before presentation to our institution . we repeated a colonoscopy showing her rectum to contain pseudopolyps within a nodular , friable , ulcerated rectal mucosa extending from 5 to 10 cm from the anal verge ( fig . endoscopic ultrasound of the affected area was performed and showed that the area was hypoechoic and diffusely thickened to the muscularis propria . anorectal manometry was performed which showed no evidence for pelvic floor dyssynergia , but evidence of rectal hypersensitivity was present . a defecating proctogram was performed which showed a nodular prominence posteriorly overlying the sling musculature measuring approximately 2 cm in diameter . colonoscopic biopsies showed eroded hyperplastic mucosa with fibromuscularization of the lamina propria and hyperplastic glandular changes ( fig . after 8 months of follow - up she was doing well without recurrence of her symptoms . it is largely a disorder of younger adults , more than 80% of patients in the literature are under the age of 50 . the name of this disorder is in itself misleading , since often the lesions are neither solitary nor ulcerated . most lesions occur on the anterior rectal wall within 10 cm of the anal verge . often a careful history will elicit prior symptoms of constipation and/or description of rectal prolapse . srus is unfortunately a disorder that often goes undiagnosed for prolonged periods of time due to misdiagnosis and lack of awareness of the condition by physicians . examined 98 patients with srus and found that 26% of them had been initially misdiagnosed , with a median duration of incorrect diagnosis of 5 years . nearly one - third of these patients had been on high doses of prednisone for more than 3 months prior to srus diagnosis . the diagnosis of srus is made using a combination of diagnostic tools including a careful history and physical exam in concert with endoscopy and biopsy . anorectal manometry and defecography will often be obtained to support the diagnosis and/or to understand the etiology of the patient 's symptoms . endoscopy can reveal a large variety of findings extending from mild mucosal erythema to multiple , large ulcerations in the rectum . these ulcers can measure up to 4 cm but usually are less than 1.5 cm . characteristic microscopic findings include the presence of mucosal architectural distortion without inflammation ; this lack of inflammation differentiates srus from ibd . anorectal manometry is performed to evaluate for concomitant or other defecatory disorders such as dyssynergic defecation . it is thought that a combination of rectal prolapse and paradoxical puborectalis contraction leads to the generation of high pressures within the rectum , leading to ischemia and , ultimately , ulceration . additionally , paradoxical puborectalis contraction creates shear forces on the rectal mucosa , and this is thought to be another etiologic factor in this disorder . these are simply theories , however , as not all patients with srus have evidence of paradoxical contraction and there have been cases where correction of rectal prolapse does not resolve the symptoms , leading to a supposition that rectal prolapse is not a causative but rather a concomitant process associated with srus . medical therapeutic options include systemic and topical medications such as corticosteroid and sucralfate enemas [ 6 , 7 ] , human fibrin sealant and sulfasalazine , both orally and topically [ 9 , 10 ] . biofeedback improves coordination of the pelvic musculature in combination with anal relaxation techniques to minimize the shear stress and potential for ischemia in the rectum that was due to dyssynergic defecation . rao et al . performed a prospective trial of biofeedback therapy in 11 patients with medically refractory srus . in this population , 82% of patients showed evidence of pelvic dyssynergia as well as higher anal pressures and lesser anal relaxation with straining compared to a population of 15 healthy controls . after a 12-week period of biofeedback therapy , none of these patients re - demonstrated dyssynergic defecation , and anal residual pressures and percentage of anal relaxation both significantly decreased . on repeat endoscopic evaluation , 54% of patients had 50% ulcer healing . biofeedback has also been shown to improve rectal blood flow via doppler mucosal flowmetry , and this improvement was correlated with subjective improvement in symptoms and endoscopic improvement in ulceration . unfortunately not all patients respond to medical or behavioral intervention and some will require surgical intervention . common surgical techniques include transabdominal rectopexy , delorme procedure ( transrectal mucosal stripping with mucosectomy ) , low anterior resection and occasionally colostomy . choi et al . reviewed 49 patients with histopathologically diagnosed srus and found postoperative symptomatic improvement in approximately 70% of patients . transabdominal rectopexy and perineal rectosigmoidectomy comprised the majority of surgical procedures performed in this series . in another series involving 66 patients undergoing surgery for srus , rectopexy was the predominant technique performed with a success rate of approximately 55% . this study also identified fecal incontinence and inability to complete evacuation as preoperative predictors of poor surgical outcome . other retrospective studies have been performed with similar results , and it is usually recommended that patients undergo a trial of medical management before undergoing surgery . srus is an uncommon disorder which is often mistaken for other conditions such as ibd or neoplasm . the diagnosis of srus can be significantly delayed . medical , surgical and behavioral therapies have all been used and it is generally accepted that before proceeding to surgery , patients undergo a trial of medical and , if appropriate , behavioral therapy in the form of biofeedback . physicians should be aware of this diagnosis , especially in patients who are not improving with conventional therapies directed towards ibd .

solitary rectal ulcer syndrome ( srus ) is an uncommon disorder which can present in patients being evaluated for defecatory disorders or which can present as a primary process often involving hematochezia , rectal pain and tenesmus . unfortunately the diagnosis of this disorder is often delayed due to misdiagnosis and/or physician unfamiliarity with the condition . we present a 24-year - old female who presented with 6 months of bloody diarrhea and weight loss . she had been receiving treatment for a presumed diagnosis of inflammatory bowel disease ( ibd ) due to an endoscopic picture of rectal thickening , edema and ulceration and had been on prednisone for 2 months prior to presentation without relief of her symptoms . after further testing including repeat endoscopy with biopsies , defecography and anorectal manometry , the diagnosis of srus was made and treatment was changed . medical management was unsuccessful and she ultimately required surgical intervention . this case highlights the difficulty in diagnosing srus due to its resemblance to other gastrointestinal diseases and should serve as a reminder that if a patient is not responding to ibd therapy , another etiology should be considered .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Rancher Preservation Act''. SEC. 2. SPECIAL REQUIREMENTS REGARDING BLACK-TAILED PRAIRIE DOG. (a) In General.--Section 13 of the Endangered Species Act of 1973 is amended to read as follows: ``special requirements regarding black-tailed prairie dog ``Sec. 13. (a) Use of Best Scientific and Commercial Data Available.--In any case in which the Secretary is required by this Act to use the best scientific and commercial data available with respect to determining whether the black-tailed prairie dog (Cynomys ludovicianus) is an endangered species or a threatened species, the Secretary-- ``(1) in evaluating comparable data, shall give greater weight to scientific or commercial data that are empirical or have been field-tested or peer-reviewed; and ``(2) shall include, in data used with respect to that species, data regarding population numbers of the species. ``(b) Field Data.-- ``(1) Requirement.--The Secretary may not determine under section 4 that the black-tailed prairie dog (Cynomys ludovicianus) is an endangered species or a threatened species unless the determination is supported by data obtained by observation of the species in the field. ``(2) Data from landowners.--The Secretary shall-- ``(A) accept and acknowledge receipt of data regarding the status of that species that is collected by an owner of land through observation of the species on the land; and ``(B) include the data in the rulemaking record compiled for any determination that the species is an endangered species or a threatened species. ``(c) Independent Scientific Review Requirements.-- ``(1) Definitions.--In this subsection: ``(A) Action.--The term `action' means-- ``(i) the determination that the black- tailed prairie dog (Cynomys ludovicianus) is an endangered species or a threatened species under section 4(a); and ``(ii) the determination under section 4(a) that the black-tailed prairie dog should be removed from any list published under section 4(c)(1). ``(B) Qualified individual.--The term `qualified individual' means an individual with expertise in the biological sciences-- ``(i) who through publication of peer- reviewed scientific literature or other means, has demonstrated scientific expertise on the black-tailed prairie dog or a similar species or other scientific expertise relevant to the decision of the Secretary under section 4(a) or (f); ``(ii) who does not have, or represent any person with, a conflict of interest with respect to the determination that is the subject of the review; ``(iii) who is not a participant in any petition or proposed or final determination before the Secretary; and ``(iv) who has no direct financial interest, and is not employed by any person with a direct financial interest, in opposing the action under consideration. ``(2) List of independent scientific reviewers.--The Secretary shall solicit recommendations from the National Academy of Sciences and develop and maintain a list of qualified reviewers to participate in independent scientific review of actions. ``(3) Appointment of independent scientific reviewers.--(A) Before any action shall become final, the Secretary shall appoint randomly, from among the list prepared in accordance with this section, 3 qualified individuals who shall review and report to the Secretary on the scientific information and analyses on which the proposed action is based. ``(B) The selection and activities of the reviewers selected pursuant to this section shall not be subject to the Federal Advisory Committee Act (5 U.S.C. App.). ``(C) Reviewers shall be compensated for conducting the independent review. ``(4) Opinion of peer reviewers.--Independent reviewers shall provide the Secretary, within 3 months, their opinion regarding all relevant scientific information and assumptions relating to the taxonomy, population models, and supportive biological and ecological information for the black-tailed prairie dog. ``(5) Final determination.--If the referees have made a recommendation on a proposed action, the Secretary shall evaluate and consider the information that results from the independent scientific review and include in the final determination-- ``(A) a summary of the results of the independent scientific review; and ``(B) in a case in which the recommendation of a majority of the referees who conducted the independent scientific review is not followed, an explanation as to why the recommendation was not followed. ``(6) Public notice.--The report of the peer reviewers shall be included in the official record of the proposed action and shall be available for public review prior to the close of the comment period on the proposed action.''. (b) Conforming Amendment.--The table of sections in the first section of such Act is amended by striking the item relating to section 13 and inserting the following: ``Sec. 13. Special requirements regarding black-tailed prairie dog.''.

Rancher Preservation Act - Amends the Endangered Species Act of 1973 to provide that, in any case in which the Secretary of the Interior is required to use the best scientific and commercial data available with respect to determining whether the black-tailed prairie dog is an endangered or threatened species, the Secretary: (1) in evaluating comparable data, shall give greater weight to scientific or commercial data that are empirical or have been field-tested or peer-reviewed; and (2) shall include data regarding population numbers of the species.Prohibits the Secretary from determining that the black-tailed prairie dog is an endangered or threatened species unless the determination is supported by data obtained by observation of the species in the field.Directs the Secretary to: (1) accept and acknowledge receipt of data regarding the status of that species that is collected by an owner of land through observation of the species on the land, and include the data in the rule-making record compiled for any determination that the species is an endangered or threatened species; (2) solicit recommendations from the National Academy of Sciences and develop and maintain a list of qualified reviewers to participate in independent scientific review of actions; and (3) appoint randomly from among the list, before any action becomes final, three qualified individuals who shall review and report to the Secretary on the scientific information and analyses on which the proposed action is based.

sonoluminescence ( sl ) is an intriguing phenomenon , which consists of light emission by small collapsing bubbles inside liquids @xcite . such bubbles are created by ultrasonic waves when the pressure of the liquid is reduced relatively to the pressure of the gas present in the medium @xcite . in general , the appearance of a cavity within a liquid implies the existence of a surface ( the wall ) dividing the region into two parts , each one occupied by a fluid : the inner cavity consisting of a gas and/or liquid vapor , and the liquid portion outside . the bubble initially expand to a maximum volume , and then collapse . at the final stages of the collapse , the gas inside the bubble radiate light . it is observed that the light emission is enhanced when atoms of noble gas are present inside the bubble . in the 90s , gaitan et al . @xcite obtained in laboratory the necessary conditions to create and trap a single bubble the size of a few microns , levitating in a bottle of water under the action of a strong , stationary - wave sound field , emitting periodically flashes of light in each acoustic cycle . the trapping of a single sonoluminescent bubble in the liquid , yielding what is called single - bubble sonoluminescence ( sbsl ) , and the production of repeated cycles of expansion and contraction , excited by ultrasonic acoustic waves , allowed a more accurate study of the phenomenon . this stability of the bubble made possible more detailed studies about the duration of the flash of light and the size of the bubble . the conversion of the energy of sound waves into flashes of light occurring in such bubbles with few microns in size is an interesting field of research , if one considers the difficulties inherent to the process , the inadequacy of some theories and models proposed , and experimental limitations . despite the existence of a wide variety of theories and models , the phenomenon is not completely explained , and there are still many open questions . among them , we can cite the heating mechanism of the gas inside the bubble ; the process of light emission ; the role of temperature of the liquid in the intensity of the emitted radiation ; the reason why water is one of the ideal fluids for observing the phenomenon . up to now , the phenomenon has been extensively studied , but its detailed mechanisms remain still unclear . the study of sl involves topics of physics such as hydrodynamics and thermodynamics , besides electromagnetism , statistical mechanics and atomic physics if one wants to go into the emitting mechanism . the dynamics of the bubble can be described by the navier - stokes equation @xcite , provided the initial state of the bubble is defined by a set of physical parameters . the energy of one photon emitted in sbsl , if compared with the energy of one atom vibrating in the sound wave which gave rise to it , typically provides a value of of order @xmath0 , which shows the high focalization of energy in this effect @xcite . the temperature in the interior of the bubble can reache thousands of degrees kelvin during the collapse phase @xcite . in this work we carry out a modeling of sbsl hydrodynamics , using the radius of the bubble as the variable of interest . there are several models that describe the time evolution of the radius of the bubble . the most common are : the rayleigh - plesset model , the herring - trilling model , and the keller - miksis model @xcite . all of these models are derived from the navier - stokes equation , using different simplifying assumptions @xcite . rayleigh - plesset equation describes the behaviour of compressible or incompressible fluids , and can therefore be used to compare the effects of the compressibility of the liquid on the time evolution of the bubble radius . other physical parameters like the liquid viscosity , the properties of the gas inside the bubble , and the superficial tension of the wall can be taken into account in these models . in order to compare the effects of these factors , we define in this work an useful parameter , the _ damping factor _ , which is defined as the ratio between the first and second highest values of the bubble radius . this parameter is relevant , since it compares two values of the radius : one before and the other one after the light emission . a detailed study of the bubble behaviour , including the variation of the wall speed as a function of time , is also carried out . this work is addressed mainly to ( under)graduate students and teachers . the subject requires the domain of calculus and many concepts from various fields of physics at intermediate level . the work can be useful in physics courses at university level , as well as an illustrative example of numerical calculus applied to a highly nonlinear phenomenon . it may also be valuable as an introductory - level text on sbsl addressed to young researchers . the work is the result of a research project in sonoluminescence carried out together with undergraduate students . the behaviour of a nonrelativistic fluid is described by the navier - stokes equation , which is valid at each point of the fluid and can be written as @xmath1 where @xmath2 is the fluid mass density , @xmath3 is the velocity field inside the fluid , @xmath4 is the resultant of body forces ( e.g. , gravity ) per unit volume of the fluid , @xmath5 is the pressure field inside the fluid and @xmath6 is the fluid viscosity . the term @xmath7 on the left - hand side of the above equation is the material derivative of the velocity of the fluid element . the material derivative is given by the operator @xmath8 where the first term on the right - hand side is the time derivative with respect to a fixed reference point of space ( the euler derivative ) , and the second term represents the changes of the field velocity along the movement of the fluid . the quantity @xmath9 on the right - hand side stands for the acceleration originated from the body forces acting on the fluid element , such as gravity or electromagnetic forces , for example . the second and third terms represent respectively the hydrostatic force and the viscous force , both per unit volume . the form navier - stokes equation is written above means that we are considering the fluid as newtonian . now , we remember that the flow inside and around the bubble is restricted to the radial direction , in other words , the problem exhibits spherical symmetry , which in fact is valid even beyond the neighborhood of the bubble , provided the shape of the flask is spherical , a typical experimental situation . thus , we take into account only the expansion and contraction motion of the bubble s radius . besides , we assume as a first approach that the compressibility of the liquid is much smaller than that of the gas inside the bubble . in this case , one derives from eq . ( [ 1 ] ) the rayleigh - plesset equation ( a dot stands for one time derivative , @xmath10 , etc ) : @xmath11 where @xmath12 is the bubble s radius , @xmath13 is the variable gas pressure inside the bubble ( @xmath13 is assumed to be uniform in our model ) , @xmath14 is the pressure of the liquid measured at any remote point from the bubble ( typically , @xmath15 atm ) , @xmath16 is the driven acoustic pressure at the point where the bubble is placed , and @xmath17 is the liquid surface tension at the bubble wall . @xmath16 is assumed to be sinusoidal and starting an expansion cycle in @xmath18 , that is , @xmath19 @xmath20 being the amplitude of the driven pressure and @xmath21 the ultrasound angular frequency in resonance with the natural oscillations of the flask , such that the driven pressure generates a stationary ultrasound wave that traps the bubble at its center , on a pressure antinode . often , the effects of the compressibility of a liquid can be neglected in many problems of hydrodynamics . however , in the case of sbsl this approach is no longer justified , because a large amount of the acoustic energy driven to the bubble is emitted back from it to the liquid , in the form of a spherical shock wave ( only a small amount is in fact converted into light ! ) , which obviously could not exist in an incompressible medium ( the acoustical wave emitted by the bubble is experimentally important , since its detection by a hydrophone signals the presence of the trapped bubble at the center of the spherical flask ) . it follows that when the compressibility of the liquid is considered , a new term is added to the right - hand side of eq . ( [ 3 ] ) , leading to the modified rayleigh - plesset equation @xcite @xmath22 where @xmath23 is the speed of sound in the liquid ( which henceforth we will assume to be water ) . we adopt a van der walls equation of state for describing the gas pressure inside the bubble , which reads @xmath24 where @xmath25 is the static bubble radius , that is , the ambient bubble radius when it is not acoustically forced , @xmath26 is the characteristic van der waals hard - core radius of the gas inside the bubble and @xmath27 is the ratio between the specific heats of the gas at constant pressure and at constant volume ( the adiabatic index ) . so , the gas pressure varies with time only by means of the bubble radius , @xmath12 . it was assumed in eq . ( [ 3.2 ] ) that the gas undergoes a so fast cycle of expansion and collapse that it is adiabatic . however , a more accurate analysis @xcite allows one to conclude that the expansion is approximately isotermic ( @xmath28 ) and only the final part of the collapse is indeed adiabatic . our simplified model here consider the whole cycle as adiabatic . in eq . ( [ 4 ] ) , the time derivative of the gas pressure is explicitly given by @xmath29 equations ( [ 3 ] ) and ( [ 4 ] ) are second - order differential equations for the radius @xmath12 , which have no analytical solution . so , in order to solve numerically these equations for a given set of system parameters , we used the mathematical program matlab ( the corresponding program codes can be requested by email to any of the authors ) . let us first consider the case in which the compressibility of the liquid is neglected . figure [ fig:100 ] shows the solution of eq . ( [ 3 ] ) for a given set of parameters describing some properties of the gas and the liquid , and at forcing pressure @xmath30 atm . the parameters used are shown in table [ table1 ] , where the noble gas argon is considered because it is well - known in sbsl literature @xcite that , after some cycles , it is the only remaining constituent of the initial air bubble , due to chemical reactions that the other components participate , which carry them to the water outside . the solution shown in fig . [ fig:100 ] is qualitatively similar to the experimental results @xcite , but quantitatively very different : the experimental afterbounces are much smaller than those that appear in fig . [ fig:100 ] . this is in agreement with the fact that indeed a considerable amount of energy is lost in the first contraction ( collapse ) , which , as we have already pointed out , is due to sound radiation by the bubble , an effect that is impossible theoretically under the assumptions that led to eq . ( [ 3 ] ) . .[table1 ] parameters used in the numerical simulation . [ cols= " < , < " , ] we can see from table [ table2 ] that the superficial tension strongly affects the dynamics of the bubble , when compared with the other two properties considered here , since it substantially reduces the damping factor . according to the experimental results existing in the literature for sbsl @xcite , the damping factor lies between the two extreme values shown in the table , and closer to the lower values , thus pointing out the importance of including the surface tension in the calculations . in this work we have presented a model describing a single bubble sonoluminescence . we obtained solutions for the equations of the model in the cases of compressible and incompressible liquids . comparing figs . [ fig:100 ] and [ fig:200 ] with the experimental results , we show that the modified rayleigh - plesset equation valid for a compressible liquid , given by eq . ( [ 4 ] ) , describes the bubble dynamics with a better accuracy @xcite , which is due to the experimentally observed acoustic radiation from the bubble , a fact that demands the liquid compressibility to be different from zero . we introduced the damping factor in order to compare the effects of some properties of the system on the dissipation of energy of the bubble after the collapse ( first compression ) . we pointed out that the superficial tension of the liquid can not be neglected in any model describing sbsl dynamics , as we summarized in table [ table2 ] . it is worth to mention that chemical effects was not considered in the present work . the chemical factors clearly affect the thickness of the bubble wall , thereby also contributing to the generation of a shock wave . of course , a more realistic treatment must include such kind of ingredient . also , as mentioned above , the process that the bubble gas undergoes is not adiabatic during the whole cycle , as we considered here , but instead isotermic during the expansion , which affects the value of the exponent @xmath27 . however , as pointed out in ref . @xcite , just modifying the numerical calculation in order to interpolate between @xmath31 and @xmath32 is not sufficient to completely describe the behaviour of @xmath12 in all of its details . matlab routines that generates our results can be requested by email to any of the authors and we hope that the simulations presented here will be valuable for teachers , ( under)graduate students and young researchers in order to have a first contact with single - bubble sonoluminescence and some of its remarkable features . the authors thank the brazilian foundations cnpq , faperj and capes for the financial support .

sonoluminescence ( sl ) is the phenomenon in which acoustic energy is ( partially ) transformed into light . it may occur by means of many or just one bubble of gas inside a liquid medium , giving rise to the terms multi - bubble- and single - bubble sonoluminescence ( mbsl and sbsl ) . in the last years some models have been proposed to explain this phenomenon , but there is still no complete theory for the light emission mechanism ( especially in the case of sbsl ) . in this work , we will not address this more complicated particular issue , but only present a simple model describing the dynamical behaviour of the sonoluminescent bubble , in the sbsl case . using simple numerical techniques within the software matlab , we discuss solutions considering various possibilities for some of the parameters involved : liquid compressibility , superficial tension , viscosity , and type of gas . the model may be used as an introductory study of sonoluminescence in physics courses at undergraduate or graduate levels , as well as a quite clarifying example of a physical system exhibiting large nonlinearity .

gravitational potential wells that are deep enough to trap gas hotter than @xmath0 can generally be detected in the thermal x - ray emission of the trapped gas . these potential wells range in size from those of massive elliptical galaxies through groups of galaxies to clusters of galaxies . as one proceeds down this sequence , the fraction of the system s baryons that are contained in the virial - temperature gas rises from @xmath1 to @xmath2 . the central cooling time @xmath3 is defined to be the ratio of the central energy density to the central luminosity density due to radiative cooling . in many , perhaps most , systems , @xmath3 is shorter than the hubble time . in the case of an elliptical galaxy such as ngc 4472 , @xmath4 , while in a cluster of galaxies such as hydra @xmath5 . hence , we must ask how these systems endure for times that greatly exceed @xmath3 . in the absence of heating , radiative losses cause the central density to rise inexorably as the central temperature falls . the density reaches arbitrarily large values in a time @xmath6 that is slightly shorter than @xmath7 ( murray & balbus , 1992 ) . kaiser & binney ( 2003 ) present a semi - analytic model of this process , which ends in a ` cooling catastrophe ' . the xmm - newton and chandra satellites have established two facts for which there was sketchy evidence in earlier data . first , although the temperature drops as one approaches the centre of one of these systems , it is bounded below by a ` floor ' temperature @xmath8 , where @xmath9 is the ` virial temperature ' characteristic of the bulk of the x - ray emitting gas . second , the x - ray emitting plasma is clearly being heated by outflows from a centrally located active galactic nucleus that is surely an accreting black hole ( bh ) . these facts have greatly strengthened the case that in the long run the energy radiated by the hot gas is replaced by energy released by accretion of gas onto the bh . consequently , in these systems gas is neither cooling nor flowing inwards as has traditionally been supposed , and their established designation as ` cooling flows ' is unfortunate . a more appropriate name is ` cuspy atmosphere ' since the defining characteristic of these systems is a sharply peaked x - ray surface - brightness profile , which proves to be associated with a central depression in the temperature of the gas . many questions about cuspy atmospheres remain open . these include ( 1 ) the mechanism by which energy is transported from the solar - system scale of the bh to the @xmath10 to @xmath11 scale of the thermal plasma , and ( 2 ) the timescale between eruptions of the bh and the corresponding depth of the excursions in the central density of the cuspy atmosphere . two extreme views are possible on this second point . a violent outburst of the bh might stir the trapped gas into something approaching an adiabatic atmosphere one in which the specific entropy @xmath12 is everywhere the same . if heating then stops completely , the specific entropy profile @xmath13 steepens as the system drifts towards a cooling catastrophe , at which another violent outburst of the bh reheats to a state of near - uniform @xmath12 ( kaiser & binney 2003 ) . in this picture , systems such as hydra and virgo are observed @xmath14 before their next cooling catastrophe . the opposite extreme was explored by tabor & binney ( 1993 ) , who conjectured that steady central heating generates a uniform - entropy core , which gradually expands as material falls into it at the base of an enveloping cuspy atmosphere . observations cast doubt on this last picture in two ways . first , cuspy atmospheres appear not to have adiabatic cores ( kaiser & binney 2003 ) . second , there is much evidence that bhs eject energy in discrete bursts rather than continuously . the absence of adiabatic cores is a clue to the way in which bhs heat the system . if photons carried the energy from the relativistic region , the energy would be thermalized deep down and then convected outwards , as it is in a late - type star with a convective core . if jets carry the energy away from the bh , it will thermalize over a wide range of radii , including radii in excess of the @xmath15 scale of the cuspy atmosphere . so with jet heating an adiabatic core need not arise ( binney & tabor 1995 ) . the most relevant evidence for discrete bursts of heating also confirms that jets are the intermediaries : we see ` cavities ' or ` bubbles ' in the x - ray emitting plasma that are surely inflated where a jet is disrupted as it impacts the denser thermal plasma . several systems show more than one generation of cavity , and the cavities nearer the bh are younger and thus more luminous in synchrotron radiation from extremely energetic electrons ( lorentz factors @xmath16 ) . it is generally agreed that these cavities move outwards at approximately the speed of sound ( @xmath17 ) in the ambient plasma ( gull & northover 1973 ; churazov _ et al . _ 2001 ; quilis _ et al . _ 2001 ; brggen & kaiser 2001 , 2002 ; brggen _ et al . _ 2002 ) . .parameters for five clusters with cavities . [ cols="<,^,^,^ , < " , ] does trapped virial - temperature gas drift far towards a cooling catastrophe during inter - outburst intervals , so that it must be radically restructured during an outburst ? the rate of evolution of the density profile of x - ray emitting gas accelerates slowly at first , and very rapidly towards the end of a drift to a cooling catastrophe . hence , if most sources are drifting towards the next cooling catastrophe , many sources will be seen in configurations near those produced by an outburst , and only a few sources will be found close to a cooling catastrophe . from the fact that @xmath18 of x - ray clusters have cusped cooling cores in which cooling times @xmath19 occur ( peres _ et al . _ 1998 ) , it follows that near - adiabatic states are not produced by outbursts , and the time between outbursts is @xmath19 . kaiser & binney ( 2003 ) concluded that the scarcity of gas at @xmath20 is compatible with the sources cycling between the least centrally concentrated configurations observed and cooling catastrophes . however , the data do not require such deep cycles . the sizes and locations of cavities in clusters such as perseus ( fabian _ et al . _ 2000 ) , mkw3s ( mazzotta _ et al . _ 2002 ) and abell 2597 ( mcnamara _ et al . _ 2001 ) suggest that a new pair of cavities is produced every @xmath21 , and simple estimates of the energy injected into the thermal plasma over the lifetime of a cavity ( churazov et al . 2002 ) suggest that in this case heating by the bh can balance radiative cooling . table 1 illustrates this point by giving for five clusters an estimate of pressure times volume for a pair of cavities , the x - ray luminosity of the cuspy atmosphere @xmath22 ( mostly from the classic @xmath23 value ) and the characteristic time @xmath24 . the _ minimum _ work done by an agn in blowing a cavity is @xmath25 , rising to @xmath26 if the fluid within the cavity is relativistic . since the inflation of cavities is likely to be highly irreversible , especially in its early stages and from the perspective of the ambient medium , the actual work done will be larger . if we conservatively assume that the work done is @xmath27 , then heating will balance cooling if the intervals between the creation of cavities equals the quantity @xmath28 listed in table 1 . these intervals agree to within the errors with the values estimated from hydrodynamic models . the suggestion that heating balances cooling is puzzling for two reasons . first , there is much evidence bhs release energy very unsteadily , and second because there is a gross mismatch between the @xmath29 to @xmath30 timescale on which the thermal plasma adjusts its configuration and the @xmath31 timescale on which the energy output of massive bhs is known to change by factors of 2 . so what mechanisms could enable a bh to hold fairly constant the density profile in the vastly bigger atmosphere of x - ray emitting gas ? one condition for establishing a steady state is that the energy output of the bh should increase when the cuspy atmosphere s central density increases , and do so with a delay that is small compared to the central cooling time @xmath32 . the bondi radius @xmath33 is the distance from the bh at which the bh s kepler speed equals the sound speed . in the cases of sgr a@xmath34 at the centre of the galaxy and of m87 , @xmath33 , which bounds the bh s sphere of influence , is resolved by _ chandra_. hence we can be pretty certain of the rate at which gas flows into the sphere of influence . gas with temperature @xmath35 flows at the sound speed @xmath36 through the spherical surface of area @xmath37 where @xmath38 , with @xmath39 the molecular weight . the particle density is @xmath40 , where @xmath41 is the pressure just above the surface . hence , the accretion rate @xmath42 rises at least as fast as @xmath43 , and any drop in @xmath35 will quickly lead to an increase in the bh s power output . the luminosity of the cooling core is @xmath44 which has a very similar dependence on @xmath35 when one takes into account the tendency of @xmath41 to rise slightly as @xmath35 declines . hence the mass falling into the sphere of influence during an outburst is expected to be roughly proportional to the energy radiated by the thermal plasma in the cooling core . we are unsure what fraction of the material that enters the sphere of influence is accreted by the bh rather than being blown out in a wind or jet . how much energy is released when a given mass of gas is swallowed by the bh is also controversial . fortunately observations of the best observed system suggest resolutions of these questions . in m87 the bondi accretion rate ( [ mdoteq ] ) is @xmath45 , which yields a luminosity @xmath46 if @xmath47 of energy is released for accretion of mass @xmath48 onto the bh ( di matteo _ et al . the x - ray luminosity from the central @xmath49 of the cuspy atmosphere is @xmath50 ( nulsen & bhringer 1995 ) , while that of the agn is @xmath51 . estimates of the mechanical luminosity of the jet that emerges from the agn range from @xmath50 ( reynolds et al 1996 ) to @xmath52 ( bicknell & begelman 1999 ; owen et al 2000 ) . thus the data for m87 suggest that the bh is accreting at a substantial fraction of the bondi rate , and that the energy released is passing along the jets to reheat the cuspy atmosphere on @xmath53-scales . radiative losses near the bh are negligible . this is precisely the situation envisaged by binney & tabor ( 1995 ) . material that falls into the sphere of influence is likely to form an accretion disk or torus . in the case of m87 , a disk of ionized gas has actually been seen with hst ( harms _ et al . _ 1994 ) . the accretion disk will introduce a lag between a drop in the central temperature of the cuspy atmosphere and an increase in the power of the bh equal to the time it takes material to spiral through the disk . if this delay exceeded @xmath54 , large - amplitude feedback oscillations would probably occur . evidence that cuspy atmospheres are in near steady - states therefore suggests that material either accretes directly from the bondi flow , or spirals through the accretion disk in @xmath21 . for a steady state to be reached , the radial profile of energy deposition by the jets at outburst must coincide with the radial profile of radiative losses between outbursts . energy is transferred from a jet to the ambient plasma when the latter disrupts the jet , either in part or totally , as at the hot spot of a fanaroff riley ( fr ) ii radio source . the more powerful a jet is , the further out it will go before it is strongly disrupted . so the fraction of a jet s energy that is deposited at large radii should increase with jet power . conversely , the higher the ambient density is near the bh , the smaller will be the radii at which a given jet is disrupted and its energy thermalized . motivated by these considerations , omma & binney ( 2004 ) repeatedly simulated the dynamical evolution of cluster gas from an initial state that resembles the current state of the hydra cluster . each simulation was fully three - dimensional and used the adaptive - mesh code enzo ( bryan 1999 ) . the rate of radiative cooling was calculated for an optically thin plasma in thermal equilibrium . hence a cooling catastrophe arose in the absence of jet heating . in simulation 1 the jets fire after @xmath55 of cooling . they have a total power of @xmath46 and run for @xmath56 , during which time they inject @xmath57 . the jets in simulation 2 fire after @xmath58 of cooling , by which time an extra @xmath57 has been lost to radiation , and they inject @xmath59 at @xmath60 . thus the later ignition of the jets in simulation 2 is compensated for by enhanced energy injection along the lines suggested by the model of bondi accretion . it is instructive to compare these energies with what would be available through bondi accretion onto a bh of mass @xmath61 under the assumption that accretion of mass @xmath48 by the bh releases @xmath47 of energy . if the atmosphere were isothermal in the numerically unresolved region from a radius @xmath62 to the bh s radius of influence , the energy available from bondi accretion would be @xmath63 over @xmath55 , and @xmath64 over @xmath58 . thus for black hole masses @xmath65 of the expected order , @xmath66 of what flows into the bh s sphere of influence needs ultimately to be accreted by the bh . for a bh of this mass the bh s mechanical luminosity in simulation 1 is @xmath67 , where @xmath68 is the eddington luminosity at which free - electron scattering causes radiation pressure to balance gravity . in figure [ densfig ] the dotted curve shows the density profile of the cluster gas at the start of both simulations . the data points show the density in the hydra cluster as deduced by david _ et al . _ ( 2000 ) . the upper full curve shows the density profile at the ignition of the jets in simulation 1 , while the dashed curve labelled @xmath69 shows the density profile at the ignition of the jets in simulation 2 . the effect on the density profile of @xmath14 of passive cooling is evident . the bottom full curve shows the spherically averaged density profile @xmath70 after the firing of the jet in simulation 1 , while the bottom dashed curve shows the same data for simulation 2 . at that time , @xmath71 after the jets extinguished , the curves are quite similar to the initial profile and the data . thus in both simulations the injected energy has effectively reversed the effect of @xmath58 of cooling . most crucially , the dashed curve of simulation 2 now lies _ below _ the full curve , implying that the system that cools for longer and has the most centrally concentrated density profile when its jets ignite , ends up with the _ less _ centrally concentrated profile . the density profiles at times later than those shown in figure [ densfig ] confirm that the greater central concentration of simulation 1 at @xmath72 is not an aberration : the profile for simulation 1 remains on top of that of simulation 2 , and moves upwards faster . consequently , when the profiles are next similar to those labelled @xmath69 in figure [ densfig ] , we can expect simulation 1 to be the scene of the more energetic outburst slamming into the more centrally concentrated icm . when the dust settles after this second outburst , the profile of simulation 2 will be the more centrally concentrated and the pair of simulations will have come full cycle . hence these simulations suggest that the density profiles of cuspy - atmosphere clusters are oscillating around an attracting profile . it has long been suggested that the cuspy - atmosphere phenomenon is fundamental for the galaxy - formation process ( e.g. , fabian 1994 ) . i agree , but i want to persuade you that cuspy atmospheres do not tell us how galaxies formed , but why they ceased forming ( binney 2004 ) . the standard picture of galaxy formation starts from the assumption that when gas falls into a potential well , it shock heats to the virial temperature ( rees & ostriker 1977 ; white & rees 1978 ) . there is increasing evidence that this assumption is significantly misleading : only a fraction of infalling gas is heated to the virial temperature , and this fraction is large only for potential wells that are deeper than those associated with galaxies ( binney 1977 ; katz _ et al . _ 2003 ; birnboim & dekel , 2003 ) . on account of the shape of the cooling curve of optically thin plasma , the temperature of infallen gas is bimodal . it seems likely that stars form from a fraction of the cold gas , and energy released by these stars strongly heats the remaining gas . if the potential well has a virial velocity below @xmath73 ( roughly that of an @xmath74 galaxy ) , the heated gas flows out of the potential well and star formation ceases until more cold gas can fall in . through repeated accretion of cold gas , a disk galaxy slowly builds up . a merger may convert this to an early - type galaxy , but subsequent infall of cold gas and star formation can restore its status as a disk galaxy . through mergers and gas accretion , the depth of the potential well increases . when its virial velocity reaches @xmath73 , gas heated by star formation can no longer be driven out ( dekel & silk , 1986 ) . consequently , an atmosphere of virial - temperature gas builds up . such atmospheres have been called a cooling flows because their central cooling times are short . actually the temperature of such a system is thermostatically controlled by the nuclear bh , which grew to its current size during merging episodes as large quantities of cold gas were driven to the centre , stimulating bursts of star formation , and permitting the bh to gorge itself at @xmath68 . as the density and temperature of the virial - temperature atmosphere increases , the environment becomes hostile to cold gas : filaments of infalling cold gas are shredded by kelvin - helmholtz instability and evaporated by electron conduction ( nipoti & binney , 2004 ) . this evaporation of cold gas can happen far from the bh , although the energy required to heat the cold gas ultimately comes from the bh , which underwrites the atmosphere s temperature . the elimination of filaments of infalling cold gas gradually throttles star formation , because the hot atmosphere never produces cold gas : the coldest part of the atmosphere surrounds the bh , and energy released by the bh reheats it long before it can reach the kinds of temperatures ( @xmath75 ) at which stars can form . the effect of the hot atmosphere on the star - formation rate is not sudden , however , because a sufficiently massive filament on a sufficiently low - angular - momentum orbit can always get through to the atmosphere s cooling core , where it can survive thermal evaporation for a significant time and lead to the formation of some stars . in the centres of clusters such as perseus we see such filaments and infer that they have embedded star formation ( mcnamara _ et al . _ 1996 ; conselice _ et al . _ 2001 ; fabian _ et al . _ these filaments have often been supposed to have formed through catastrophic cooling of the hot atmosphere , but their dust content and morphology are more consistent with the infall hypothesis ( soker _ et al . _ 1991 ; sparks _ et al . _ 1989 ; sparks 1992 ) . the galaxy luminosity function differs profoundly from the mass function of dark - matter halos in all cold - dark matter ( cdm ) cosmogonies . specifically , there are both fewer faint galaxies than low - mass halos , and fewer luminous galaxies than high - mass halos . the dearth of low - luminosity galaxies can be plausibly ascribed to the effects of photoionization at redshifts @xmath76 ( efstathiou 1992 , dekel 2004 ) and to the ability mentioned above , of star formation to heat residual gas and drive it out of shallow potential wells . in a recent examination of this problem in the context of semi - analytic galaxy formation models , benson _ et al . _ ( 2003 ) found that when feedback was strong enough to make the number of low - luminosity galaxies agree with observation , too many high - luminosity objects formed because gas ejected from shallow potential wells later fell into deep potential wells . the crucial ingredients missing from the benson _ et al . _ models are ( a ) the ability of the central black hole to prevent cooling of virial - temperature gas , and ( b ) the infall of cold gas , together with the tendency of a hot atmosphere to destroy filaments of cold infalling gas . the demography of quasars and radio galaxies indicates that most of the energy released in the formation of a massive bh has emerged in bursts of accretion that have driven the luminosity to near @xmath68 . thus yu & tremaine ( 2002 ) found that the total energy emitted in the optical and uv bands by agn lies remarkably close to the energy released in the growth of massive bhs . they also showed that a high efficiency @xmath77 for the conversion of accretion energy to optical / uv photons and radiation at @xmath78 must be assumed if the formation of the known population of bhs is to generate as many luminous quasars as are observed . the mass of a bh that radiates at @xmath68 exponentiates on the salpeter time @xmath79 . if bhs form with masses @xmath80 , then they require @xmath81 to grow to their current @xmath82 . thus yu & tremaine require them to have radiated at @xmath83 for @xmath84 and accreted at @xmath85 for the remaining @xmath86 . the tight correlation between bh mass and the velocity dispersion of the host spheroid tells us that bh growth is dominated by periods of rapid formation of spheroid stars . this conclusion is reinforced by the similarity in time and space of the densities of luminous quasars and luminous star - forming galaxies . it seems clear that these episodes of rapid bh and spheroid growth occur when there is plenty of cool gas at the galaxy centre . these episodes are short because a combination of star formation , aided by radiation from the bh ( ostriker ) , and mass loss in a galactic wind , quickly lowers the gas density to the point at which it can be heated to @xmath0 . star formation and bh growth then all but cease . the hot gas flows out of shallower potential wells , but is confined by wells with virial velocities @xmath87 . once the host potential is deep enough to trap supernova - heated gas , and a hot atmosphere builds up , the bh becomes more regularly active . its mode of operation changes significantly , in the sense that its energy output becomes predominantly mechanical . in general terms it is natural that photons should diminish in prominence as distributors of the bh s energy production once the bh starts accreting optically thin , virial - temperature gas . but this mode switch has yet to be properly understood . observations of m87 leave no doubt that the switch occurs , however . the rate at which the bh s mass grows in the new regime is determined by the rate at which the cuspy atmosphere radiates , which for a typical cluster lies in the range @xmath88 to @xmath52 . at the canonical @xmath89 accretion efficiency , these luminosities imply mass accretion rates @xmath90 to @xmath91 . growth at rates of this order for @xmath92 does not have a significant impact on the mass of a bh that already contains @xmath93 . this is why the combined radiative output of quasars already accounts for the observed bh mass density . fresh supplies of cold gas can revive star formation . if the gas has high angular momentum and accumulates in a disk , there can be significant star formation without enhanced bh growth . gas infall enhances bh growth only if the gas tumbles to the galactic centre to form spheroid stars . hence the bh s mass is correlated with the properties of the spheroid rather than with those of the whole galaxy . although some loose ends remain , i am impressed by the way in which disparate strands of theory and observation are coming together to form a coherent picture of galaxy formation , and the symbiosis of bhs with spheroids and cuspy atmospheres . in this picture bhs play a major role in preventing gas that is heated to the virial temperature from cooling . galaxies that are in potential wells deep enough to trap supernova - heated gas soon cease to form stars , even from cold infalling gas of high angular momentum , because trapped gas at the virial temperature evaporates infalling gas before stars can form from it . hence bhs cause the cutoff above @xmath74 in the galaxy luminosity function . bhs are effective thermostatic heaters for two reasons . first , they sample the coldest gas , and the rate at which they are fed increases rapidly as the temperature of this gas falls . moreover , the mass accreted in any time interval is roughly proportional to the energy radiated by the central part of the atmosphere in that interval . second , they inject energy through jets , and the radial range over which a jet s energy is thermalized is smaller when the pre - outburst atmosphere is more centrally concentrated . this phenomenon causes the density profile of an atmosphere to fluctuate around an attracting profile that appears to be similar to those observed . for more than two decades the theory of steady - state cooling flows with mass dropout held up progress in appreciating the role that agn play in structuring galaxies . this theory was finally swept away by damning evidence from the _ chandra _ and _ xmm - newton _ missions , but its internal contradictions should have left it without proponents a decade ago . meanwhile , evidence has emerged for the intimate connection between bhs and both quasars and spheroids , and for the strength of mass outflows from star - forming galaxies . the last piece of the jigsaw that gives a coherent picture of galaxy formation is the still tentative evidence for the importance of cold infall . over the next decade i hope that this picture will be consolidated by understanding ( a ) the relation between extra - planar gas around spiral galaxies and the infall and outflow phenomena , and ( b ) why bh accretion sometimes produces the eddington luminosity and rapid bh growth , and in other circumstances yields jets with high efficiency . finally , we must come to an understanding of how it is that infalling cold gas frequently has enough angular momentum to form a galactic disk . katz , n. , keres , d. , dav , r. & weinberg , d. h. 2003 in _ the igm / galaxy connection : the distribution of baryons at @xmath94 _ , assl conference proceedings vol . 281 , ( eds j. l. rosenberg & m. e. putman ) , kluwer , dordrecht , p. 185

cooling flows galaxies : nuclei galaxies : formation galaxies : jets galaxies : luminosity function in cuspy atmospheres , jets driven by supermassive black holes ( bhs ) offset radiative cooling . the jets fire episodically , but often enough that the cuspy atmosphere does not move very far towards a cooling catastrophe in the intervals of jet inactivity . the ability of energy released on the sub - parsec scale of the bh to balance cooling on scales of several tens of kiloparsecs arises through a combination of the temperature sensitivity of the accretion rate and the way in which the radius of jet disruption varies with ambient density . accretion of hot gas does not significantly increase bh masses , which are determined by periods of rapid bh growth and star formation when cold gas is briefly abundant at the galactic centre . hot gas does not accumulate in shallow potential wells . as the universe ages , deeper wells form , and eventually hot gas accumulates . this gas soon prevents the formation of further stars , since jets powered by the bh prevent it from cooling , and it mops up most cold infalling gas before many stars can form . thus bhs set the upper limit to the masses of galaxies . the formation of low - mass galaxies is inhibited by a combination of photo - heating and supernova - driven galactic winds . working in tandem these mechanisms can probably explain the profound difference between the galaxy luminosity function and the mass function of dark halos expected in the cold dark matter cosmology . [ firstpage ]

rosai dorfman disease ( rdd ) was originally called sinus histiocytosis with massive lymphadenopathy when described by rosai and dorfman over 30 years ago . this disease typically presents as massive but painless bilateral cervical lymph node enlargement accompanied sometimes by fever , in the first two decades of life . microscopic examination of an affected lymph node shows dilated sinusoids packed with foamy histiocytes , which contain intact lymphocytes and/or plasma cells within their cytoplasm , termed emperipolesis . however , numerous reports of rdd affecting a variety of sites in the head and neck , intracranial , breast , gastrointestinal tract and other abdominal sites are available . fine needle aspiration findings of rdd are well described with the largest experience being from our institute . emperipolesis has always been described as the critical diagnostic feature of rdd in these cytology reports . we report here an unusual case of rdd where a number of samples , both biopsy and fine needle aspirates , were obtained from the same patient at various intervals in the course of the disease . microscopic findings varied at different periods of disease progression , serving as evidence for the morphological evolution process in rdd . the differential diagnostic implications of this variation are discussed . a 44-year - old male patient , a general medical practitioner by profession , presented with slowly progressive swelling of left submandibular gland for 10 years and cervical lymph nodes . the patient was a non - insulin - dependent diabetic , on treatment with oral hypoglycemics and insulin at different periods . patient continued to have enlarging cervical lymphadenopathy which would swell to three or four times the usual size over three to four days , accompanied by fever of around 38c and rising blood sugar levels . subsequently the nodes would regress to stable size over the next 10 - 15 days , with gradual subsidence of fever . a magnetic resonance imaging ( mri ) scan of the head showed a left nasal mass and multiple cervical lymph nodes . routine hemogram and serum biochemistry were normal except for the erythrocyte sedimentation rate , which was raised at 62 mm in the first hour . details of biopsies and aspirations performed in sequential order , with clinical state at the time of biopsy , diagnosis rendered and the extent of emperipolesis seen within foamy histiocytes the patient stabilized over the next three months with regression of nodes followed by a stable cervical lymphadenopathy . fine needle aspiration cytology ( fnac ) of both left and right cervical stable nodes was performed , and reported as rdd [ table 1 , specimen 3 ] . patient continued to have flare - ups with nasal mass causing obstruction , for which repeated excisions were performed . as detailed in table 1 , repeated biopsies were not diagnosed as rdd in view of absent emperipolesis and the possibility of rhinoscleroma was considered . antinuclear antibodies , rheumatoid factor and antineutrophil cytoplasmic antibodies were negative . since histopathology had always been performed during exacerbations and in one instance during involution , patient was kept on follow - up until he stabilized . biopsy of a stable left cervical lymph node was performed , which yielded a diagnosis of rdd [ table 1 , specimen 8 ] . tissue for histopathology was fixed in 10% neutral buffered formalin and subjected to routine paraffin - embedded sections with hematoxylin and eosin staining . special stains for acid - fast bacilli ( afb ) , periodic acid schiff ( pas ) , grocott 's silver methanamine for fungus ( grocott ) , perl 's stain for iron , van kossa stain for calcium , giemsa and modified gram 's stain for tissue sections were performed following standard protocols . aspirations were performed using 10 ml syringe fitted on a syringe holder , using a 23-gauge needle , in an outpatient setting without anesthesia . aspirates were smeared on glass slides and wet - fixed in 95% alcohol for papanicolaou stain and air - dried for may - grnwald - giemsa stain , both stains being done in all aspirates . extra smears for immunocytochemistry were similarly prepared and wet - fixed in 95% alcohol . as a control group , four aspirates from cervical lymph nodes diagnosed as rdd were selected from the records of the cytopathology laboratory . four biopsies , also diagnosed as rdd , including two from nasal mucosa and two from cervical lymph node were also included from the records of the pathology department as control cases . the clinical details and timing of biopsy / has not been reported previously in the literature , this information was obtained as detailed below . emperipolesis in these cells was quantified by counting the first 100 histiocytic cells fitting the above description in randomly selected fields . fields were selected from the centre and tails of smears since larger cells aggregate near the tail . cells were categorized into four groups based on extent of emperipolesis , yielding four groups : nil , 1 - 3 lymphocytes/ plasma cells , 3 - 10 lymphocytes/ plasma cells and > 10 lymphocytes/ plasma cells in a histiocyte . emperipolesis in biopsies was quantified in s100-positive histiocytes , using the same four categories as for cytology . immunocytochemistry for s100 was done using 1:100 dilution with overnight incubation . for cd 68 and alpha-1-antichymotrypsin ( act ) prediluted primary antibodies with one - hour incubation the specimens available from the patient in chronological order with date of sampling , phase of disease and quantification of the extent of emperipolesis in percentage are given in table 1 . the first specimen was left submandibular gland excision which was enlarged to four cm size . microscopic examination showed foci of normal salivary gland and large areas of marked chronic sialadenitis with atrophy of salivary acini . the inflammatory infiltrate consisted of lymphocytes and plasma cells along with a few lymphoid follicles , fibrosis and focal necrosis . one of the pieces showed small collections of foamy histiocytes , negative with afb , pas , giemsa , perl 's and gram 's stains . both aspirates showed numerous large histiocytes with emperipolesis in a background of lymphocytes and plasma cells [ figure 1 ] . the histiocytes had abundant foamy cytoplasm and round nuclei with considerable variation in nuclear size and shape , some with prominent nucleoli . aspirate from left cervical lymph node in stable phase showing many large histiocytes with numerous lymphocytes and plasma cells packed within the cytoplasm ( emperipolesis ) , obscuring the histiocyte nucleus . occasional histiocytes in the background with less degree of emperipolesis are also seen ( papanicolaou , 100 ) fourth and fifth specimens were nasal mucosal excisions , received in multiple fragments showing chronic inflammation with extensive fibrosis and numerous foamy histiocytes [ figure 2 ] . immunocytochemistry for s100 was strongly positive in the cytoplasm and nuclei of the foamy histiocytes while cd 68 and act were negative [ figure 3 ] . additional small histiocytic and mononuclear cells positive for cd68 and act were identified amongst the surrounding inflammatory cells . definite emperipolesis is not evident ( h and e , 200 ) biopsy from nasal mass in exacerbation showing s100 to be positive in foamy cells ( a ) , while cd68 is negative ( b ) . ( immunocytochemistry for s100 ( a ) and cd68 ( b ) , 200 ) in view of discrepancy between cytology and histology , a repeat aspiration of left cervical lymph node was done when patient had exacerbation of symptoms . aspirate showed numerous histiocytes with emperipolesis , although to a lesser extent than in previous aspirates [ figure 4 ; sixth specimen , table 1 ] . cd68 and act were negative in the large histiocytes but numerous small mononuclear histiocytic cells in the background were positive for both these markers [ figure 3 inset ] . aspirate from left cervical lymph node in mild exacerbation , showing numerous histiocytes with large nuclei . inset : immunocytochemistry for cd68 is negative in the large rdd histiocytes with emperipolesis ( arrow ) but positive in scattered mononuclear cells in the background ( papanicolaou , 400 , inset : cd68 immunocytochemistry , 100 ) a left cervical lymph node biopsy was obtained during involution phase [ seventh specimen , table 1 ] . the lymph node measured one cm in size . slides showed extensive lymph nodal necrosis and apoptosis with perinodal fibrosis . in a few foci occasional foamy histiocytes a right cervical lymph node was biopsied in stable phase [ eighth specimen , table 1 ] . the lymph node measured 2.5 cm in size and showed maintained architecture with perinodal fibrosis . most of the lymph node substance was occupied by dilated sinuses filled with foamy histiocytes which showed emperipolesis of lymphocytes and plasma cells [ figure 5 ] . biopsy from left cervical lymph node in stable phase showing dilated sinuses containing foamy histiocytes with emperipolesis . numerous plasma cells are seen in the perisinusoidal lymphoid tissue ( h and e , 200 ) control cases showed variable extent of emperipolesis which has been quantified as detailed in table 2 . it was more in cytology specimens as compared to histopathology specimens and varied from case to case and sample to sample . rdd to this date remains an idiopathic entity , the etiology of which remains unknown despite intense investigations over the last 20 years.[714 ] in the absence of understanding regarding pathogenesis , numerous reports in the literature have concentrated on unusual sites of involvement by rdd . this feature is always identified and is requisite for making a histopathological diagnosis of rdd . immunohistochemical investigations into the nature of histiocytes in rdd have , however , thrown up many markers which have diagnostic utility . histiocytes of rdd are s100-positive , setting them apart from the more usual sinus histiocytes and phagocytic cells in general . unlike langerhans cells which are also s100-positive , histiocytes of rdd are cd1a - negative . cd68 , a marker for phagocytic histiocytes is also positive in histiocytes of rdd as is act . thus the histiocytes of rdd have some features of antigen - presenting cells or langerhans cells ( s100-positive ) and some features of phagocytic histiocytes ( positivity for cd68 , act , pan - macrophage markers like ebm11 , ham 56 , and leu - m3 ; antigens functionally associated with phagocytosis like fc receptor for igg and complement receptor 3 ; lysosomal enzymes like lysozyme , act and alpha 1-antitrypsin ) . morphologically and electron microscopically , however , rdd histiocytes have none of the features of mature langerhans cells , the immature cells of langerhans cell histiocytosis , or phagocytic cells . antigens associated with early inflammation ( mac-387 , 27e10 ) , antigens found on circulating monocytes but not tissue macrophages ( okm5 , leu - m1 ) and activation antigens ( ki-1 , transferrin receptor and interleukin 2 ) are also expressed by these histiocytes . these features suggest that rdd histiocytes are functionally activated macrophages recently derived from circulating monocytes . it has also been shown that the sinuses of rdd nodes , in addition to the classic histiocytes with emperipolesis , also contain large numbers of small - sized mononuclear cells negative for s100 but positive for cd11b , cd11c , cd14 , cd16 , cd33 , cd36 , lysozyme , mac 387 and hla - dr . in the same study , the rdd histiocytes with emperipolesis were positive for s100 , cd11c , cd14 , cd33 , cd68 , and ln 5 . these findings suggested that monocytes derived from the marrow migrate into the sinuses of rdd nodes where they are transformed into the rdd histiocytes , possibly by local cytokine modulation . the common expression of s100 , fascin , cathepsin d and cathepsin e by rdd histiocytes points towards antigen - presenting cell differentiation . expression pattern of mrna suggests that rdd histiocytes express tumor necrosis factor ( tnf ) alpha , interleukin ( il ) 1 and il 6 . in contrast , mature langerhans cells in dermatopathic lymphadenitis did not express any of these cytokines . immature langerhans cells of langerhans cell histiocytosis mostly expressed tnf alpha , although occasional cases expressed il-1 . the current working hypothesis on pathogenesis of rdd is therefore recruitment of marrow monocytes from peripheral blood into lymph nodal sinuses or extranodal sites and their transformation into the immunophenotypically distinct rdd histiocytes which demonstrate emperipolesis and functional uniqueness in terms of cytokine expression profile . release of cytokines like tnf alpha from these cells is responsible for the genesis of fever and other systemic symptoms . however , the morphological counterpart of such an evolutionary transformation or variation in morphology with timing of biopsy are not well documented . in the present case , rdd has been biopsied at various times in the course of the disease , with emperipolesis not always being identified . these findings fit well with the current working hypothesis detailed above . rapidly enlarging nodes and extra - nodal tissue affected with rdd showed less degree of emperipolesis , with predominance of s100-positive foamy histiocytes . in aspirates and biopsies in stable phase , emperipolesis was easy to find . these features suggest that early transformation of monocytes into rdd histiocytes occurs in exacerbation and that emperipolesis takes more time to be well developed . small mononuclear cells positive for cd68 and act but negative for s100 seen in the background may indicate progressive disease activity . since two different types of histiocytic cells are present together in rdd , accurate interpretation of immunocytochemical findings is essential . the variability in extent of emperipolesis observed in this patient indicates that it is a dynamic event which takes time to develop . variable extent of emperipolesis was also seen in eight aspirates and biopsies from other patients [ table 2 ] , although these were from patients with unequivocal diagnosis of rdd on initial sampling . although it is not possible to identify the exact nature of the apoptotic cells , it is reasonable to assume these were the mononuclear and histiocytic cell components which may be involuting in response to changes in the cytokine milieu . sampling of stable disease therefore yields diagnostically useful tissue whereas sampling during exacerbation and involution phases yields tissue inadequate for definitive diagnosis . if emperipolesis is focal in certain stages of rdd , these cases will be missed on biopsy . rhinoscleroma was an important differential diagnostic consideration in the present case in view of the foamy histiocytes without emperipolesis presenting in the nose . therefore , presence of foamy histiocytes in the correct clinical context should prompt a dif ferential diagnosis of rdd even in the absence or focality of emperipolesis . similarly , extensively necrotic and apoptotic nodes can be from an involuting stage of rdd . the rdd histiocytes are very large , from 50 to 100 microns or more in size . a five - micron section would sample only a tenth or less of the rdd histiocyte cytoplasm . if emperipolesis is restricted to just one or two lymphocytes in only a few of the rdd histiocytes , as seen in many cells of the second aspirate , biopsy diagnosis of rdd would be difficult . in cytology smears on the other hand , the entire rdd histiocyte is sampled and with the transparent papanicolaou stain , can be analysed in its entirety . because of these reasons quantification of emperipolesis in biopsies may not correlate with that seen in aspirates , although it has been performed in this study for comparison . the factors initiating this peculiar inflammatory response of recruitment of monocytes and their transformation in situ remain unknown . the etiology of emperipolesis and its nature are also unknown . without understanding the pathogenetic mechanisms underlying these two key factors in rdd ,

this study examines variation of morphologic features , including emperipolesis , during the evolution of a case of rosai dorfman disease ( rdd ) . a 44-year - old male patient with rdd affecting the salivary glands , cervical lymph nodes , nasal and maxillary sinus mucosa had a waxing and waning course over two and a half years , with episodic sudden increase in size followed by involution and then a static course with moderate sized swellings . multiple aspirations and biopsies were performed , which form the basis of this study . four classical cases of rdd on aspirates and another four on biopsy were analyzed for comparison , with quantification of the number of lymphocytes engulfed by histiocytes ( emperipolesis ) . three nasal biopsies and one salivary gland excision of the index case , performed during acute exacerbation , showed chronic inflammation and foamy histiocytes without emperipolesis , the aspirate showing emperipolesis nil in 45% , 1 - 3 lymphocytes in 15% , 4 - 10 in 36% and > 10 in 4% . two aspirations and one lymph node biopsy done from static phase showed classical features of rdd with extensive emperipolesis , the aspirate from left cervical lymph node showing emperipolesis nil in 2% , 1 - 3 in 5% , 4 - 10 in 35% and > 10 in 58% while right cervical lymph node aspirate showed emperipolesis nil in 9% , 1 - 3 in 21% , 4 - 10 in 29% and > 10 in 41% . a biopsy performed from involuting cervical lymph node showed extensive apoptosis and vasculitis without foamy histiocytes or emperipolesis . for comparison , eight classical rdd cases showed abundant emperipolesis with mild variation . emperipolesis is variable in rdd depending on disease activity , which has differential diagnostic relevance and demonstrates the natural history of this rare disease .

the vertex spectrometer ( ves ) setup is a large aperture magnetic spectrometer including the system of proportional and drift chambers , a multichannel threshold erenkov counter , beam - line erenkov counters , a lead - glass @xmath9-detector ( lgd ) and trigger hodoscope . this permits full identification of multi - particle final states . the setup runs on the negative particle beam with the momentum of 36.6 @xmath3 . the description of the setup can be found in @xcite . in this report we present some results of partial wave analysis of the @xmath0 system in the reaction @xmath10 for different @xmath5 regions @xmath11 @xmath12 . the discussed results are based upon the statistics of about @xmath13 events . our previous results were published in @xcite . the pwa has been performed in the 0.82.6 @xmath7 mass region in 50 mev bins for different @xmath5 regions . modified version of the illinois pwa program @xcite with maximum likehood method has been used for the analysis . amplitudes were written using isobar model and relativistic covariant helicity formalism according to @xcite . explicit @xmath5-dependence @xmath14 was included for waves with nonzero projection of spin on gj z - axis . density matrix of full rank was used to describe final state . the set of 42 partial waves in the form @xmath15 @xcite was used in the analysis . full wave set and parameterization of isobars including special treatment of @xmath16 s - wave can be found in @xcite . for the channels with @xmath17 , @xmath18 , @xmath19 largest waves are assigned to their own density matrix elements and are enabled to freely interfere with each other . at @xmath20 @xmath12 in a ) full density matrix , b ) largest eigenvalue ; + wave @xmath21 at @xmath20 @xmath12 in c ) full density matrix , d ) largest eigenvalue . ] results of pwa are represented in general by _ density matrix_. for physical analysis _ amplitudes _ are much more convenient . we present here a new type of amplitude analysis extraction of largest eigenvalue of density matrix . density matrix can be represented by its eigenvalues and eigenvectors : @xmath22 single out leading term : @xmath23 here @xmath24 is coherent part of density matrix and @xmath25 is the rest ( incoherent part ) . to be of physical meaning , this decomposition must be _ stable _ with respect to variations of density matrix elements . this is so if eigenvalues are _ well separated _ in comparison with errors in @xmath26 matrix : @xmath27 . this is the case for @xmath28 where @xmath29 , @xmath30 . extraction of largest eigenvalue has the following advantages . by construction matrix @xmath24 has rank one , so phases are well defined . it quantitatively uses information about coherence factors , which is often ignored . practical experience shows that resonance structures tend to concentrate in @xmath24 and leakage ( see below ) is suppressed in @xmath24 . nevertheless , @xmath25 can contain different non - leading exchanges , albeit it often contains garbage . we can also note that if the wave is small in @xmath24 , its phase with respect to largest waves can not be measured . as a restriction this method requires a lot of data for good fit with small errors . it is not applicable if eigenvalues are not separated . in this case sometimes a group of clustered eigenvalues can be extracted . it is also not applicable if all eigenvalues except one are not statistically significant , as it is the case for unnatural sector for @xmath28 system . an example of separation of largest eigenvalue is present in figure [ fig - lev ] . on sub - figures a ) and b ) one can see a huge difference between wave @xmath31 in the full density matrix and in the largest eigenvalue . it was already noted @xcite that at low @xmath5 region this wave is large and highly incoherent with others at @xmath32 @xmath7 and have only a relatively small shoulder at @xmath33 @xmath7 , which corresponds to well known @xmath34 . our analysis confirms this as shown in figure [ fig - lev ] a ) . contrary to this in the largest eigenvalue this wave is dominated by physical @xmath34 . the bump at low @xmath35 is at least ten times suppressed , which is consistent with its low coherence with other waves . the physical nature of this phenomena is still unknown . in figures [ fig - lev ] c ) , d ) one can see the difference between full density matrix and largest eigenvalue for the wave @xmath21 at @xmath20 @xmath12 . at both figures we can see at @xmath36 @xmath7 a signal for @xmath37 while in fig.[fig - lev ] c ) we can also see a bump at @xmath38 @xmath7 which is absent in fig.[fig - lev ] d ) . this bump is a leakage from @xmath39 with intensity about 0.2% of total number of events or about 7.5% of @xmath40 wave in this low @xmath41 region . this leakage is at least ten times suppressed in coherent part of density matrix . at @xmath42 @xmath12 in : a ) real data , full @xmath26 matrix ; b ) real data , largest eigenvalue ; c ) leakage , full @xmath26 matrix ; d ) leakage , largest eigenvalue . ] we have used the following method to study a possible leakage effects due to finite setup resolution and limited knowledge of setup acceptance . at first , we fit real data with small but representative wave set 12 largest waves . the result of this step is a reasonably accurate representation of multidimensional distribution of real events . next we generate monte - carlo events according to density matrix from this fit , smear these events according to modeled setup resolution and fit them as usual using standard wave set with all 42 waves . to study dependence of results of variation of modeled acceptance , we have used monte - carlo events without smearing , but used corrupted mc program ( with hodoscope trigger logic excluded ) for final fits with 42 waves . the results of leakage study for exotic wave @xmath43 are shown in fig . [ fig - leak ] . one can see that exotic wave can contain 3050% of leakage , but can not be described by leakage . the structure of density matrix in the real data and leakage is quite different in the coherent part of @xmath26 leakage is 2050 times suppressed . most other waves can contain 510% of leakage . at different @xmath41 regions : a d ) full density matrix ; e h ) largest eigenvalue ; i l ) phase difference @xmath45 , full density matrix . ] waves with exotic quantum numbers @xmath46 were included in our analysis with all possible projections @xmath47 . waves with @xmath48 are small in comparison with @xmath49 ( except for @xmath50 @xmath7 ) and are not considered by us as significant . wave @xmath51 in four different @xmath5 regions is shown in fig . [ fig - onemp ] . in the full density matrix ( fig . [ fig - onemp ] a d ) at low @xmath5 this wave consists mainly of a bump around @xmath52 @xmath7 and a shoulder at @xmath53 @xmath7 . at higher @xmath5 regions the bump diminishes while the shoulder remains approximately the same . from figures [ fig - onemp ] e h ) one can see that this shoulder corresponds mainly to the coherent part of the density matrix , and this part remains stable over investigated @xmath5 region . the bins over @xmath5 are selected so that numbers of events in @xmath39 peak are approximately the same for all bins , namely about 20000 events/50 mev , so @xmath5 distribution for coherent part of exotic wave is roughly the same as for @xmath39 while its crossection is only 23% of it . one can see a sharp drop on the coherent part of exotic wave at @xmath54 @xmath7 . we can see analogous effect in some other @xmath55 waves and it can be connected with worse description of high @xmath35 region . phase difference @xmath56 is shown in fig . [ fig - onemp ] i this phase difference is not constant , visible drop corresponds to phase raise of @xmath34 resonance . again the shape of phase variation is more or less stable over inspected @xmath5 region . in general we can not see here narrow exotic object with @xmath53 @xmath7 . results of pwa for the wave @xmath57 in different @xmath5 regions are presented in figure [ fig - zeromp ] . at low @xmath5 two peaks are visible which corresponds to @xmath8 and @xmath58 . at higher @xmath5 peak for @xmath8 is clearly suppressed . relative strength of @xmath8 and @xmath58 signals together with relative number of events in @xmath59 @xmath7 and @xmath60 @xmath7 bands is shown in fig [ fig - zeromp]c ) in ten @xmath5 regions . one can see that @xmath5 distribution for @xmath8 is much more steep than for @xmath58 or even for the total number of events in corresponding @xmath35 band . a possible explanation of this phenomena can be given if the @xmath8 bump is at least partially non - resonant and produced by deck - type final state scattering . : a ) @xmath61 @xmath12 region ; b ) @xmath62 @xmath12 region ; c ) relative @xmath41 dependence of @xmath8/@xmath58 signals and corresponding @xmath35 bands . ] partial wave analysis of @xmath28 final state at different @xmath5 regions was performed on ves data . new type of amplitude analysis was suggested extraction of the coherent part of density matrix . its advantages and limitations were briefly discussed . wave @xmath63 was studied in different @xmath5 regions @xmath64 0.0100.0700.1500.3000.800 @xmath12 . wave shape is broad and more or less the same in all @xmath5 regions studied . clear phase variation with respect to @xmath34 is visible in all @xmath5 regions . no narrow object around @xmath6 @xmath7 is found . waves @xmath17 were studied in the same @xmath5 regions . abnormally steep @xmath5 distribution for @xmath8 was established . this phenomena can be understood if @xmath17 wave in @xmath8 region is partially consists of deck - type background .

the results on partial wave analysis of @xmath0 system in reaction @xmath1 at the momentum @xmath2 @xmath3 on the beryllium target are presented . new method of amplitude analysis is suggested extraction of largest eigenvalue of density matrix . exotic wave with @xmath4 is studied in four @xmath5 regions . no narrow object around @xmath6 @xmath7 is found . unusually steep @xmath5 dependence for @xmath8 object is detected . address = department of hadron physics , ihep , protvino , russia , 142284 , [email protected]

jordan s inequality , @xmath3 has numerous extensions and generalizations . ( to simplify the notation we agree that for @xmath4 the value of @xmath5 is 1 ) . an exhaustive review of the literature is available in @xcite . one of the many types of generalizations is a sequence of the two sided inequalities . the first of them is the inequality @xmath6 by ling zhu @xcite . it is followed by @xmath7 by @xcite ; finally ling zhu verifies @xcite the general @xmath8 where @xmath9 are given by a recursion formula . see also ( * ? ? ? * section 3.7 ) . later ( [ eq : j - n ] ) was extended in @xcite to @xmath10 for @xmath11 . the proofs of inequalities ( [ eq : j-1])([eq : j - r ] ) are based on a monotone version of the lhospital rule : _ if @xmath12 and @xmath13 is increasing on @xmath14 , so is the quotient @xmath15_. the two sided inequalities ( [ eq : j - n ] ) are closely related to the infinite expansion of @xcite @xmath16 where @xmath17 and @xmath18 . see also ( * ? ? ? * section 2.3 ) . identity ( [ eq : j - series ] ) is verified by a straightforward rearrangement of a double power series . by direct integration one achieves also @xmath19 similar ideas were developed for bessel functions in a paper by baricz and wu @xcite and are summarized in @xcite . in @xcite the author uses the notation @xmath20 , normalized so that @xmath21 . without normalization the result of baricz and wu are formulated as @xmath22 for all @xmath23 and for @xmath24 , where @xmath25 and @xmath26 denotes the first positive zero of @xmath27 . the aim of this study is to develop similar ideas for the the trigonometric functions which have singularities , namely , the @xmath28 and @xmath29 functions . our attention was drawn to this subject in an attempt to refine the inequality of becker and stark @xcite @xmath30 our main result ( theorem 1 ) is that the function @xmath31 admits a sequence of upper and lower bounds and these inequalities are closely related to a laurent series expansion in powers of @xmath1 . the same approach will be applied also to @xmath32 and @xmath29 . in spite of the similarity , there are several essential differences between our result and those of ling zhu and for @xmath5 and of baricz for the bessel functions . + ( a ) bessel functions and , consequently @xmath33 , are solutions of simple linear second order differential equations . this is a useful tool in @xcite . unfortunately , we do not know any simple linear differential equation for the tan function . on the contrary , the results for @xmath34 are influenced by its poles at @xmath2 . + ( b ) we start our study with the infinite series and the upper and lower bounds appear as consequences of this alternating series . we do not use the monotone lhospital rule . our method uses partial fractions expansions . + in analogy with ( [ eq : j - r ] ) and ( [ eq : baricz ] ) we also expand @xmath35 into a laurent series of @xmath36 , with @xmath37 . this expansion has different properties from that which corresponds to @xmath38 . in this section we present an infinite series expansion for the tan function and two sets of upper and lower bounds , one with an even number of terms and one with odd number of terms . [ thm : tan ] ( a ) we have the infinite expansion @xmath39 , \ ] ] where @xmath40 } \binom{2p-2m-1}{p-1 } \zeta(2 m ) - \binom{2p-1}{p-1 } \right ] , \qquad p=1,2,\ldots \ .\ ] ] all the coefficients @xmath41 are positive . the infinite series in ( [ eq : tan - laurent ] ) converges for @xmath42 . ' '' '' + ( b ) for all even number @xmath43 and @xmath44 , we have the pair of inequalities @xmath45 \qquad\qquad\qquad\qquad \\ & \qquad\qquad\qquad\qquad \le \ \frac { \tan ( \pi x / 2 ) } { \pi x / 2 } \ \le \ \frac { 8}{\pi^2 } \left [ \frac{1 } { 1 - x^2 } + \sum _ { k=0 } ^{2n } ( -1)^k \frac { t_{k+1 } } { 4^{k+1 } } ( 1-x^2)^k \right ] , \end{aligned}\ ] ] where @xmath46 and @xmath47 . the left hand side inequality of ( [ eq : tan-2n ] ) is strict for @xmath4 . + ( c ) ' '' '' for all odd number @xmath48 and @xmath44 , we have @xmath49 \ \le \ \frac { \tan ( \pi x / 2 ) } { \pi x / 2 } \qquad\qquad \\ & \qquad\qquad \le \ \frac { 8}{\pi^2 } \left [ \frac{1 } { 1 - x^2 } + \sum _ { k=0 } ^{2n } ( -1)^k \frac { t_{k+1 } } { 4^{k+1 } } ( 1-x^2)^k - h_{2n+2 } ( 1-x^2)^{2n+1 } \right ] , \end{aligned}\ ] ] where @xmath50 and @xmath51 . the right hand side inequality of ( [ eq : tan-2n+1 ] ) is strict for @xmath4 . * examples . * the first coefficients are @xmath52 , @xmath53 and @xmath54 . accordingly , @xmath55 the first two special cases of ( [ eq : tan-2n ] ) ( for @xmath56 ) and ( [ eq : tan-2n+1 ] ) ( for @xmath57 ) are @xmath58 and @xmath59 * proof of theorem [ thm : tan ] * for sake of convenience we divide the proof into several steps . _ ( i ) the infinite expansion for tan . _ our starting point is the partial fraction expansion @xmath60 which holds in every domain which contains no poles . it follows that @xmath61 .\ ] ] each term of the series may be expanded into a geometric series , provided that @xmath62 for @xmath63 , i.e. , for @xmath64 . this yields @xmath65 \\ = & \frac { 8}{\pi^2 } \left [ \frac{1 } { 1 - x^2 } + \sum _ { k=0 } ^\infty \left ( \sum _ { n=1 } ^\infty \frac{1 } { n^{k+1 } ( n+1)^{k+1 } } \right ) \frac { ( -1)^k } { 4^{k+1 } } ( 1-x^2)^k \right ] . \end{aligned}\ ] ] the expansion ( [ eq : tan - laurent ] ) will follow if we show that the sums @xmath66 are given explicitly by ( [ eq : tp - zeta ] ) for @xmath67 . the proof is based on the following identity ( * ? ? ? * ex . 39 , p. 246 ) : _ if @xmath68 , then for every _ @xmath69 , @xmath70 ( [ eq : xm - yk ] ) may be verified by mathematical induction on @xmath71 and @xmath72 . we take in ( [ eq : xm - yk ] ) @xmath73 , @xmath74 , @xmath75 , and conclude that @xmath76 .\ ] ] to calculate @xmath41 we sum ( [ eq : x=-1/n ] ) for @xmath77 and separate @xmath78 from @xmath79 : @xmath80 \\ & = \binom{2p-2 } { p-1 } \sum_{n=1}^\infty \left [ -\frac{1}{n } + \frac{1}{n+1 } \right ] + \sum_{j=2}^p \binom{2p - j-1 } { p-1 } \big [ ( -1)^{j } \zeta(j ) + \big ( \zeta(j ) - 1 \big ) \big ] \\ & = \binom{2p-2}{p-1 } \cdot ( -1 ) + \sum _ { j = 2 } ^ { p } \binom{2p - j-1}{p-1 } \big [ \big ( ( -1)^{j } + 1 \big ) \zeta(j ) - 1 \big ) \big ] \\ & = 2 \sum _ { 2 \le 2 m \le p } \binom{2p-2m-1}{p-1 } \zeta(2 m ) - \sum_{j=1}^{p } \binom{2p - j-1}{p-1 } . \end{aligned}\ ] ] since @xmath81 , formula ( [ eq : tp - zeta ] ) is verified and part ( a ) of the theorem follows . we remark that similar sums @xmath82 are mentioned in ( * ? ? ? * , ( 373 ) ) for @xmath83 and @xmath84 . _ ( ii ) the inequalities . _ let us write the series ( [ eq : tan - laurent ] ) as @xmath85 , \ ] ] with the remainder term @xmath86 for each @xmath87 , @xmath88 , the series @xmath89 and its derivative series @xmath90 are alternating series with smaller and smaller terms . indeed , @xmath91 thus @xmath92 and similarly @xmath93 thus , by properties of alternating series , @xmath94 and @xmath95 are positive functions for @xmath88 . consequently @xmath94 increases for @xmath88 , and is bounded from below and from above by @xmath96 the lower bound of @xmath94 , @xmath97 may be written as a finite sum : for @xmath4 , ( [ eq : tan - laurent ] ) yields @xmath98 , \ ] ] so @xmath99 . \end{aligned}\ ] ] consequently @xmath100 is bounded for @xmath101 and for @xmath102 , respectively , by @xmath103 and parts ( b ) and ( c ) of the theorem follow . the remainder term satisfies @xmath104 hence it decreases rapidly , in particular near the poles @xmath105 . for example , for @xmath106 and @xmath107 we have @xmath108 . the bounds in ( [ eq : tan-2n+1 ] ) and ( [ eq : tan-2n ] ) are also very precise near the poles @xmath2 . indeed , the difference between the @xmath71-th upper and lower bounds ( @xmath109 odd or even ) is less then @xmath110 . it is interestiong to compare the convergence of the series ( [ eq : tan - laurent ] ) with that of the taylor series ( * ? ? ? * section 3:14 ) @xmath111 where @xmath112 denotes the dirichlet lambda function . since @xmath113 , the remainder of the series ( [ eq : tan - lambda ] ) after @xmath109 terms is @xmath114 here @xmath115 is uniformly small for large values of @xmath109 . on the other hand , we saw above that the remainder of the series ( [ eq : tan - laurent ] ) after @xmath109 terms is @xmath116 . after extracting @xmath109-th root from the two remainders for large @xmath109 , we compare , up to @xmath117 , @xmath118 with @xmath119 . the consequence is that after @xmath120 terms , for large @xmath109 , the taylor series ( [ eq : tan - lambda ] ) yields a smaller remainder for @xmath121 , while for @xmath122 , the series ( [ eq : tan - laurent ] ) has a smaller remainder . @xmath123 due to ( [ eq : j - r ] ) and ( [ eq : baricz ] ) it is also natural to expand @xmath124 into power series of @xmath36 . formally we follow ( [ eq : tan - fractions ] ) and ( [ eq : tan ( pi x/2 ) ] ) : @xmath125 . \\ = & \frac { 8}{\pi^2 } \sum _ { k=0 } ^\infty ( -1)^k \frac { \tilde{t}_{k+1}(r ) } { 4^{k+1 } } ( r^2-x^2)^k \ , , \end{aligned}\ ] ] with @xmath126 note that @xmath127 differs from @xmath41 by it s range of summation and it is not defined for @xmath38 . equations ( [ eq : tan - r2-x2 ) ] ) and ( [ eq : tan ( pi x/2 ) ] ) are superficially similar . however , they describe different phenomena . ( [ eq : tan ( pi x/2 ) ] ) describes the function @xmath128 in the interval @xmath129 , including its singularities at @xmath2 . expansion ( [ eq : tan - r2-x2 ) ] ) is valid when @xmath130 for all @xmath131 . assuming @xmath132 , this holds when @xmath133 , i.e. , @xmath134 which includes the points @xmath135 and their neighborhoods . note that in the complex plane @xmath136 is the interior of a lemniscate with focal points @xmath137 . inequalities analogous to ( [ eq : tan-2n ] ) and ( [ eq : tan-2n+1 ] ) may be deduced from expansion ( [ eq : tan - r2-x2 ) ] ) . we do not attempt to calculate the sums ( [ eq : t - p - r ] ) explicitly as functions of @xmath138 . rather we shall obtain a recursive formula for the coefficients @xmath127 . the function @xmath139 satisfies the first order , quadratic riccati differential equation @xmath140 . it easy to see that @xmath141 satisfies @xmath142 for @xmath143 . if we let @xmath144 and @xmath145 , then @xmath146 satisfies @xmath147 for @xmath148 . substitution of @xmath149 , @xmath150 and comparison of coefficients lead to the following quadratic recursion formula for @xmath151 , @xmath37 : @xmath152 expansions and inequalities of similar type are available for the @xmath32 and @xmath29 functions . in this section we present the results for the secant function . we remind , in analogy with inequalities ( [ eq : beckerstark ] ) and ( [ eq : chen - qi - cot ] ) , that @xmath153 to prove ( [ eq : sec - beckerstark ] ) , it is sufficient to show that the even function @xmath154 increases for @xmath88 . this indeed holds , since by ( [ eq : beckerstark ] ) @xmath155 \ge 0 .\ ] ] the constants in ( [ eq : sec - beckerstark ] ) follow now by the limit values for @xmath4 and as @xmath156 . our aim is to generalize the right hand side of ( [ eq : sec - beckerstark ] ) into an infinite sequence of inequalities . [ thm : sec ] ( a ) we have the infinite expansion @xmath157 , \ ] ] where @xmath158 \eta(2 m ) \right]\ ] ] for @xmath159 and @xmath160 denotes the dirichlet eta function . all the coefficients @xmath161 are positive . ' '' '' + ( b ) for all even number @xmath43 and @xmath162 , we have the pair of inequalities @xmath163 \le \ \sec ( \pi x /2 ) \\ & \qquad\qquad \le \ \frac{4}{\pi } \left [ \frac{1 } { 1 - x^2 } - \sum _ { k=0 } ^{2n-1 } ( -1)^k \frac { s_{k+1 } } { 4^{k+1 } } ( 1-x^2)^k - j_{2n+1 } ( 1-x^2)^{2n } \right ] , \end{aligned}\ ] ] where @xmath164 and @xmath165 . the right hand side inequality of ( [ eq : sec-2n ] ) is strict for @xmath4 . + ( c ) ' '' '' for all odd number @xmath48 and @xmath166 , we have @xmath167 \\ & \qquad\qquad \le \ \sec ( \pi x /2 ) \le \ \frac{4}{\pi } \left [ \frac{1 } { 1 - x^2 } - \sum _ { k=0 } ^{2n+1 } ( -1)^k \frac { s_{k+1 } } { 4^{k+1 } } ( 1-x^2)^k \right ] , \end{aligned}\ ] ] where @xmath168 and @xmath169 . the left hand side inequality of ( [ eq : sec-2n+1 ] ) is strict for @xmath4 . * examples . * the first coefficients are @xmath170 , @xmath171 and @xmath172 . accordingly , @xmath173 for @xmath56 we get on @xmath166 @xmath174 \le \sec ( \pi x / 2 ) \le \frac { 4}{\pi } \left [ \frac{1 } { 1 - x^2 } - 1 + \frac{\pi}{4 } \right]\ ] ] and for @xmath175 , @xmath176 \le \sec ( \pi x / 2 ) \le \frac { 4}{\pi } \left [ \frac{1 } { 1 - x^2 } - \frac{1}{4 } + \frac{\pi^2 -6}{96 } ( 1 - x^2 ) \right ] \ .\ ] ] * proof . * we start with the partial fraction expansion @xmath177 . then for @xmath166 , @xmath178 \\ & = \frac { 4}{\pi } \left [ \frac{1 } { 1 - x^2 } - \sum _ { k=0 } ^\infty \left ( \sum _ { n=1 } ^\infty \frac { ( -1)^{n-1 } ( 2n+1 ) } { n^{k+1 } ( n+1)^{k+1 } } \right ) ( -1)^k \frac { ( 1-x^2)^k } { 4^{k+1 } } \right ] \\ & = \frac { 4}{\pi } \left [ \frac{1 } { 1 - x^2 } - \sum _ { k=0 } ^\infty ( -1)^k \frac { s_{k+1 } } { 4^{k+1 } } ( 1-x^2)^k \right ] , \end{aligned}\ ] ] where @xmath179 for @xmath180 . the coefficients @xmath161 may be presented explicitly by finite sums of the dirichlet @xmath160 function . let us multiply ( [ eq : x=-1/n ] ) by @xmath181 and separate @xmath78 from @xmath182 : @xmath183 \\ & + \sum_{j=2}^p \binom{2p - j-1 } { p-1 } \left [ 2\frac { ( -1)^j } { n^{j-1 } } + \frac { ( -1)^j } { n^j } + 2\frac { 1 } { ( n+1)^{j-1 } } - \frac { 1 } { ( n+1)^j } \right ] . \end{aligned}\ ] ] we multiply the last equation by @xmath184 and sum it for @xmath185 . with the dirichlet eta function @xmath186 we get @xmath187 \\ & + \sum _ { j=2 } ^p \binom{2p - j-1 } { p-1 } \big [ 2(-1)^j \eta(j-1 ) + ( -1)^j \eta(j ) + 2 \big(-\eta(j-1 ) + 1 \big ) - \big(-\eta(j ) + 1 \big ) \big ] \\ & = -\binom{2p-2 } { p-1 } + \sum _ { j=2 } ^p \binom{2p - j-1 } { p-1 } + \sum _ { j=2 } ^p \binom{2p - j-1 } { p-1 } \big [ 2 \big ( ( -1)^j - 1 \big ) \eta(j-1 ) + \big ( ( -1)^j + 1 \big ) \eta(j ) \big ] \\ & = - \binom{2p-2 } { p-1 } + \binom{2p-2 } { p } + \sum _ { 2 \le 2 m \le p } 2 \big [ \binom{2p-2m-1 } { p-1 } - 2 \binom{2p-2m-2 } { p-1 } \big ] \eta(2 m ) \\ & = \binom{2p-2 } { p-2 } - \binom{2p-2 } { p-1 } + 2 \sum _ { 2 \le 2 m \le p } \big [ \binom{2p-2m-2 } { p-2 } - \binom{2p-2m-2 } { p-1 } \big ] \eta(2 m ) . \end{aligned}\ ] ] here we used the facts that @xmath188 and that @xmath189 thus , ( [ eq : sp - eta ] ) is proved . the inequalities ( [ eq : sec-2n ] ) and ( [ eq : sec-2n+1 ] ) are verified as in theorem [ thm : tan ] . @xmath123 the coefficients @xmath41 and @xmath161 are easily related . in the ( [ eq : sec - derivative ] ) we substitute @xmath190 and @xmath191 , respectively , by the series ( [ eq : tan - laurent ] ) and ( [ eq : sec - laurent ] ) and compare powers of @xmath1 , the result is @xmath192 we outline some other results which may be verified by similar arguments . for the cotangent function , let us recall the inequality ( * ? ? ? * eq . ( 17 ) ) @xmath193 it is possible generalize the left hand side of ( [ eq : chen - qi - cot ] ) into the infinite expansion @xmath194 \ , \ ] ] @xmath195 , \quad p \ge 1 . \end{aligned}\ ] ] all @xmath196-s are positive . the infinite series in ( [ eq : cot - laurent ] ) converges for @xmath197 . for example , @xmath198 . inequalities in the style of theorems [ thm : tan ] and [ thm : sec ] may be proved for @xmath199 . ( [ eq : cot - laurent ] ) is obtained from the expansion @xmath200 . for the calculation of @xmath196 in ( [ eq : cp - zeta ] ) , it is useful to take in ( [ eq : xm - yk ] ) , @xmath73 , @xmath201 and sum the result for @xmath202 . for the summation of the series , one has to use the binomial identity @xmath203 ( * ? ? ? * , eq . 5.20 ) . @xmath123 for the cosecant function we remind , in analogy with ( [ eq : beckerstark ] ) , ( [ eq : sec - beckerstark ] ) and ( [ eq : chen - qi - cot ] ) , the double inequality ( * ? ? ? * eq . ( 19 ) ) @xmath204 the right hand side of ( [ eq : chen - qi - cosec ] ) may be generalized into the expansion @xmath205 , \ ] ] where @xmath206 . \end{aligned}\ ] ] here @xmath207 . expansion ( [ eq : cosec - laurent ] ) follows from the partial fraction expansion @xmath208 . @xmath209 is calculated similarly to @xmath196 . @xmath123 if we substitute the series ( [ eq : cot - laurent ] ) and ( [ eq : cosec - laurent ] ) into the identity @xmath210\ ] ] and compare powers of @xmath211 , it follows that @xmath212 and @xmath213 are related by @xmath214 finally we show that our methods are applicable also to bessel functions and they provide a short proof of ( [ eq : baricz ] ) , based on other principles than those of baricz and wu in @xcite . an expansion of the form @xmath215 holds for all @xmath87 in the complex plane . to see this , put @xmath144 , i.e. , @xmath216 . since @xmath217 is an even analytic function in the whole complex plane , it follows that @xmath218 is analytic for all @xmath219 and may be expanded as @xmath220 . consequently ( [ r2-x2-expansion ] ) holds for all @xmath87 . to calculate the @xmath221-s , let us apply the identity ( * ? ? ? 9.1.30 ) @xmath222 to expansion ( [ r2-x2-expansion ] ) . since @xmath223 , we get @xmath224 for @xmath225 we obtain that @xmath226 . consequently , @xmath227 to prove the inequalities ( [ eq : baricz ] ) , we have to estimate the remainder of the expansion ( [ baritz - expansion ] ) , namely @xmath228 let @xmath229 denote the first positive zero of @xmath230 . it is well known that @xmath231 and that @xmath232 in @xmath233 . see figure 1 . if @xmath236 satisfies @xmath237 , all the coefficients in the tail series @xmath238 are positive for all @xmath23 , hence @xmath239 . so , in the left hand side of ( [ eq : baricz ] ) , @xmath240 ; and on the right hand side of ( [ eq : baricz ] ) , @xmath241 @xmath242 may be written as a finite sum . as @xmath243 , we get from ( [ baritz - expansion ] ) for @xmath4 that @xmath244 thus , @xmath245

the function @xmath0 is expanded into a laurent series of @xmath1 , where the coefficients are given explicitly as combinations of zeta function of even integers . this is used to achieve a sequence of upper and lower bounds which are very precise even at the poles at @xmath2 . similar results are obtained for other trigonometric functions with poles . * keywords * : trigonometric inequalities , jordan inequality , laurent series , zeta function , dirichlet functions + * mathematics subject classification ( 2010 ) * : 26d05

A young Google executive who helped ignite Egypt's uprising energized a cheering crowd of hundreds of thousands Tuesday with his first appearance in their midst after being released from 12 days in secret detention. "We won't give up," he promised at one of the biggest protests yet in Cairo's Tahrir Square. Egyptian anti-Mubarak protesters shout out during a protest in al Manoura, Egypt, Tuesday, Feb.8, 2011. Tens of thousands of Egyptians have been demonstrating in Cairo and other cities, in an ongoing... (Associated Press) Egyptian Wael Ghonim, a Google Inc. marketing manager, talks at Tahrir Square in Cairo, Egypt, Tuesday, Feb. 8, 2011. A young leader of Egypt's anti-government protesters, newly released from detention,... (Associated Press) A volunteer serves tea to anti-government protesters as they sit in front of an Egyptian army tank in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a... (Associated Press) An anti-government protester puts up a poster with a caricature of Egyptian President Hosni Mubarak in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a... (Associated Press) Egyptian Muslim clerics file through the crowd in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir Square into a makeshift... (Associated Press) Anti-government protesters demonstrate in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir Square into a makeshift village... (Associated Press) Egyptian Wael Ghonim, center, a 30-year-old Google Inc. marketing manager who was a key organizer of the online campaign that sparked the first protest on Jan. 25, gestures to the crowd in Tahrir Square,... (Associated Press) Thousands of anti-Mubarak protesters are seen next to an Egyptian army tank as they take part in a demonstration at Tahrir square in Cairo, Egypt, Tuesday, Feb. 8, 2011. (AP Photo/Emilio Morenatti) (Associated Press) Egyptian Wael Ghonim, a Google Inc. marketing manager, who has become a hero of the demonstrators since he went missing on Jan. 27, two days after the protests began, hugs the mother of Khaled Said, a... (Associated Press) Egyptian anti-Mubarak protesters shout in front of Egypt's parliament in Cairo, Egypt, Tuesday, Feb. 8, 2011. Tens of thousands of Egyptians have been demonstrating in Cairo and other cities, calling... (Associated Press) An anti-government protester puts up a poster with a caricature of Egyptian President Hosni Mubarak in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a... (Associated Press) Egyptian Wael Ghonim, center, the 30-year-old Google Inc. marketing manager who was a key organizer of the online campaign that sparked the first protest on Jan. 25, talks to the crowd in Tahrir Square,... (Associated Press) Anti-government protesters stand among makeshift tents in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir Square into a... (Associated Press) Anti-government protesters demonstrate in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir Square into a makeshift village... (Associated Press) Egyptian Wael Ghonim, center, a 30-year-old Google Inc. marketing manager who was a key organizer of the online campaign that sparked the first protest on Jan. 25, talks to the crowd in Tahrir Square,... (Associated Press) Egyptian Wael Ghonim, center, a 30-year-old Google Inc. marketing manager who was a key organizer of the online campaign that sparked the first protest on Jan. 25, talks to the crowd in Tahrir Square,... (Associated Press) A young Egyptian anti-Mubarak protester carries an Egyptian flag in Alexandria, Egypt, Tuesday, Feb.8, 2011. Tens of thousands of Egyptians have been demonstrating in Cairo and other cities, calling for... (Associated Press) Egyptian Wael Ghonim, a Google Inc. marketing manager, who has become a hero of the demonstrators since he went missing on Jan. 27, two days after the protests began, hugs the mother of Khaled Said, a... (Associated Press) Egyptian Wael Ghonim, center, the 30-year-old Google Inc. marketing manager who was a key organizer of the online campaign that sparked the first protest on Jan. 25, talks to the crowd in Tahrir Square,... (Associated Press) Thousands of Egyptian anti-Mubarak protesters take part in a demonstration in Tahrir Square in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir... (Associated Press) Egyptian muslim clerics pray in Tahrir Square, in Cairo, Egypt, Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning Tahrir Square into a makeshift village with tens... (Associated Press) Anti-government protesters hold an Egyptian flag during demonstrations in Tahrir Square in downtown Cairo, Egypt Tuesday, Feb. 8, 2011. Protesters appear to have settled in for a long standoff, turning... (Associated Press) Once a behind-the-scenes Internet activist, 30-year-old Wael Ghonim has emerged as an inspiring voice for a movement that has taken pride in being a leaderless "people's revolution." Now, the various activists behind it _ including Ghonim _ are working to coalesce into representatives to push their demands for President Hosni Mubarak's ouster. With protests invigorated, Vice President Omar Suleiman issued a sharply worded warning, saying of the protests in Tahrir, "We can't bear this for a long time, and there must be an end to this crisis as soon as possible," in a sign of growing impatience with 16 days of mass demonstrations. For the first time, protesters made a foray to Parliament, several blocks away from their camp in the square. Several hundred marched to the legislature and chanted for it to be dissolved. In Tahrir, the massive, shoulder-to-shoulder crowd's ranks swelled with new blood, including thousands of university professors and lawyers who marched in together as organizers worked to draw in professional unions. The crowd rivaled the biggest demonstration so far, a week ago, that drew a quarter-million people. Some said they were inspired to turn out by an emotional television interview Ghonim gave Monday night just after his release from detention. He sobbed over those who have been killed in two weeks of clashes and insisted, "We love Egypt ... and we have rights." "I cried," a 33-year-old upper-class housewife, Fifi Shawqi, said of the interview with Ghonim, who she'd never heard of before the TV appearance. She came to the Tahrir protest for the first time, bringing her three daughters and her sister. "I felt like he is my son and all the youth here are my sons." Tuesday's huge turnout gave a resounding answer to the question of whether the protesters still have momentum even though two weeks of steadfast pressure have not achieved their goal of ousting 82-year-old Mubarak, Egypt's authoritarian leader for nearly three decades. Suleiman rejected any departure for Mubarak or "end to the regime. He told a gathering of newspaper editors that the regime prefers to deal with the crisis using dialogue, adding, "We don't want to deal with Egyptian society with police tools." He warned that the alternative to dialogue was "a coup" _ a possible hint of an imposition of military rule. However, editors present at the meeting said he then explained he didn't mean a military coup but that "a force that is unprepared for rule" could overturn state institutions. U.S. Vice President Joe Biden spoke by phone with Suleiman, saying Washington wants Egypt to immediately rescind emergency laws that give broad powers to security forces _ a key demand of the protesters. Ghonim's reappearance gave a clearer picture of the stunning trajectory of the protests, which swelled from the online organizing of small Internet activist groups into the first and greatest mass challenge ever to Mubarak's rule. Ghonim is an Egyptian who oversees Google Inc.'s marketing in the Middle East and Africa from Dubai, one of the United Arab Emirates. He vanished two days after the protests began on Jan. 25, snatched off the street by security forces and hustled to a secret location. Earlier this year, Ghonim _ anonymously _ launched a Facebook page commemorating Khaled Said, a 28-year-old businessman in Alexandria who was beaten to death by two policemen in June. The page became a rallying point for a campaign against police brutality, with hundreds of thousands joining. For many Egyptians, it was the first time to learn details of the extent of widespread torture in their own country. Small-scale protests over Said's death took place for months. The Khaled Said group worked online with other activists, including the April 6 movement named after the date of 2008 labor protests and the campaign of Nobel Peace laureate and democracy advocate Mohamed ElBaradei. Ghonim's page was "the information channel," said Ziad al-Oleimi, a pro-ElBaradei organizer. Together they decided to hold a larger gathering on Jan. 25, announced on Ghonim's page, to coincide with Police Day _ a state holiday honoring security forces. By phone and Internet, they got out the word to supporters in Cairo and other cities, but didn't expect much. "We really thought that on Jan. 25, we will be arrested in five minutes. I am not kidding," said al-Oleimi. They were surprised to find thousands turning out at several locations in Cairo, many inspired by mass protests in Tunisia. On the fly, organizers made a change in plans, said al-Oleimi: All protesters were to march on Tahrir Square. There, they were met by security forces that unleashed a powerful crackdown, firing water cannons and rubber bullets in battles that lasted until the evening. Even after Ghonim's arrest, his Facebook page was an organizing point. Activists weighed in with postings on strategies and tactics. "When we say let's organize a protest, let's think, five people sit together and plan. Imagine now 50,000 heads are put together through the Internet. Lots of creativity and greatness," said Abdel-Galil el-Sharnoubi, website manager for the fundamentalist Muslim Brotherhood, which balked at joining the first protest but two days later threw its weight behind the movement. Ghonim's page called a Jan. 28 protest labeled "the day of rage" which brought out greater numbers. Despite a new police crackdown that day, the movement had legs. Even when the government shut down the Internet for an unprecedented five days trying to snuff out the protests, organizers now could bring out mass numbers by telephone or word of mouth. Throughout the days that followed, Ghonim had no idea what was happening in the streets. He was in detention, often blindfolded and questioned repeatedly, he said in a Monday night television interview. The interview, on the privately owned satellite channel Dream TV, was for most Egyptians the first time they had seen or even heard of the goateed young man. It was not even widely known that Ghonim was the administrator for the Khaled Said Facebook page. He struck a modest tone and even said he gained respect for some of those who interrogated him in detention. But he was passionate in declaring Egyptians wanted their rights and an end to humiliation. He repeated over and over, "We are not traitors." When the hostess of the show showed pictures of young men killed in the protests, Ghonim slumped in sobs, saying, "It is the fault of everyone who held on tight to authority and didn't want to let go," before cutting short the interview. Over the next 20 hours, about 130,000 people joined a Facebook page titled, "I delegate Wael Ghonim to speak in the name of Egypt's revolutionaries." Ghonim appeared to strike a chord among the broader public, where some have absorbed a state-fueled image of the protesters as disrupting life for no reason and being directed by foreign hands. A retired army general, Essam Salem, said the interview "showed a face of the truth which the state media tried to cover up for so long. ... Many people are coming because they saw the truth." On Tuesday afternoon, Ghonim arrived in Tahrir, greeted by cheers and hustled up to a stage. He spoke softly and briefly to the huge crowd, offering his condolences to the families of those killed. "We are not giving up until our demands are met," he proclaimed before shaking his fist in the air, chanting, "Mubarak, leave, leave." The crowd erupted in cheering, whistling and deafening applause. Despite the excitement Ghonim injected into an already feverish gathering, organizers and the crowds themselves refused the idea of a single leader for their movement. Many contend its strength lies in its lack of leaders and in its nature as a mass popular uprising _ perhaps wary in part of personal splits that have sabotaged past opposition movements. Ghonim and three others were added to a now 10-member committee that represents the various activist groups to coordinate protest activities and push through the groups' demands, said al-Oleimi. "No one can say they lead the revolution. There are leaders and units that organized inside the revolution, and they get their legitimacy from the demands of the revolution," he said. "We don't represent the people in the square. We represent the organized groups." Some activists were seen collecting names and phone numbers of some in the crowds, talking of holding some sort of poll over who they support to represent them. "Ghonim cannot be a leader by himself, unless he is elected by a committee elected and composed of different groups that represent all these people," said Shayma Ahmed, a 20-year-old student among the Tahrir crowds. Ghonim as well appeared to be dismissing talk of himself as a leader. "I'm not a hero. I was writing on a keyboard on the Internet and I wasn't exposing my life to danger," he said in the interview. "The heroes are the one who are in the street." The protesters say they will not begin negotiations with the government over future democratic reforms until Mubarak steps down. Vice President Suleiman has tried to draw them into talks, promising extensive but still unclear change. Many protesters fear he aims to fragment the movement with partial concessions and gestures. There were demonstrations calling for the president's ouster around the country as well with 18,000 people cramming into the main square of Alexandria, Egypt's second largest city. Some 3,000 service workers for the Suez Canal demonstrated in Suez city, while 8,000 people chanted anti-Mubarak slogans in the southern city of Assiut. Even after nightfall, thousands remained in Tahrir, with larger numbers camping out than previously, including significant numbers of women and children. Popular singers entertained them with concerts. ___ AP correspondents Lee Keath and Hamza Hendawi contributed to this report. ||||| Egyptian vice-president said the alternative to dialogue is a coup. [EPA] Omar Suleiman, the Egyptian vice-president, warned on Tuesday that his government "can't put up with continued protests" for a long time, as tens of thousands of pro-democracy protesters rallied in Cairo's Tahrir Square for the sixteenth day in a row. In a sharply worded statement reflecting the regime's impatience and frustration with the mass demonstrations, the newly appointed Suleiman said the crisis must be ended as soon as possible. Increasingly the public face of the embattled government, Suleiman said there will be "no ending of the regime" and no immediate departure for President Hosni Mubarak, according to the state news agency MENA, reporting on a meeting between the vice-president and independent newspapers. The immediate departure of Mubarak is a key demand for the pro-democracy demonstrators. Mubarak's pledge to not seek another term later this year didn't tame the angry protests. Meanwhile, the UN secretary-general, Ban Ki-moon added his voice to host of countries calling for "an orderly transition" in Egypt. Speaking at the United Nations headquarters in New York, Moon said Egyptian government must heed the call from its people for greater reform immediately. Subtle threat Suleiman reportedly told the editors of the newspapers that the regime wants dialogue to resolve protesters' demands for democratic reform, adding, in a veiled warning, that the government doesn't "want to deal with Egyptian society with police tools." Click here for more on Al Jazeera's special coverage At one point in the roundtable meeting, Suleiman warned that the alternative to dialogue "is that a coup happens, which would mean uncalculated and hasty steps, including lots of irrationalities. We don't want to reach that point, to protect Egypt." Pressed by the editors to explain the comment, he said he did not mean a military coup but that "a force that is unprepared for rule" could overturn state institutions, said Amr Khafagi, editor-in-chief of the privately-owned Shorouk daily, who attended the briefing. "He doesn't mean it in the classical way." "The presence of the protesters in Tahrir Square and some satellite stations insulting Egypt and belittling it makes citizens hesitant to go to work," he said. Egyptian military, widely hailed for professionalism and restraint, has vowed not to use force against peaceful protesters. President Mubarak, his deputy and the new prime minister, Ahmed Shafiq, are all retired military officers with deep links to the institution. Sticks and carrots Suleiman warned that calls by some protesters for a campaign of civil disobedience are "very dangerous for society and we can't put up with this at all." This comes a day after Suleiman announced a slew of constitutional reforms, to be undertaken by yet to be formed committees. Suleiman said that one committee would carry out constitutional and legislative amendments to enable a shift of power while a separate committee will be set up to monitor the implementation of all proposed reforms. The two committees will start working immediately, he said. Suleiman stressed that demonstrators will not be prosecuted and that a separate independent fact-finding committee would be established to probe the violence on February 2.

– Let's hope these two developments don't collide in a bad way: On a day when Tahrir Square saw perhaps its largest demonstration yet, the nation's new vice president issued what both AP and al-Jazeera described as a "sharply worded" statement that the government is losing its patience. "We can't bear this for a long time, and there must be an end to this crisis as soon as possible," said Omar Suleiman. At another point, he said there will be "no ending of the regime." Speaking with newspaper editors, Suleiman also raised eyebrows in his call for dialogue by noting that the alternative "is that a coup happens, which would mean uncalculated and hasty steps, including lots of irrationalities. We don't want to reach that point, to protect Egypt." Pressed on the issue, however, he said he didn't mean a military coup or the imposition of military rule. The government doesn't "want to deal with Egyptian society with police tools," he said.

terrestrial gamma ray flashes ( tgfs ) were first observed above thunderclouds by the burst and transient source experiment ( batse ) ( fishman et al . , 1994 ) . it was soon understood that these energetic photons were generated by the bremsstrahlung process when energetic electrons collide with air molecules @xcite ; these electrons were accelerated by some mechanism within the thunderstorm . since then , measurements of tgf s were extended and largely refined by the reuven ramaty energy solar spectroscopic imager ( rhessi ) ( cummer et al . , 2005 ; smith et al . , 2005 , grefenstette et al . , 2009 , smith et al . , 2010 ) , by the fermi gamma - ray space telescope @xcite , by the astrorivelatore gamma a immagini leggero ( agile ) satellite which recently measured tgfs with quantum energies of up to 100 mev @xcite , and by the gamma - ray observation of winter thunderclouds ( growth ) experiment @xcite . hard radiation was also measured from approaching lightning leaders ( moore et al . , 2001 ; dwyer et al . , 2005 ) ; and there are also a number of laboratory experiments where very energetic photons were generated during the streamer - leader stage of discharges in open air ( stankevich and kalinin , 1967 ; dwyer et al . , 2005b ; kostyrya et al . , 2006 ; dwyer et al . , 2008b ; nguyen et al . , 2008 ; rahmen et al . , 2008 ; repev and repin , 2008 ; nguyen et al . , 2010 ; march and montany , 2010 ; shao et al . , 2011 ) . next to gamma - ray flashes , flashes of energetic electrons have been detected above thunderstorms @xcite ; they are distinguished from gamma - ray flashes by their dispersion and their location relative to the cloud - as charged particles in sufficiently thin air follow the geomagnetic field lines . in december 2009 nasa s fermi satellite detected a substantial amount of positrons within these electron beams @xcite . it is now generally assumed that these positrons come from electron positron pairs that are generated when gamma - rays collide with air molecules . two different mechanisms for creating large amounts of energetic electrons in thunderclouds are presently discussed in the literature . the older suggestion is a relativistic run - away process in a rather homogeneous electric field inside the cloud ( wilson , 1925 ; gurevich , 1961 ; gurevich et al . , 1992 ; gurevich , 2001 dwyer , 2003 , 2007 ; milikh and roussel - dupr , 2010 ) . more recently research focusses on electron acceleration in the streamer - leader process with its strong local field enhancement ( moss et al . , 2006 ; li et al . , 2007 ; chanrion and neubert , 2008 ; li et al . , 2009 ; carlson et al . , 2010 ; celestin and pasko , 2011 ; li et al . , 2012 ) . whatever the mechanism of electron acceleration in thunderstorms is , ultimately one needs to calculate the energy spectrum and angular distribution of the emitted bremsstrahlung photons . as the electrons at the source form a rather directed beam pointing against the direction of the local field , the electron energy distribution together with the angles and energies of the emitted photons determine the photon energy spectrum measured by some remote detector . the energy resolved photon scattering angles are determined by so - called doubly differential cross - sections that resolve simultaneously energy @xmath0 and scattering angle @xmath1 of the photons for given energy @xmath2 of the incident electrons . the data is required for scattering on the light elements nitrogen and oxygen with atomic numbers @xmath3 and @xmath4 , while much research in the past has focussed on metals with large atomic numbers @xmath5 . the energy range up to 1 gev is relevant for tgf s ; we here will provide data valid for energies above 1 kev . as illustrated by fig . 1 , the full scattering problem is characterized by three angles . the two additional angles @xmath6 and @xmath7 determine the direction of the scattered electron relative to the incident electron and the emitted photon . the full angular and energy dependence of this process is determined by so - called triply differential cross - sections . a main result of the present paper is the analytical integration over the angles @xmath6 and @xmath7 to determine the doubly differential cross - sections relevant for tgf s . as the cross - sections for the production of electron positron pairs from photons in the field of some nucleus are related by some physical symmetry to the bremsstrahlung process , we study these processes as well ; we provide doubly differential cross - sections for scattering angle @xmath8 and energy @xmath9 of the emitted positrons for given incident photon energy @xmath0 and atomic number @xmath5 . + with the doubly differential cross sections for bremsstrahlung and pair production a feedback model can be constructed tracing bremsstrahlung photons and positrons as a possible explanation of tgfs ( dwyer , 2012 ) . , scattered electron @xmath10 and emitted photon @xmath11 form the angles @xmath12 and @xmath13 , and @xmath7 is the angle between the planes spanned by the vector pairs @xmath14 and @xmath15 . the scattering nucleus has atomic number @xmath5 . ] our present understanding of bremsstrahlung and pair production was largely developed in the first half of the 20th century . it was first calculated by bethe and heitler ( 1934 ) . important older reviews are by heitler ( 1944 ) , by hough ( 1948 ) , and by koch and motz ( 1959 ) . we also used some recent text books ( greiner and reinhardt , 1995 ; peskin and schroeder , 1995 ) ; together with heitler ( 1944 ) and hough ( 1948 ) , they provide a good introduction into the quantum field theoretical description of bremsstrahlung and pair production . the calculation of these two processes is related through some physical symmetry as will be explained in chapter [ pair ] . as drawn in fig . 1 , when an electron scatters at a nucleus , a photon with frequency @xmath16 can be emitted . the geometry of this process is described by the three angles @xmath1 , @xmath6 and @xmath7 . cross sections can be total or differential . total cross sections determine whether a collision takes place for given incident electron energy , singly differential cross sections give additional information on the photon energy or on the angle between incident electron and emitted photon , and doubly differential cross sections contain both . triply differential cross sections additionally contain the angle at which the electron is scattered . as two angles are required to characterize the direction of the scattered electron , one could argue that this cross section should actually be called quadruply differential , but the standard terminology for the process is triply differential . koch and motz ( 1959 ) review many different expressions for different limiting cases , but without derivations . moreover , some experimental results are discussed and compared with the presented theory . bethe and heitler ( 1934 ) , heitler ( 1944 ) , hough ( 1948 ) , koch and motz ( 1959 ) , peskin and schroeder ( 1995 ) , greiner and reinhardt ( 1955 ) use the born approximation to derive and describe bremsstrahlung and pair production cross sections . several years later new ansatzes were made to describe bremsstrahlung . elwert and haug ( 1969 ) use approximate sommerfeld - maue eigenfunctions to derive cross sections for bremsstrahlung under the assumption of a pure coulomb field . they derive a triply differential cross section and beyond that also numerically a doubly differential cross section . furthermore they compare with results obtained by using the born approximation . they show that there is a small discrepancy for high atomic numbers between the bethe - heitler theory and experimental data , and they provide a correcting factor to fit the bethe - heitler approximation better to experimental data for large @xmath5 . however , they only investigate properties of bremsstrahlung for @xmath17 ( aluminum ) and @xmath18 ( gold ) . tseng and pratt ( 1971 ) and fink and pratt ( 1973 ) use exact numerical calculations using coulomb screened potentials and furry - sommerfeld - maue wave functions , respectively . they investigate bremsstrahlung and pair production for @xmath17 and for @xmath18 and show that their results with more accurate wave functions do not fit with the bethe heitler cross section exactly . this is not surprising as the bethe - heitler approximation is developed for low atomic numbers @xmath5 and for @xmath5 dependent electron energies as discussed in section [ valid ] . + shaffer et al . ( 1996 ) review the bethe heitler and the elwert haug theory . they discuss that the bethe heitler approach is good for small atomic numbers and give a limit of @xmath19 for experiments to deviate from theory . for @xmath20 the theory of bethe and heitler , however , is stated to be in good agreement with experiments for energies above the kev range . they calculate triply differential cross sections using partial - wave and multipole expansions in a screened potential numerically for @xmath21 ( silver ) and @xmath18 and compare their results with experimental data . actually their results are close to the elwert haug theory which fits the experimental data better than their theory . shaffer and pratt ( 1997 ) also discuss the theory of elwert and haug ( 1969 ) and compare it with the bethe heitler theory and , additionally , with the bethe heitler results multiplied with the elwert factor and with the exact partial wave method . they show that all theories agree within a factor 10 in the kev energy range , and that the elwert - haug theory fits the exact partial wave method best . however , they only investigate bremsstrahlung for atomic nuclei with @xmath21 , 53 ( iodine ) , 60 ( neodymium ) , 68 ( erbium ) and 79 , but not for small atomic numbers @xmath3 and 8 as relevant in air . in summary , elwert and haug ( 1969 ) , tseng and pratt ( 1971 ) , fink and pratt ( 1973 ) , shaffer et al . ( 1996 ) and shaffer and pratt ( 1997 ) calculate cross sections for bremsstrahlung and pair production for atomic numbers @xmath17 and @xmath22 numerically , but not analytically , and they do not provide any formula or data which can be used to simulate discharges in air . the eedl database consists mainly of experimental data which have been adjusted to nuclear model calculations . for the low energy range geant4 takes over this data and gives a fit formula . the singly differential cross section related to @xmath16 which is used in the geant4 toolkit is valid in an energy range from 1 kev to 10 gev and taken from seltzer and berger ( 1985 ) . the singly differential cross section related to @xmath1 is based on the doubly differential cross section by @xcite and valid for very high energies , i.e. , well above @xmath23 mev . but in the preimplemented cross sections of geant4 the dependence on the photon energy is neglected in this case so that it is actually a singly differential cross section describing @xmath1 . table [ brems.tab ] gives an overview of the available literature and data for total or singly , doubly or triply differential bremsstrahlung cross sections ; parameterized angles or photon energies are given , as well as the different energy ranges of the incident electron . furthermore , the table shows the atomic number @xmath5 investigated and includes some further remarks . for calculating the angularly resolved photon energy spectrum of tgf s , we need a doubly differential cross section resolving both energy and emission angle of the photons ; we need it in the energy range between 1 kev and 1 gev for the small atomic numbers @xmath3 and 8 . therefore most of the literature reviewed here is not applicable . however , the bethe - heitler approximation is valid for atomic numbers @xmath20 and for electron energies above 1 kev @xcite . how the range of validity depends on the atomic number @xmath5 is discussed in section [ valid ] . we therefore will use the triply differential cross section derived by bethe and heitler ( 1934 ) to determine the correct doubly differential cross . .available data for bremsstrahlung cross sections . besides the available information on total or singly , doubly or triply differential cross - sections , the range of validity of the incident electron energy and of the atomic number is given . if not stated otherwise , these are theoretical expressions . [ cols="^,^,^,^,^",options="header " , ] i carlson et al . ( 2009 , 2010 ) use geant 4 , a library of sotware tools with a preimplemented database to simulate the production of terrestrial gamma - ray flashes . but geant 4 does not supply an energy resolved angular distribution as it does not contain a doubly differential cross section , parameterizing both energy and emission angle of the bremsstrahlung photons ( see table [ brems.tab ] ) . furthermore , it is designed for high electron energies . it also includes the landau - pomeranchuk - migdal ( lpm ) ( landau and pomeranchuk , 1953 ) effect and dielectric suppression ( ter - mikaelian , 1954 ) which do not contribute in the kev and mev range . we will briefly discuss the cross sections and effects implemented in geant 4 in [ app_geant4 ] . lehtinen has suggested a doubly differential cross section in his phd thesis ( lehtlinen , 2000 ) that is also used by xu et al . lehtinen s ansatz is a heuristic approach based on factorization into two factors . the first factor is the singly differential cross section of bethe and heitler ( 1934 ) that resolves only electron and photon energies , but no angles . the second factor is due to jackson ( 1975 , p. 712 , it depends on the variable @xmath24\;/\ ; ( 1-\beta\cos\theta_i)^4 $ ] , where @xmath25 measures the incident electron velocity on the relativistic scale . however , this factor derived in jackson ( 1975 , p. 712 is calculated in the classical and not quantum mechanical case , and it is valid only if the photon energy is much smaller than the total energy of the incident electron . we will compare this ansatz with our results in [ app_leht ] . dwyer ( 2007 ) chooses to use the triply differential cross section by bethe and heitler ( 1934 ) , but with an additional form factor parameterizing the structure of the nucleus @xcite . we will show in [ app_form ] that this form factor , however , does not contribute for energies above 1 kev . this cross section depends on all three angles as shown in fig . 1 . if one is only interested in the angle @xmath1 between incident electron and emitted bremsstrahlung photon , the angles @xmath6 and @xmath7 have to be integrated out either numerically , or the analytical results derived in the present paper can be used . in chapter [ brems ] we introduce the triply differential cross section derived by bethe and heitler then we integrate over the two angles @xmath6 and @xmath7 to obtain the doubly differential cross section which gives a correlation between the energy of the emitted photon and its direction relative to the incident electron . furthermore , we investigate the limit of very small or very large angles and of high photon energies ; this also serves as a consistency check for the correct integration of the full expression . in chapter [ pair ] we perform the same calculations for pair production , i.e. , when an incident photon interacts with an atomic nucleus and creates a positron electron pair . as we explain , this process is actually related by some physical symmetry to bremsstrahlung , therefore results can be transferred from bremsstrahlung to pair production . we get a doubly differential cross section for energy and emission angle of the created positron relative to direction and energy of the incident photon . the physical interpretation and implications of our analytical results is discussed in chapter [ disc ] . energies and emission angles of the created photons and positrons are described in the particular case of scattering on nitrogen nuclei . for electron energies below 100 kev , the emission of bremsstrahlung photons in different directions varies typically by not more than an order of magnitude , while for higher electron energies the photons are mainly emitted in forward direction . for this case , we derive an analytical approximation for the most likely emission angle of bremsstrahlung photons and positrons for given particle energies . in chapter [ concl ] we will briefly summarize the results of our calculations . details of our calculations can be found in [ app_res ] - [ app_theta ] . beyond that we provide a c++ code the c++ code can be downloaded directly from the website of the journal . if an electron with momentum @xmath26 approaches the nucleus of an atom , it can change its direction due to coulomb interaction with the nucleus ; the electron acceleration creates a bremsstrahlung photon with momentum @xmath27 that can be emitted at an angle @xmath1 relative to the initial direction of the electron . the new direction of the electron forms an angle @xmath6 with the direction of the photon . the angle @xmath7 is the angle between the planes spanned by the vector pairs @xmath14 and @xmath15 . this process is shown in figure 1 . a virtual photon ( allowed by heisenberg s uncertainty principle ) transfers a momentum @xmath28 between the electron and the nucleus . therefore both energy and momentum are conserved in the scattering process . the corresponding triply differential cross section was derived by bethe and heitler ( 1934 ) : @xmath29 . \label{bcs.1}\end{aligned}\ ] ] here @xmath5 is the atomic number of the nulceus , @xmath30 is the fine structure constant , @xmath31 js is planck s constant , @xmath32 and @xmath33 m / s is the speed of light . the kinetic energy @xmath34 of the electron in the initial and final state is related to its total energy and momentum as @xmath35 where @xmath36 kg is the electron mass . the conservation of energy implies @xmath37 which determines @xmath38 as a function of @xmath2 and @xmath0 . the directions of the emitted photon with energy @xmath0 and of the scattered electron are parameterized by the three angles ( see fig . 1 ) @xmath39 the differentials are @xmath40 furthermore one can get an expression for the absolute value of the virtual photon @xmath41 with the help of the momenta , the photon energy @xmath0 and the angles ( [ bcs.3 ] ) - ( [ bcs.5 ] ) . its value is @xmath42 the cross sections of bethe and heitler ( [ bcs.1 ] ) are valid if the born approximation @xcite holds @xmath43 for nitrogen with @xmath3 and for oxygen with @xmath4 , this holds for electron velocities @xmath44 m / s and @xmath45 m / s ; this is equivalent to a kinetic energy of @xmath46 this means that incident electron energies above 1 kev can be treated with eq . [ bcs.1 ] , for lower energies , one can not calculate with free electron waves anymore , but has to use coulomb waves ( heitler , 1944 ; greiner und reinhardt , 1995 ) ; in this case one can not derive cross sections like ( [ bcs.1 ] ) analytically any more . thus the bethe heitler cross section and our results must not be used for energies of the electron in the initial and final state smaller than 1 kev . however , for higher energies of the electron in the initial and final state , the approximation by bethe and heitler becomes more accurate ; thus this approximation is better if @xmath47 kev . the easiest way is to integrate over the angle @xmath7 between the scattering planes first ( see fig . [ start_fig.1 ] ) . for this purpose it is useful to redefine some quantities in the following way ; therefore ( [ bcs.1 ] ) can be written much more simply : @xmath48 with ( [ int.1 ] ) - ( [ int.7 ] ) , eq . ( [ bcs.1 ] ) can be written as : @xmath49 thus the integration over @xmath7 simply reads @xmath50 \label{int.9}\end{aligned}\ ] ] where @xmath51 and @xmath52 still depend on @xmath6 and @xmath1 . these integrals can be calculated with the help of the residue theorem which is reviewed briefly in [ app_res ] . if @xmath53 is a rational function without poles on the unit circle @xmath54 , then @xmath55 where @xmath56 is a complex function which is defined as @xmath57 the residuum of a pole @xmath58 of order @xmath59 is defined as @xmath60.\end{aligned}\ ] ] to integrate the functions in eq . ( [ int.9 ] ) , we write @xmath61 and get from ( [ int.11 ] ) @xmath62 the poles of the functions @xmath63 in ( [ int.16 ] ) - ( [ int.19 ] ) are given by @xmath64 for @xmath65 poles are of order one and for @xmath66 of order two . in addition @xmath67 has a pole at @xmath68 according to ( [ int.10 ] ) one needs poles with @xmath69 . for @xmath70 it is quite clear that @xmath71 . as the angles @xmath1 and @xmath6 are between @xmath72 and @xmath73 , the expression @xmath74 in eq . ( [ int.1 ] ) . furthermore @xmath75 , @xmath76 and @xmath77 . hence @xmath78 therefore @xmath79 in eq . ( [ int.20 ] ) is a negative real number . furthermore @xmath80 and @xmath81 . thus @xmath82 it follows immediately that @xmath83 and @xmath84 . for all residua one obtains @xmath85 with the knowledge of these residua and using ( [ int.10 ] ) , the integral in ( [ int.9 ] ) can be calculated elementarily @xmath86 . \label{int.27}\end{aligned}\ ] ] after having obtained an expression for the `` triply '' differential cross section , there is still the integration over @xmath6 left . this calculation is mainly straight forward , but rather tedious . using expression ( [ int.27 ] ) , it is @xmath87\sin\theta_f . \label{theta.1}\end{aligned}\ ] ] let s now consider the first integral of ( [ theta.1 ] ) . if one inserts ( [ int.1 ] ) and ( [ int.5 ] ) , it becomes @xmath88 where the substitution @xmath89 was made in the second step . ( [ theta.3 ] ) is rather simple and yields @xmath90 this was a quite simple calculation . all the other integrals can be calculated similarly , but with more effort . as another example let s consider the last integral . before inserting ( [ int.1 ] ) , ( [ int.2 ] ) and ( [ int.7 ] ) one can define for simplicity @xmath91 the expression @xmath52 from eq . ( [ int.2 ] ) is then @xmath92 thus the regularly appearing term @xmath93 can be written as @xmath94 where the definitions @xmath95 have been introduced . by using ( [ int.1 ] ) , ( [ int.7 ] ) and ( [ theta.9 ] ) , the last integral of ( [ int.27 ] ) becomes @xmath96 where @xmath97 has been substituted again . + this integration can be performed elementarily by finding the indefinite integral @xmath98 by inserting @xmath99 and @xmath100 as upper and lower limit , using ( [ theta.10 ] ) and ( [ theta.11 ] ) and simplifying . the integral in ( [ theta.12 ] ) is then finally @xmath101 . \label{theta.15}\end{aligned}\ ] ] all the other integrals can be calculated similarly where one always has to substitute @xmath97 . with this technique the whole doubly differential cross section finally becomes @xmath102 with the following contributions : @xmath103 , \label{theta.17}\\ i_2&=&-\frac{2\pi ac}{p_f(e_i - cp_i\cos\theta_i)}\ln\left ( \frac{e_f+p_fc}{e_f - p_fc}\right ) , \label{theta.18 } \\ i_3&=&\frac{2\pi a}{\sqrt{(\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i } } \nonumber \\ & \times&\ln\bigg(\big((e_f+p_fc)(4p_i^2p_f^2\sin^2\theta_i(e_f - p_fc)+(\delta_1+\delta_2 ) ( ( \delta_2e_f+\delta_1p_fc ) \nonumber\\ & -&\sqrt{(\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i}))\big)\big((e_f - p_fc ) ( 4p_i^2p_f^2\sin^2\theta_i(-e_f - p_fc ) \nonumber \\ & + & ( \delta_1-\delta_2 ) ( ( \delta_2e_f+\delta_1p_fc)-\sqrt{(\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i}))\big)^{-1 } \bigg ) \nonumber\\ & \times&\left[-\frac{(\delta_2 ^ 2 + 4p_i^2p_f^2\sin^2\theta_i)(e_f^3+e_fp_f^2c^2)+p_fc(2 ( \delta_1 ^ 2 - 4p_i^2p_f^2\sin^2\theta_i)e_fp_fc+\delta_1\delta_2(3e_f^2+p_f^2c^2))}{(\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i}\right.\nonumber\\ & -&\frac{c(\delta_2e_f+\delta_1p_fc)}{p_f(e_i - cp_i\cos\theta_i ) } \nonumber\\ & -&\frac{4e_i^2p_f^2(2(\delta_2e_f+\delta_1p_fc)^2 - 4m^2c^4p_i^2p_f^2\sin^2\theta_i)(\delta_1e_f+\delta_2p_fc)}{((\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i)^2 } \nonumber \\ & + & \left.\frac{8p_i^2p_f^2m^2c^4\sin^2\theta_i(e_i^2+e_f^2)-2\hbar^2\omega^2p_i^2\sin^2\theta_ip_fc(\delta_2e_f+\delta_1p_fc)+ 2\hbar^2\omega^2p_f m^2c^3(\delta_2e_f+\delta_1p_fc ) } { ( e_i - cp_i\cos\theta_i)((\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i)}\right ] , \nonumber\\ \label{theta.19}\\ i_4&=&-\frac{4\pi ap_fc(\delta_2e_f+\delta_1p_fc)}{(\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i } -\frac{16\pi e_i^2p_f^2 a(\delta_2e_f+\delta_1p_fc)^2}{((\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i)^2 } , \label{theta.20 } \\ i_5&=&\frac{4\pi a}{(-\delta_2 ^ 2+\delta_1 ^ 2 - 4p_i^2p_f^2\sin^2\theta_i ) ( ( \delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i ) } \nonumber\\ & \times&\left[\frac{\hbar^2\omega^2p_f^2}{e_i - cp_i\cos\theta_i}\right.\nonumber\\ & \times&\frac{e_f[2\delta_2 ^ 2(\delta_2 ^ 2-\delta_1 ^ 2)+8p_i^2p_f^2\sin^2\theta_i(\delta_2 ^ 2+\delta_1 ^ 2 ) ] + p_fc[2\delta_1\delta_2(\delta_2 ^ 2-\delta_1 ^ 2)-16\delta_1\delta_2p_i^2p_f^2\sin^2\theta_i]}{\delta_2 ^ 2 + 4p_i^2p_f^2\sin^2\theta_i } \nonumber\\ & + & \frac{2\hbar^2\omega^2 p_i^2\sin^2\theta_i(2\delta_1\delta_2 p_fc+2\delta_2 ^ 2e_f+8p_i^2p_f^2\sin^2\theta_i e_f)}{e_i - cp_i\cos\theta_i}\nonumber\\ & + & \frac{2e_i^2p_f^2\{2(\delta_2 ^ 2-\delta_1 ^ 2)(\delta_2e_f+\delta_1p_fc)^2 + 8p_i^2p_f^2\sin^2\theta_i[(\delta_1 ^ 2+\delta_2 ^ 2)(e_f^2+p_f^2c^2 ) + 4\delta_1\delta_2e_fp_fc]\}}{((\delta_2e_f+\delta_1p_fc)^2 + 4m^2c^4p_i^2p_f^2\sin^2\theta_i)}\nonumber\\ & + & \left.\frac{8p_i^2p_f^2\sin^2\theta_i(e_i^2+e_f^2)(\delta_2p_fc + \delta_1 e_f)}{e_i - cp_i\cos\theta_i}\right ] , \label{theta.21}\\ i_6&=&\frac{16\pi e_f^2p_i^2\sin^2\theta_i a}{(e_i - cp_i\cos\theta_i)^2 ( -\delta_2 ^ 2+\delta_1 ^ 2 - 4p_i^2p_f^2\sin^2\theta_i)}. \label{theta.22}\end{aligned}\ ] ] eq . ( [ theta.16 ] ) depends explicitly on @xmath104 and @xmath1 while @xmath38 and @xmath105 are functions of @xmath2 and @xmath16 through ( [ bcs.2 ] ) and ( [ bcs.2b ] ) . ( [ theta.16 ] ) is the final result of the integration of ( [ bcs.1 ] ) over @xmath7 and @xmath6 with the help of the residue theorem and some basic calculations . now this result can be used both as input for monte carlo code and for discussing some basic properties of the behaviour of produced bremsstrahlung photons . + actually ( [ theta.16 ] ) is also valid for @xmath106 , as will be shown in the next section , but the simple way just to set @xmath106 in ( [ theta.16 ] ) will fail , especially for numerical purposes , because the logarithmic part in ( [ theta.17 ] ) tends to @xmath107 for @xmath108 and so fails for numerical applications . thus we need an additional expression for @xmath106 which has to be consistent with ( [ theta.16 ] ) . for some special cases the integration of ( [ bcs.1 ] ) over @xmath7 and @xmath6 is easier . this information can also be used to verify ( [ theta.16 ] ) by checking consistency and use them for monte carlo codes . if one is only interested in forward and backward scattering , one can set @xmath106 or @xmath111 before integrating ; then ( [ bcs.1 ] ) becomes @xmath112 where the momentum @xmath41 of the virtual photon can be written as @xmath113 here the upper sign corresponds to @xmath106 and the lower one to @xmath111 . + as ( [ small.1 ] ) and ( [ small.2 ] ) do not depend on @xmath7 at all , the @xmath7 integration simply gives a factor of @xmath114 , and ( [ small.1 ] ) becomes @xmath115 finally this expression has to be integrated over @xmath6 in order to obtain the doubly differential cross section . similarly to the total integration of ( [ theta.1 ] ) it is convenient to define @xmath116 where @xmath117 , with definitions ( [ theta.5 ] ) and ( [ theta.6 ] ) . eq . ( [ small.2 ] ) can then be rewritten as @xmath118 and @xmath119 \sin\theta_f \nonumber \\ \label{small.7}\end{aligned}\ ] ] where the integration is rather elementary and can be performed by substituting @xmath97 again . thus ( [ small.7 ] ) yields @xmath120 . \label{small.8}\end{aligned}\ ] ] this expression is much simpler than ( [ theta.16 ] ) , but only valid for @xmath106 or @xmath111 . actually this expression has also been obtained by calculating the limit @xmath121 or @xmath122 in ( [ theta.16 ] ) ; hence the consistency check is succesful . details can be found in [ app_small ] . the other case which can be investigated easily is when almost all kinetic energy of the incident electron is transferred to the emitted photon , i.e. , @xmath124 and @xmath125 and consequently from eq . ( [ bcs.7 ] ) @xmath126 with these limits it follows for the triply differential cross section ( [ bcs.1 ] ) @xmath127.\nonumber\\ \label{limit.5}\end{aligned}\ ] ] actually ( [ limit.5 ] ) depends neither on @xmath7 , nor on @xmath6 . therefore @xmath128 which leads to a very simple expression for the doubly differential cross section @xmath129 . \label{limit.7}\end{aligned}\ ] ] although taking the limit @xmath123 contradicts eq . ( [ born.2 ] ) as the energy of the emitted electron should be larger than @xmath130 kev ( [ born.2 ] ) , ( [ limit.7 ] ) can be used for two purposes . + as ( [ limit.7 ] ) can be obtained , as well , by taking the limit @xmath131 in ( [ theta.16 ] ) , the complicated expression ( [ theta.16 ] ) is checked for consistency analytically . for further details the reader is referred to [ app_large ] . furthermore we will see in section [ max_scat.sec ] that the most probable scattering angle does not depend on the photon energy for @xmath132 mev . therefore this cross section can be used for calculating the most probable scattering angle in this energy range . pairs of electrons and positrons can be produced if a photon interacts with the nucleus of an atom . this process is related by some symmetry to the production of bremsstrahlung photons . bremsstrahlung occurs when an electron is affected by the nucleus of an atom , scattered and then emits a photon . so there are three real particles involved : incident electron , scattered electron and emitted photon . as the photon has no antiparticle one can change the time direction of the photon . for antimatter it is well known that antiparticles can be interpreted as the corresponding particles moving back in time . so one can substitute the incident electron by an positron moving forward in time . thus by substituting emitted photon by incident photon and incident electron by emitted positron ( due to time reversal and changing its charge ) it is possible to describe pair production from bremsstrahlung . thus the emitted photon in the bremsstrahlung process has to be substituted by the incident photon from the nucleus and the incident electron by the produced positron . with these two replacements one gets the differential cross section for pair production @xcite @xmath133 , \nonumber \\ \label{pair.1}\end{aligned}\ ] ] where @xmath5 , @xmath134 , @xmath135 , @xmath136 and @xmath137 are the same parameters as in eq . ( [ bcs.1 ] ) . @xmath16 is the frequency of the incident photon , @xmath138 and @xmath139 are the total energy and the momentum of the positron / electron with @xmath140 similarly to ( [ bcs.1 ] ) there are three angles , @xmath141 between the direction of the photon and the positron / electron direction , @xmath142 , and @xmath7 is the angle between the scattering planes @xmath143 and @xmath144 . the absolute value of the momentum of the virtual photon is @xmath145 algebraically one obtains ( [ pair.1 ] ) from ( [ bcs.1 ] ) by replacing @xmath146 where the quantities on the left hand side are for bremsstrahlung , and those on the right hand side for pair production . at the end one has to multiply with an additional factor to get the correct prefactor . with all the mentioned substitutions it is @xmath147 because of this symmetry the results for pair production follow easily from those for bremsstrahlung . + the direction of the positron relative to the incident photon is given by integrating ( [ pair.1 ] ) over @xmath7 and @xmath148 . but this is the same exercise as to integrate ( [ bcs.1 ] ) over @xmath7 and @xmath6 . because of the symmetry between bremsstrahlung and pair production one can take ( [ theta.16 ] ) and substitute ( [ pair.8 ] ) - ( [ pair.15 ] ) to obtain a doubly differential cross section @xmath149 with the following contributions @xmath150 , \nonumber\\ \label{pair.19}\\ i_2&=&\frac{2\pi ac}{p_-(e_+-cp_+\cos\theta_i)}\ln\left ( \frac{e_-+p_-c}{e_--p_-c}\right ) , \label{pair.20 } \\ i_3&=&\frac{2\pi a}{\sqrt{(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i } } \nonumber \\ & \times&\ln\bigg(\big((e_-+p_-c)(4p_+^2p_-^2\sin^2\theta_i(e_--p_-c)+(\delta^{(p)}_1+\delta^{(p)}_2 ) ( ( \delta^{(p)}_2e_-+\delta^{(p)}_1p_-c ) \nonumber\\ & -&\sqrt{(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i}))\big)\big((e_--p_-c ) ( 4p_+^2p_-^2\sin^2\theta_i(-e_--p_-c ) \nonumber\\ & + & ( \delta^{(p)}_1-\delta^{(p)}_2 ) ( ( \delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)-\sqrt{(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i}))\big)^{-1}\bigg ) \nonumber\\ & \times&\left[\frac{c(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)}{p_-(e_+-cp_+\cos\theta_i)}\right.\nonumber\\ & + & \big[((\delta^{(p)}_2)^2 + 4p_+^2p_-^2\sin^2\theta_i)(e_-^3+e_-p_-c)+p_-c(2 ( ( \delta^{(p)}_1)^2 - 4p_+^2p_-^2\sin^2\theta_i)e_-p_-c \nonumber\\ & + & \delta^{(p)}_1\delta^{(p)}_2(3e_-^2+p_-^2c^2))\big]\big[(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i\big]^{-1 } \nonumber\\ & + & \big[-8p_+^2p_-^2m^2c^4\sin^2\theta_i(e_+^2+e_-^2)-2\hbar^2\omega^2p_+^2\sin^2\theta_ip_-c(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c ) \nonumber\\ & + & 2\hbar^2\omega^2p_- m^2c^3(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)\big ] \big[(e_+-cp_+\cos\theta_i)((\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i)\big]^{-1 } \nonumber\\ & + & \left.\frac{4e_+^2p_-^2(2(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 - 4m^2c^4p_+^2p_-^2\sin^2\theta_i)(\delta^{(p)}_1e_-+\delta^{(p)}_2p_-c)}{((\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i)^2}\right ] , \label{pair.21}\\ i_4&=&\frac{4\pi ap_-c(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)}{(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i } + \frac{16\pi e_+^2p_-^2 a(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2}{((\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i)^2 } , \label{pair.22 } \\ i_5&=&\frac{4\pi a}{(-(\delta^{(p)}_2)^2+(\delta^{(p)}_1)^2 - 4p_+^2p_-^2\sin^2\theta_i ) ( ( \delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i ) } \nonumber\\ & \times&\left[\frac{\hbar^2\omega^2p_-^2}{e_+cp_+\cos\theta_i } \big[e_-[2(\delta^{(p)}_2)^2((\delta^{(p)}_2)^2-(\delta^{(p)}_1)^2)+8p_+^2p_-^2\sin^2\theta_i((\delta^{(p)}_2)^2+(\delta^{(p)}_1)^2 ) ] \right.\nonumber\\ & + & p_-c[2\delta^{(p)}_1\delta^{(p)}_2((\delta^{(p)}_2)^2-(\delta^{(p)}_1)^2)-16\delta^{(p)}_1\delta^{(p)}_2p_+^2p_-^2\sin^2\theta_i]\big]\big[(\delta^{(p)}_2)^2 + 4p_+^2p_-^2\sin^2\theta_i\big]^{-1 } \nonumber\\ & + & \frac{2\hbar^2\omega^2 p_{+}^2 \sin^2\theta_i(2\delta^{(p)}_1\delta^{(p)}_2 p_-c+2(\delta^{(p)}_2)^2e_-+8p_+^2p_-^2\sin^2\theta_i e_-)}{e_+-cp_+\cos\theta_i}\nonumber\\ & - & \big[2e_+^2p_-^2\{2((\delta^{(p)}_2)^2-(\delta^{(p)}_1)^2)(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 8p_+^2p_-^2\sin^2\theta_i[((\delta^{(p)}_1)^2+(\delta^{(p)}_2)^2)(e_-^2+p_-^2c^2 ) \nonumber\\ & + & 4\delta^{(p)}_1\delta^{(p)}_2e_-p_-c]\}\big]\big[(\delta^{(p)}_2e_-+\delta^{(p)}_1p_-c)^2 + 4m^2c^4p_+^2p_-^2\sin^2\theta_i\big]^{-1}\nonumber\\ & -&\left.\frac{8p_+^2p_-^2\sin^2\theta_i(e_+^2+e_-^2)(\delta^{(p)}_2p_-c + \delta^{(p)}_1 e_-)}{e_+-cp_+\cos\theta_i}\right ] , \label{pair.23}\\ i_6&=&-\frac{16\pi e_-^2p_+^2\sin^2\theta_i a}{(e_+-cp_+\cos\theta_i)^2 ( -(\delta^{(p)}_2)^2+(\delta^{(p)}_1)^2 - 4p_+^2p_-^2\sin^2\theta_+ ) } \label{pair.24}\end{aligned}\ ] ] with @xmath151 and with @xmath152 defined as @xmath153 if electrons are scattered at nuclei , they can produce hard bremsstrahlung photons with frequency @xmath16 and direction @xmath1 relative to the direction of the electrons . + figure [ exp.fig ] compares our equation ( [ theta.16 ] ) with experimental results for for bremsstrahlung as a function of the scattering angle @xmath1 between emitted photon and incident electron for gold @xmath18 where 1 mb = @xmath154 m@xmath155 . the energies are a ) @xmath156 kev , @xmath157 kev and b ) @xmath158 kev , @xmath159 kev . the solid lines shows our result ( [ theta.16 ] ) ; the dotted lines show experimental values ( aiginiger,1966).,title="fig : " ] for bremsstrahlung as a function of the scattering angle @xmath1 between emitted photon and incident electron for gold @xmath18 where 1 mb = @xmath154 m@xmath155 . the energies are a ) @xmath156 kev , @xmath157 kev and b ) @xmath158 kev , @xmath159 kev . the solid lines shows our result ( [ theta.16 ] ) ; the dotted lines show experimental values ( aiginiger,1966).,title="fig : " ] a ) @xmath156 kev , @xmath157 kev b ) @xmath158 kev , @xmath159 kev + gold ( @xmath18 ) for different electron and photon energies ( aiginger , 1966 ) . for @xmath18 the minimal electron energy ( [ born.2 ] ) for the born approximation to be valid , is @xmath160 kev . figure [ exp.fig ] shows that the cross sections agree overall in size for @xmath156 kev , @xmath157 kev and for @xmath158 kev , @xmath159 kev . however , for the first case , the energy of the electron in the final state is @xmath161 kev @xmath162 kev , thus close to the velocity limit . therefore there is a larger deviation , especially for small angles , than for the second case where a very good agreement can be observed . figure [ disc_fig.1 ] shows the doubly differential cross section ( [ theta.16 ] ) for bremsstrahlung for several electron and photon energies . for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath163 kev , b ) @xmath164 kev , c ) @xmath165 mev and d ) @xmath166 mev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron.,title="fig : " ] for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath163 kev , b ) @xmath164 kev , c ) @xmath165 mev and d ) @xmath166 mev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron.,title="fig : " ] + a ) @xmath163 kev b ) @xmath164 kev + for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath163 kev , b ) @xmath164 kev , c ) @xmath165 mev and d ) @xmath166 mev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron.,title="fig : " ] for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath163 kev , b ) @xmath164 kev , c ) @xmath165 mev and d ) @xmath166 mev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron.,title="fig : " ] + c ) @xmath165 mev d ) @xmath166 mev + at first , the probability for generating photons decreases with increasing photon energy for fixed electron energy . this can be understood easily by applying ( [ limit.7 ] ) . as can be seen there , the doubly differential cross section grows linearly in the momentum of the electron in the final state which is equivalent to @xmath169 for high photon energies . so , if all kinetic energy is transferred from the electron onto the photon , the final momentum @xmath170 vanishes , and thus @xmath171 for nonrelativistic electron and photon energies the scattering angle tends to be mainly equally distributed , i.e. the photons do not have a preference for a particular direction . when the photon energy increases , photons are mainly emitted in forward direction , but the ratio between forward and backward scattering is at least three orders of magnitude lower than for a relativistic electron . this case belongs to the classical case where the velocity is small compared to the speed of light . namely , it is @xmath172 and non - relativistic equations will be enough to describe these phenomena . in the relativistic case ( @xmath173 and @xmath174 ) the differential cross section becomes more and more anisotropic . forward scattering is preferred to backward scattering although the maximal cross section does not lie precisely at @xmath106 as can be seen in figure [ disc_fig.1 ] c ) . but the more the electron energy increases the more the maximum wanders to smaller angles , for example , it seems in figure [ disc_fig.1 ] d ) that the maximal emission is indeed for @xmath1=0 . as mentioned in section [ theta_int ] and in [ app_small ] , formula ( [ theta.17 ] ) can not be evaluated directly at @xmath106 . however , for this purpose , we derived ( [ small.8 ] ) which is valid for @xmath106 and @xmath111 . as in figure [ disc_fig.1 ] for a smaller angular range , title="fig : " ] as in figure [ disc_fig.1 ] for a smaller angular range , title="fig : " ] + a ) @xmath165 mev b ) @xmath166 mev ) @xmath175 and the maximum of this cross section @xmath176 vs. the kinetic energy of the incident electron for different ratios between photon and electron energies in a a ) linear and b ) logarithmic scale for @xmath3 .,title="fig : " ] ) @xmath175 and the maximum of this cross section @xmath176 vs. the kinetic energy of the incident electron for different ratios between photon and electron energies in a a ) linear and b ) logarithmic scale for @xmath3 .,title="fig : " ] + a ) b ) figure [ disc_fig.2 ] shows again ( [ theta.16 ] ) for two relativistic electron and different photon energies but for a smaller range of angles . it shows in more detail that the angle of maximal scattering is small , but not 0 . + figure [ disc.ratio ] shows the ratio between the cross section for backward scattering and forward scattering . it can be clearly seen that the tendency for backward scattering decreases for increasing electron energy . the lower the electron energy becomes , the more forward and backward scattering become similar and in general , the scattering tends to be isotropic . only for ratios between photon energies and electron energies close to 1 , forward scattering is preferred for the whole range of energies , but still decreases with increasing electron energies . + in energetic electron avalanches electrons scatter frequently which leads to a large velocity dispersion . it depends on the direction of the applied electric field whether electrons move forward or whether their directions are distributed arbitrarily . if so , however , this implies that photons will not necessarily move in a preferred direction , but in the direction of the incident electron . their motion and thus change of direction depend on photon processes , such as compton scattering . the tendency of forward scattering in the case of relativistic incident electrons can be understood by applying the laws of relativistic transformations . imagine a non - quantum field theoretical description of bremsstrahlung @xcite . if one regards an inertial system in which the incident particle is at rest ( fig . [ disc_fig.3 ] a ) ) , radiation is emitted isotropically with a small - angle deflection . \a ) b ) if the physical laws for this process are relativistically transformed into the laboratory system where the nucleus is at rest and the electron moving , most of the radiation is emitted in forward direction relative to the electron direction ( fig . [ disc_fig.3 ] b ) ) . because this transformation is valid for a non - quantum field theoretical , relativistic electron , it must also be true for a relativistic quantum theoretical description , therefore we see that the forward scattering of photons can simply be explained as a result of the relativistic transformation . + for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath177 kev , b ) @xmath178 kev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron . , title="fig : " ] for bremsstrahlung ( @xmath3 ) versus the scattering angle @xmath1 between emitted photon and incident electron . the electron energies are a ) @xmath177 kev , b ) @xmath178 kev . in each plot the the photon energy @xmath0 amounts to @xmath167 and @xmath168 of the kinetic energy of the incident electron . , title="fig : " ] + a ) @xmath177 kev b ) @xmath179 kev + the forward scattering can moreover be understood by using the conservation laws of energy and momentum . they predict that photons have to be scattered in forward direction if electron and photon energy are high . the interested reader is referred to [ app_cons ] . + although figure [ disc_fig.1 ] shows that the maxima of the doubly differential cross section form with increasing electron energy , it is difficult to determine in these plots when these maxima really start to be generated clearly . figure [ disc_fig.4 ] shows the doubly differential cross section in dependence of the incident electron energy for @xmath177 kev and @xmath178 kev when the kinetic energy is equal to the rest energy . for @xmath180 kev and for @xmath181 the cross section for forward scattering is already two orders of magnitude larger than for backward scattering , but a clear maximum can not be seen . however , for the same kinetic energy , but for @xmath182 there is already a clear maximum formed . but if the kinetic energy grows up to @xmath183 kev which is equal to the rest energy of the electron , there is even a maximum for @xmath184 . this can be expected due to the relativistic transformation . if @xmath185 , then the photon emission is relatively isotropic . but if the kinetic energy is approximately equal to the rest energy of the electron , relativistic laws are valid . especially for @xmath186 @xmath187 therefore the electron has to be treated relativistically and clear maxima close to @xmath106 form for every possible photon energy . figure [ disc_fig.1 ] shows that for both slow and relativistic electrons the doubly differentical cross section also varies with the photon energy for fixed electron energies . for fixed electron energy , lower photon energies are more likely . moreover , photons are more likely for certain angles . they are more likely for lowly energetic electrons in the limit @xmath188 and for highly energetic electrons in the limit @xmath189 . figure [ disc_fig.6 ] shows the doubly differential cross section in another way . now the photon energy is fixed and the electron energy differs within one plot . for all cases it is more likely that low energetic electrons create photons than relativistic electrons do , in the limit @xmath190 . but for small angles , i.e. for forward emission of photons , the probability rapidly increases for relativistic electrons and exceeds the probability at small electron energies . for bremsstrahlung ( @xmath3 ) vs. the scattering angle @xmath1 for several electron and photon energies . in each panel the photon energy @xmath0 is fixed and the cross section is plotted for various kinetic energies of the incident electron . , title="fig : " ] for bremsstrahlung ( @xmath3 ) vs. the scattering angle @xmath1 for several electron and photon energies . in each panel the photon energy @xmath0 is fixed and the cross section is plotted for various kinetic energies of the incident electron . , title="fig : " ] + a ) @xmath157 ev b ) @xmath191 ev + for bremsstrahlung ( @xmath3 ) vs. the scattering angle @xmath1 for several electron and photon energies . in each panel the photon energy @xmath0 is fixed and the cross section is plotted for various kinetic energies of the incident electron . , title="fig : " ] for bremsstrahlung ( @xmath3 ) vs. the scattering angle @xmath1 for several electron and photon energies . in each panel the photon energy @xmath0 is fixed and the cross section is plotted for various kinetic energies of the incident electron . , title="fig : " ] + c ) @xmath191 kev d ) @xmath192 kev figure [ disc_fig.1 ] also shows that the angle for which maximal scattering takes place , is rather independent of the photon energy . hence , one can use ( [ limit.7 ] ) to determine a formula for that scattering angle . actually this derivation leads to a quartic equation which can , however , be approximated for small angles , i.e. @xmath193 , through a quadratic equation . the reader is referred to [ app_theta ] for the detailed calculation . the solution of the quadratic equation reads @xmath194 -|\mathbf{p}_i|\delta_0c-\frac{\hbar\omega}{e_f}c|\mathbf{p}_i|\delta_0 } } \label{disc.9}\end{aligned}\ ] ] with @xmath195 @xmath123 , e.g. @xmath196 and @xmath197 for maximal scattering vs. incident electron energy in a a ) semilog and b ) loglog plot for @xmath3 . besides ( [ disc.9 ] ) for @xmath196 , the exact solution of the quartic equation and various data for different @xmath198 are shown.,title="fig : " ] for maximal scattering vs. incident electron energy in a a ) semilog and b ) loglog plot for @xmath3 . besides ( [ disc.9 ] ) for @xmath196 , the exact solution of the quartic equation and various data for different @xmath198 are shown.,title="fig : " ] + a ) b ) figure [ disc_fig.7 ] shows ( [ disc.9 ] ) and manually extracted values for @xmath1 for different photon energies . it shows much better than figure [ disc_fig.1 ] that @xmath1 is rather independent of the photon energy for relativistic electron energies . besides ( [ disc.9 ] ) , the solution of the quartic equation , is shown . moreover , it shows that ( [ disc.9 ] ) gives a good approximation for those angles @xmath1 for which scattering is maximal . actually , we see that the exact solution describes the angle for maximal scattering better , especially for low energies , but for high energies both curves fit very well . + by inserting @xmath199 into ( [ disc.9 ] ) one obtains a formula which relates the photon energy to the most probable scattering angle . + we now proceed from bremsstrahlung to pair production . one photon with energy @xmath0 creates two particles , namely an electron and a positron , both with rest energy @xmath200 . therefore @xmath201 follows for the kinetic energies of these two particles . thus the photon energy has to be @xmath202 mev for pair production and the kinetic energy of the particles is bounded as @xmath203 . as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed photon energies a ) @xmath204 mev , b ) @xmath205 mev , c ) @xmath157 mev and d ) @xmath159 mev . in each panel different positron energies @xmath9 relative to the available photon energy @xmath206 are plotted . , title="fig : " ] as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed photon energies a ) @xmath204 mev , b ) @xmath205 mev , c ) @xmath157 mev and d ) @xmath159 mev . in each panel different positron energies @xmath9 relative to the available photon energy @xmath206 are plotted . , title="fig : " ] + a ) @xmath204 mev b ) @xmath205 mev + as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed photon energies a ) @xmath204 mev , b ) @xmath205 mev , c ) @xmath157 mev and d ) @xmath159 mev . in each panel different positron energies @xmath9 relative to the available photon energy @xmath206 are plotted . , title="fig : " ] as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed photon energies a ) @xmath204 mev , b ) @xmath205 mev , c ) @xmath157 mev and d ) @xmath159 mev . in each panel different positron energies @xmath9 relative to the available photon energy @xmath206 are plotted . , title="fig : " ] + c ) @xmath157 mev d ) @xmath159 mev figure [ disc_fig.8 ] shows the doubly differential cross section ( [ pair.18 ] ) for different photon and positron energies . forward scattering is dominant , there is almost no case now of more isotropic scattering . this results from the fact that almost all positron energies in figure [ disc_fig.8 ] are relativistic . for very highly energetic photons , e.g. @xmath207 mev and @xmath208 mev , and thus relativistic positron energies in fig . [ disc_fig.8 ] there are clear maxima for forward scattering . for energies @xmath209 mev , however , the maxima are @xmath210 , but forward scattering is still preferred . pair production is symmetric in positron and electron energy . thus for the singly differential cross section @xmath211 the probability of the creation of a positron with a given energy is as large as the probability to create an electron with this energy : @xmath212 + as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed positron energies a ) @xmath213 kev and b ) @xmath214 mev . in each panel curves for the photon energies @xmath215 5 mev , 10 mev , 50 mev and 100 mev are included.,title="fig : " ] as a function of the angle @xmath8 between incident photon and created positron for @xmath3 : the cross section is shown for fixed positron energies a ) @xmath213 kev and b ) @xmath214 mev . in each panel curves for the photon energies @xmath215 5 mev , 10 mev , 50 mev and 100 mev are included.,title="fig : " ] + a ) @xmath213 kev b ) @xmath214 mev figure [ disc_fig.9 ] shows the doubly differential cross section ( [ pair.18 ] ) for fixed positron and different photon energies . again positrons which are generated with high velocities predominantly scatter forward while this tendency vanishes if the positron energy is very low . this can be traced back to the relativistic behaviour again . if a positron is very energetic , it has to be treated relativistically and the relativistic transformation leads to forward scattering ( this is the same explanation as for bremsstrahlung ) . we also see that the creation of positrons is more likely for highly energetic photons . as for bremsstrahlung one can get a simple formula for the preferred direction . performing the same calculation as for bremsstrahlung one obtains @xmath216 -|\mathbf{p}_+|\delta^{(p)}_0c \nonumber\\ & -&\frac{\hbar\omega}{e_-}c|\mathbf{p}_+|\delta^{(p)}_0\big)^{-1}\bigg]^{\frac{1}{2 } } \label{disc.14}\end{aligned}\ ] ] with @xmath217 and @xmath218 figure [ disc_fig.10 ] for maximal scattering vs. incident photon energy in a a ) semilog and b ) loglog plot for @xmath3 . besides ( [ disc.14 ] ) for @xmath219 various data for different @xmath220 are shown.,title="fig : " ] for maximal scattering vs. incident photon energy in a a ) semilog and b ) loglog plot for @xmath3 . besides ( [ disc.14 ] ) for @xmath219 various data for different @xmath220 are shown.,title="fig : " ] + a ) b ) shows that ( [ disc.14 ] ) is a good approximation for @xmath8 for high photon energies and high ratios between photon and positron energy . the smaller the ratio between photon and positron energy , however , is , the worse ( [ disc.14 ] ) becomes for low photon energies . if the photon energy is larger than 50 mev , relativistic positrons are created ; therefore forward scattering takes place and @xmath8 can be calculated with ( [ disc.14 ] ) . we have reviewed literature relevant for bremsstrahlung in terrestrial gamma - ray flashes ( tgfs ) ( bethe and heitler , 1934 ; heitler , 1944 ; elwert and haug , 1969 ; seltzer and berger , 1985 ; shaffer et al . , 1996 ; agostinelle et al . , 2003 ) . focussing on atomic numbers @xmath3 ( nitrogen ) and @xmath4 ( oxygen ) and an energy range of 1 kev to 1 gev , no good parametrization of an energy resolved angular distribution in the form of doubly differential cross section is available . the theory of bethe and heitler covers this energy range for @xmath221 , but it parameterizes the direction of the scattered electron as well ; therefore we integrated their triply differential cross section to obtain the correct energy resolved angular distribution for bremsstrahlung and pair production . other authors ( lehtinen , 2000 ; dwyer , 2007 ; carlson et al . , 2009 , 2010 ) used different approaches , as discussed in the introduction . they use singly or triply differential cross sections which do not give a direct relation between the photon energy and the direction of the photon relative to the motion of the electron . as positrons are created within a thundercloud as well @xcite , we used a symmetry between the production of bremsstrahlung and the creation of an electron - positron pair both in the field of a nucleus to obtain a cross section which relates the energy of the created positron with its direction . we have seen that emitted bremsstrahlung photons are mainly released in forward direction if the electron which interacts with the nucleus has such a high energy that it has to be treated relativistically . for lower energies scattering tends to be more isotropic . for the case that almost all kinetic energy of the incident electron is transformed into photon energy , we derived an approximation for the most probable photon emission angle as a function of the incident electron energy and of the photon energy . the expression is valid for all ratios of photon over electron energy if the electron motion is relativistic . so , when photons have been created within a thundercloud or discharge , they are mainly scattered in forward direction as long as the electrons move relativistically , i.e. if their kinetic energy is at least as large as their rest energy . similar results hold for pair production . next to the doubly differential cross section we derived a simple approximation for the most probable positron emission angle for the case that the photon energy is larger than 10 mev ( for ratios between the kinetic energy of the positron and available photon energy down to 25% ) or than 100 mev ( for ratios lower than 25% ) . we have seen that for very highly energetic photons that almost all positrons are scattered in forward direction . if , however , the photon energy decreases , the probability of forward scattering decreases as well . instead the maximal cross section can be found at @xmath222 for low ratios between @xmath9 and @xmath206 and is , beyond that , symmetric to this angle . our analytical results for the doubly differential cross - sections for bremsstrahlung and pair production are also supplied in the form of two functions written in c++ . in this form the functions can be implemented into monte carlo codes simulating energetic processes like the production of gamma - rays or electron positron pairs in thunderstorms . + + * acknowledgements : * we dedicate this article to the memory of davis d. sentman . he was a great inspiration and discussion partner in the summer of 2011 when c.k . worked on this project , and he was an invaluable colleague and co - organizer for u.e . for many years . we acknowledge fruitful and motivating discussions with brant carlsson . c.k . acknowledges financial support by stw - project 10757 , where stichting technische wetenschappen ( stw ) is part of the netherlands organization for scientific research nwo . in this appendix the method how to calculate integrals of the form @xmath223 shall be discussed where @xmath224 is a rational function without poles on the unit circle @xmath54 . but before explaining this method let s briefly review some general facts about residua . let @xmath225 , be a holomorphic function and @xmath226\rightarrow\mathbb{c},t\mapsto \gamma(t)$ ] , a closed curve in the complex plane . then one can calculate complex curve integrals via @xmath227 where the sum has to be taken over all poles @xmath58 of @xmath56 and complex curve integrals are defined as @xmath228 the residuum of a pole @xmath58 can be calculated via @xmath60 \label { res.4}\end{aligned}\ ] ] where @xmath59 denotes the order of the pole . with the help of the ( [ res.2 ] ) one can simply perform the integration of ( [ res.1 ] ) . for that purpose define @xmath229 and choose the unit circle @xmath230 \label{res.6}\end{aligned}\ ] ] as closed curve ; hence ( [ res.3 ] ) becomes @xmath231 where the identities @xmath232 and @xmath233 were used in the last step . + finally with ( [ res.2 ] ) and ( [ res.7 ] ) one gets a simple formula to calculate ( [ res.1 ] ) : @xmath234 with @xmath56 being defined in ( [ res.5 ] ) . in order to get ( [ small.8 ] ) from ( [ theta.16 ] ) it is rather straight forward to set @xmath106 or @xmath111 . especially it is @xmath235 but there is one case which should be considered a bit more thoroughly . + this regards the logarithm in ( [ theta.17 ] ) . for @xmath111 it is @xmath236 ; thus @xmath237 and @xmath238 which is a very simple calculation . however , for @xmath106 it is @xmath239 which can be both negative or positive depending on values of @xmath240 and @xmath241 if @xmath242 then equations ( [ appc.3 ] ) - ( [ appc.5 ] ) are valid again . if @xmath243 , however , it follows for the argument of the logarithm @xmath244 hence it is necessary to use the rule of lhpital : @xmath245 with ( [ appc.10 ] ) the whole limit yields @xmath246 which is and has to be identical with ( [ appc.5 ] ) . so in both cases , @xmath243 and @xmath242 , ( [ appc.5],[appc.12 ] ) are generated by setting @xmath109 ; therefore one does not have to distinguish between the these cases in ( [ small.8 ] ) . + but it is of importance to mention that due to ( [ appc.7 ] ) one can get numerical problems if one only implements ( [ theta.16 ] ) and wants to calculate the doubly differential cross section for @xmath106 . thus it is useful to distinguish for @xmath247 and @xmath106 and to use ( [ small.8 ] ) instead for the latter case . + for the rest of limiting forward and/or backward scattering it is , however , straight forward to insert @xmath109 and thus can deduce ( [ small.8 ] ) from ( [ theta.16 ] ) with the additional help of ( [ appc.10 ] ) . there are three contributions from ( [ theta.16 ] ) which lead to ( [ limit.7 ] ) in the limit @xmath249 : @xmath250 \label{appd.3}\end{aligned}\ ] ] while all other integrals which appear in ( [ theta.16 ] ) cancel each other ( which will be shown in an example later ) . it can be verified easily that @xmath251 according to definitions ( [ theta.5 ] ) , ( [ theta.6 ] ) and ( [ limit.3 ] ) . with these limits the behavior of @xmath252 for small @xmath105 can be calculated in a straight forward way : @xmath253 for ( [ appd.2 ] ) and ( [ appd.3 ] ) , however , there is more effort to be invested . as it is @xmath254 and @xmath255 for @xmath256 , one has to use the rule of lhpital . if one rewrites @xmath257 with @xmath258 this rule leads to @xmath259 \nonumber \\ & = & -\frac{2}{\delta } ; \label{appd.9}\end{aligned}\ ] ] thus @xmath260 the limit of ( [ appd.3 ] ) can also be calculated by using ( [ appd.7 ] ) . it is @xmath261 \ ] ] while @xmath105 can simply be reduced in the fractions , one has to use the rule of lhpital again for the logarithmic part because it is @xmath262 and the logarithm @xmath263 for @xmath256 . its limit is @xmath264 \nonumber \\ & = & \left.-\frac{2}{e_f\delta_1}\right|_{p_f \rightarrow 0 } = -\frac{2}{e_f\delta } \label{appd.12};\end{aligned}\ ] ] thus the whole limit yields after some further calculations @xmath265 finally , if one inserts ( [ int.3 ] ) , the sum of ( [ appd.6 ] ) , ( [ appd.10 ] ) and ( [ appd.13 ] ) leads to ( [ limit.7 ] ) . + all other terms which appear in ( [ theta.16 ] ) vanish . for this purpose one should regroup all terms according to their origin . as an example let s consider the three contributions which have arisen from @xmath266 . for this integral it follows @xmath267 \nonumber \label{appd.14 } \\ & \xrightarrow{\hbar\omega\rightarrow e_{kin , i } } & \frac{2\pi ac}{e_i - cp_i\cos\theta_i}\left[-\frac{2c}{e_f } + \psi\left(-\frac{2}{\delta}\right)+\left(\psi e_f+\delta c\right ) \frac{2}{e_f\delta}\right ] \label{appd.15 } \nonumber \\ & = & 0 \label{appd.16}\end{aligned}\ ] ] where we have used ( [ appd.9 ] ) , ( [ appd.12 ] ) and @xmath268 in the limiting step . of course , this term has to vanish because @xmath269 , but the concrete calculation after having integrated over @xmath7 and @xmath6 is much more complicated . therefore we have just given an example here . similarly , all other terms cancel so that only the limits of @xmath270 , stay . as mentioned in the introduction , preimplemented cross sections for bremsstrahlung can be found in the geant 4 software library ( agostinelli et al . , 2003 ; geant4.cern.ch ) . geant 4 contains data for the total cross section @xmath271 , the singly differential cross section @xmath272 and a singly differential cross section @xmath273 depending on @xmath1 , but not on @xmath16 . + the singly differential cross section @xmath272 by bethe and heitler is appropriate for small @xmath5 ; it is ( bethe and heitler , 1934 ; heitler , 1944 ) @xmath274 with @xmath275 with the quantities as described in section [ brems_def ] . + geant 4 uses a fit formula which is appropriate for large @xmath5 ; it is ( agostinelli et al . , 2003 ) @xmath276 where @xmath277 is a constant which is not specified in the geant 4 documentation , nor in the source code . @xmath278 is defined as @xmath279 where @xmath280 is the kinetic energy of the incident electron . @xmath281 and @xmath282 are defined as @xmath283 with @xmath284 , @xmath285 and @xmath286 where @xmath287 is the ratio between the photon energy and the total energy of the incident electron . + @xmath288 and @xmath289 in ( [ geant.2 ] ) are defined as @xmath290 with @xmath291 . the @xmath292 are directly defined in the geant 4 source code as @xmath293^{\frac{1}{3}}\left(a_{hj,1}+[z(z+1)]^{\frac{1}{3}}a_{hj,2}\right),\ j\in\{1,2,3\ } , \nonumber \\ \label{geant.9 } \\ b_{hj}&=&b_{hj,0}[z(z+1)]^{\frac{1}{3}}\left(b_{hj,1}+[z(z+1)]^{\frac{1}{3}}b_{hj,2}\right),\ j\in\{1,2,3\ } , \nonumber \\ \label{geant.10 } \\ a_{lj}&=&a_{lj,0}[z(z+1)]^{\frac{1}{3}}\left(a_{lj,1}+[z(z+1)]^{\frac{1}{3}}a_{lj,2}\right),\ j\in\{1,2,3\ } , \label{geant.11 } \\ b_{lj}&=&b_{lj,0}[z(z+1)]^{\frac{1}{3}}\left(b_{lj,1}+[z(z+1)]^{\frac{1}{3}}b_{lj,2}\right),\ j\in\{1,2,3\ } , \label{geant.12 } \end{aligned}\ ] ] where all the coefficients are also defined in the source code : + @xmath294 with @xmath295 and @xmath296 . in ( [ geant.13 ] ) - ( [ geant.16 ] ) the first index denotes columns , the second one denotes rows . + ) and ( [ geant.1 ] ) as a function of the kinetic energy @xmath297 of the incident electron for @xmath3 ( nitrogen ) and for fixed photon energy a ) @xmath205 kev , b ) @xmath159 kev and c ) @xmath298 mev.,title="fig : " ] ) and ( [ geant.1 ] ) as a function of the kinetic energy @xmath297 of the incident electron for @xmath3 ( nitrogen ) and for fixed photon energy a ) @xmath205 kev , b ) @xmath159 kev and c ) @xmath298 mev.,title="fig : " ] + a ) @xmath205 kev b ) @xmath159 kev + ) and ( [ geant.1 ] ) as a function of the kinetic energy @xmath297 of the incident electron for @xmath3 ( nitrogen ) and for fixed photon energy a ) @xmath205 kev , b ) @xmath159 kev and c ) @xmath298 mev.,title="fig : " ] + c ) @xmath298 mev figure [ comp.fig ] compares the bethe heitler cross section ( [ bethe.1 ] ) with that of geant 4 ( [ geant.1 ] ) where we have chosen @xmath299 for all energies in such a way that the orders of magnitude of ( [ bethe.1 ] ) and ( [ geant.1 ] ) agree with each other . it shows that ( using exactly the values provided in the source code of geant 4 ) that there is a good quantitative and qualitative agreement for electron energies of @xmath300 mev and @xmath301 mev . but above and below that , both cross sections certainly differ . + that is because geant 4 was developed for high energy energy physics in particle accelerators and thus for high atomic numbers . thus the cross sections used in geant 4 are not appropriate to describe the production of bremsstrahlung photons in air . the bethe - heitler theory for the energy range we consider , is used for small atomic numbers . + geant 4 also includes dielectric suppression , i.e. the suppression of the emission of lowly energetic photons because of their interaction with the electrons of the background medium ( ter - mikaelian , 1954 ) , and the landau - pomeranchuk - migdal ( lpm ) effect ( landau and pomeranchuk , 1953 ) , i.e. the suppression of photon production due to the multiple scattering of electrons . + the influence of the dielectric effect can be estimated by @xmath302 where @xmath303 is the density of free electrons . for densities between @xmath304 m@xmath305 and @xmath306 m@xmath305 , @xmath278 is almost @xmath130 . ( [ dielec.1 ] ) vs. the photon energy for different electron energies for a ) @xmath307 m@xmath305 and b ) @xmath308 m@xmath305,title="fig : " ] ( [ dielec.1 ] ) vs. the photon energy for different electron energies for a ) @xmath307 m@xmath305 and b ) @xmath308 m@xmath305,title="fig : " ] a ) @xmath307 m@xmath305 b ) @xmath309 m@xmath305 figure [ dielec_fig ] shows ( [ dielec.1 ] ) for different photon energies , electron energies and densities . dielectric suppression has a very small effect when @xmath310 gev ; thus it can be neglected . + the lpm effect is not important , either . the lpm threshold energy is @xmath311 ev ( bertou et al . , 2000 ) ; this is much higher than typical energies of electrons in the atmosphere . + the preimplemented cross sections used in geant 4 are supposed to be used for high electron energies @xmath312 mev and high atomic numbers @xmath5 . in the case of tgfs it is necessary to treat electron energies in the kev and mev range and small atomic numbers where the lpm effect and dieletric suppression are not significant . figure [ leht.fig ] shows the comparison of ( [ theta.16 ] ) and ) of the integration of ( [ bcs.1 ] ) for different electron energies ( @xmath3 ) : doubly differential cross section versus the scattering angle @xmath1 between incident electron and emitted photon . the ratio between the photon energy @xmath0 and the kinetic electron energy @xmath297 is fixed to 0.001% and 90% . the born approximation ( [ born.2 ] ) is valid in all cases . , title="fig : " ] ) of the integration of ( [ bcs.1 ] ) for different electron energies ( @xmath3 ) : doubly differential cross section versus the scattering angle @xmath1 between incident electron and emitted photon . the ratio between the photon energy @xmath0 and the kinetic electron energy @xmath297 is fixed to 0.001% and 90% . the born approximation ( [ born.2 ] ) is valid in all cases . , title="fig : " ] + a ) @xmath164 kev , @xmath313 b ) @xmath164 kev , @xmath314 + ) of the integration of ( [ bcs.1 ] ) for different electron energies ( @xmath3 ) : doubly differential cross section versus the scattering angle @xmath1 between incident electron and emitted photon . the ratio between the photon energy @xmath0 and the kinetic electron energy @xmath297 is fixed to 0.001% and 90% . the born approximation ( [ born.2 ] ) is valid in all cases . , title="fig : " ] ) of the integration of ( [ bcs.1 ] ) for different electron energies ( @xmath3 ) : doubly differential cross section versus the scattering angle @xmath1 between incident electron and emitted photon . the ratio between the photon energy @xmath0 and the kinetic electron energy @xmath297 is fixed to 0.001% and 90% . the born approximation ( [ born.2 ] ) is valid in all cases . , title="fig : " ] + a ) @xmath165 mev , @xmath313 b ) @xmath165 mev , @xmath314 + the doubly differential cross section used by lehtinen . lehtinen uses a product ansatz for the angular and the frequency part ; here the angular part is a non - quantum mechanical expression taken from @xcite . this cross section is only valid if @xmath315 . there is a good agreement for low ratios between photon and electron energy , but a large deviation for larger ratios . therefore this cross section is not appropriate for high ratios needed to obtain photons with energies up to several tens of mev to determine the high energy tail of the tgf spectrum where almost all electron energy is converted into photon energy . dwyer ( 2007 ) uses the triply differential cross section by bethe and heitler ( 1934 ) , but with an additional form factor @xmath316 parameterizing the structure of the nucleus @xcite . @xmath317 is defined as @xmath318 where @xmath5 is the atomic number and @xmath319 the charge density @xmath320 with @xmath321 where @xmath322 is the reduced compton wave length of the electron . the delta function describes the nucleus itself and the debye term describes the electrons of the shell . performing the fourier transformation in ( [ form.1 ] ) gives @xmath323 with @xmath41 as in eq . ( [ bcs.7 ] ) . we calculated the value of @xmath316 for different angles , electron and photon energies [ a ) @xmath166 kev , @xmath205 kev , @xmath324 ; b ) @xmath166 kev , @xmath325 kev , @xmath326 ; c ) @xmath163 mev , @xmath298 mev , @xmath327 and d ) @xmath328 mev , @xmath205 mev , @xmath329 . in all these cases the atomic form factor is 1 . hence , it can be neglected . as it makes the integration over @xmath7 and @xmath6 more complicated , it is useful not to use @xmath316 . as equation ( [ theta.16 ] ) is rather complicated , it is interesting to see which terms have the most important contribution . ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a semilog plot for different electron and photon energies ( @xmath3).,title="fig : " ] ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a semilog plot for different electron and photon energies ( @xmath3).,title="fig : " ] + a ) @xmath166 kev , @xmath298 kev b ) @xmath166 kev , @xmath330 kev + ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a semilog plot for different electron and photon energies ( @xmath3).,title="fig : " ] ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a semilog plot for different electron and photon energies ( @xmath3).,title="fig : " ] + c ) @xmath163 mev , @xmath159 kev d ) @xmath163 mev , @xmath331 mev ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a linear plot for different electron and photon energies ( @xmath3).,title="fig : " ] ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a linear plot for different electron and photon energies ( @xmath3).,title="fig : " ] + a ) @xmath166 kev , @xmath298 kev b ) @xmath166 kev , @xmath330 kev + ) - ( [ theta.22 ] ) to ( [ theta.16 ] ) in a linear plot for different electron and photon energies ( @xmath3).,title="fig : " ] + c ) @xmath163 mev , @xmath159 kev figure [ contr_fig.1 ] shows the contribution of all parts to the final result in a logarithmic scale while fig . [ contr_fig.2 ] shows the same in a linear scale . in all cases , i.e. low and high electron energies and low and high ratios between @xmath0 and @xmath297 , the main contribution comes from ( [ theta.19 ] ) . it is important to state that not all contributions can be seen in figure [ contr_fig.1 ] because some of the terms have negative values which , however , are shown in figure [ contr_fig.2 ] . so one might think that for @xmath166 kev and @xmath298 kev , equation ( [ theta.22 ] ) has the largest contribution , but as figure [ contr_fig.2 ] shows , ( [ theta.21 ] ) has nearly the same absolute value , but opposite sign ; therefore they cancel . thus the third integral ( [ theta.19 ] ) is the most important one . the same holds for other electron energies and ratios between @xmath0 and @xmath297 . we conclude that ( [ theta.19 ] ) is the dominant contribution for all relevant parameter values . one can also gain information on the scattering angle @xmath1 for high electron energies from the conservation of energy and momentum , @xmath332 where @xmath333 and @xmath334 are the energy and the momentum of the electron in the initial and final state . @xmath11 is the momentum of the photon which is related to its energy @xmath0 through @xmath335 and @xmath336 and @xmath41 are the energy and the momentum of the virtual photon between electron and nucleus . @xmath41 changes the momentum of the nucleus . but the contribution to the kinetic energy can be neglected ; thus @xmath337 and @xmath338 squaring ( [ cons.6 ] ) and using @xmath339 , the angle @xmath1 is : @xmath340 by using ( [ cons.5 ] ) and the relativistic energy - momentum relation ( [ bcs.2 ] ) we get an expression for the momentum of the electron in the final state @xmath341 which leads to @xmath342 although this is an analytical expression for the scattering angle @xmath1 one should take into account that it depends on the vector @xmath41 of the virtual photon which is not known in forehand . thus , depending on @xmath41 , only a statistical statement can be made about @xmath1 . + it is , however , possible to investigate the limit of ( [ cons.9 ] ) for high electron energies which yields @xmath343 as @xmath344 $ ] and @xmath345 we can conclude that @xmath346 especially for @xmath347,@xmath348 , i.e. , the photon is mainly emitted in forward direction . + if , additionally , the photon energy @xmath0 also increases more and more ( for high electron energies ) it is @xmath349 thus @xmath350 hence , we conclude from simple considerations about energy and momentum conservation that the photon is mainly scattered in forward direction if the energies of electron and photon are both very high . in order to obtain ( [ disc.9 ] ) we calculate the derivative of ( [ limit.7 ] ) after @xmath1 : @xmath351 \nonumber\\ \label{disc.5}\end{aligned}\ ] ] with definition ( [ limit.3 ] ) for @xmath352 . in order to calculate the extrema one has to set equation ( [ disc.5 ] ) equal to zero : @xmath353 ( e_i - c|\mathbf{p}_i|\cos\theta_i)^3 \nonumber\\ & + & \delta(\theta_i)\left[2(e_i\cos\theta_i -c|\mathbf{p}_i|)(4e_f^2+\delta(\theta_i)c^2 ) \right . \nonumber \\ & -&2\hbar c\omega|\mathbf{p}_i|\sin^2\theta_i ( e_i - c|\mathbf{p}_i|\cos\theta_i ) \nonumber \\ & + & \frac{2\hbar^2\omega^2}{e_f}\left(2\cos\theta_i ( e_i - c|\mathbf{p}_i|\cos\theta_i)^2 \right . \nonumber\\ & -&\left.\left.c|\mathbf{p}_i|\sin^2\theta_i(e_i - c|\mathbf{p}_i|\cos\theta_i)\right)\right ] . \label{disc.6}\end{aligned}\ ] ] as @xmath354 , expression ( [ disc.6 ] ) is quartic in @xmath355 ; therefore ( [ disc.6 ] ) can be solved analytically in principle , but the solution will be long and complicated . figure [ disc_fig.1 ] also shows that the angles for maximal scattering are very small for relativistic electrons , therefore one can approximate @xmath356 and @xmath357 . this leads to @xmath358 and @xmath359 \nonumber\\ & + & \delta_0 \left[2(4e_f^2+\delta_0c^2)-2\hbar c\omega|\mathbf{p}_i|\theta_i^2 + \frac{2\hbar^2\omega^2}{e_f}\left(2(e_i - c|\mathbf{p}_i|)-c|\mathbf{p}_i| \theta_i^2\right)\right ] \nonumber \\ \label{disc_app.8}\end{aligned}\ ] ] with solution @xmath194 -|\mathbf{p}_i|\delta_0c-\frac{\hbar\omega}{e_f}c|\mathbf{p}_i|\delta_0 } } \label{disc_app.9}\end{aligned}\ ] ] xxx99 s. agostinelli et al . , 2003 . g4-a simulation toolkit . methods phys . res . , sect . 250 - 303 h. aiginger , 1966 . elektron - bremsstrahlungwirkungsquerschnitte von 180 und 380 kev - elektronen . zeitschrift fuer physik , vol . 8 - 25 l. p. babich , 2003 . high - energy phenomena in electric discharges in dense gases . theory , experiment and natural phenomena . istc science and technology series , vol . 2 futurepast xavier bertou et al . , lpm effect and pair production in the geomagnetic field : a signature of ultra - high energy photons in the pierre auger observatory , astro . 121 - 130 h. a. bethe and w. heitler , 1934 . on the stopping of fast particles and on the creation of positive electrons . london , vol . 146 , pp . 83 - 112 m. briggs et al . , 2010 . first results on terrestrial gamma ray flashes from the fermi gamma - ray burst monitor . j. geophys . 115 , a07323 m. s. briggs et al . , 2011 . electron - positron beams from terrestrial lightning observed with fermi gbm . 38 , l02808 b. e. carlson , n. g. lehtinen and u. s. inan , 2009 . terrestrial gamma ray flashes production by lightning current pulses . j. geophys . 114 , a00e08 b. e. carlson , n. g. lehtinen and u. s. inan , 2010 . terrestrial gamma ray flash production by active lightning leader channels . j. geophys . 115 , a10324 o. chanrion and t. neubert , 2008 . a pic - mcc code for simulation of streamer propagation in air . j. comput . 7222 - 7245 o. chanrion and t. neubert , 2010 . production of runaway electrons by negative streamer discharges . j. geophys . 115 , a00e32 d.e . cullen , s.t . perkins and s.m . seltzer , 1991 . tables and graphs of electron interaction cross 10 ev to 100 gev derived from the llnl evaluated electron data library ( eedl ) , z = 1 - 100 . lawrence livermore national laboratory , ucrl-50400 , vol . 31 s. a. cummer , y. zhai , w. hu , d. m. smith , l. i. lopez , m. a. stanley , 2005 . measurements and implications of the relationship between lightning and terrestrial gamma ray flashes . 32 , l08811 j. r. dwyer , 2003 . a fundamental limit on electric fields in air . geophys . 2055 j. r. dwyer and d. m. smith , 2005 . a comparison between monte carlo simulations of runaway breakdown and terrestrial gamma - ray flashes . 32 , l22804 j. r. dwyer et al . , 2005a . x - ray bursts associated with leader steps in cloud - to - ground lightning . geophys . 32 , l01803 j. r. dwyer et al . , 2005b . x - ray bursts produced by laboratory sparks in air . 32 , l20809 j. r. dwyer , 2007 . relativistic breakdown in planetary atmospheres , physics of plasmas . 042901 j. r. dwyer et al . , 2008a . a study of x - ray emission from laboratory sparks in air at atmospheric pressure . j. geophys . 113 , d23207 j. r. dwyer et al . , 2008b . high - energy electron beams launched into space by thunderstorms . 35 , l02815 j. r. dwyer , 2012 . the relativistic feedback discharge model of terrestrial gamma ray flashes . journal of geophy . res . - space phys . 117 , a02308 g. elwert and e. haug , 1969 . calculation of bremsstrahlung cross sections with sommerfeld - maue eigenfunctions . 183 , pp . 90 - 105 j. k. fink and r. h. pratt , 1973 . use of furry - sommerfeld - maue wave functions in pair production and bremsstrahlung . a , vol . 7 , pp . 392 - 403 g. j. fishman et al . , 1994 . discovery of intense gamma - ray flashes of atmospheric origin . science , vol . 1313 - 1316 i. gallimberti et al . , 2002 . fundamental processes in long air gap discharges . c. r. physique , vol . 1335 - 1359 t. gjesteland , n. ostgaard , a.b . collier , b.e . carlson , m.b . cohen , n.g . lehtinen , 2011 . confining the angular distribution of terrestrial - gamma ray flash emission . j. geophys . 116 , a11313 b. w. grefenstette , d. m. smith , b. j. hazelton and l. i. lopez , 2009 . first rhessi terrestrial gamma ray flash catalog . j. geophys . 114 , a02314 w. greiner and j. reinhardt , 1995 . quantenelektrodynamik , verlag harri deutsch a. v. gurevich , 1961 . on the theory of runaway electrons . soviet physics jetp - ussr , vol . 904 - 912 a. v. gurevich , g. milikh , r. roussel - dupr , 1992 . runaway electron mechanism of air breakdown and preconditioning during a thunderstorm . 463 - 468 a. v. gurevich and k. p. zybin , 2001 . runaway breakdown and electric discharges in thunderstorms . physics - uspekhi , vol . 44 , pp . 1119 - 1140 w. heitler , 1944 . the quantum theory of radiation . oxford university press p.v.c . hough , 1948 . the angular distribution of pair - produced electrons and bremsstrahlung . 74 , pp . 80 - 86 u. s. inan and n. g. lehtinen , 2005 . production of terrestrial gamma - ray flashes by an electromagnetic pulse from a lightning return stroke . 32 , l19818 j. d. jackson , 1975 . classical electrodynamics . john wiley & sons h. w. koch and j. w. motz , 1959 . bremsstrahlung cross - section formulas and related data . phys . , vol . 920 - 956 i. d. kostyrya , v. f. tarasenko , a. n. tkachev and s. i. yakovlenko , 2006 . x - ray radiation due to nanosecond volume discharges in air under atmospheric pressure . 356 - 361 l. landau and i. pomeranchuk , 1953 . nauk sssr , vol . 535 - 536 n.g . lehtinen , 2000 . relativistic runaway electrons above thunderstorms . ph.d . thesis , stanford university , stanford , ca c. li , w. j. m. brok , u. ebert and j. j. a. m. van der mullen , 2007 . deviations from the local field approximation in negative streamer heads . 123305 c. li , u. ebert and w. hundsdorfer , 2009 . 3d hybrid computations for streamer discharges and production of runaway electrons . 202003 c. li , u. ebert and w. hundsdorfer , 2010 . spatially hybrid computations for streamer discharges with generic features of pulled fronts : i. planar fronts . j. comput . 200 - 220 g. lu , s. a. cummer , j. li , f. han , d. m. smith and b. grefenstette , 2011 . characteristics of broadband magnetic lightning emissions associated with terrestrial gamma - ray flashes . j. geophys . 116 , a03316 v. march and j. montany , 2010 . influence of the voltage - time derivative in x - ray emission from laboratory sparks . 37 , l19801 m. marisaldi et . al . , 2010 . detection of terrestrial gamma ray flashes up to 40 mev by the agile satellite . j. geophys . 115 , a00e13 g. milikh and r. roussel - dupr , 2010 . runaway breakdown and electrical discharges in thunderstorms . j. geophys . 115 , a00e60 c. b. moore , k. b. eack , g. d. aulich and w. rison , 2001 . energetic radiation associated with lightning stepped - leaders . 2141 - 2144 g. d. moss , v. p. pasko , n. y. liu and g. veronis , 2006 . monte carlo model for analysis of thermal runaway electrons in streamer tips in transient luminous events and streamer zones of lightning leaders . j. geophys . res . , vol . 111 , a02307 w. nackel , 1994 . the elementary process of bremsstrahlung . rep . , vol . 317 - 353 c. v. nguyen , a. p. j. van deursen and ute ebert , 2008 . multiple x - ray bursts from long discharges in air . d - appl . phys . , 234012 c. v. nguyen , a. p. j. van deursen e. j. m. van heesch and g. j. j. winands , 2010 . x - ray emission in streamer - corona plasma . 025202 p. e. penczynski and h. l. wehner , 1970 . measurement of the energetic and angular dependence of the external bremsstrahlung asymmetry . z. physik , vol . 237 , pp . 75 - 85 m. e. peskin and d. v. schroeder , 1995 . an introduction to quantum field theory , westview press a. v. phelps , b. m. jelenkovic and l. c. pitchford , 1987 . simplified models of electron excitation and ionizattion at very high e / n . phys . rev . a , vol . 5327 m. rahman , v. cooray , n. a. ahmad , j. nyberg , v. a. rakov and s. sharma , 2008 . x - rays from 80 cm long sparks in air . geophys . 35 , l06805 a. g. repev and p. b. repin , 2008 . spatiotemporal parameters of the x - ray radiation from a diffuse atmospheric - pressure discharge . 53 , pp . 73 - 80 s.m.seltzer and m.j.berger , 1985 . bremsstrahlung spectra from electron interactions with screened atomic nuclei and orbital electrons . inst . meth . 95 - 134 c. d. shaffer , x. m. tong and r. h. pratt , 1996 . triply differential cross section and polarization correlations in electron bremsstrahlung emission . 4158 - 4163 c. d. shaffer and r. h. pratt , 1997 . comparison of relativistic partial - wave calculations of triply differential electron - atom bremsstrahlung with simpler theories . . a , vol . 3653 - 3658 t. shao , c. zhang , z. niu , p. yan , v. f. tarasenko , e. k. baksht , a. g. burahenko and y. b. shutko , 2011 . diffuse discharge , runaway electron , and x - ray in atmospheric pressure air in a inhomogeneous electrical field in repetitive pulsed modes . appl . 021506 d. m. smith , l. i. lopez , r. p. lin and c. p. barrington - leigh , 2005 . terrestrial gamma - ray flashes observed up to 20 mev . science , vol . 1085 - 1088 d. m. smith et al . terrestrial gamma ray flashes correlated to storm phase and tropopause height . j. geophys . 115 , a00e49 d. m. smith , j. dwyer , b. hazelton , b. greffenstette , g. f. m. martinez - mckinney , z. zhang , a. lowell , n. kelley , m. splitt , s. lazarus , w. ulrich , m. schaal , z. saleh , e. cramer , h. rassoul , s.a . cummer , g. lu and r. blakeslee , 2011 . the rarity of terrestrial gamma - ray flashes . 38 , l08807 y. l. stankevich and v. g. kalinin , 1967 . fast electrons and x - ray radiation during the initial stage of growth of a pulsed spark discharge in air . 1042 - 1043 m. tavani et al . , 2011 . terrestrial gamma - ray flashes as powerful particle accelerators . 018501 m. l. ter - mikaelian , 1954 . nauk sssr , vol . 94 , p 1033 t. torii , t. nishijima , zl . kawasaki , t. sugita , 2004 . downward emission of runaway electrons and bremsstrahlung photons in thunderstorm electric fields . 31 , l05113 y - s . tsai , 1974 . phys , vol . 46 , p. 815 tsai , 1977 . phys , vol . 49 , p. 421 h. k. tseng and r. h. pratt , 1971 . exact screened calculations of atomic - field bremsstrahlung . rev . a , vol . 100 - 115 h. tsuchiya , t. enoto , s. yamada , t. yuasa , k. nakazawa , t. kitaguchi , m. kawaharada , m. kokubun , h. kato , m. okano , k. makishima , 2011 . long - duration gamma ray emissions from 2007 and 2008 winter thunderstorms . j. geophys . 116 , d09113 c. wilson , 1925 . the electric field of a thundercloud and some of its effects . london , vol . 37a , pp . 32d-37d w. xu , s. celestin and v. p. pasko , 2012 . source altitudes of terrestrial gamma - ray flashes produced by lightning leaders , geophys . 39 , l08801 * christoph khn * studied physics in kiel and hamburg , germany from 2005 till 2010 . after having finished his diploma thesis on six - dimensional supergravity , he started his phd studies at cwi amsterdam , the netherlands . + * ute ebert * studied physics at the university of heidelberg , germany , and she wrote her phd thesis at the university of essen , germany . after a postdoc period at the university of leiden , netherlands , she became staff member at cwi amsterdam , netherlands . since 2002 she leads a research group at cwi and is part time professor at eindhoven university of technology . the research of her group concentrates on transient electrical discharges , both in plasma technology and in atmospheric electricity . + * analytical results on doubly differential cross - sections for typical tgf parameters * distribution of emission angles and energies for bremsstrahlung photons * distribution of emission angles and energies for positrons in pair production * c++ code with the analytical cross section results provided

within thunderstorms electrons can gain energies of up to hundred(s ) of mev . these electrons can create x - rays and gamma - rays as bremsstrahlung when they collide with air molecules . here we calculate the distribution of angles between incident electrons and emitted photons as a function of electron and photon energy . we derive these doubly differential cross - sections by integrating analytically over the triply differential cross - sections derived by bethe and heitler ; this is appropriate for light atoms like nitrogen and oxygen ( z=7,8 ) if the energy of incident and emitted electron is larger than 1 kev . we compare our results with the approximations and cross section used by other authors . we also discuss some simplifying limit cases , and we derive some simple approximation for the most probable scattering angle . we also provide cross sections for the production of electron positron pairs from energetic photons when they interact with air molecules . this process is related to the bremsstrahlung process by some physical symmetry . therefore the results above can be transferred to predictions on the angles between incident photon and emitted positron , again as a function of photon and positron energy . we present the distribution of angles and again a simple approximation for the most probable scattering angle . our results are given as analytical expressions as well as in the form of a c++ code that can be directly be implemented into monte carlo codes . bremsstrahlung , pair production , analytical integration of bethe - heitler equation , distribution of scattering angles

respiratory dysfunction in stroke patients is caused by weakening of the trunk and respiratory muscles and reduced physical activity due to loss of normal postural control resulting from a lesion in the central nervous system . because weakening of respiratory muscles decreases exercise endurance , functional locomotion , and independent walking ability , strengthening of respiratory muscle plays an important role in the functional recovery of post - stroke patients . post - stroke patients have partial or total weakening of the diaphragm , intercostal , and abdominal muscles on the affected side . there is also a significant decrease in maximal respiratory pressure in post - stroke patients compared with that in healthy individuals . about 40% of stroke patients show a reduction in diaphragm displacement and a decrease in lung function to 50% of the age - expected values . both residual volume ( rv ) and vital capacity ( vc ) are affected , leading to respiratory muscle weakness . recent research reported that inspiratory muscle training is effective in improving activities of daily living , walking ability , quality of life , respiratory muscle strength , and endurance in stroke patients . thus , assessment of respiratory muscle strength may be useful to monitor the improvement in patient health over time , identify those at risk of hypoventilation , and determine the impact of respiratory muscle training , and can assess respiratory muscle weakness and quantify its severity . maximal inspiratory pressure ( mip ) is a widely used , clinically relevant indicator of the effect of respiratory training . the mip is generated during the mller maneuver , which involves a forced expiration , followed by an attempt at inspiration made with the mouth and nose closed , which leads to a negative pressure in the chest and lungs . it is the volitional force output of the inspiratory muscles working in synergy , and is an established and reliable measure of global inspiratory muscle strength . previous studies have reported that respiratory muscle training improves muscle function in acute stroke patients and inspiratory muscular weakness is evident in chronic stroke survivors . however , data on the reliability of measurements used in inspiratory muscle training and respiratory functions for post - stroke patients are lacking . peak inspiratory flow ( pif ) , at a given volume , depends on the airway caliber as well as the strength and speed of shortening of the inspiratory muscles . the muscle - training device is an electronic inspiratory loading device , and can provide automatically processed information for the mip , pif , and vc during loaded breathing tasks . the purpose of this study was to determine the intra- and inter - reliability for measurement of pulmonary function values , mip , pif and vc . our hypothesis is that the electronic inspiratory loading device is sufficiently reliable for pulmonary function tests in post - stroke patients . fifty post - stroke patients from the m rehabilitation hospital in seoul , republic of korea , volunteered and participated in this study . a physical assessment and interview were initially conducted with all individuals to collect anthropometric and demographic data ( gender , age , height , weight , body mass index [ bmi ] , affected side , onset time of stroke , and use of medications ) . a questionnaire was administered to gather information related to the work environment , smoking history , recent respiratory infections , and the presence or absence of lung and heart disease . the data were used as parameters for both the analyses and interpretation of the pulmonary function tests . the inclusion criteria were as follows : no history of cardiovascular or respiratory problems , first episode of unilateral stroke with hemiparesis during the previous 6 months , mini mental status evaluation score > 24 , no facial palsy , no receptive aphasia , and no prior thoracic or abdominal surgery . the exclusion criteria were as follows : use of medications that could affect neuromuscular control or provoke drowsiness , evidence of restrictive lung disease based on lung volumes , history of asthma , and use of psychotropic drugs or alcohol abuse . the study s protocol was approved by the institutional review board of the sahmyook university in seoul and participants gave signed consent after receiving verbal and written information about the study . examiner 1 had been a physical therapist for 2 years , and examiner 2 had been a physical therapist for 12 years . neither of the examiners had evaluated pulmonary function using the device in their rehabilitation clinic . before beginning the study , both examiners underwent 24 hours of specific training in educational and experimental methods for patients , with a professional instructor ( ph.d . ) experienced with the measurement protocol used in this study . two measurements were performed on the same day to assess inter - rater reliability and to ensure that the pulmonary function parameters were unchanged . after a week , 1 examiner measured the variables again at the same time of a day to assess intra - rater reliability . the measurements were performed in exactly the same way . the electronic inspiratory loading device ( powerbreathe k5 , 2010 , hab international ltd , uk ) was used to provide automatically processed information on pulmonary function ( mip , pif , and vc ) during loaded breathing tasks . subjects were comfortably seated in a chair with their feet on the ground , their back unsupported , and their trunk at a 90 angle to their hips . to record mip , participants were instructed to perform inspirations against an obstructed airway at near - rv . subjects could choose their own breathing frequency , but were instructed to perform forceful and deep inspirations followed by complete expirations . complete expiration was indicated by an acoustic signal provided by the handheld loading device upon cessation of flow . subjects performed a minimum of 3 efforts and the value used was the best of these . subjects were allowed to practice twice and immediately afterwards were asked to repeat the trial until 3 acceptable measurements were obtained . measurements were considered acceptable if they were maintained , without an air leak , for duration of at least 1 second and if 2 readings were taken with a maximum difference of 10% . between the measurements , 20 minutes of break time was given to patients to minimize the bias for the mip , pif , and vc due to inter - rater reliability test . signals from the pneumotachograph were captured electronically using j - lab software version 5.22.1.50 ( cardinal health gmbh , hoechberg , germany ) . to describe the intra- and inter - rater reliability of the electronic inspiratory loading device for pulmonary functions , intra - class correlation coefficients ( iccs ) were calculated for mip , pif , and vc . iccs of the type ( 3 , 1 ) were used to evaluate the inter - rater reliability and type ( 1 , 1 ) for intra - rater reliability . bland - altman plots and 95% confidence intervals ( cis ) are given to provide a visual representation of pressure and volume and to determine the agreement between the 2 measurements . icc and bland - altman plots have been advocated as the statistical methods of choice in reliability studies . iccs 0.25 were considered poor , 0.260.49 low , 0.500.69 moderate , 0.700.89 high , and 0.901.00 very high . if the slope of the scatter plot of 2 variables in bland - altman plot is y=0 , the 2 tests will have little error . to assess measurement , standard error of measurement ( sem ) the 95% minimal detectable change ( mdc ) was calculated as 1.96 * sem * 2 . sem and mdc are often used to determine the standard error of the measurement ; their reliability ensures the accuracy and precision of the smaller observed standard error of the measured variable . results were considered significant at p<0.05 , and statistical analyses were performed using spss ( version 18.0 ) . fifty post - stroke patients from the m rehabilitation hospital in seoul , republic of korea , volunteered and participated in this study . a physical assessment and interview were initially conducted with all individuals to collect anthropometric and demographic data ( gender , age , height , weight , body mass index [ bmi ] , affected side , onset time of stroke , and use of medications ) . a questionnaire was administered to gather information related to the work environment , smoking history , recent respiratory infections , and the presence or absence of lung and heart disease . the data were used as parameters for both the analyses and interpretation of the pulmonary function tests . the inclusion criteria were as follows : no history of cardiovascular or respiratory problems , first episode of unilateral stroke with hemiparesis during the previous 6 months , mini mental status evaluation score > 24 , no facial palsy , no receptive aphasia , and no prior thoracic or abdominal surgery . the exclusion criteria were as follows : use of medications that could affect neuromuscular control or provoke drowsiness , evidence of restrictive lung disease based on lung volumes , history of asthma , and use of psychotropic drugs or alcohol abuse . the study s protocol was approved by the institutional review board of the sahmyook university in seoul and participants gave signed consent after receiving verbal and written information about the study . examiner 1 had been a physical therapist for 2 years , and examiner 2 had been a physical therapist for 12 years . neither of the examiners had evaluated pulmonary function using the device in their rehabilitation clinic . before beginning the study , both examiners underwent 24 hours of specific training in educational and experimental methods for patients , with a professional instructor ( ph.d . ) experienced with the measurement protocol used in this study . two measurements were performed on the same day to assess inter - rater reliability and to ensure that the pulmonary function parameters were unchanged . after a week , 1 examiner measured the variables again at the same time of a day to assess intra - rater reliability . the electronic inspiratory loading device ( powerbreathe k5 , 2010 , hab international ltd , uk ) was used to provide automatically processed information on pulmonary function ( mip , pif , and vc ) during loaded breathing tasks . subjects were comfortably seated in a chair with their feet on the ground , their back unsupported , and their trunk at a 90 angle to their hips . to record mip , participants were instructed to perform inspirations against an obstructed airway at near - rv . subjects could choose their own breathing frequency , but were instructed to perform forceful and deep inspirations followed by complete expirations . complete expiration was indicated by an acoustic signal provided by the handheld loading device upon cessation of flow . subjects performed a minimum of 3 efforts and the value used was the best of these . subjects were allowed to practice twice and immediately afterwards were asked to repeat the trial until 3 acceptable measurements were obtained . measurements were considered acceptable if they were maintained , without an air leak , for duration of at least 1 second and if 2 readings were taken with a maximum difference of 10% . between the measurements , 20 minutes of break time was given to patients to minimize the bias for the mip , pif , and vc due to inter - rater reliability test . signals from the pneumotachograph were captured electronically using j - lab software version 5.22.1.50 ( cardinal health gmbh , hoechberg , germany ) . to describe the intra- and inter - rater reliability of the electronic inspiratory loading device for pulmonary functions , intra - class correlation coefficients ( iccs ) were calculated for mip , pif , and vc . iccs of the type ( 3 , 1 ) were used to evaluate the inter - rater reliability and type ( 1 , 1 ) for intra - rater reliability . bland - altman plots and 95% confidence intervals ( cis ) are given to provide a visual representation of pressure and volume and to determine the agreement between the 2 measurements . icc and bland - altman plots have been advocated as the statistical methods of choice in reliability studies . iccs 0.25 were considered poor , 0.260.49 low , 0.500.69 moderate , 0.700.89 high , and 0.901.00 very high . if the slope of the scatter plot of 2 variables in bland - altman plot is y=0 , the 2 tests will have little error . to assess measurement , standard error of measurement ( sem ) the 95% minimal detectable change ( mdc ) was calculated as 1.96 * sem * 2 . sem and mdc are often used to determine the standard error of the measurement ; their reliability ensures the accuracy and precision of the smaller observed standard error of the measured variable . results were considered significant at p<0.05 , and statistical analyses were performed using spss ( version 18.0 ) . a summary of results for intra - rater reliability between examiners for the 3 sessions is given in table 2 . the iccs for mip , pif , and vc were 0.986 , 0.992 , and 0.959 , respectively . a summary of results for inter - rater reliability between tests for the 3 sessions performed is shown in table 3 . the iccs for mip , pif , and vc were 0.984 , 0.985 , and 0.933 , respectively . sem for mip , pif , and vc varied between 3.575 and 4.380 mmh2o , 0.003l / s and 0.057l / s , 0.122 and 0.179 , respectively , and 95% minimal detectable change ranged from 4.917 to 7.370 mmh2o for mip , 0.000 to 3.615l / s for pif , and 0.057 to 0.123 l / s for tlc . bland - altman plots indicated good agreement , and the plots for inter- and intra - rater reliability are shown in figure 1 . inspiratory muscle training has been used to investigate cardiopulmonary function and exercise tolerance for chronic and subacute post - stroke patients . following a stroke , patients experience respiratory dysfunction because of reduction in vital capacity , inspiratory capacity , total lung capacity , maximum inspiratory capacity , and expiratory reserve volume . furthermore , the efficiency of the unaffected muscles may be decreased due to instability of the chest wall and an inactive lifestyle . the aim of this study was to quantify the reliability of a respiratory muscle test device for assessing pulmonary function in post - stroke patients and to determine the implications of the results . the main finding suggests that the described protocols produce reliable measurements for most of the inspiratory muscle function tests considered . jandt et al . studied the relationship between trunk control , respiratory muscle strength , and pulmonary function in stroke patients , and found a positive correlation between trunk control and respiratory muscle strength , particularly in the case of the expiratory muscles . in a study involving individuals with multiple sclerosis , inspiratory muscle training significantly increased inspiratory muscle strength and resulted in generalized improvements in expiratory pulmonary function . in addition , inspiratory muscle training has been associated with breathing retraining and was found to be feasible and effective in patients with generalized myasthenia gravis . improvements in respiratory muscle strength , chest wall mobility , respiratory pattern , and respiratory endurance were also observed . however , other researchers have argued that there is insufficient evidence to support inspiratory muscle training as an effective treatment to improve function after stroke , and no evidence relating to the safety of inspiratory muscle training . although electronic inspiratory loading devices have previously been used to train and examine pulmonary function , their reliability when used with post - stroke patients has not been reported , and their clinical use to date has been limited . the current study evaluated the intra- and inter - rater reliability of measures of mip , pif , and vc , and found that the electronic inspiratory loading device had very high intra - rater reliability and very high inter - rater reliability . the 95% cis for the inter- and inter - rater reliability of mip were narrow ( 0.986 and 0.0.984 , respectively ) . similarly , the 95% cis for the intra- and inter - rater reliability of pif ( 0.992 and 0.985 , respectively ) and vc ( 0.959 and 0.933 , respectively ) were also narrow . the high inter- and intra - reliability for mip , pif , and vc suggests that the current study had high power . romer and mcconnell investigated the inter - test reliability of non - invasive measures of respiratory muscle function , and suggested that measures of maximum inspiratory and expiratory pressure and flow all had good reliability . reported the reliability of a threshold - loading device in healthy subjects and in patients with chronic obstructive pulmonary disease ( copd ) . in both groups , only small variations in pressure were observed despite large variations in flow . the threshold is a reliable and reproducible device for loading inspiratory muscles in patients with copd as well as in healthy subjects , and , similar to previous studies , showed good inter - rater ( 0.8810.992 ) and intra - rater ( 0.9280.992 ) reliability . however , these reliabilities ranged from high to very high and the results showed that the procedure for the respiratory muscle test was compromised to increase reliabilities . when sem is less than 10% of the mean value and mdc is less than 20% of the measured value , they are reliable because the measurement error is estimated low . in the present study , sem values of mip , pif , and vc were less than 10% of the average measured values . also , mdc values appeared to be less than 10% of all the 3 variables and they increased the confidence level . to use electronic inspiratory loading devices for rehabilitation in post - stroke patients , high and constant intra- and inter - reliability during inspiration training with patients is very important . the results of pulmonary function tests for the mip , pif and vc can be affected by the examiner s experience . in the current study , although the 2 examiners had clinical careers of different durations , the intra - examiner reliability was high to very high in both cases . these results show that following a consistent procedure might be adequate for the measurement of pulmonary function , despite differences in clinical experience . therefore , the pulmonary function test device can be useful in goal - setting for post - stroke patients even when it is performed by therapists with different experience . first , the findings of this study are valid in post - stroke patients only and may not necessarily be generalizable to other patients . further studies should be conducted with other patients who have impaired pulmonary function and weakened inspiratory muscles to investigate the effect of respiratory muscle training on pulmonary function . intra- and inter - rater reliability of this study confirm previous results and indicate that mip , pif , and vc can be reliably measured with an electronic inspiratory loading device , even by newly trained physical therapists . the smaller inter - rater reliability could be explained by the operator - dependence of this device . the potential use of electronic inspiratory loading device in clinical evaluation of the mip , pif , and vc remains unknown , but this study provides a basis for future research in clinical populations .

backgroundthe purpose of this study was to examine the inter- and intra - rater reliability of an electronic inspiratory loading device for the assessment of pulmonary functions : maximum inspiratory pressure , peak inspiratory flow , and vital capacity.material/methodssubjects were 50 patient volunteers in a rehabilitation hospital who had experienced their first episode of unilateral stroke with hemiparesis during the previous 6 months ( 26 men , 24 women ; mean age [ sd ] , 55.96 [ 12.81 ] years ) , with no use of medications that could induce drowsiness , evidence of restrictive lung disease , history of asthma , use of psychotropic drugs , or alcohol consumption habit.maximum inspiratory pressure , peak inspiratory flow , and vital capacity for pulmonary functions were assessed using an electronic inspiratory loading device ( powerbreathe , k5 , 2010 ) by 2 examiners , with patients in an unassisted sitting position , and 1 examiner re - assessed with same patients at the same time of a day after 1 week . intra - class correlation coefficients were used to assess reliability.resultsintra-rater reliability ranged from intra - class correlation coefficients ( iccs)=0.959 to 0.986 in variables . for the inter - rater reliability between 2 examiners , the iccs ranged from 0.933 to 0.985 . intra - rater and inter - rater reliability were good in variables ( maximal inspiratory pressure , peak inspiratory flow , and vital capacity).conclusionsthe intra- and inter - examiner reliability of the pulmonary function measurements , maximum inspiratory pressure , peak inspiratory flow , and vital capacity , for the post - stroke patients was very high . the results suggest that the electronic inspiratory loading device would be useful for clinical rehabilitative assessment of pulmonary function .

failure to grasp the rationale behind cleaning and shaping concepts can increase the incidence of procedural complications such as blockage , ledge formation , apical transportation and perforations . according to the glossary of endodontic terms of the american association of endodontists , canal transportation is defined as follows : removal of canal wall structure on the outside curve in the apical half of the canal due to the tendency of files to restore themselves to their original linear shape during canal preparation ; may lead to ledge formation and possible perforation . various undesirable apical preparation outcomes such as damage to the apical foramen , elbow formation , zip formation and perforation have been described as possible results of canal transportation . perforation represents a communication between the root canal space and the external root surface , causing irritation of the periradicular tissues . similar terms describing the shape of a zipped apical part of the root canal are an hourglass shape , a teardrop or a foraminal rip . it can result in a poorly cleaned root canal , which fails to provide a resistance form to compact gutta percha , and leads to obturation which is vertically overextended but internally under - filled . apical transportation can be categorized into : type 1 : represents a minor movement of the position of the physiologic foramen , resulting in its iatrogenic relocation . type ii : represents a moderate movement of the physiologic position of the foramen , resulting in a considerable iatrogenic relocation on the external root surface . in this type , a larger communication with the periapical space exists , and attempt to create a more coronal shape may weaken or perforate the root . type iii : represents a severe movement of the physiologic position of the canal , resulting in a significant iatrogenic relocation of the physiologic foramen . canals exhibiting type i transportation can be cleaned and obturated , if sufficient residual dentin is maintained and shape created above the foramen . type ii cases are managed by placing a barrier to control bleeding and provide a backstop to pack against during subsequent obturation procedures . in type iii situations , a barrier technique is usually not feasible ; it requires obturation as best as possible followed by corrective surgery . a healthy 21-year - old young male presented with the intention of seeking relief from discomfort and swelling associated with a painful endodontically retreated maxillary central incisor . five months ago , he had undergone root canal treatment for the resolution of a lesion of endodontic origin associated with 11 and 12 . clinical examination revealed non - carious , discoloured , tender 11 and incisally fractured non - tender 12 . softness to palpation indicated loss of buccal cortical plate over root apices of 11 and 12 . iopa radiograph , obtained at the time of visit , exhibited periradicular radiolucency involving insufficiently obturated 11 and overfilled 12 . periradicular curettage and removal of extruded gutta percha , after raising a mucoperiosteal flap under local anesthesia , exposed the apical canal transportation of 11 . repair of this canal defect by packing a wet sand consistency mix of white mineral trioxide aggregate ( mta ) ( angelus , brazil ) , with distilled water , restored it . cold compaction by a ball burnisher , after removal of overextended gutta - percha , sealed the root apex of 12 . a decrease in the size of radiolucency in iopa radiograph supports the clinical finding [ figures 1a g ] and [ figures 2a and b ] . ( a ) previous occlusal radiograph , ( b ) preoperative iopa radiograph , ( c ) exposed lesion , ( d ) exposed apical transportation , ( e ) defect repaired by mta , ( f ) third month recall , ( g ) recall radiograph ( a ) preoperative radiograph , ( b ) fourth month recall radiograph it is important to understand the objectives for shaping and cleaning the root canal system . the factors associated with an increased risk of canal transportation include insufficiently designed access cavities , use of inflexible instruments , instrumentation technique , insufficient irrigation during mechanical enlargement , degree and radius of a canal curvature , unseen canal curvatures in two dimensional radiography and experience of operator . canal transportation may result in inadequately cleaned root canals , over - reduction of sound dentin and destruction of the integrity of the root . mineral trioxide aggregate is the material of choice for managing various undesirable apical preparation outcomes . the sealing ability of this non - absorbable material is not adversely affected by blood contamination . cementum grows adjacent and onto this radiopaque material , thus allowing for a normal periodontal attachment apparatus . in this case , mta was used to repair apical transportation defect , as it has above - mentioned advantages over other materials . apicoectomy or root - end preparation was avoided as it would have further removed the sound dentin . many endodontic complications , including canal transportation , can be prevented while cleaning and shaping . apical transportation may lead to post - operative flare - up , surgery and extraction . however , depending upon the extent of occurrence , it can be managed . in the present case , the outcome of this case , indicate that the result of these procedures , is predictable and successful .

procedural accidents leading to complications such as canal transportation have been ascribed to inapt cleaning and shaping concepts . canal transportation is an undesirable deviation from the natural canal path . herewith a case of apical transportation of root canal resulting in endodontic retreatment failure and its management is presented . a healthy 21-year - old young male presented discomfort and swelling associated with painful endodontically retreated maxillary incisor . radiograph revealed periradicular radiolucency involving underfilled 11 and overfilled 12 . insufficiently obturated 11 exhibited apical transportation of canal . this type iii transportation was treated by periradicular surgery and repair using white mineral trioxide aggregate ( mta ) . comfortable asymptomatic patient presented uneventful healing at third and fourth month recall visits . a decrease in the size of radiolucency in radiograph supported the clinical finding . in the present case , mta is useful in repairing the transportation defect . the result of these procedures is predictable and successful .

@xcite presented um673 ( @xmath2 ) as a `` new case of gravitational lensing '' . the two lensed images originate from a quasar at a redshift @xmath3 , while the lensing galaxy is much closer to the milky way ( @xmath4 ) . the angular separation between component @xmath5 and @xmath6 was found to be @xmath7 , while the magnitude of the qso images and the lens galaxy , at the time of discovery , was @xmath8 , @xmath9 and @xmath10 magnitude , resulting in a total magnitude @xmath11 , with a standard deviation of the order of 0.2 magnitude . they concluded that um673 appeared to be one of the most luminous quasars , due to the amplification of image @xmath5 by gravitational lensing . a spectroscopic study of this gravitational lens was published by @xcite , in order to investigate the size of the corresponding @xmath12 clouds . since they found that the equivalent widths of the @xmath12 lines in the spectra of @xmath5 and @xmath6 are well correlated , they concluded that both light beams actually cross the same clouds . data from this paper were used by @xcite to test their model for the minihalo of the @xmath12 forest for the case of um673 . @xcite observed um673 from 1987 to 1993 . the observations were performed in the @xmath6-band , to eliminate any possible contamination originating from the deflecting galaxy . they mainly derived the magnitude difference of the two qso components , because the observing conditions were of modest quality for most of the nights . the photometric zero point was computed for the nights of 1988 october 31 , 1988 december 17 and 1991 october 27 . the respective joint @xmath6 magnitude of the two qso components ( no contribution from the galaxy in the @xmath6-band ) was 168 , 169 and 167 . their results led to the conclusion that the quasar was not showing any significant variability , but the accuracy of the relative photometry was of the order of 0.05 to 0.2 magnitude . the mean @xmath6-band magnitude difference was @xmath13 . in a later report based on an eso key - program for photometric monitoring of gravitational lenses , @xcite confirmed the above conclusions . during a 2-days workshop held in hambourg , @xcite presented some _ preliminary _ results from the 1988 - 1994 monitoring of the lens . the relative photometry of component @xmath5 , with respect to a reference magnitude @xmath14 , was indicating variations of the order of 0.2 magnitude ! unfortunately , nothing more was ever published , and therefore no additional information concerning the reduction method used or the reference magnitude could be found . in a recently published paper concerning @xmath15 observations of gravitational lenses , @xcite reported on observations of um673 performed in november 1994 . the @xmath0 magnitude of the components @xmath5 , @xmath6 , and the galaxy was @xmath16 and @xmath17 respectively , resulting in an integrated magnitude of @xmath18 . the error on the total magnitude is of the order of @xmath19 . the sloan digital sky survey ( @xmath20 ) also observed um673 . having their own photometric system under preparation @xcite , they presented their measurements in a preliminary red filter , designated as @xmath21 ( see section [ comparison with the literature ] ) . observations in the @xmath21 filter were performed in 1995 november 24 and 1996 december 12 . for the first period , @xcite reported @xmath22 , while for the second period @xcite reported @xmath23 . we report in this paper about a photometric monitoring through the years 1995 - 2000 , with conclusions to significant variations in the total light of the gravitational lens system . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars , situated in the neighborhood of um673 . these results , based on data which were accumulated during a period of 3.5 months , consist in a preliminary tool for directly checking the photometric variability of the quasar . during the six - year monitoring period , we performed ccd photometry of um673 from four different observing sites . in detail , we observed at : \(a ) la silla ( chile ) in november 1995 , december 1996 and october 1997 . during the first two periods , we used the 0.6 m ( f/15 ) bochum telescope , in conjunction with the th7882 ccd ( 384@xmath24576 , 22 @xmath25m@xmath26 pixels ) ; in 1997 , the observations were performed with the 0.9 m dutch ( f/11 ) telescope and the tektronix tk512cb ccd ( 512@xmath24512 , 27 @xmath25m@xmath26 pixels ) . the above configurations gave a scale of 0.55@xmath27 pixel@xmath28 and 0.463@xmath27 pixel@xmath28 , corresponding to a field of view of 3.2@xmath29 and @xmath30 , respectively . all observations were carried out through the standard johnson @xmath0 filter . the exposure time for the first , second , and third period was 180 , 300 and 1200 sec , respectively . \(b ) kryonerion ( greece ) in 1998 october 29 , using the 1.2 m ( f/13 ) telescope and the class i si502 ccd chip ( 512@xmath24512 , 24 @xmath25m@xmath26 pixels ) , resulting in a scale of 0.30@xmath27 pixel@xmath28 with a field of view of 2.65@xmath31 . the images were taken using the @xmath0 filter , with an integration time of 120 sec per exposure . a dark current subtraction was also included in the preliminary data reduction pipeline . \(c ) tenerife ( spain ) in 2000 august 23 , using the 1.0 m ogs telescope ( f/13.3 at the ritchey - chrtien ) combined with a thomson ccd ( 1024@xmath241024 , 19@xmath25m@xmath26 pixels ) giving a scale of 0.3@xmath27 pixel@xmath28 and a field of view of 5.12@xmath32 . this time the object was observed in both the @xmath33 and @xmath0 filters , with a same exposure time of 120 sec . \(d ) skinakas , crete ( greece ) from 2000 september to 2000 december , using the 1.3 m ( f/7.7 ) ritchey - chrtien telescope . the si003b ccd chip ( 1024@xmath241024 , 24 @xmath25m@xmath26 pixels ) was the detector , giving a scale of 0.5@xmath27 pixel@xmath28 and a field of view of 8.57@xmath34 . the observations were performed in the standard johnson @xmath33 and @xmath0 filters , with an exposure time of 240 sec per image . most of the nights um673 was monitored for many hours and we have obtained , in total , images from 29 clear nights . individually , the median seeing at the bochum telescope was 15 and better at the dutch telescope , around 11 . for the night 1998 october 29 the seeing varied between 20 - 30 , while on 2000 august 23 it was of sub - arsecond quality . finally , a value between 08 to 15 was measured for the period september - december 2000 . the observational details are summarized in table [ logbook ] . no study has ever been performed on neighbouring field stars to check the variability of the quasar , since um673 lies in a quasi - empty region of the sky . therefore , the only possibility for almost all sets of observations ( the skinakas data were the single exception ) , was to use photometric standard stars ( equatorial in our case ) to calibrate our measurements ( extinction and zero point correction ) . we mainly used the blue star hd12021 for the 1995 - 1998 missions . this photometric standard ( hipparcos identifier hip 9155 ) has been extensively observed by different observers @xcite and its properties are known with high precision . its equatorial co - ordinates are : @xmath35 and @xmath36 ; @xcite report : @xmath37 @xmath380.015 and @xmath39 . in 2000 august 23 the calibration was performed by taking exposures at different airmasses of the photometric standard 113191 @xcite . for the skinakas observations , apart from hd12021 we also used the geneva photometric standard with identification gen + 7.0093407 @xcite . > from the photometric standards observed in each mission a mean extinction coefficient and zero point were computed for every ( photometric ) night , which were then applied to the data of um673 . the data reduction was performed by developing scripts in the eso - midas environment . we applied aperture photometry on our ccd frames in order to study the photometric behavior of the _ total _ light of um673 , which is composed of the two lensed images and the lensing galaxy . we used a circular aperture of 15 to 185 diameter for this purpose , depending on the observing run conditions ( i.e. exposure time , quality of optics , seeing ) . the no - mans - land " was properly set , to avoid contamination from the faint galaxy seen at the south of um673 . a precise calculation of the sky background near the gravitational lens was performed by using a 25 width ring , external to no - mans - land " . the incorporation of errors , apart from the aperture photometry errors , included the uncertainty due to the extinction correction and the zero point correction , as computed with the help of the photometric standard stars . the reduction of the data showed that the contribution of the first factor on the daily averaged values was practically negligible ( of the order of a few milli - magnitude ) , thanks to the numerous exposures and the good observing conditions . the error due to the zero point and extinction correction was of the order of 0055 , 004 , 0015 , 004 and 0015 for the 1995 to 2000 missions , respectively . table [ photometricresults ] contains the @xmath0-band photometric results . column 2 presents the daily averages for each run , with their accuracy , composed of all exposures of each night . column 3 contains the mean value and its standard deviation for each run . our results , together with the two @xmath0-band measurements available in the literature ( @xcite , @xcite ) are plotted in fig . [ variability ] . the variability of the gravitational lens system is clearly seen in the graph . thanks to the relatively large field of view of the configuration of the skinakas 1.3 m telescope , it was possible to perform aperture photometry on ten field stars in the neighborhood of um673 , which were present in the majority of our frames . although almost all of them are fainter than the lens , an optimized combination of several factors ( i.e. photometric conditions , high quality telescope optics , precise tracking by means of an autoguider ) resulted in a large set of good quality data ( 81 frames in @xmath0 and 60 frames in @xmath33 , obtained during a period of 3.5 months ) , from which significant information on these field stars could be extracted . the variability of the field stars was checked by properly co - adding all the frames of the given night and then performing aperture photometry on them . this operation gave a set of eight frames per filter . for every frame we computed the magnitude difference , @xmath40 , of the star @xmath41 with respect to the star @xmath42 and finally obtained a mean magnitude difference , @xmath43 , for every pair of stars in the whole data set . the results obtained from the differential photometry showed that for most cases the mean errors in the magnitude differences were between 0.01 - 0.03 magnitude , except for three stars . therefore , we finally decided to reject them , and to use the rest for checking the variability of the lens . a finding chart with the identification of the field stars is given in fig . [ findingchart ] . by using the same photometric standards that were used for the lens , we performed a zero - point and extinction correction , converting the instrumental values to @xmath33 and @xmath0 magnitudes . second order extinction correction and colour transformation were not performed . we also performed a preliminary astrometric identification with the help of the @xmath44 software , developed by e. downey ( 2000)-an interactive astronomical ephemeris program for @xmath45 windows _ is available at http://www.clearskyinstitute.com/xephem ] . by correlating our results with the co - ordinates presented in @xcite , we identified the seven field stars . table [ referencestars ] lists the ra - dec co - ordinates of the reference stars , their @xmath0 magnitude and @xmath46 colour , including errors associated with the determination of the instrumental magnitudes . although it is approximately fifteen years since the discovery of the lens , um673 has hardly been observed . consequently , the very few existing measurements can not provide a clear view concerning the photometric behavior of the gravitational lens system before 1995 . the closest ( in time ) observations to our measurements are those performed by the @xmath20 , with a photometric system consistsing of five passbands ( @xmath47 and @xmath48 ) . since the definition of the system is still under progress , the observations are performed using filters which are similar but _ not _ identical to the final ones , designated as @xmath49 and @xmath50 . um673 was observed by the @xmath20 group in 1995 november 24 , and in 1996 december 12 . for the first period , @xcite report @xmath51 , while for the second period @xcite report @xmath52 and @xmath53 , respectively . the transformation of the @xmath20 measurements to the johnson @xmath54 and cousins @xmath55 photometric system is a complicated task ( cf @xcite and @xcite ) and , as a consequence , a direct comparison of the @xmath20 with our measurements is not possible . nevertheless , since both we and the @xmath20 have data obtained during the same periods ( november 1995 and december 1996 ) , we tried to derive some additional conclusions on the variability of the lens by comparing the observations obtained by @xmath20 in the two different periods . the comparison of the 1995 and 1996 @xmath20 measurements yielded ambiguous results , since the decrease of the @xmath56 magnitude shows that the lens became brighter , while a comparison of the @xmath57 and @xmath21 measurements gave the opposite conclusion . as it is mentioned in @xcite , the main task of the 1996 @xmath20 observations was to explore the detection of qsos , based on colour selection criteria . for this reason , observations were performed even if the conditions were non - photometric . as a consequence , we conclude that a comparison of the 1995 and 1996 @xmath20 measurements does not give any supplementary information on the variability of the quasar . the instrumentation used during our 1995 - 1996 missions did not allow us any additional exploitation of the data ( e.g. profile fitting of the qso components ) . hence , both a microlensing scenario and an internal variability of the quasar could equivalently explain the brightening of um673 . however , our measurements , which are characterized by a photometric precision of the order of a few hundredths of a magnitude , clearly demonstrate the 1996 peak in brightness . at the same time , they indicate that since 1997 the quasar seems to be in a less variable state , but the situation of a quiet phase can not be ruled out . we have been monitoring the gravitational lens um673 through the years 1995 - 2000 . to measure the total light of the lens ( component @xmath5 + component @xmath6 + lensing galaxy ) we constrained ourselves to aperture photometry . the numerous observations obtained during each run ( several hours per night ) , allowed us to reach a photometric precision of a few hundredths of a magnitude . the photometric calibration was performed with the help of several photometric standard stars . although the observations were performed using several configurations , all measurements agree with the conclusion that the qso has undergone a long term variability , that corresponds to a brightening in the total light of the system of @xmath58 0.3 magnitude in respect to its discovery value , in 1987 . from the agreement between the 1995 and 1997 measurements we see that this variability had its peak ( additional 02 brightening ) in 1996 . the @xmath0 magnitude of um673 we derived was [email protected] in november 1995 , [email protected] in december 1996 , [email protected] in october 1997 , [email protected] in october 1998 and [email protected] for the last quarter of 2000 ( fig . [ variability ] ) . thanks to the optimized configuration of the skinakas observatory , we managed to have @xmath33 and @xmath0 measurements of seven field stars in the vicinity of um673 during the period september - december 2000 . although more observations are needed for a better knowledge about the stability of these stars over a longer time - basis , the photometric reduction showed no significant variability at the level 002 - 003 . the measurements obtained after 1996 seem to form a plateau at around @xmath60 , indicating that since 1997 the quasar seems to be in a less variable , or even quiet , state . nevertheless , we propose a systematic monitoring of um673 at a rate of a few images at fixed time intervals . with the help of the reference stars , differential photometry would directly show any new variability in the system . we also suggest new measurements with instruments allowing analysis of the spectra of the components for comparison with earlier ones , and photometric observations to derive the fluxes of the two qso components . we thank dr . a. erikson ( dlr , berlin ) for his introduction to the 0.6 m bochum telescope and for his help to convert our ccd data to fits format , and a. kougentakis for his excellent assistance during the observations at skinakas observatory . t.n . would like to thank n. shatsky , visiting astronomer at rob , for the helpful discussions . + the authors would like to acknowledge prof . j. surdej , for his useful comments . finally , it is a pleasure to thank the referee , dr . r. schild , for his constructive suggestions . + this research ( d.s . ) was mainly carried out in the framework of the projects `` service centres and research networks '' , and `` ples dattraction interuniversitaires '' p4/05 , both initiated and financed by the belgian federal scientific services ( dwtc / sstc ) . t.n . acknowledges support from the project `` chercheurs supplmentaires aux etablissements scientifiques federaux '' . acknowledges support from a p.en.e.d . " program of the general secretariat of research and technology of greece , and the royal observatory of belgium for financing his visit in brussels . + skinakas observatory is a collaborative project of the university of crete , the foundation for research and technology - hellas and the max - planck - institut fr extraterrestrische physik . daulie , g. , hainaut , o. , hutsmkers , d. , magain , p. , remy , m. , smette , a. , surdej , j. & van drom , e. 1993 , in 31st lige international astrophysical colloquium , gravitational lenses in the universe , ed . surdej , j. , fraipont - caro , d. , gosset , e. , et al . , ( lige : univ . of lige press ) , 181 rrrrr 1995 nov 03/09 - 10 & 0.6 m bochum & th 7882 & r & 180 + 1996 dec 09 - 19 & 0.6 m bochum & th 7882 & r & 300 + 1997 oct 22 - 26 & 0.9 m dutch & tektronix tk512cb & r & 1200 + 1998 oct 29 & 1.2 m kryonerion & class i si502 & r & 120 + 2000 aug 23 & 1.0 m ogs & thomson & r & 120 + 2000 sep 03/11/18 & 1.3 m skinakas & tektronix si003b & r & 240 + 2000 nov 02 - 03/23 & 1.3 m skinakas & tektronix si003b & r & 240 + 2000 dec 14 - 15 & 1.3 m skinakas & tektronix si003b & r & 240 + rrr 1995 nov 03 & 16.27 @xmath38 0.06 & + 1995 nov 09 & 16.31 @xmath38 0.06 & 16.30 @xmath38 0.02 + 1995 nov 10 & 16.32 @xmath38 0.06 & + 1996 dec 09 & 16.11 @xmath38 0.05 & + 1996 dec 10 & 16.12 @xmath38 0.05 & + 1996 dec 11 & 16.10 @xmath38 0.05 & + 1996 dec 12 & 16.09 @xmath38 0.05 & + 1996 dec 13 & 16.05 @xmath38 0.05 & + 1996 dec 14 & 16.07 @xmath38 0.05 & 16.08 @xmath38 0.01 + 1996 dec 15 & 16.08 @xmath38 0.05 & + 1996 dec 16 & 16.11 @xmath38 0.05 & + 1996 dec 17 & 16.07 @xmath38 0.05 & + 1996 dec 18 & 16.08 @xmath38 0.05 & + 1996 dec 19 & 16.04 @xmath38 0.05 & + 1997 oct 22 & 16.29 @xmath38 0.02 & + 1997 oct 23 & 16.30 @xmath38 0.02 & + 1997 oct 24 & 16.30 @xmath38 0.02 & 16.30 @xmath38 0.01 + 1997 oct 25 & 16.30 @xmath38 0.02 & + 1997 oct 26 & 16.29 @xmath38 0.02 & + 1998 oct 29 & 16.23 @xmath38 0.05 & 16.23 @xmath38 0.05 + 2000 aug 23 & 16.30 @xmath38 0.02 & + 2000 sep 03 & 16.34 @xmath38 0.02 & + 2000 sep 11 & 16.35 @xmath38 0.02 & + 2000 sep 18 & 16.31 @xmath38 0.03 & + 2000 nov 02 & 16.35 @xmath38 0.02 & 16.34 @xmath38 0.01 + 2000 nov 03 & 16.34 @xmath38 0.02 & + 2000 nov 23 & 16.35 @xmath38 0.02 & + 2000 dec 14 & 16.34 @xmath38 0.02 & + 2000 dec 15 & 16.35 @xmath38 0.02 & + rrrr 1 & 01 45 12.05 @xmath6109 47 49 & 15.92 @xmath38 0.02 & 0.51 @xmath38 0.03 + 2 & 01 45 07.15 @xmath6109 49 01 & 16.61 @xmath38 0.02 & 0.94 @xmath38 0.03 + 3 & 01 45 08.73 @xmath6109 43 13 & 17.12 @xmath38 0.02 & 0.33 @xmath38 0.03 + 4 & 01 45 03.43 @xmath6109 44 18 & 17.37 @xmath38 0.02 & 0.84 @xmath38 0.04 + 5 & 01 44 57.90 @xmath6109 44 09 & 17.42 @xmath38 0.02 & 0.84 @xmath38 0.04 + 6 & 01 44 56.26 @xmath6109 44 15 & 17.80 @xmath38 0.02 & 0.42 @xmath38 0.04 + 7 & 01 44 56.63 @xmath6109 43 02 & 16.75 @xmath38 0.03 & 0.38 @xmath38 0.04 +

we present the results of a photometric ccd monitoring of the gravitational lens system um673 , that took place from 1995 to 2000 . in total , the doubly - imaged quasar was observed in the @xmath0-band during 29 photometric nights , using optical telescopes with dimensions in the range 0.6 m to 1.3 m . we detected a significant variability in the total light of the um673 system , that is , in the light of the two qso images plus the lensing galaxy . with respect to the magnitude of the gravitational lens system at its discovery , in 1986 , um673 was 0.3 magnitude brighter . furthermore , our december 1996 measurements show that between november 1995 and october 1997 the system became even brighter , reaching a magnitude difference of 0.5 magnitude with respect to its discovery value . we also present @xmath0 magnitudes and @xmath1 colours of seven field stars situated in the vicinity of the lens , based on a 3.5-month monitoring during the year 2000 .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Strategy To Oppose Predatory Organ Trafficking Act'' or the ``STOP Organ Trafficking Act''. SEC. 2. FINDINGS. Congress finds the following: (1) The World Health Organization (WHO) estimates that approximately 10 percent of all transplanted kidneys worldwide are illegally obtained, often bought from vulnerable impoverished persons or forcibly harvested from prisoners. (2) In 2004, the World Health Assembly passed a resolution urging its member-states to take measures to protect the poorest as well as vulnerable groups from exploitation by organ traffickers. (3) On February 13, 2008, the United Nations Global Initiative to Fight Human Trafficking (UNGIFT) hosted the ``Vienna Forum to Fight Human Trafficking'', and subsequently reported that a lack of adequate illicit organ trafficking laws has provided opportunity for the illegal trade to grow. (4) On March 21, 2011, the Council of the European Union adopted rules supplementing the definition of criminal offenses and the level of sanctions in order to strengthen the prevention of organ trafficking and the protection of those victims. (5) In 2005, the United States ratified the Protocol to Prevent, Suppress and Punish Trafficking in Persons, Especially Women and Children, a supplement to the United Nations Convention against Transnational Organized Crime, which includes the removal of organs as a form of exploitation under the definition of ``trafficking in persons''. (6) According to a 2013 United Nations report from the Special Rapporteur on trafficking in persons, especially women and children, the economic and social divisions within and among countries is notably reflected in the illicit organ trafficking market, in which the victims are commonly poor, unemployed, and more susceptible to deceit and extortion. SEC. 3. SENSE OF CONGRESS. It is the sense of Congress that-- (1) the kidnapping or coercion of individuals for the purpose of extracting their organs for profit is in contradiction of the ideals and standards for ethical behavior upon which the United States has based its laws; (2) the illegal harvesting of organs from children is a violation of the human rights of the child and is a breach of internationally accepted medical ethical standards described in WHO Assembly Resolution 57.18 (May 22, 2004); (3) the illegal harvesting and trafficking of organs violates the Universal Declaration of Human Rights, in Article 3 which states that ``Everyone has the right to life, liberty and security of person.'', and in Article 4 which states that ``No one shall be held in slavery or servitude.''; and (4) establishing efficient voluntary organ donation systems with strong enforcement mechanisms is the most effective way to combat trafficking of persons for the removal of their organs. SEC. 4. STATEMENT OF POLICY. It shall be the policy of the United States to-- (1) combat the international trafficking of persons for the removal of their organs; (2) promote the establishment of voluntary organ donation systems with effective enforcement mechanisms in bilateral diplomatic meetings, as well as in international health forums; and (3) promote the dignity and security of human life in accordance with the Universal Declaration of Human Rights. SEC. 5. REVOCATION OR DENIAL OF PASSPORTS TO INDIVIDUALS WHO ARE ORGAN TRAFFICKERS. The Act entitled ``An Act to regulate the issue and validity of passports, and for other purposes'', approved July 3, 1926 (22 U.S.C. 211a et seq.), which is commonly known as the ``Passport Act of 1926'', is amended by adding at the end the following: ``SEC. 4. AUTHORITY TO DENY OR REVOKE PASSPORT. ``(a) Issuance.--The Secretary of State may refuse to issue a passport to any individual who has been convicted of an offense under section 301 of the National Organ Transplant Act (42 U.S.C. 274e) if such individual used a passport or otherwise crossed an international border in the commission of such an offence. ``(b) Revocation.--The Secretary of State may revoke a passport previously issued to any individual described in paragraph (1).''. SEC. 6. AMENDMENTS TO THE TRAFFICKING VICTIMS PROTECTION ACT OF 2000. (a) Definitions.--Section 103 of the Trafficking Victims Protection Act of 2000 (22 U.S.C. 7102) is amended-- (1) in paragraph (9)-- (A) in subparagraph (A), by striking ``or'' at the end; (B) in subparagraph (B), by striking the period at the end and inserting: ``; or''; and (C) by adding at the end the following new subparagraph: ``(C) trafficking of persons for the removal of their organs (as defined in paragraph (13)).''; (2) by redesignating paragraphs (13) through (15) as paragraphs (14) through (16), respectively; and (3) by inserting after paragraph (12) the following new paragraph: ``(13) Trafficking of persons for the removal of their organs.-- ``(A) In general.--The term `trafficking of persons for the removal of their organs' means the recruitment, transportation, transfer, harboring, or receipt of a person, either living or deceased, for the purpose of removing one or more of the person's organs, by means of-- ``(i) coercion; ``(ii) abduction; ``(iii) deception; ``(iv) fraud; ``(v) abuse of power or a position of vulnerability; or ``(vi) transfer of payments or benefits to achieve the consent of a person having control over a person described in the matter preceding clause (i). ``(B) Organ defined.--In subparagraph (A), the term `organ' has the meaning given the term `human organ' in section 301(c)(1) of the National Organ Transplant Act (42 U.S.C. 274e(c)(1)).''. (b) Interagency Task Force to Monitor and Combat Trafficking.-- Section 105(d)(3) of the Trafficking Victims Protection Act of 2000 (22 U.S.C. 7103(d)(3)) is amended by inserting after the first sentence the following new sentence: ``Such procedures shall include collection and organization of data from human rights officers at United States embassies on host country's laws against trafficking of persons for the removal of their organs and any instances of violations of such laws.''. SEC. 7. REPORTING. (a) In General.--Not later than 1 year after the date of the enactment of this Act, and annually thereafter through 2024, the Secretary of State shall submit to the appropriate congressional committees a comprehensive report that includes the following information: (1) A description of the sources, practices, methods, facilitators, and recipients of trafficking of persons for the removal of their organs during the period covered by each such report. (2) A description of activities undertaken by the Department of State, either unilaterally or in cooperation with other countries, to address and prevent trafficking of persons for the removal of their organs. (3) A description of activities undertaken by countries to address and prevent trafficking of persons for the removal of their organs. (b) Matters To Be Included.--The reports required under subsection (a) shall include the collection and organization of data from human rights officers at United States diplomatic and consular posts on host countries' laws against trafficking of persons for the removal of their organs, including enforcement of such laws, or any instances of violations of such laws. (c) Additional Matters To Be Included.--The reports required under subsection (a) may include-- (1) information provided in meetings with host country officials; (2) information provided through cooperation with United Nations or World Health Organization agencies; (3) communications and reports provided by nongovernmental organizations working on the issue of trafficking of persons for the removal of their organs; and (4) any other reports or information sources the Secretary of State determines to be necessary and appropriate. SEC. 8. DEFINITIONS. In this Act: (1) Appropriate congressional committees.--The term ``appropriate congressional committees'' means the Committee on Foreign Affairs of the House of Representatives and the Committee on Foreign Relations of the Senate. (2) Organ.--The term ``organ'' has the meaning given the term ``human organ'' in section 301(c)(1) of the National Organ Transplant Act (42 U.S.C. 274e(c)(1)). (3) Trafficking of persons for the removal of their organs.--The term ``trafficking of persons for the removal of their organs'' means the recruitment, transportation, transfer, harboring, or receipt of a person, either living or deceased, for the purpose of removing one or more of the person's organs, by means of-- (A) coercion; (B) abduction; (C) deception; (D) fraud; (E) abuse of power or a position of vulnerability; or (F) transfer of payments or benefits to achieve the consent of a person having control over a person described in the matter preceding clause (i). SEC. 9. LIMITATION ON FUNDS. No additional funds are authorized to be appropriated to carry out this Act or any amendment made by this Act. Passed the House of Representatives June 13, 2016. Attest: KAREN L. HAAS, Clerk.

Strategy To Oppose Predatory Organ Trafficking Act or the STOP Organ Trafficking Act (Sec. 3) This bill expresses the sense of Congress that: kidnapping or coercion of individuals to extract their organs for profit contradicts the standards for ethical behavior upon which the United States has based its laws; illegal harvesting of organs from children is a violation of the chid's human rights and a breach of international medical ethical standards; illegal harvesting and trafficking of human organs violates the Universal Declaration of Human Rights; and establishing efficient national organ donation systems with strong enforcement mechanisms is the most effective way to combat trafficking of persons for the removal of their organs. (Sec. 4) It shall be U.S. policy to: (1) combat trafficking of persons for the removal of their organs, (2) promote the establishment of voluntary organ donation systems with effective enforcement mechanisms, and (3) promote the dignity and security of human life. (Sec. 5) The Passport Act of 1926 is amended to authorize the Department of State to refuse to issue a passport to, and revoke a previously issued passport from, a person convicted of trafficking in human organs who used a passport or otherwise crossed an international border in committing such offense. (Sec. 6) The Trafficking Victims Protection Act of 2000 is amended to define &quot;trafficking of persons for the removal of their organs&quot; as the recruitment, transportation, transfer, harboring, or receipt of a person, either living or dead, for the purpose of removing one or more of the person's organs by: coercion, abduction, deception, fraud, abuse of power, or transfer of payments or benefits to achieve the consent of an individual having control over such person for the purpose of removing the person's organs. &quot;Organ&quot; means the human (including fetal) kidney, liver, heart, lung, pancreas, bone marrow, cornea, eye, bone, and skin or any subpart thereof and any other human organ specified by the Department of Health and Human Services. Trafficking of persons for the removal of their organs is included in the definition of "severe forms of trafficking in persons." The Interagency Task Force To Monitor and Combat Trafficking is tasked with collecting and organizing data from human rights officers at U.S. embassies on host country's laws against trafficking of persons for the removal of their organs and any instances of violations of such laws. (Sec. 7) The State Department shall report annually through 2024 to Congress regarding: (1) the trafficking of persons for the removal of their organs, and (2) preventive activities undertaken by the State Department and other countries.

when introducing the concept of observable quantity in equilibrium thermodynamics , one must keep in mind the fact that the observation itself should be carried out in discrete intervals of time that are widely separated from one another . when standing on a purely mathematical point of view , one of the presently most noted physicists told him that the asymptotics near the turning points can not be considered as semiclassics because the landau criterion for being semiclassical is violated there . the author , as a mathematician , believed that the asymptotics even in the domain of deep shadow and the `` instantons '' obtained for the imaginary number @xmath3 can still be considered as the semiclassical asymptotics . recently , yu . m. kagan clearly explained the author that the physicists mean only the case @xmath4 when speaking about the bose einstein distribution . but the author , as a mathematician , believed that this restriction is artificial and considered system ( 1)(4 ) in the general case , without any restrictions on the number @xmath5 of particles at the @xmath6th energy level . but the natural restriction @xmath7 , @xmath8 , still exists and is taken into account by the author . einstein condensate also exists but in a small neighborhood of the zeroth energy level ( small compared with @xmath9 ) rather than at a single point . the author continues to use the name `` bose einstein '' for the obtained distribution and the condensate phenomenon . the general asymptotics is constructed for @xmath10 , and this asymptotics holds for @xmath11 . ] , one must agree that the processes of establishing an equilibrium require infinite time . however , in mathematics there are some concepts which are similar to the notion of `` half - life '' in physics . for example , one can introduce a time interval during which the difference between the current state and the state of equilibrium in the course of relaxation becomes @xmath12 times less . in approximation theory and in the theory of numerical methods , especially after the well - known paper of mandelshtam and leontovich @xcite , the following relaxation process was in use : at first , a reacting system is brought to some equilibrium . then one rapidly changes one of the conditions ( e.g. , the temperature or the pressure ) and traces the evolution of the system towards a new equilibrium ( see , for example , the article `` method relaxation '' in the great encyclopedia of oil and gas , http://www.ngpedia.ru [ in russian ] ) . since the observation intervals should be `` equal '' to the relaxation time , they are large enough , and one can refer to the process as the _ multi - step relaxation process _ ( mrp ) . economic and historical processes , and also biological processes in a living organism , belong to phenomena of this kind , and therefore , from time to time , thermodynamic models of these processes arise . the formation of clusters , according to the scheme suggested below in sec . 3.2 , can serve as an example of a multi - step relaxation process . the fact that time intervals of observation are discrete is the most important point to be taken into account when speaking about the instruments of observation . the difference between readings of measuring macro- and microinstruments in thermodynamics is related to the following aspects . a macroinstrument does not take into account the motions of nuclei , of electrons , and even of atoms within a molecule and regards any molecule as an individual particle . mathematically , this corresponds to imposing rigid constraints on the elements forming the molecule . that is , we must modify those axioms of mechanics in which we consider all elementary particles and their behavior in the configuration space whose dimension is equal to the tripled number of elementary particles . \2 . a macroinstrument measuring density counts the number of particles in a fragment of the volume ; however , it can not trace the movements of particles with different numbers during discrete finite time intervals . at each discrete time moment , this device counts the number of particles in the same fragment ; however , it can not notice what is the exact position of any particle indexed at the previous time moment and whether or not this particle really is within the chosen fragment . mathematically , this means that the arithmetical law of rearrangement of summands holds . the sum does not depend on the way in which we have indexed the particles . in this sense , the laws of classical mechanics are even modified in a more substantial way . let us quote from the textbook @xcite on quantum mechanics , where the authors define the basic property of classical mechanics : `` in classical mechanics , identical particles ( e.g. , electrons ) do not lose their ` personality , ' despite the identity of their physical properties . specifically , you can imagine that the particles forming a given physical system are ` indexed ' at some time moment and then one can trace the motion of each of the particles along its own trajectory ; then the particles can be identified at any time moment . in quantum mechanics , it is fundamental that there is no way to trace each of the identical particles separately and thus to distinguish them . we can say that , in quantum mechanics , identical particles completely lose their individuality '' ( russian p. 252 ) . a macroinstrument does not keep this basic property either . mathematically , this means that , to take this property into account , we should impose some new constraints , which are already explicitly nonholonomic , on the mechanics of many particles and , which is especially important , we should take into account the permutability of particles in the definition of density , namely , _ any permutation of particles does not modify the density_. in thermodynamics , the gas molecule density is measured . although the gas molecules differ from each other and the boltzman approach to studying the molecules is consistent with the objective reality , the difference between the molecules does not play any role when the molecule density is determined . if the density is considered in a small fragment of the vessel , which contains approximately a million of particles , then it turns out that the density in this fragment coincides with the average density in the entire vessel up to a thousand of particles ( up to 0.1 % ) and is independent of the particle numeration . it follows from these considerations that the entropy ( in contrast to the boltzmann shannon entropy ) should take into account the permutability of the indices of the particles ( cf . @xcite , sec . hence , for an ideal gas @xmath13 @xmath14 where @xmath15 stands for the average number of particles in each of the @xmath16 states of the @xmath17th group and @xmath18 and @xmath19 are some constants ( see @xcite , the footnote on p. 184 , and also @xcite and @xcite ) , the entropy must be of the form @xmath20 @xmath21.\tag{4}\ ] ] in other words , the entropy has exactly the same form as in the bose einstein quantum case . this face is proved for balls and boxes in @xcite in the footnote in sec . 46 ; also see @xcite . we have noted above that a macroinstrument and its measurements force mathematicians to reorganize even the axioms of classical mechanics . however , mathematicians are forced to do so by entering the corresponding small parameters and passing to the related limits . a macroinstrument and its measurements still reduce the time spent to perform constructions of this kind . however , when one speaks of the axioms of thermodynamics , which is based on laws derived by great physicists who used ancient experiments conducted on earth , it then turns out that the above considerations modify the classical concept of thermodynamics completely . meanwhile , microinstruments of a molecule is much less than the typical length of the vessel ( provided that the shape of the vessel is given ) '' , i.e. , there are two scales in the problem , which correspond to macro- and microinstruments . ] also play a role in classical thermodynamics ; they enable one to calculate the dimension related to the number of atoms in the molecule . in the mathematical literature , as a rule , the number of degrees of freedom coincides with the number of independent generalized coordinates . however , there notions are distinct in the standard thermodynamics , because the volume is three - dimensional , which is established by the macrodevice , whereas the number of degrees of freedom is related to the number of atoms in a molecule and is measured by the microdevice . let us explain the following experimental fact . in some cases , the number of degrees of freedom for diatomic and polyatomic molecules is an integer . in our opinion , this happens because the intramolecular communications ( the distances between the atoms of the molecule ) are very hard , and , when the temperature increases , no new degrees of freedom arise . generally speaking , the number of degrees of freedom fundamentally depends on the energy of the molecules , and the energy of different molecules of the same gas is different , and , apparently , to the average energy ( the temperature ) there must correspond the average number of degrees of freedom , which is hence must be noninteger . however , on one hand , tight connections enable one to excite almost all molecules for a sufficiently high ( room ) temperature and , on the other hand , to give the molecules no possibility to excite new degrees of freedom ( e.g. , the vibrational ones ) . if the connections are not so rigid , then the number of degrees of freedom depends on temperature , and hence on energy , and is not an integer in general . this is clear from the comparison of the values of the heat capacity @xmath22 with the experiment : for hydrogen sulfide with three atoms , the theory gives 5.96 , and the experiment 6.08 , for carbon dioxide , the experiment gives a greater value @xmath23 ( @xmath24 , @xmath25 ) , and , for carbon disulfide , the vale is almost two times larger , namely , 9.77 . in the case of diatomic molecules , say , for nitrogen , the theory gives 4.967 and the experiment shows 4.93 ; for the chlorine , the value is almost 20% higher , namely , 5.93 , etc . it turns out that the number of degrees of freedom coincides with the dimension of the generalized bose gas which is regarded as a distribution of a classical gas . landau and lifshitz notice this fact for the three - dimensional bose gas . they write that these equations ( @xmath26 ) coincide with the equations of the adiabatic line for an ordinary monatomic gas . `` however , we stress , '' the authors write further , `` that the exponents in the formulas @xmath27 and @xmath28 are not related now to the ratio of specific heat capacities ( since the relations @xmath29 and @xmath30 fail to hold ) '' @xcite , p. 187 . one can show in a quite similar way that , for the five - dimensional and six - dimensional bose gas , the `` poisson adiabatic line '' coincides with the poisson adiabat for the two - atomic and three - atomic molecule ( see @xcite , sec . 47 , diatomic gas with molecules of different atoms . rotation of molecules ) . with regard to the above stipulation , as @xmath31 , we obtain precisely both the condition @xmath30 and the ratio @xmath32 coinciding with relations well known in the old thermodynamics . the three - dimensional case of the bose einstein - type distribution can be represented as @xmath33 @xmath34 the bose einstein `` average '' values @xmath35 of the occupation numbers @xmath36 depend only on the energy , i.e. , on the sum @xmath37 , and @xmath38 so that @xmath39 the transition to integer dimensions is similar ; the fractional dimensions are obtained by passing from factorials to @xmath40-functions . a more rigorous approach in described in @xcite . let us now proceed with finding the number of degrees of freedom for for a low temperature that does not exceed the critical one : @xmath43 . the maxwell boltzmann equation for the ideal gas is of the form @xmath44 where @xmath45 stands for the pressure , @xmath46 for the volume , @xmath47 for the number of particles , and @xmath48 for the temperature . denote by @xmath49 the dimensionless quantity @xmath50 which is called the _ compressibility factor_. equation can be represented in the form @xmath51 let us express the bose einstein - type distribution for the fractional dimension @xmath52 using polylogarithms . represent the thermodynamic potential of the bose gas of the fractional dimension @xmath53 in the form @xmath54 where @xmath48 stands for the temperature , @xmath55 for the mass , @xmath56 is a constant , @xmath57 is the activity , @xmath58 is the chemical potential , and @xmath40 stands for the euler gamma function . the function @xmath59 introduced in is referred to as a polylogarithm and is defined by the rule @xmath60 where @xmath61 stands for the riemann zeta function . to pass to the dimensionless units , we introduce the temperature @xmath62 in such a way that @xmath63 . the expressions for the dimensionless pressure @xmath64 and for the number of particles @xmath47 that correspond to the thermodynamic potential are of the form @xmath65 @xmath66 we have ( for the definition of @xmath67 , see below ) @xmath68 the following formula can thus be obtained for the compressibility factor @xmath49 : @xmath69 in particular , for @xmath70 ( i.e. , for @xmath71 ) , we have @xmath72 as is well known , in the bose einstein theory , the value @xmath71 corresponds to the so - called degeneration of the bose gas . for a classical gas satisfying the same relations , the _ degeneration coincides with the critical point _ @xmath73 , @xmath74 , and @xmath75 . consequently , one can write @xmath76 for @xmath75 in , namely , @xmath77 and to every pure classical gas there corresponds its own value of @xmath67 . the entropy in the dimension @xmath78 can be evaluated in the standard way . the great thermodynamical potential is considered , @xmath79 where @xmath80 , the dimension @xmath52 is equal to @xmath81 , @xmath48 stands for the temperature , and @xmath82 for the activity . the number of particles is @xmath83 the compressibility factor is @xmath84 let us evaluate the entropy , @xmath85.\end{aligned}\ ] ] for @xmath71 , @xmath86 , and @xmath64 , the specific entropy is equal to @xmath87 e. m. apfelbaum [ apfelbaum ] and v. s. vorobev @xcite compared the bose distributions of fractional dimension @xmath88 in the @xmath89 diagram with the experimental critical isotherms for various gases . we present these graphs in figs . 15 . in fig . 5a , the graphs for the nitrogen and oxygen are shown , which have been constructed by professor v. s. vorobev . ( i.e. , for the ideal `` bose gas '' ) , @xmath90 , @xmath91 , and @xmath92 . ( b ) isobars of density for the van der waals equation are shown by solid lines . line 1 is the binodal . the circles correspond to isobars of the `` bose gas '' for @xmath93 . ] . ] , @xmath94 , and @xmath92 . ( b ) the same for water , @xmath95 . ( c ) the same for copper , @xmath96 . ] we shall show that the bose condensate in classical thermodynamics is the condensate of gas ( vapor ) into liquid ( in contrast to the statement presented in the manual @xcite in the footnote on p. 199 ) . * example 1 . * consider the example given by a famous theorem in number theory , namely , the solution of an ancient problem , which has the latin title `` partitio numerorum . '' this task involves an integer @xmath97 which is decomposed into @xmath47 terms , for example , if @xmath98 and @xmath99 , then @xmath100 which gives two solutions to the problem , @xmath101 . if @xmath102 and @xmath103 , then the decomposition has only one version , and @xmath104 . if @xmath102 and @xmath105 , then there is also only one version of decomposition , namely , the sum of ones , i.e. , @xmath106 . obviously , there is a number @xmath107 for a fixed @xmath97 such that the number of versions of the decomposition , @xmath108 , is maximal possible ( this number is not unique in general ) . the number @xmath109 is referred to as the _ hartley entropy_. at the point at which @xmath110 reaches its maximum , there is a maximum entropy . let a partition @xmath111 of @xmath97 into @xmath47 summands be given . denote by @xmath112 the number of summands on the right - hand side that are precisely equal to @xmath17 . then the total number of summands is @xmath113 , and this number is equal to @xmath47 , since we know that the total number of summands is @xmath47 . further , the sum of the parts equal to @xmath17 is @xmath114 , since there are @xmath112 summands , and then the sum of all summands can be obtained by summing these expressions over all possible @xmath17 , i.e. , @xmath115 , and this sum is equal to @xmath97 . namely , @xmath116 the very nonuniqueness of the above maximum and an uncertainty concerning the number of the maxima enabled erds to obtain results with accuracy up to @xmath117 only . thus , the erds theorem holds for the system of two diophantine equations @xmath118 the maximum number of solutions of the system is achieved provided that the following relation holds : @xmath119 and the coefficient @xmath120 is defined by the formula @xmath121 . if one increases the number @xmath47 in problem and keeps the number @xmath97 constant , then the number of solutions decreases . if the sums in are counted from zero rather than from one , i.e. , @xmath122 then the number of solutions does not decrease and remains constant . let us explain this fact . the erds lehner problem @xcite is to decompose a number @xmath123 into @xmath124 summands . the decomposition of the number 5 into two summands has two versions . if we include also 0 , then we obtain three versions , 5 + 0 = 3 + 2 = 4 + 1 . thus , the inclusion of zero gives the opportunity to say that we decompose the number into @xmath125 summands . indeed , the expansion of the number 5 into 3 summands includes all previous versions : 5 + 0 + 0 , 3 + 2 + 0 . and 4 + 1 + 0 and adds new options that do not contain zero . here the maximum does not change much @xcite ; however , the number of options can not decrease , because the zeros enable the maximum to remain constant , and the entropy never decreases ; after reaching the maximum , it becomes constant . this very remarkable property of entropy enables us to construct a general unbounded probability theory @xcite . in physics , the effect is identical to the so - called phenomenon of bose condensate . let us pose the following question : what is the difference between arithmetic , together with the problem of `` partitio numerorum , '' and the boltzmann shannon statistics ? if we assume that @xmath126 and @xmath127 are two different versions , then we obtain the boltzmann shannon statistics . the number of versions of decomposition , @xmath108 , is growing rapidly . thus , the `` noncommutativity '' of the addition gives additionally a huge number of versions of decomposition , and the hartley entropy ( which is equal to the logarithm of the number of versions ) coincides with the boltzmann shannon entropy . therefore , we have proved that , if we add zero to the family of possible summands and decompose a number @xmath97 into @xmath47 summands , then this is equivalent to solving equations , i.e. , to imposing relations for the number of particles and for energy . here the number of zeros increases drastically ; if @xmath98 , then , for @xmath128 , the number of zeros is 22 . however , the number of ones is also large , although it is twice smaller than the number of zeros . it is very visible to consider the bose condensate as the number of zeros ; however , this is inaccurate . the bose condensate occurs in a neighborhood of a point at which the energy vanishes rather than at the point itself . nevertheless , if one writes @xmath129 ( where @xmath130 stands for the density and the vector @xmath131 is the momentum ) for the bose condensate at rest , then this notation is true , because the density is the limit @xmath132 where @xmath47 stands for the number of particles , @xmath46 for the volume , and @xmath55 for the mass of the particle . this means that , as @xmath133 , the bell - shaped function near the zero energy is converted to the @xmath134 function . by an ideal ( or perfect ) liquid we mean a liquid without attraction and without any surface tension this is a liquid which can exist for a positive pressure only together with a saturated steam . in this case , the perfect liquid is the result of an optical illusion , and this `` perfect liquid '' is the same ideal gas in the condensate , with another density . it can be described , as in the case of a consideration of a bose condensate , in the form @xmath129 , where @xmath135 stands for the density of the condensate . it can not exist without a volume trap , which is similar to the case in which a container with gas has a hole , and there is a vacuum outside the vessel , in which case this liquid , which looks as if it is boiled , is going away together with the gas . the mean speed of the particles inside the liquid is the same as the mean speed of the gas particles . this corresponds to the condition that the temperature in the system `` liquid saturated steam '' is the same in the liquid and in the gas . the liquid in a closed vessel is a fluctuation standing at a fixed place ( @xmath136 ) , or , speaking in a simpler way , this liquid is a `` resting '' bose condensate ( cf . @xcite , p.204 ) . small crystals that occur in a supersaturated solution coincide with the bose condensate only if they are not composed of mutually connected particles , and , moreover , if the particles are continuously exchanged with the particles in the solution ; moreover , the small crystals , as solids , are an optical illusion , namely , we simply do not see that the particles of crystals are permanently transposed with particles of the solution . in other words , this is by no means a crystal , this is a fluctuation ; however , this fluctuation is relatively immobile . thus , the bose condensate for classical particles represents some `` special density fluctuations ; '' only this , and nothing more . a. i. anselm constructed his theory starting from the eyring formula for free energy . the liquid structure model accepted by eyring is in fact closer to the strongly compresses gas model @xcite . one can talk about the density in a `` special cluster fluctuation '' of a part of our vessel with gas . if we speak of the density in this cluster only , this means that ( as in the example of a small volume with one million of particles ) one can not speak of the number of particles that are placed in the cluster as if they are frozen and do not move . this is only an appearance , and all of the particles or a part of them can be replaced in a minute by another ones , and the indexing inside the `` fluctuation '' cluster can change every minute . at the next time step , this can be the same picture but probably with different particles involved . we speak about some fragment of the volume . in fact , the particles that are more concentrated can be spread out over the entire vessel . however , if there is at least a little gravity of the earth , then the fluctuations with more concentrated particles accumulate near the bottom . if we consider a vessel with gas in the form of a perfectly reflecting sphere ( see @xcite@xcite ) , then , due to the repulsive force occurring at the border , fluctuations of this kind are located near the center of the ball . from the standpoint of our observation , in discrete time intervals at far distances from each other , the denser fragment of the volume , i.e. , the bose condensate , is at rest and hence corresponds to a small momentum in the bose einstein - type distribution . mathematically , the mrp model corresponds to this phenomenon . this property will be called the _ relativity principle for mrp_. let us repeat once again that the only fact which can be guaranteed by the generalized theory of bose condensate is that there will be a higher density of particles at the bottom . * example 2 . * let a gas be contained in a closed vessel at a room temperature , and let the gas be almost satisfying the clausius relation @xmath137 we cool the vessel down to a temperature @xmath138 . at some temperature @xmath139 , a liquid is formed . the temperature @xmath140 is referred to as the dew point . according to the standard conception , the fluctuations above the temperature of the dew point are of the order of @xmath141 . after the formation of liquid , the gas , which is called a saturated steam in the physical literature , also satisfies relation . it is quite rarefied . according to the van der waals model , there are no singularities at the dew point under the gas - liquid passage ( on the so - called binodal ) . according to experimental data , there are no large fluctuations either in the usual sense at the dew point . finally , the most important thing . the experiment shows that , at @xmath142 , the gas is rarefied , and it remains an ideal gas in the sense of relation , i.e. , in the boltzmann - maxwell sense . there is , however , a fluctuation of the type of a stationary bose einstein condensate . in this fluctuation , the molecules by themselves placed inside this fluctuational fragment can possibly move with the same velocities as those of the gas molecules and , if it were possible to enumerate them , then the numbers will be changed very quickly . if shall refer to this fluctuation ( of the form of the bose - einstein condensation ) as liquid , then actual molecules of the liquid move in it with the same speeds as the gas molecules ( of the `` saturated vapor '' ) . to represent this picture in a more visible way , imagine a bunting which winds from one roller to the other . between the rollers , under the material , a strong wind blows from a hose . we see a `` hump '' is formed between the rollers ; however , it can be assumed that we do not see that the bunting moves . nevertheless , as the density of the bose condensate increases , our macroinstrument can fix the bound of the density and show us that there is a more dense phase and a less dense phase . hence , only the original macroinstrument can show us the bound of this abstract liquid , i.e. , of the second phase . first , the bose - condensate at rest , i.e. , the gas compaction , is being formed ( because of the relativity principle for mrp ) , and then there arise quantum forces , i.e. , attraction forces ( see below ) , acting on the `` nearest neighborhoods '' , the more so because the molecules move slower at a low temperature . if liquid droplets occur below the temperature of the `` dew point , '' then the droplets are spherical , even under the presence of the gravity of the earth ( physicists refer to the very gravity , as a rule , when claiming that the border between gas and liquid is flat ) . the pressures in the droplet and in the gas ( the saturated vapor ) are different , due to the surface tension . therefore , the main rule of the equilibrium `` vapor - liquid , '' namely , the coincidence of the of pressures , really holds at the dew point only if we neglect the surface tension , and thus neglect the attraction of liquid molecules , because these two effects are inseparably linked with each other . our concept of a new ideal gas is based on the very assumption on the absence of attraction between the molecules . the picture in which the attraction and the surface tension play no role can be is observed in experiments if the temperature is equal to the temperature @xmath143 of the gas - liquid transition ( i.e. , at a point of the `` binodal '' ) and @xmath143 is still greater than the temperature at which a droplet of critical radius has been already formed . then , at @xmath142 , the incipient drops spontaneously shrink and occur at another point . these drops can not live without the surrounding saturated vapor ; one can see these drops but can not feel them . if the vessel is spherical and the mean free path is comparable to the size of the vessel ( similar to the so - called knudsen criterion ; see @xcite@xcite , then the probability of such a virtual drop is larger at the center of the vessel . in this case , if we make the labelling of several molecules by launching few isotopes which can be traced , then these isotopes will pass freely through the liquid to vapor and back , and they will form a a denser structure near the center of the ball , in such a way that , when illuminated by parallel rays , it will provide a shade . however , it is impossible to take this drop from the gas medium . one can see an ideal liquid but can not feel it . possibly it is better to refer to it as a `` virtual liquid . '' this approach is unusual for the majority of physicists . although everyone knows that , say , when photons are collected at a focus at which their `` density '' is high , then it is impossible to separate the focus from the `` photon medium . '' a mathematical analog of the quantum bose condensate for a classical gas is a liquid without attraction in which the speeds of the molecules are approximately the same as the speeds of the molecules in the saturated vapor . the attraction between molecules results in a significant correction provided that the radius of a drop is greater than the critical one ; however , this correction abolishes the conditions of the vapor liquid equilibrium for the pressure . therefore , the problem must be divided into two separate problems , namely , 1 ) an ideal gas and a perfect liquid without attraction , and 2 ) the consideration of the attraction for the case in which the decay into two phases has already been carried out and the radius of the drop exceeds the critical value . we define the temperature from the overcondensate part of the system , i.e. , from the gas until the volume of particles in the condensate is comparatively small , i.e. , until the surface tension is formed and a drop of critical radius size appears . the drop of critical radius size is the result of a different mr - process , i.e. , of the quantum dipole - dipole interaction clusterization according to the scheme given in sec . the nucleation process consists of two mutually related mr - processes . the bose condensate in the first mr - process is the nucleation starting mechanism including the quantum effect of dipole - dipole attraction and the quantum effect of exchange interaction of identical particles . in the manual by landau and lifshitz and in other manuals , the spectrum is calculated by the weyl courant formula . such calculations require the use of the phase volume , and the volume @xmath46 of the configuration space naturally arises . we determine the spectrum starting from the number of degrees of freedom and actually use the volume only in the final result to pass from the number of particles to the density . as was already seen , the number of degrees is equal to the dimension of the bose einstein - type distribution . the gas spinodal , which is defined in a new way as the locus of isotherms of a new ideal gas , is formed at the maximum entropy at the points at which the chemical potential @xmath58 vanishes . therefore , on the diagram @xmath144 , the spinodal is a segment @xmath145 , @xmath75 in the case of the van der waals normalization @xmath86 and @xmath64 . until now we , maximally following the traditional notation used in [ 3 ] . preserve the volume @xmath46 , although _ neither the equation for the @xmath146-potential given in _ [ 3 , $ 28 ] @xmath147 _ nor relations _ ( 1)(4 ) _ contain the volume @xmath46_. we interpret the bose einstein condensate as a liquid phase , and because for @xmath148 the number of overcondensate particles remains constant , the liquid is `` incompressible '' . for @xmath149 , the bose condensate occurs and , consequently , for the liquid phase on the spinodal , the quantity @xmath150 remains constant on the liquid isotherm . this means that the isotherm of the liquid phase that corresponds to a temperature @xmath62 is given by @xmath151 all isotherms of the liquid phase ( including the critical isotherm at @xmath152 ) pass through the origin @xmath153 , @xmath154 and then fall into the negative region ( or to the second sheet ) . the point @xmath153 corresponds to the parameter @xmath155 , and hence to the continuation to @xmath156 , since , for @xmath71 , the pressure @xmath157 can be continued to @xmath158 . we shall see below that the value of @xmath49 as @xmath159 is also positive , and therefore the spinodal for @xmath160 gives the second sheet on the diagram @xmath161 ; it is more convenient to map this sheet onto the negative quadrant . under the assumption that the transition to the liquid phase is not carried out for @xmath152 , we equate the chemical potentials @xmath58 and @xmath162 for the `` liquid '' and `` gaseous '' phase on the isotherm @xmath152 ( this fact is proved below ) . after this , we find the value of the chemical potential corresponding to the transition to the `` liquid '' phase for @xmath163 by equating the chemical potentials of the `` liquid '' and `` gaseous '' phases . in this section , we find the point of the isotherm - isochore of the liquid as the quantity @xmath164 tends to zero . first of all , we take into account the fact that @xmath107 is finite , although it is large , and hence we must use the obtained correction . in fact , the transition to integral ( 6 ) from the integral over momenta in @xcite by using the replacement @xmath165 corresponds to the transition to the energy oscillatory `` representation '' or , which is the same , to the natural series . the differential @xmath166 means that the discrete series must be taken with the same series in @xmath167 , and this is precisely the natural series multiplied by a small parameter . historically , such a representation was present already in the initial plank distribution . the transition from the discrete representation of the natural series to the integral representation will be described in this section . this representation associates the bose einstein distribution with the number theory considered in example 1 . on the other hand , it stresses that the discrete bose plank distribution depends only on the number of degrees of freedom and is independent of the three - dimensional volume @xmath46 . obviously , the discrete decompositions leading to integral ( 6 ) are not unique . usually , the physicists reduce discrete decompositions to integrals over momenta and try to relate them to the volume @xmath46 ( and the phase volume , respectively ) . using the natural series and the parameter @xmath168 , we thus stress the difference between these approaches . let us construct the thermodynamics of the ideal bose gas with boundedly many states at a given quantum level . since @xmath8 because of the left equality in formula , this condition can not be an additional restriction . summing the finite geometric progression , we obtain @xmath169 the potential @xmath146 is equal to the sum @xmath170 over @xmath6 : @xmath171 for the number of particles , we have the formula @xmath172 ( see ( 20 ) ) . omitting the volume @xmath46 , we obtain @xmath173}-1}\right).\tag{25}\ ] ] the volume @xmath46 in relations was required only for the normalization , for the transition form the number @xmath47 to the density . for @xmath174 , it does not interfere with the asymptotics as @xmath175 , because the term containing @xmath176 in the right - hand side is small . at the same time , it agrees with the pressure , because @xmath177 . for @xmath178 , we omit the volume @xmath46 , because even for @xmath155 due to example 1 , there appears a term of the form @xmath179 which must be taken into account and @xmath155 , there is no area @xmath180 . and this confuses specialists in thermodynamics . indeed , on one hand , @xmath181 , but on the other hand , it follows from ( 17 ) that @xmath182 , and hence , by ( 17 ) , the limit of @xmath183 as @xmath184 and @xmath185 tends to infinity . this finally leads to a false conclusion that the bose - condensate exists only for @xmath186 in the two - dimensional case . in fact , it exists for @xmath187 , and this is not a very small value ( see corollary 1 below ) . ] , because we have @xmath188 in the two - dimensional case . in the two - dimensional trap , the number @xmath47 is significantly less , but even for @xmath11 , @xmath189 , we can use the asymptotic formulas given below . on the other hand , the relation between thermodynamic parameters allows us to decrease the number of independent variables from three to two ( cf . fig . 9 in the variables @xmath190 and figs . 1116 in the variables @xmath191 ) . * estimates*. @xmath192 taking the parameter @xmath168 into account we use the euler maclaurin formula to obtain @xmath193 where @xmath194 , @xmath195 , @xmath196 , and @xmath197 . here the remainder @xmath198 satisfies the estimate @xmath199 we calculate the derivative and obtain @xmath200 \tag{27}\\ \big|\frac{k^2e^{k(y+\varkappa)}}{(e^{k(y+\varkappa)}-1)^2 } -\frac{e^{y+\varkappa}}{(e^{y+\varkappa}-1)^2}\big|\,dy^\alpha . \nonumber\end{aligned}\ ] ] we also have @xmath201 by setting @xmath202 and @xmath203 , we obtain the estimate for @xmath198 : @xmath204 with a certain constant @xmath56 . for example , if @xmath205 , then @xmath206 preserves the estimate@xmath207 . @xmath192 the energy will be now denoted by @xmath97 , because without multiplication by the volume @xmath46 , this is not the usual thermodynamics but rather a certain analog of the number theory ( see example 1 ) . taking account of the fact that , for the value of @xmath97 , the correction in can be neglected for the value of @xmath97 , we obtain @xmath208 where @xmath194 , @xmath209 . therefore , @xmath210 we obtain ( see @xcite ) @xmath211 by setting @xmath212 , we finally obtain @xmath213 [ erds formula ] it can be proved that @xmath214 gives the number @xmath47 with satisfactory accuracy . hence , @xmath215 consider the value of the integral ( with the same integrand ) taken from @xmath167 to @xmath216 and then pass to the limit as @xmath217 . after making the change @xmath218 in the first term and @xmath219 in the second term , we obtain @xmath220 on the other hand , making the change @xmath218 in , we obtain @xmath221 this gives @xmath222 now let us find the next term of the asymptotics by setting @xmath223 furthermore , using the formula @xmath224 and expanding @xmath225 in @xmath226 we obtain @xmath227 thus , we have obtained the erds formula @xcite . the relation @xmath228 is consistent with the linear relation @xmath229 , where @xmath230 , for @xmath231 . we can normalize the activity @xmath232 at the point @xmath2 , and we can find @xmath233 by matching the liquid and gaseous branches at @xmath234 for the pressure @xmath235 , in order to prevent the phase transition on the critical isotherm at @xmath152 . in what follows , we normalize the activity for @xmath163 with respect to the value of @xmath233 computed below . then the chemical potentials ( in thermodynamics , the thermodynamic gibbs potentials for the liquid and gaseous branches ) coincide , and therefore there can be no `` gas liquid '' phase transition at @xmath152 . now , for the isochore isotherm of the `` incompressible liquid '' to take place , we must construct it with regard to the relation @xmath236 , i.e. , @xmath237 we obtain the value @xmath238 from the implicit equation @xmath239 thus , for each @xmath163 we find the spinodal curve ( i.e. , the points at which @xmath240 ) in the domain of negative @xmath168 @xcite , @xmath241 in the set of two values of @xmath168 corresponding to the solution , we choose the value associated with the largest entropy , i.e. , the quantity largest in absolute value and denote it by @xmath242 . for @xmath152 , we choose the value of @xmath243 so that both solutions @xmath244 coincide , and we write @xmath245 . let @xmath246 be the activity of the gas , and let @xmath247 be the activity of the liquid . w e present the condition for the coincidence of @xmath97 and of the activities at the point of the phase transition : @xmath248 @xmath249 the relation @xmath250 will be called the normalization of activity on the critical isotherm . relations determine the value of the chemical potential @xmath251 at which the `` gas liquid '' phase transition occurs . let @xmath252 . thus , for every @xmath253 , we obtain a value of the reduced activity of the liquid @xmath254 ( @xmath255 is the activity of the liquid ) that corresponds to the van der waals normalization . in thermodynamics , the critical values @xmath2 , @xmath256 , and @xmath257 are evaluated experimentally for almost all gases , and therefore the critical number of degrees of freedom can be set in advance . according to numerical calculations for a real gas , the parameter @xmath258 ( @xmath259 , @xmath260 ) determining the point @xmath261 ensures that the binodal passes through the triple point ( see sec . 3.4 ) . the triple point can be determined experimentally with a sufficient accuracy . the molecules of an ideal gas can be thought of as tiny balls . let us imagine holes , excitons in glass , also as balls which are empty , without the substance of a molecule . obviously , if one mixes these balls in a glass in a chaotic way , then the chaos in the glass becomes increased . this means that the entropy increases in the presence of holes . therefore , to achieve the maximum of the entropy , we must also additionally mix holes into this glass . in our conception , holes occur for @xmath262 . in the ideal gas model , we ignore the attraction , and this means that , when `` stretching '' the liquid , which results in holes , the liquid does not resist ( as the sand , which is incompressible under the compression and does not resist under `` tension ; '' cf . the appendix to the book @xcite ) . once there is no attraction , there is no negative pressure under the `` tension '' , i.e. , there is no formation of holes . if @xmath156 , then the plane @xmath161 is positive again , and therefore it is covered by the other sheet . it can readily be seen that the lines entering the point @xmath153 , @xmath263 ( i.e. , to the point @xmath155 ) are reflected on this second sheet back , along the same line . this means that it is geometrically convenient to arrange the reflection of vectors on the second sheet by using the matrix @xmath264 , where @xmath265 stands for the two - dimensional identity matrix , i.e. , to flip ( carry out the mirror reflection for ) the sheet @xmath266 to the negative quadrant . note that this procedure is compliance with the concepts of dirac hole theory , just in the opposite direction , namely , to a hole we assign a negative pressure , i.e. , a negative energy . now the straight lines can be continued through the origin to the negative quadrant , although the pressure really does not change its sign . this is only a convenient geometric `` uniformization . '' note also that , due to absence of attraction , an ideal liquid is completely plastic ; namely , it does not try to return to the original state ( the state before stretching ) . in this sense , the bose condensate for @xmath262 , which leads to this `` kind '' of liquid , can also be treated more visually as a glass or an amorphous solid . this makes it possible to interpret the state of the liquid for @xmath262 more intuitively . the author has come to the revision of the thermodynamics when studying economics in which money is the very particles , according the correspondence principle derived by irving fisher . fisher himself did not referred to his observation as the correspondence principle . however , since he was a disciple of gibbs , there is a clear reason for the fact that the relation of the basic law of economics @xmath267 where @xmath268 stands for the amount of goods , @xmath97 for the number of money , @xmath269 for the turnover rate , and @xmath45 for the price of goods , is obviously related to the correspondence of economical and thermodynamical quantities , namely , the volume @xmath46 corresponds to the amount of goods @xmath268 , the number of money @xmath97 to the number of particles @xmath47 , the rate @xmath269 to the temperature @xmath48 . the price of goods @xmath45 is related to pressure to a lesser extent ; however , it is denoted by the same symbol . in this correspondence principle , it is natural to correspond holes to debts and acquitting to annihilation . as mentioned above , the locus on which the chemical potential is zero gives the points of maximum entropy . we refer to these points as the `` new spinodal . '' in economics , this new spinodal means a kind of limit for debts @xcite . thus , according to the relations thus obtained , we face a double covering of the plane @xmath270 for @xmath271 and @xmath272 . the meaning of the second sheet is that , for @xmath272 , the chaotic state of liquid ( as a phenomenon associated with the bose condensate ) increases when the number of holes of the type of frenkel excitons increases , and the holes are placed in the liquid , which is fluctuationally concentrated on a rather slow - moving domain ( _ from the point of view of the device discussed above _ ) , in the form of chaotic nanoholes , then the structure of the liquid becomes chaotically stretched . here the holes - excitons can not be indexed by our device , as well as the particles , and we can speak only of the density of holes . as was already said above , it is more convenient to place the second sheet under consideration in the quadrant @xmath273 $ ] , by continuing the straight lines through the singular point of @xmath153 , @xmath263 to the negative quadrant . in other words , to make a reflection with the help of the matrix @xmath274 , where @xmath275 stands for the identity matrix . thus , it becomes convenient to speak of `` negative pressure '' , although we neglect the attraction of particles , and hence there can be no negative pressure at all . as a rule , the pressure , as well as the temperature , is regarded as a positive quantity . we stretch the liquid , and it becomes plastically frozen up in this stretched state and does not tend to shrink back . let us explain from the point of view of physics why the extension to the negative square is natural . we compare the new ideal liquid with sand , which is incompressible under the `` compression '' and `` dost not resist '' under stretching , because there is no attraction between the grains . * example 3 . * consider a cylindrical vessel , filled with sand , whose lid is attached to the piston , in the room of the space station . the increase in the vessel with the piston leads only to a rearrangement of sand and its transformation to a floating `` dust '' in the new volume ( see @xcite ) . if we take into account the gravitational attraction between the grains , then the phenomenon of pulling the piston creates a negative pressure , and thus it is natural to pass to the negative quadrant on the @xmath276 diagram , and then to neglect the gravitational attraction . neglecting the presence of attraction here is just as `` legitimate '' as it is in the theory of vapor - liquid equilibrium , where the condition that the pressures are equal is possible only if we neglect the surface tension . this also explains a smooth transition ( without a phase discontinuity of the first kind ) of this structure into ice , namely , a frozen glass crystallizes . mishchenko and the author @xcite considered the transition to a two - dimensional lagrangian manifold in the four - dimensional phase space , where the pressure @xmath45 and the temperature @xmath48 ( the intensive variables ) play the role of coordinates and the extensive variables ( the volume @xmath46 and the entropy @xmath277 ) play the role of momenta for the lagrangian manifold , where the entropy is the action generating the lagrangian structure . seemingly , there is no global canonical transformation leading to a change of this kind . this does not confuse physicists . for example , in 25 of @xcite , `` equilibrium of a solid in an external field , '' it is said that `` from the equation @xmath278 represented in the form @xmath279 we see '' however , formula the expression `` represented in the form '' . nevertheless , this `` implies '' the following conclusion : `` if the field is absent and both @xmath58 and @xmath48 are constant , then the pressure is automatically also constant . '' at the same time , the same textbook states that , at a temperature slightly below the `` dew point , '' when the radius of the drop becomes greater than the critical value , it can be seen that the pressure of the liquid inside the drop differs from the pressure in the saturated vapor . the external field is absent . is this still thermodynamics ? other words are used ; one speaks of a vapor instead of gas and of the process of nucleation instead of the vapor - liquid equilibrium . and then a patch is immediately put on the same hole , namely , an extra term is added to . the old thermodynamics has many patches of this kind . it turns out that this complex transformation , leading to relation , can be carried out , as we have seen , only by continuing to the domain of negative energies . after this , one can justify the maxwell transition by introducing a small dissipation ( viscosity ) . the introduction of an infinitesimal dissipation enables one to simultaneously solve the problem of critical exponents , without using the scaling hypothesis , on which the method of renormalization group is based . let us show this . in thermodynamics , the viscosity is absent . however , generally speaking , without an infinitesimal dissipation , an equilibrium in thermodynamics should not be attained . therefore , it is natural to implement the occurrence of this infinitesimal viscosity and then pass to the limit as the viscosity tends to zero . the geometric quantization of the lagrangian manifold ( see @xcite , 11.4 ) is usually associated with the introduction of the constant @xmath280 . the author introduced the term of wiener ( or tunnel ) quantization to describe the case in which the number @xmath281 is purely imaginary @xcite . let us apply the wiener quantization to thermodynamics . the thermodynamic potential @xmath282 is the action @xmath283 on the two - dimensional lagrangian manifold @xmath284 in the four - dimensional phase space @xmath285 , where @xmath286 and @xmath287 are the pressure @xmath45 and the temperature @xmath48 , respectively , @xmath288 is equal to the volume @xmath46 , and @xmath289 is equal to the entropy of @xmath277 taken with the opposite sign . all other potentials , namely , the internal energy @xmath275 , the free energy @xmath290 , and the enthalpy @xmath291 are the results of projecting the lagrangian manifold to the coordinate planes @xmath292 , @xmath293 under the wiener quantization , we have @xmath294 consequently , the role of time @xmath295 in the quantization , is played by @xmath296 , @xmath297 note that the tunnel quantization of the van der waals equation ( vdw ) as @xmath298 gives maxwell s rule ( see below ) . as we shall see below , the critical point and the spinodal point are focal points . and therefore , as @xmath298 there points do not come to the `` classical '' picture , i.e. , to the van der waals model . the spinodal points , which are similar to turning points in quantum mechanics , can be approached by the airy function , whereas the critical point , which is the point at which two turning points are generated ( two airy functions ) , can be approached by the weber function ( see @xcite ) . it is the very weber function which is used to express the creation point of the shock wave for @xmath299 in the burgers equation is expressed . if one passes to the limit as @xmath300 outside these points , then we obtain the vdw maxwell model . however , the passage to the limit is violated at these very points . therefore , the so - called landau `` classic '' critical exponents @xcite drastically differ from the experiment . the weber function give singularities of the form @xmath301 , whereas the airy function gives a feature of the form @xmath302 . let us present a more detailed consideration of the burgers equation . consider the heat equation @xmath303 where @xmath304 is a small parameter . as is known , all linear combinations @xmath305 of solutions @xmath306 and @xmath307 of equation are solutions of this equation . let us make the change @xmath308 we obtain the following nonlinear equation : @xmath309 which is referred to as the integrated burgers equation and by using the substitution @xmath310 . ] . obviously , to any solution @xmath311 of equation we can assign a solution @xmath312 of the equation , @xmath313 . to the solution of equation we assign a solution @xmath314 of the equation where @xmath315 , ( @xmath316 ) . since @xmath317 we obtain the @xmath318 algebra of the tropical mathematics @xcite . to find solutions for @xmath319 , hopf suggested to consider the burgers equation @xmath320 and to refer to the function @xmath321 ( riemann waves ) as a ( generalized ) solution of the equation @xmath322 the solution @xmath269 of the burgers equation can be expressed in terms of the logarithmic derivative @xmath323 of the solution @xmath324 of the heat equation @xmath325 thus , the original problem reduces to the study of the logarithmic limit of a solution of the heat equation . as is known , the solution of problem is of the form @xmath326 the asymptotics of the integral can be calculated by the laplace method . for @xmath327 , we have @xmath328 here @xmath329 and the integral is evaluated along a lagrangian curve @xmath330 ; @xmath331 is a point on @xmath332 . for @xmath333 , there are three points @xmath334 , @xmath335 , and @xmath336 on @xmath330 whose projections to the @xmath337 axis are the same ; in other words , the equation @xmath338 for @xmath339 has three solutions @xmath340 , @xmath341 , and @xmath342 . write @xmath343 @xmath344 , and @xmath345 where @xmath346 for @xmath347 $ ] . these arguments enable us to obtain a generalized discontinuous solution of for the times @xmath333 . it is defined by a function @xmath348 defining the significant areas @xcite of the curve @xmath332 . note that this , in particular , this implies the rule of equal areas , which is known in hydrodynamics for finding the front of a shock wave whose evolution is described by equation . note that this precisely corresponds to the maxwell rule for the vdw equation . the solution @xmath349 of the burgers equation at the critical point @xmath350 is evaluated by the formula @xmath351 as @xmath352 , after the change @xmath353 , we obtain @xmath354 what does this mean in terms of classical theory and classical measurement , when the condition referred to in the book @xcite as the `` semiclassic condition '' is satisfied ( i.e. , for the case in which we are outside the focal point ) ? for the laplace transform , this means that we are in a domain in which the laplace asymptotic method can be applied indeed , i.e. , in the domain where @xmath355 if the solution of the relation @xmath356 is nondegenerate , i.e. , @xmath357 at the point at which @xmath358 then the reduced integral is bounded as @xmath217 . for this integral to have a zero of the order of @xmath359 , we must integrate it with respect to @xmath360 after applying the fractional derivative @xmath361 . the value of @xmath362 as applied to 1 ( the value of @xmath363 is approximately equal to @xmath364 . by @xcite , the correspondence between the differentiation operator and a small parameter of the form @xmath365 is preserved for the ratio @xmath366 , while the leading term of the asymptotic behavior is not cancelled in the difference between @xmath367 and @xmath368 due to the uncertainty principle ( see remark 5 ) . let us repeat the calculations in @xcite with regard to the fact that , on this class of functions , @xmath369 has the properties @xmath370 and @xmath371 consider the obvious inequality @xmath372 where @xmath232 is an arbitrary real constant . when evaluating this integral , we have @xmath373 @xmath374 @xmath375 we obtain @xmath376 for this quadratic trinomial ( in @xmath232 ) to be positive for all values of @xmath232 , it is necessary that the following condition be satisfied : @xmath377 or @xmath378 thus , the tunnel quantization explains both the condition @xmath379 for photons and the condition @xmath380 for bosons . in the case of thermodynamics , the role of @xmath337 is played by the pressure @xmath45 , and the role of the momentum @xmath381 is the played by the volume @xmath382 . therefore , @xmath383 , i.e. , @xmath384 this is the very jump of the critical exponent . one van similarly obtain other critical exponents ( see @xcite ) . for the comparison with experimental data , see the same paper . unfortunately , thermodynamics does not use the concept of lagrangian manifold which was introduced by the author in 1965 @xcite . it is especially suitable for thermodynamics , in which there are pairs of intensive and extensive quantities . intensive quantities , roughly speaking , are the quantities for which one can not create the concept of `` specific '' quantity . these are the temperature @xmath48 , the pressure @xmath45 , and the chemical potential @xmath58 . to these intensive quantities , there correspond related extensive quantities , namely , the entropy @xmath277 , the volume @xmath46 , and the number of particles @xmath47 . altogether , they form the phase space , where the role of coordinates is played by the intensive quantities and the role of momenta is played by the extensive quantities . in this case , a lagrangian manifold is a three - dimensional submanifold ( of the six - dimensional phase space ) on which there is an action , an analog of the integral @xmath385 , @xmath386 in mechanics . it is locally independent of the path . usually a 4-dimensional phase space @xmath387 is considered . this space corresponds to @xmath388 , @xmath389 , @xmath390 , @xmath391 , @xmath392 : @xmath393 depending on the coordinate plane of the form @xmath394 ; @xmath395 ; @xmath396 ; @xmath397 to which the lagrangian manifold is projected . the lagrange property means that the number of planes can not coincide ( there are no planes of the form @xmath398 and @xmath399 ) . to every projection there corresponds some potential ( @xmath400 is the thermodynamic potential , etc . ) . this is an obvious correspondence . if it were more elaborated , then , on one hand , the transition from the action @xmath401 to the `` action''coordinate @xmath402 would be not `` so obvious '' ( see formulas ) . on the other hand , it would be natural to use the semiclassical ( wiener feynman ) quantization of action rather than the scaling hypothesis . ( the quantization of the lagrangian manifold differs from the full quantization of thermodynamics @xcite in the same way in which the semiclassical bose sommerfeld geometric quantization differs from the quantization of schrdinger , heisenberg , and feynman . the term `` dequantization , '' which is well - known in the tropical mathematics @xcite , means the wiener or tunnel quantization of the lagrangian manifold , and then the passage to the limit as the quantization parameter ( the viscosity ) tends to zero . the second quantization is always associated with the identity of particles , and , if it is carried out for classical particles , then it is tacitly assumed that the particles are indistinguishable for the observer . instead of an @xmath47-dimensional problem , we arrive at the three - dimensional picture in which @xmath47 particles are distributed . the vlasov equation @xcite is obtained from the second quantization of classical mechanics . however , the original arguments used by vlasov were actually based on the assumption that the particles can be regarded as identical ones . in the classical system of hamilton equations for @xmath47 particles , even if the hamiltonian is invariant under any permutation of the particles , the initial conditions need not have this property . however , the initial conditions of the liouville equation can be regarded as data satisfying the conditions of symmetry . indeed , let @xmath403 are initial conditions for the hamiltonian system whose hamiltonian is invariant under every permutation @xmath404 and also under every permutation @xmath405 . for example , let @xmath406 substituting the initial conditions into the hamiltonian , we obtain the energy @xmath407 the energy is conserved along the trajectories of the hamiltonian system . consider further the liouville equation corresponding to the hamiltonian system @xmath408 where @xmath409 stands for the poisson bracket , with the initial condition @xmath410 where @xmath275 satisfies . this equation describes the distribution corresponding to the hamiltonian system with the initial conditions given above . the liouville equation and the initial conditions are symmetric with respect to any transposition of @xmath411 and @xmath412 and to any transposition of @xmath413 and @xmath414 . this symmetry is preserved for the solutions . according to the gibbs distribution for the gibbs ensemble , every distribution can be expressed in terms of energy . therefore , it is symmetric with respect to any permutation of the particles . schnberg @xcite carried out a second quantization of this system in the fock space . in @xcite , the vlasov equation was obtained under the assumption that the interaction is small and the number of particles is large . the bbkki chains are also symmetric with respect to these permutations . hence , for any distribution in the many - body problem , such a symmetry follows . thus , we arrive at the invariance with respect to the permutations of the particles , and thus to a `` distribution of bose einstein type '' for the statistical physics of classical particles . other mathematically rigorous arguments which lead to a `` distribution of bose einstein type , '' in the form of lemmas and theorems ( see @xcite ) , and hence also the distributions of classical particles , obey the laws of number theory . although a modern macroinstrument can not trace the motion of every particle ( because of discreteness of the observation times in relaxationally stepwise process ) , which is possible at the classical level , but it can distinguish between molecules and dimers or clusters . the clusters consisting of more than two molecules occur in gas much less frequently than dimers . dimers are observable at all temperatures , and a macroinstrument can calculate their average percentage at a given temperature . this is an important new phenomenon in experiment , and this phenomenon was not available to the great who formulated the basic laws of thermodynamics . dimers occur and become immediately split by monomers ( single molecules ) , and they are created and annihilated in different places . they occur because there are _ quantum _ forces of attraction between molecules ( the dipole - dipole interaction ) . the dimers are virtual , as the ideal liquid is . to take into account this important phenomenon ( the creation and annihilation of dimers ) mathematically , one obviously needs to make the `` second '' quantization and introduce the creation and annihilation operators for dimers , i.e. , for pairs . the author referred to this `` second '' quantization as the `` ultrasecond '' quantization due to the introduction of creation and annihilation operators for pairs . in the special case of the bardeen model , this quantization was introduced in essence @xcite , @xcite ; however , since this model is , roughly speaking , exactly solvable , these operators turned out to be hidden in the model in a sense . in general , the ultrasecond quantization and the asymptotic behaviors associated with it are rather cumbersome and lead to quantum equations involving the planck constant @xmath281 . the passage to the limit as @xmath415 , and then the passage to the limit as the viscosity tends to zero , are cumbersome , and we present here only a part of this passage , which is related , as in the previous section , with the introduction of an infinitesimal viscosity into the classical scattering problem ( for @xmath416 ) . this means that we introduce the viscosity and , after manipulations , pass to the limit as the viscosity tends to zero . this procedure will enable us to find the boyle temperature @xmath1 , and then also the boyle density @xmath417 , i.e. , the so - called zeno line , which is present in the van der waals model and which was first noticed by bachinski in experiments with pure gases . we shall further obtain the so - called law of corresponding states . the attraction between the particles occurs in the quantum mechanical consideration of the dipole - dipole interaction . in the standard semiclassical limit , if the distance between neutral molecules is fixed ( does not depend on the parameter @xmath281 , i.e. , on a dimensionless parameter proportional to @xmath281 ) , then , as @xmath415 , the attraction disappears . in this sense , the use of an attraction potential in molecular dynamics using the classical newton equations for many particles is at least baseless . however , if , along with @xmath281 , the problem involves other small and large parameters , then the attraction potential can be kept for some relationships among these parameters under the passage to the limit as @xmath415 . since the scattering problem has another parameter tending to infinity , for example , the time of scattering is considered in the interval from @xmath418 to @xmath419 , it can happen that , as @xmath420 and @xmath421 simultaneously ( provided that there is a dependence between these parameters ) , an attractive potential of the order of @xmath422 is kept ( as @xmath415 ) , where @xmath423 stands for the distance between the particles . as we see below , to obtain a `` rough '' thermodynamics leading to the law of corresponding states , it is sufficient to determine the values of the boyle temperature @xmath1 and the boyle density @xmath424 only for mercury . as is known , the mercury isotherms are very close to the van der waals model ( see fig . 14 ) , and hence the lennard jones potential model must provide a good description of the following two important facts : 1 ) attraction existence ; 2 ) collision of molecules due to a rapidly increasing repulsive potential . we present only a typical example of studying the relation between the actual gas and the interaction potential , which corresponds to the case of a small intermolecular distance such that quantum effects must inevitably arise . but the natural choice of the potential @xmath146 for an actual gas and and the fact that the zeno lines are taken into account give us mercury isotherms in sec . 3.5 . as an example , we consider the lennard jones potential , noting that , in our fundamental manipulations , the repulsive part of the potential does not play any role . the only essential quantity is the so - called effective radius @xmath232 , because it determines a one - dimensional elementary length . as is known , in the radially symmetric case , @xmath425 in the original scattered particles , we prescribe an energy @xmath275 and an impact parameter @xmath426 . the momentum @xmath97 , as well as the energy @xmath275 , is preserved . we also know that @xmath427 expressing the energy @xmath275 , we obtain for the attraction @xmath428 in the domain @xmath429 . in the scattering problem , for the interaction potential , one considers the lennard jones potential @xmath430 where @xmath167 stands for the energy at the well depth , @xmath232 for the effective radius , and @xmath431 for the distance between two particles with radius vectors @xmath432 and @xmath433 . in the two - particle problem , in the absence of external potential , the problem is reduced to a one - dimensional radially symmetric problem . in problem , for different values of @xmath426 , there are other barriers and wells . at the stationary points @xmath434 and @xmath435 , the velocity vanishes , and thus these values can be evaluated by using the potential term only . we speak now of a pair of particles with the mass center which is caught by the trap ( rather than of a single particle ) . therefore , the difference @xmath436 is the very energy which is needed to knock out the pair ( dimer ) from the trap . after formation of a dimer at @xmath41 , one should consider the collision of a dimer with a monomer according to the same scheme , assuming that the pair - dimer ( a @xmath58-particle ) has already been formed . further , one considers the scattering problem already for the dimer at @xmath437 and a particle of the same mass @xmath55 . the successive consideration of such a multistep procedure leads to formation of a three - dimensional cluster , and we obtain a temperature significantly lower than @xmath2 . it is important that the first step gives an upper bound , and this restriction is natural . in an experiment , the percentage of dimers in gas can be calculated . it can be seen how dimers are created and how they are annihilated ( broken by monomers ) . after this , the average number of these events is calculated . the higher is the temperature , the higher is the average energy of the monomers , and the smaller is the number of dimers . the main point is that , under this approach , there are only two values , @xmath435 and @xmath434 , which are kept in the skeleton of the scattering problem ( cf . the skeleton of the amoeba in the tropical mathematics @xcite ) . for @xmath438 , the well disappears . for the attractive part of the lennard jones potential , this energy is equal to @xmath439 . with regard to the standard clausius considerations this very ratio is of interest for us . ] , we can see that the average energy of the particles is equal to @xmath440 . the average energy is the temperature , and @xmath441 . above this temperature , there is no well . in thermodynamics , for physical reasons , this is the so - called boyle temperature @xmath1 . in our framework , the boyle temperature is defined as the temperature above which the dimers are practically absent . this is a new approach . according to this conception , the boyle temperature for argon ( ar ) is @xmath442 and for krypton ( kr ) it is @xmath443 , while the tables of the experimental work @xcite give @xmath444 for ar and @xmath445 for kr . the discrepancy between the theoretical and experimental values is of the order of 23% . the critical temperature @xmath435 must correspond to the deepest well , i.e. , to the maximum value of the difference @xmath446 for all impact parameters @xmath426 . this difference determines the drop of the energy of a dimer after this dimer was captured by the `` trap , '' and thus determines the energy which a monomer must have to knock out the dimer from the well ( i.e. , for the dimer to collapse ) . the height of the barrier `` protects '' the created pair whose reduced mass was captured by the trap of `` dimers '' and `` clusters '' from `` shocks '' of monomers . as the temperature decreases , @xmath447 , the height of the barrier reduces , and , to survive , the clusters must create their own barrier in the form of a microanalog of the surface film . thus , a `` domain '' must occur , a three - dimensional cluster ( the so - called elementary cluster ) which has at least one particle which is protected by other particles . this is a new definition of the critical temperature @xmath2 as the temperature below which clusters are formed from dimers . calculations give @xmath448 at the point @xmath449 . the impact parameter at this point is equal to @xmath450 . let us now obtain analytical formulas for the zeno line in dependence on the potential . . ] stands for the radius vector of the dimer ; it is marked on the abscissa axis . a `` particle '' falls from the left , from the point @xmath451 , where @xmath426 stands for the impact parameter . after reflection from the `` wall '' , i.e. , from the potential , in the presence of viscosity , the particles meet the barrier and then after rather many reflections from the barrier and the `` wall '' drop on the well bottom in a greater time interval . ] let us use considerations of dimensional analysis for the scattering problem and the definition of the one - particle ( the so - called thermal ) attraction potential . the scattering problem is considered for the lennard jones potential , and therefore there is an additional parameter of length in the problem , the parameter @xmath232 , which is the effective radius . the attraction potential occurs in the quantum theory of the dipole dipole interaction . if we fix the distance between the particles and assume that the semiclassical parameter @xmath281 tends to zero , then the attractive potential vanishes . this means that , as @xmath415 , the distance between the particles decreases . it follows that the attractive potential acts between `` nearest neighbors '' only . therefore , it is natural to use the expansion of an attraction single - particle potential in powers of the radius @xmath423 up to @xmath452 only . the `` dressed '' or thermal potential @xmath453 is attracting . as is well known , it was derived from the fact that the correlation sphere for the @xmath47-particle for the gibbs distribution is finite @xcite . one of the most interesting points of independence of a macroinstrument of a microinstrument manifests itself when applying the dimension theory @xcite . a macroinstrument determines the volume @xmath46 . according to the independence of the thermodynamic quantities on the shape of the volume @xmath46 , the volume @xmath46 ensures us that we have the dimension in the dimension theory is three ; however , this volume does not give us any one - dimensional measure . which is the typical length in the thermodynamic process . a microinstrument determines the effective radius of the molecule and the mean free path . however , in dimension theory , we can not measure the typical length of the macrothermodynamics by using the radius of the molecule or the mean free path , even if the volumeis a torricelli tube and its typical thickness is small as compared with the case in which the vessel is a ball . these considerations show that the only possible dimensionless combination for the argument of @xmath454 is @xmath455 since @xmath456 , it follows that the expansion is @xmath457 the constant @xmath458 gives no contribution to the scattering problem , and the thermal `` single - particle '' potential turns out to be proportional to the density . on the plane @xmath459 , the maximum of the binodal ( according to fig . 8 for @xmath73 ) is equal with respect to @xmath460 to the very value @xmath257 , which enables us to find the proportionality coefficient . it turns out to be equal to one . the situation in which the thickness of the tube is `` commensurable '' to the radius of the molecule leads to quite different effects : to the superfluidity of water in a nanotube and to the freezing of water at @xmath461 ( see @xcite ) . @xmath460-diagram for gases corresponding to simple liquids . here @xmath462 and @xmath463 . the zeno line ( the straight line @xmath464 ) in the phase diagram . for the states @xmath465 ( the hard fluids ) , the repulsive forces dominate ; for the states @xmath466 ( soft fluids ) , the attraction forces dominate . ] expanding @xmath467 we can make the separation of variables in the two - particle problem to a scattering problem for a pair of particles and to the problem of their joint motion for @xmath468 , just as it was done in @xcite . in this case , in the scattering problem , a quadratic attraction potential ( an upturned parabola ) @xmath469 is added to the lennard jones interaction potential , and @xmath470 for the isochoric process . in the scattering problem thus obtained , there are two points of rest , namely , the stable one , @xmath434 , and the unstable point @xmath435 . their ratio is a dimensionless quantity . as follows from the previous section , @xmath471 , where @xmath45 stands for the pressure , @xmath47 for the number of particles , @xmath48 for the temperature , and , due to the fact that a stable stationary point has the meaning of temperature , it follows that the ratio @xmath472 enables us to wrote the curves @xmath473 in the graph @xmath48 , @xmath474 . the curve at @xmath475 is called the _ zeno line _ ( or the _ bachinski parabola _ ) , and the locus of the beginnings of the curves @xmath476 ( for @xmath477 and @xmath478 ) is referred to as the _ binodal_. thus , in our view , the zeno line determines the temperatures for which the dimers become practically nonexistent for a given density . denote by @xmath479 the value of @xmath460 at the maximal point of the binodal and denote the endpoint of this curve on the @xmath460 axis by @xmath424 . in @xcite . this point was referred to as the hypothetical point @xmath424 ( the boyle point ) . calculating the value of @xmath480 , we obtain @xmath481 , which coincides with the values of @xmath480 for the noble gases up to thousandths . the ratio @xmath482 also coincides with the values of this quantity for the noble gases . table 1 shows the data corresponding to the resulting diagram ( for @xmath483 in `` molecular '' values ) , and note the discrepancy between the basic dimensionless relations obtained by the data of molecular dynamics and the theoretical relations obtained by physicists from the chain bbkki and the @xmath47-partial gibbs distribution . table 1 @xmath484 on the top line of the table , the theoretical values for @xmath480 , @xmath482 , and @xmath485 , obtained using the above theory are presented . the second line contains the values of the same quantities evaluated according to the latest data of molecular dynamics and results of theoretical physicists for the lennard jones potential . the third line gives the values obtained from the van der waals equation , which is empirical . the value of @xmath486 can be computed in the experiment very accurately , and it is equal to @xmath487 for noble gases , nitrogen , oxygen , and propane . the value of @xmath482 ( the ratio of the critical value of @xmath460 critical to @xmath424 , i.e. , to the entire length of the segment with respect to @xmath488 on which the zeno - line `` cuts '' the abscissa axis away ) evaluated in the above theory coincides with the corresponding values for water , argon , xenon , krypton , ethylene , and a number of other gases . let us present detailed calculations to find the zeno - line . consider the potential @xmath489 its first derivative is equal to @xmath490 and the second derivative is @xmath491 we obtain a solution of the equation in the form @xmath492 substituting the value @xmath493 into , we find @xmath494 , the zeno - line , i.e. , a segment , which is straight up to 3% , @xmath495 where @xmath424 stands for the maximal density as @xmath496 . .,title="fig : " ] + we have @xmath497 where @xmath498 is an isotherm - isochore . therefore , @xmath499 let us express @xmath49 in terms of @xmath500 for @xmath501 and @xmath156 and for @xmath502 , @xmath503 where @xmath86 and @xmath64 . the value of @xmath504 is defined in this very normalization . therefore , @xmath505 on the other hand , @xmath506 consequently , @xmath507 and @xmath508 substituting this into , we obtain @xmath509 and @xmath510 as @xmath511 . therefore , as @xmath511 , the value @xmath512 is negligible . consequently , @xmath513 here @xmath67 corresponds to @xmath514 , which is the minimal value of @xmath49 on the critical isotherm for @xmath515 ( see fig , 9 ) . since @xmath516 where @xmath262 , it follows that @xmath517 where @xmath518.\ ] ] hence , @xmath519 the expression @xmath520 tends as @xmath521 to @xmath522 , where @xmath167 stands for the lower limit of the integral expression for @xmath523 at @xmath524 . similarly , the expression @xmath525 at @xmath526 is equal to @xmath527 . hence @xmath528 as @xmath529 and @xmath530 therefore , @xmath531 for all values of @xmath168 . hence , by , @xmath532 moreover , it is clear that @xmath533 as @xmath534 and @xmath529 . the value of @xmath535 determines the minimum of @xmath536 and the maximal density of holes . to determine the gas - liquid transition , as in sec . 2.3 , with the correction to the zeno line taken into account , we derive equations of the form - , by normalized the activity for the critical isotherm . ) . ] . the inclined line is the continuation of the theoretical critical isotherm shown in fig . 9 to the domain of negative values of @xmath45 and @xmath49 . the initial point of the curve @xmath537 ( @xmath258 ) is at a distance from the point @xmath263 , and the starting point @xmath538 ( @xmath539 ) of the curve coincides with the point of intersection of the dashed line and the solid line . ] obviously , the rougher is the device , the greater is the dissipation parameter , and therefore the more important is the uncertainty principle . if our device does not distinguish some molecules from one another , then this is a rough instrument . it is not necessary that the device itself be so rough . it is sufficient to say that the experimenter does not want to distinguish molecules and computes the density roughly , counting all the molecules for which he wants to construct a `` rough '' thermodynamics . hence , when speaking more precisely , from the point of view of mathematics , the rougher thermodynamics we want to receive , the more rough will be the answer due to the wiener uncertainty principle . our rough instrument does not distinguish particles not only in mixtures . measuring different particles , the observer thinks that these are the same molecules , and only the measurements are somewhat scattered . this is even a more rough thermodynamics . it is referred to the fluid part , when the gas - liquid is not distinguished , clusters occur , etc . the critical points are on the boundary of the fluid domain , and we approach them from the side of the fluid domain for @xmath540 . when considering above the phase transition , we have equated the chemical potentials of the liquid and the gas phases on the critical isotherm , assuming that there is no phase transition there . we considered the case in which the viscosity vanishes , and we obtained a phase transition which was not smeared . now , when considering the problem with a coarser device , we no longer have any right to assume that the dissipation tends to zero . the uncertainty principle gives us a fairly large smearing of the phase transition ; however , it happens on a `` rough '' critical isotherm which is measured by a rough instrument . the latter can not distinguish now not only particles of a single pure gas but does not distinguish particles of different gases either . we have compared the wiener quantization of thermodynamics with the dissipation resulting in a shock wave . however , the dissipation may be different in different substances , while we are interested now in the hugoniot conditions for the entire mixture , and we do not want to distinguish stratificationally occurring internal shock waves within a common shock wave . this is particularly evident when the dissipative parameters of viscosity and thermal conductivity are different ( see @xcite , 95 ) , the viscosity @xmath541 is small , and the thermal conductivity is relatively large , @xmath542 . if the processes inside the shock wave are not of interest for us , then we pose the hugoniot conditions on a shock wave spread with respect to heat conductivity . on the other hand , if the values of viscosity in a mixture of different gases are different but not dramatically different from one another , then the width of a shock wave thus obtained is defined by the average viscosity ( see fig . [ [ coincidence - of - the - solution - of - distributions - of - boseeinstein - type - for - fractional - dimension - with - the - solutions - obtained - in - the - van - der - waals - model ] ] coincidence of the solution of distributions of bose einstein type for fractional dimension with the solutions obtained in the van - der - waals model ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ on the standard @xmath89-diagram , which is presented in all thermodynamics textbooks as illustrating the vdw equations , let us compare the gas isotherms for the temperatures less than or equal to the critical temperature . it is not hard to see that he gas spinodal for the vdw equation coincides very precisely with the quarter of an ellipse . in the general case , we know two points through which the ellipse must pass . one point is the critical point and the other one is the point at @xmath93 and @xmath543 in the case of isotherms corresponding to the vdw equation which are close to the isotherm of mercury . now that we know this , we can say that when the spinodal for @xmath263 reaches a point lower than 0.5 , then the number of degrees of freedom near this point is slightly less than 3 . but as was indicated above , the experimental isotherms can not reach this point , since the spinodal is bounded by the value @xmath544 corresponding to the temperature @xmath545 of the triple point . let us explain the reasons for which we approximate the spinodal by an ellipse . we know the two endpoints of the spinodal and the two tangents to it at these points are parallel to the coordinate axes of the @xmath161 plane . the ellipse can be transformed to a circle by changing the scale of the axes . the circle has a constant radius of curvature , and from this point of view the approximation by a circle is as natural as the simplest approximation of a curve joining two points by the line segment with those endpoints . this reminds us of the geometry of poincar s famous thermodynamical two - dimensional model of the universe , called _ poincaria _ by gindikin @xcite . in that model , there is a circle ( the absolute ) as unaccessible to the isotherms as , in the situation described above , the spinodal is unaccessible to isotherms . [ [ the - law - of - preference - of - cluster - formation - over - passage - to - liquid - state ] ] the law of preference of cluster formation over passage to liquid state ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ `` the law of economic profitability '' asserts that at the same temperature @xmath163 , smaller than @xmath2 , gas particles tend to increase the number of degrees of freedom from the initial value @xmath546 up to @xmath238 , which is critical for the given temperature @xmath62 . in economics , this preference should be understood as the preference of uniting ( associating ) over incurring debts . in thermodynamics it should be understood as preferring to form clusters over passing to the liquid state . it is easy to show that the correction to the bose einstein distribution related to this law improves the coincidence of our theoretical isotherms with the isotherms coming from the vdw equation to such an extent that they are practically undistinguishable . the geometric locus of points where the phase transition gas to liquid occurs is known as the _ binodal_. the geometric locus of points where the tangent to the isotherm is perpendicular to the @xmath45 axis in the @xmath161 diagram is known as the _ spinodal_. the point @xmath545 which lies on the binodal , and at which three phases coexist : gas , liquid , and solid , is called the triple point . so this point lies on the binodal , and isotherms for temperatures lower than that point can not be observed experimentally ( see the picture appearing in @xcite ) . a good agreement with the latest experimental values for nitrogen takes place for the isotherms from @xmath548 up to the point @xmath549 . the spinodal is the thick lower line ; it comes from the empirical model devised by the authors of the paper @xcite . here we see a significant difference from the van - der - waals model . in the latter , the spinodal is a quarter of an ellipse on the @xmath161 diagram which joins the points @xmath543 and @xmath550 . the tangency point of the isotherm with the spinodal is at the end point of the spinodal and is an accumulation point . let us define the poisson adiabat for fractional dimension . to do this , consider the limit as @xmath551 , i.e. , the case of the old ideal gas . we have @xmath552 @xmath553 on the @xmath554 diagram with @xmath64 as @xmath555 , we have @xmath556 therefore , @xmath557 we have calculated the angle at which the the gas isotherm issues from the point @xmath558 whose critical value of the compressibility factor is @xmath559 thus , we have obtained a generalization of the poisson adiabat to the case of a fractional number of degrees of freedom . the equation of the isotherm for a fixed value of @xmath560 is of the form @xmath561 where @xmath232 is the activity , @xmath562 , while @xmath563 is determined by using the coincidence of the relations @xmath564 with the spinodal constructed above . in this situation @xmath563 is determined uniquely . the final main equations of the `` critical '' isotherms of a pure gas corresponding to the value @xmath514 will be @xmath573 for the vdw equation to which the ellipse passing through the points @xmath574 and @xmath575 corresponds , the coincidence of the isotherms is so precise that on the plot they are completely undistinguishable . as v. s. vorobiev has shown , if the law of preference stated above is not taken into account , the discrepancy with the experimental data for nitrogen are greater . since , as @xmath576 , where @xmath577 is the triple point corresponding to a gas with the given value of @xmath514 , the isotherms become denser , it follows that the derivative of the spinodal with respect to @xmath45 on the @xmath0 diagram is zero . therefore , instead of ending on the line @xmath263 , the quarter of the ellipse terminates at the point @xmath578 with the corresponding value of @xmath579 ( @xmath159 ) . this uniquely determines the elliptic spinodal of the gas . consider a virtual gas whose critical temperature , denoted by @xmath580 , coincides with the temperature of the triple point of the given gas . let us consider two isotherms : the critical isotherm of the virtual gas and the isotherm of the given gas for @xmath581 . from relation , for a fixed @xmath563 with @xmath582 , we can find @xmath544 ( the value of @xmath168 at the triple point ) . for known values of @xmath583 and @xmath579 , using formula ( 13 ) , we obtain the value of @xmath584 . thereby we find on the @xmath0 diagram the terminal point of the spinodal at which the derivative of the quarter of the ellipse vanishes . we have found this by using the experimental values of the two endpoints of the quarter of the ellipse , which is our gas spinodal . thus , the positions of the _ critical point _ and the _ triple point _ ( well known from standard tables ) _ entirely determine _ the isotherms of the given gas . as was already pointed out in the author s papers , it is more natural to pass from momenta @xmath381 to energies @xmath585 and to generalize the problem of the transition of the energy @xmath586 to the energy @xmath587 , i.e. , to the hamiltonian containing repulsion . here integration of the distribution corresponding to the number of particles must be performed with respect to the measure @xmath590 ( integration over angles is omitted ) . integration of the pressure distribution must be performed with respect to the measure @xmath591 over the three - dimensional volume @xmath46 . when @xmath592 , in order to determine @xmath563 , we use parastatistics in which @xmath58 varies from minus infinity to plus infinity . in this case the isotherm issued on the @xmath593 plane from the point @xmath594 comes to the line @xmath475 for certain positive @xmath58 . in the discrete case , for @xmath156 we have the law of reflection @xmath602 since the function @xmath603 is monotone decreasing , it follows that @xmath604 hence for @xmath71 the isochor @xmath605 coincides with the isochor of the second sheet , corresponding to negative values of @xmath168 ( i.e. second phase ) for @xmath240 and @xmath606 , so , that @xmath607 and @xmath71 . [ [ refinement - of - the - asymptotic - continuation - of - a - perfect - liquid - to - the - second - sheet - according - to - the - preference - law ] ] refinement of the asymptotic continuation of a perfect liquid to the second sheet according to the preference law ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ therefore , on the diagram @xmath144 , the spinodal is a segment @xmath145 , @xmath75 ( in the case of the van - der - waals normalization @xmath86 and @xmath64 ) . for @xmath149 , the bose condensate occurs and , consequently , for the liquid phase on the spinodal , the quantity @xmath611 remains constant on the liquid isotherm . this means that the isotherm of the liquid phase that corresponds to a temperature @xmath48 is given by @xmath612 all isotherms of the liquid phase ( including the critical isotherm at @xmath152 ) pass through the origin @xmath153 , @xmath154 and then fall into the negative region ( or to the second sheet ) . the point @xmath153 corresponds to the parameter @xmath155 , and hence to the continuation to @xmath156 , since , for @xmath71 , the pressure @xmath613 can be extended to @xmath160 . we shall see below that the value of @xmath49 as @xmath614 is also positive , and therefore the spinodal for @xmath160 gives another sheet on the diagram @xmath161 ( the second one ) ; it is more convenient to take this sheet onto the negative quadrant . under the assumption that the transition to the liquid phase is not carried out for @xmath615 , we equate the chemical potentials @xmath58 and @xmath162 for the `` liquid '' and `` gaseous '' phase on the isotherm @xmath615 ( this fact is proved below ) . we can make the normalization of activity @xmath624 at the point @xmath234 , and we can find @xmath625 by matching the liquid and gaseous branches at @xmath234 for the pressure , in order to prevent the phase transition on the critical isotherm at @xmath626 . in what follows , we normalize the activity for @xmath163 with respect to the value of @xmath233 computed below . then the chemical potentials ( in thermodynamics , the thermodynamic gibbs potentials for the liquid and gaseous branches ) coincide , and therefore there can be no phase transition `` gas - liquid '' at @xmath152 . now , for the isochore - isotherm of the `` incompressible liquid '' to take place , we must construct it with regard to the relation @xmath236 , namely , @xmath627 where @xmath621 according to , remains constant on the liquid isotherm . let @xmath246 be the activity of the gas and @xmath635 the activity of the liquid . we present the condition for the coincidence of @xmath97 and of the activities at the point of the phase transition , @xmath636 @xmath637 [ [ the - positive - chemical - potential - for - the - number - of - degrees - of - freedom - less - than-2-gamma0 ] ] the positive chemical potential for the number of degrees of freedom less than 2 ( @xmath156 ) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ this relation restricts value @xmath653 , which turns out to be small . therefore , `` velocity '' at which @xmath657 reaches the line @xmath475 for @xmath658 is high , and an interval of isochor between @xmath515 and @xmath475 on the @xmath0 diagram form an almost straight line ( see figs . 1113 ) . let us note the important equality which determines the constant @xmath243 in the distribution for @xmath146 potential . according to , we have @xmath659 hence by substituting in the value @xmath243 is determined uniquely for @xmath156 . since the rightmost isochore ( which is not shown in fig . 11 ) is a segment of a straight line , it follows that all isochores of high density must also be line segments . they pass through the point @xmath660 on the zeno line and the point @xmath661 on the line @xmath662 . we thus obtain ( when including the isochores shown in fig . 11 ) a complete family of isochores for @xmath663 , @xmath664 , related to the law of corresponding states . to any point of an isochore in the plane @xmath665 there corresponds a point of temperature , and we construct isotherms which , up to the wiener uncertainty principle , correspond to the experimental law of corresponding states ( fig . 12 ) . in fig . 13 , the graph of an experimental isotherm for mercury is presented ; this graph was kindly evaluated by professor v. s. vorobev , according to the most recent data , at the instance of me . note that the passage gas liquid happens at @xmath666 along a slanting line rather than a vertical one , which is related to nonzero viscosity and the wiener uncertainty principle . this effect is of the same nature as the jump of critical exponents and `` thickness of the layer '' of a shock wave . the author is grateful to v.v . brazhkin , a.e . gekhman , b.v . egorov , d.yu . ivanov , yu.m . kagan , a.g . kulikovskii , g.a . martynov , i.v . melekhov , d.s . minenkov , v.n . ryzhov , a.s . kholevo , and a.v . chaplik for fruitful discussions . the author is especially indebted to professor v.s . vorobev who had verified all graphs and and carried out an entire series of the most important comparisons of theoretical results with experimental data . l. d. landau and e. m. lifshits , _ course of theoretical physics , _ vol . 3 : _ quantum mechanics : non - relativistic theory _ ( nauka , moscow , 1964 ; transl . of the 1st ed . , pergamon press , london paris and addison - wesley publishing co. , inc . , reading , mass . , 1958 ) . e. m. apfelbaum and v. s. vorobev , `` correspondence between the ideal bose gas in a space of fractional dimension and a dense nonideal gas according to maslov scheme '' , russ . j. math . phys . * 18 * ( 1 ) , 1925 ( 2011 ) . v. p. maslov , `` the effect of a natural trap ( the boundary of the volume ) on the bose distribution of quantum particles in the three - dimensional and two - dimensional cases , '' math . notes , * 92 * ( 6 ) 868871 , ( 2012 ) . v. p. maslov and p. p. mosolov , `` asymptotic behavior as @xmath669 of trajectories of @xmath47 point masses , interacting according to newton s gravitation law , '' izv . nauk sssr ser * 42 * ( 5 ) , 10631100 ( 1978 ) [ math . ussr - izv . * 42 * ( 5 ) , 11011119 ( 1978 ) ( 1979 ) ] . v. p. maslov , `` solution of the gibbs paradox in the framework of classical mechanics ( statistical physics ) and crystallization of the gas c60 , '' mat . zametki * 83 * ( 5 ) , 787791 ( 2008 ) [ math . notes * 83 * ( 56 ) , 716722 ( 2008 ) ] . m. schnberg , `` application of second quantization methods to the classical statistical mechanics , '' nuovo cimento * 9 * ( 12 ) , 1139 - 1182 ( 1952 ) ; `` application of second quantization methods to the classical statistical mechanics ( ii ) , '' nuovo cimento * 10 * ( 4 ) , 419472 ( 1953 ) . v. p. maslov and g. v. koval , `` on a generalization of the bardeen cooper schrieffer method for pairwise interactions , '' teoret . mat . * 154 * ( 3 ) , 584592 ( 2008 ) [ theoret . and math . * 154 * ( 3 ) , 495502 ( 2008 ) ] . v. p. maslov , `` thermodynamics of fluids : the law of redestribution of energy , two - dimensional condensate , and @xmath48-mapping , '' teoret . mat . * 161 * ( 3 ) , 422456 2009 ) [ theoret . and math . phys . * 161 * ( 3 ) , 16811713 ( 2009 ) ] . v. p. maslov and v. e. nazaikinskii , `` on the distribution of integer random variables related by a certain linear inequality : i , '' mat . zametki * 83 * ( 2 ) , 232263 ( 2008 ) [ math . notes * 83 * ( 2 ) , 211237 ( 2008 ) ] . v. p. maslov and v. e. nazaikinskii , `` on the distribution of integer random variables related by a certain linear inequality : ii , '' mat . zametki * 83 * ( 3 ) , 381401 ( 2008 ) [ math . notes * 83 * ( 3 ) , 345363 ( 2008 ) ] . v. p. maslov , `` bose - condensate in the two - dimensional case , the @xmath670-point , and the thiess - landau two - fluid model , '' teoret . mat . * 159 * ( 3 ) 174176 , ( 2009 ) ; `` taking parastatistical corrections to the bose - einstein distribution into account in the quantum and classical cases , '' teoret . * 172 * ( 3 ) 468478 , ( 2012 ) [ theoret . and math . phys . ]

in the first part of the paper , we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length , and also the relationship between these observable quantities . the concept of the number of degrees of freedom , which relates the observable quantities listed above , is generalized to the case of low temperatures . an analogy between the creation and annihilation operators for pairs ( dimers ) and the creation and annihilation operators for particles ( molecules ) is carried out . a generalization of the concept of a bose condensate is introduced for classical molecules as an analog of an ideal liquid ( without attraction ) . it is shown that the negative pressure is equivalent to the @xmath0 diagram covering by the second sheet . the negative pressure in the liquid is treated as holes ( of exciton type ) in the density of the bose condensate . the phase transition gas - liquid is calculated for an ideal gas ( without attraction ) . a comparison with experimental data is carried out . in the other part of the paper , we introduce the concept of new observable quantity , namely , of a pair ( a dimer ) , as a result of attraction between the nearest neighbors . we treat in a new way the concepts of boyle temperature @xmath1 ( as the temperature above which the dimers disappear ) and of the critical temperature @xmath2 ( below which the trimers and clusters are formed ) . the equation for the zeno line is interpreted as the relation describing the dependence of the temperature on the density at which the dimers disappear . we calculate the maximal density of the liquid and also the maximal density of the holes . the law of corresponding states is derived as a result of an observation by a macrodevice which can not distinguish between molecules of distinct gases , and a comparison of theoretical and experimental data is carried out .

Seven-time ELLE cover star Keira Knightley has confirmed her pregnancy to ELLE. We just got off the phone with her rep, who happily admitted the rumours were true, but also said that Keira will not be making any further comment. So we won't be seeing pics of the scan posted on Instagram then. Photo: Getty We're guessing the baby will be coming late March/April time. When we interviewed Keira, 29, last summer, she told us she wasn't planning children with husband James Righton just then (hah!) but babies were clearly on the brain. When we talked about her fantasy film script, she said it would be about 'The horrendous issue of trying to have a baby when you can’t. 'I’ve seen friends who’ve been through this, it seems like one of the most dramatic things that can happen to half of the population – and actually, the other half as well because, my god, the unbelievable toll it takes on male partners – and there are no good films about it.' Even then, she had pretty clear ideas of what would and wouldn't go for a daughter when she has one. Like acting, for instance: 'Oh, 100%, I’d absolutely tell her not to,' she said. "I would 150 million trillion per cent be totally discouraging. Teenage years should be done privately. You should be going out and getting unbelievably drunk, getting into ridiculous situations, making mistakes. That’s what that time of life is about and we should do that privately. 'Saying that, I don’t regret it – I wouldn’t do my life any differently, but having lived through it… There was a very long time when [interviewers] were all: "Well you’re a sh*t actress and you’re anorexic and people hate you" which, for a teenager is a very strange thing.' Will Keira's kid be as cute as this one? Or this one? ||||| It will be a very merry Christmas for Zoe Saldana and husband Marco Perego this year! The actress is said to have given birth to her twins at a Los Angeles hospital on Monday. The Guardians of the Galaxy star was reportedly carrying two little boys, but the couple has yet to release the gender of their new bundles of joy -- or any baby names. A friend did speak out, however, saying the new parents are "ecstatic" and stated both want a big family. More From The Stir: 150 Most Popular Names for Twins Looks like they're off to a good start with two babies at once! Congratulations to the happy family. We can't wait to hear the names they've chosen for their little ones! What do you think would be good names for twin boys? Image via Zoe Saldana/Instagram

– Keira Knightley and her husband of a year and a half, James Righton, are expecting their first child, Knightley's rep confirmed to Elle UK today. Multiple sources told Page Six the same thing yesterday. Rumors started swirling last month but really ramped up Sunday night, when Knightley did not imbibe during the (Moët-sponsored) British Independent Spirit Awards and wore a "billowy" dress unlike the fitted attire she usually dons. The 29-year-old is more than three months along, according to Page Six's sources; Elle guesstimates she's due in late March or April. (Click to read about another beloved actress who just gave birth to twins.)

a key issue in studying in - medium @xmath0 meson interactions concerns the strength of the attractive @xmath0 nuclear potential @xcite . related topical questions involve ( i ) the underlying free - space @xmath8 interaction and whether or not it can realistically support @xmath0 nuclear clusters ( see ref . @xcite for a recent review ) , and ( ii ) the role of @xmath0 mesons in multistrange self - bound matter @xcite and in compact stars @xcite . an order of magnitude estimate of the nuclear potential @xmath9 is provided by the leading - order ( lo ) tomozawa - weinberg ( tw ) vector term of the chiral effective meson - baryon lagrangian @xcite which in the born approximation gives @xmath10 where @xmath4 is the nuclear density , @xmath11 , and @xmath12 mev is the pion decay constant . this attraction is doubled , roughly , within chirally based coupled - channel @xmath13@xmath14@xmath15 calculations that produce dynamically a @xmath13 quasibound state loosely identified with the @xmath16 resonance @xcite . deeper potentials , in the range @xmath17(150200 ) mev are obtained in comprehensive global fits to @xmath0-atom strong - interaction shifts and widths by introducing empirical density dependent effective @xmath18 amplitudes @xcite . such strongly attractive potentials are expected to generate @xmath0 nuclear quasibound states which could prove relatively narrow once the strong transition @xmath19 becomes kinematically forbidden for binding energies exceeding about 100 mev , as conjectured by akaishi and yamazaki @xcite . experimentally , we mention the @xmath0 quasibound signals claimed for @xmath20 @xcite at and below the @xmath21 threshold . however , these reported signals are quite broad , at variance with the underlying physics . in contrast to the indications of a deep @xmath0 potential , considerably shallower potentials , @xmath17(4060 ) mev , are obtained for zero kinetic - energy kaons by introducing self energy ( se ) contributions to the in - medium @xmath22 threshold scattering amplitude , within a self - consistent procedure that includes in particular the potential @xmath9 thus generated @xcite . in a recent letter @xcite we reported on new , self consistent calculations of @xmath0 quasibound states that lead to deep @xmath0 nuclear potentials , considerably deeper than the ` shallow ' potentials deduced in refs . the basic idea is to identify the @xmath18 _ subthreshold _ energy domain required for the construction of @xmath9 . for kaonic atoms , essentially at the @xmath0 nuclear threshold , this was explored during the 1970s by wycech @xcite , bardeen and torigoe @xcite and rook @xcite who noted the dominance of the subthreshold @xmath13 quasibound state @xmath16 in causing the in - medium @xmath13 scattering amplitude to become more attractive as one goes to subthreshold @xmath18 energies . in our letter @xcite we applied this idea , introducing a new self consistency requirement , to a comprehensive study of kaonic atoms that uses scattering amplitudes derived from a chirally motivated coupled channel meson - baryon lagrangian @xcite . here we expand on these recent calculations to provide more details on derivation , systematics and results . in addition to the next to leading - order ( nlo ) model cs30 used in the letter , in the present work we report on a new lo model tw1 fitted to the new siddharta values of shift and width of the @xmath23 state in the @xmath0 hydrogen atom @xcite . the paper is organized as follows : in sec . [ sec : self ] we describe a self consistent scheme of handling in - medium subthreshold @xmath18 scattering amplitudes used in the construction of @xmath9 . in sec . [ sec : model ] we discuss the derivation of in - medium scattering amplitudes in both models tw1 and cs30 . some details are relegated to an appendix . in sec . [ sec : atoms ] we discuss kaonic atom calculations , and in sec . [ sec : bound ] we discuss calculations of @xmath0 nuclear quasibound states . sec . [ sec : concl ] concludes the work with a brief summary of the main results . in the single - nucleon approximation , the @xmath0 potential in nuclear matter of density @xmath4 is given in terms of the in - medium @xmath18 scattering amplitude @xmath24 , @xmath25 where @xmath26 reduces to the free - space two - body @xmath18 c.m . forward scattering amplitude @xmath27 and the nucleon energy @xmath28 is approximated by its mass @xmath29 in the kinematical factor in front of @xmath24 . here , @xmath30 is the relative @xmath18 momentum and @xmath31 is the lorentz invariant mandelstam variable @xmath2 which reduces to the square of the total @xmath18 energy in the two - body c.m . frame . in the laboratory frame , @xmath32 . before constructing @xmath9 for use in actual calculations , we need to prescribe how to interpret in eq . ( [ eq : t ] ) the two - body arguments @xmath30 and @xmath33 of the in - medium scattering amplitude . for @xmath2-wave amplitudes , the momentum dependence arises through the magnitude @xmath7 of the relative momentum @xmath30 which near threshold is approximated by @xmath34 averaging over angles , the square of @xmath30 assumes the form @xmath35 for @xmath33 we note that @xmath36 in the two - body c.m . system , but @xmath37 in the nuclear laboratory system which nearly coincides with the @xmath0nucleus c.m . system . averaging over angles yields @xmath38 . near threshold , neglecting quadratic terms in the binding energies @xmath39 , @xmath40 , we have @xmath41 where @xmath42 . to transform the momentum dependence into density dependence , the nucleon kinetic energy @xmath43 is approximated in the fermi gas model by @xmath44 , with @xmath45 mev , and the @xmath0 kinetic energy @xmath46 is identified in the local density approximation with @xmath47 , where @xmath48 and @xmath49 is the @xmath0 finite - size coulomb potential . under these approximations , ( [ eq : p^2 ] ) and ( [ eq : sqrts ] ) become @xmath50 , \label{eq : p^2final}\ ] ] where both terms on the r.h.s . are positive for attractive @xmath9 , and @xmath51 ( in mev ) , where _ all _ the terms following @xmath52 on the r.h.s . are negative , thus implementing the anticipated downward energy shift into the @xmath18 subthreshold energy region . ( [ eq : sfinal ] ) is used in most of the bound state applications below as is , although we also checked the effect of implementing gauge invariance through the substitution @xmath53 . gauge invariance often is not implemented in the solution of the free - space lippmann - schwinger equations of underlying chiral models simply because its effects on the two - body meson - baryon system are negligible . we note that the @xmath0 nuclear potential @xmath9 appears as an argument in expressions ( [ eq : p^2final ] ) and ( [ eq : sfinal ] ) for @xmath54 and @xmath33 , respectively , which in turn serve as arguments in expression ( [ eq : t ] ) for this same @xmath9 . this suggests to calculate @xmath9 self consistently within a scheme in which the downward energy shift into the @xmath18 subthreshold energy region is density dependent and is controlled by the outcome self - consistent @xmath55 . in the corresponding sections below we elaborate on the self consistency scheme which is applied to the solution of the wave equation satisfied by in - medium @xmath0 mesons . the synergy of chiral perturbation theory and coupled channel @xmath56-matrix resummation techniques provides successful description of @xmath57 interactions at low energies @xcite . in our approach we employ chirally motivated coupled - channel @xmath2-wave potentials that are taken in a separable form , @xmath58 with @xmath59 , @xmath60 and @xmath61 denoting baryon energy , baryon mass and meson energy in the c.m . system of channel @xmath62 . the coupling matrix @xmath63 is determined by chiral su(3 ) symmetry . the parameter @xmath64 mev represents the pseudoscalar - meson decay constant in the chiral limit , and the inverse range parameters @xmath65 are fitted to the low energy @xmath57 data . the indices @xmath62 and @xmath66 run over the meson - baryon coupled channels @xmath15 , @xmath14 , @xmath57 , @xmath67 , @xmath68 and @xmath69 , including all their appropriate charge states . details of the free - space version of this model are given in ref . @xcite . here we summarize its essential points with emphasis on in - medium modifications . the chiral symmetry of meson - baryon interactions is reflected in the structure of the @xmath63 coefficients derived directly from the lagrangian . the exact content of the matrix elements up to second order in the meson c.m . kinetic energies was specified already in ref . @xcite . in practice , one often considers only the leading order tw interaction @xcite with energy dependence given by @xmath70 the structure constants @xmath71 are listed in ref . we note that this relativistic prescription differs from the one adopted in models derived from a chiral lagrangian formulation for static baryons @xcite and expanded strictly only to second order in meson energies and quark masses . there , the energy dependence form @xmath72 is replaced by @xmath73 where the primed meson energies @xmath74 include a relativistic correction : @xmath75 , with @xmath76 denoting the meson mass in channel @xmath66 and where @xmath77 is the baryon mass in the chiral limit . in principle , approaches based on different formulations of the chiral lagrangian should give identical results for physical observables . however , this is true only when one sums up an infinite series of relevant feynman diagrams to all orders in @xmath78 , and need not hold at a given perturbative order . in other words , models based on different lagrangian formulations , or models that differ from each other in prescribing how to treat terms beyond leading order , may give within reasonable limits different predictions for physical observables . the scattering amplitudes corresponding to the separable potentials ( [ eq : vpot ] ) are also of a separable form @xmath79 with the same form factors @xmath80 and @xmath81 , and where the _ reduced _ scattering amplitude @xmath82 is given explicitly by @xmath83_{ij}\;. \label{eq : ampl}\ ] ] here the meson - baryon propagator @xmath84 is diagonal in the channel indices @xmath62 and @xmath66 . when the elementary @xmath57 system is submerged in the nuclear medium one has to consider pauli blocking and self energies ( se ) generated by the interactions of mesons and baryons with the medium . thus , the propagator @xmath84 and the reduced amplitudes @xmath85 become dependent on the nuclear density @xmath4 . the intermediate state green s function is calculated as @xmath86 here @xmath87 is the on - shell c.m . momentum in channel @xmath62 and the integration domain @xmath88 is limited by the pauli principle in the @xmath57 channels . included in the denominator of the green s function ( [ eq : green ] ) is the sum @xmath89 of meson and baryon self energies in channel @xmath62 . in particular the kaon se @xmath90 , which serves as input in eq . ( [ eq : green ] ) and therefore also in eq . ( [ eq : ampl ] ) for the output reduced amplitude @xmath91 , requires by eq . ( [ eq : t ] ) the knowledge of this same output @xmath91 . this calls for a _ self consistent _ solution of the in - medium reduced scattering amplitudes @xmath92 as was first suggested by lutz @xcite . in the present calculation , following ref . @xcite , the baryon and pion self energies were approximated by momentum independent potentials @xmath93 with real and imaginary parts of @xmath94 chosen consistently from mean - field potentials used in nuclear structure calculations and in scattering calculations , respectively . specifically , we adopted @xmath95 mev , @xmath96 mev , @xmath97 mev and @xmath98 mev . the free parameters of the separable - interaction chiral models considered in ref . @xcite and in the present work were fitted to the available experimental data on low energy @xmath57 interactions , consisting of @xmath99 low - energy cross sections for elastic scattering and reactions to the @xmath100 , @xmath101 , @xmath102 , @xmath103 and @xmath104 channels ( as listed in ref . in addition , the accurately determined @xmath99 threshold branching ratios @xmath105 , @xmath106 , @xmath107 @xcite provide a rather strict test for any quantitative model . another stringent test is provided by the recent siddharta measured values @xmath108 and @xmath109 of the @xmath0hydrogen atom @xmath23 level shift and width @xcite . .@xmath110 threshold observables calculated in several free - space lo coupled - channel chiral models . the @xmath0hydrogen atom @xmath23 shift @xmath108 and width @xmath109 ( in ev ) marked by asterisks were obtained from the calculated @xmath111 scattering length by means of a modified deser - trueman relation @xcite and are compared to the siddharta measured values @xcite . the @xmath110 threshold branching ratios @xmath105 , @xmath106 , @xmath107 are from ref . the last two columns list the calculated @xmath112 @xmath113-matrix pole positions @xmath114 ( in mev ) on the [ @xmath115 second riemann sheet of the complex energy plane . [ cols="^,^,^,^,^,^,^,^",options="header " , ] [ tab : bound3 ] table [ tab : bound3 ] presents binding energies and widths of @xmath23 @xmath0 nuclear quasibound states in several nuclei across the periodic table , calculated self - consistently within in - medium versions of cs30 chiral amplitudes . the first two sequences denoted [ wh ] and @xmath33 illustrate the role of subthreshold @xmath33 extrapolation which affects particularly the widths @xmath116 , in a similar pattern to that already shown for the tw1 model in table [ tab : bound2 ] . the next three sequences exhibit the effects of successively sophisticating the calculations : first , the in - medium ` no se ' amplitudes are dressed by self energies ( denoted ` + se ' ) , bringing the calculated widths further down ( and marginally so the binding energies ) ; then , the calculations are made dynamical ( denoted ` + dyn . ' ) taking into account the polarization of the nuclear core by the strongly bound @xmath0 , which produces higher binding energies @xmath117 and smaller widths @xmath116 ; and last , energy dependent imaginary @xmath118 terms are added self consistently to simulate two - nucleon @xmath119 absorption modes ( denoted ` + 2n abs . ' ) and their available phase space @xcite . whereas the binding energies decrease insignificantly , the resulting widths of order @xmath120 mev become comparable in light nuclei to the binding energies @xmath117 . in this work we have used several versions of in - medium @xmath13 scattering amplitudes constructed in a chirally motivated coupled channel separable potential model to derive self - consistently the @xmath0 nuclear potential for several bound state applications . the @xmath13 scattering amplitudes exhibit , invariably , a strong energy and density dependence below threshold , which reflects the dominant effect of the @xmath16 subthreshold resonance . this is precisely the energy region relevant for the self consistent construction of @xmath9 for kaonic atoms and for @xmath0 nuclear quasibound state calculations . it was found that kaonic atoms probe @xmath13 c.m . energies typically 3050 mev below threshold whereas @xmath0 nuclear @xmath23 quasibound states reach considerably lower @xmath13 subthreshold energies . thus , the chiral model versions used in the present work produced potential depths in the range @xmath121 8090 mev in kaonic atoms , and somewhat deeper potentials of depths 100110 mev for @xmath0 nuclear quasibound states . by comparing the size and shape of our subthreshold @xmath13 scattering amplitudes with those of other chiral models , as discussed for example in ref . @xcite , we expect these results to hold generally in any coupled - channel chiral model constrained by low energy @xmath110 data once our self consistency construction is applied . the density dependence of the resulting kaonic atom potentials is such that by adding adjustable phenomenological terms to be determined by fits to the data , the real part of the potential becomes twice as deep and the imaginary part about three times as deep due to a @xmath118dominated complex term which could represent @xmath122 dispersive and absorptive modifications . these substantial modifications at full nuclear density represent extrapolations from the nuclear surface region to which kaonic atoms are mostly sensitive and where such modifications appear more modest . more work is needed to explain the origin and test the existence of the sizable @xmath118 term . finally , the effects of a @xmath7-wave interaction generated by the @xmath123 subthreshold resonance are found secondary to the effects of the @xmath2-wave interaction which is dominated by the @xmath16 subthreshold resonance . stimulating discussions with wolfram weise are gratefully acknowledged . this work was supported by the gacr grant no . 202/09/1441 , as well as by the eu initiative fp7 , hadronphysics2 , under project no . the observed properties of in - medium @xmath57 interaction may be related to the dynamics of the @xmath16 resonance in the nuclear medium . this is demonstrated for model tw1 in fig . [ fig : poles1 ] which shows the motion in the complex energy plane of poles related to the @xmath14 and @xmath57 channels upon increasing the nuclear density , including pauli blocking but disregarding self energy insertions . the lower half of the energy plane , below the real axis , corresponds to the [ @xmath115 riemann sheet standardly referred to as the second riemann sheet and accessed from the physical region by crossing the real energy axis in between the @xmath124 and @xmath57 thresholds . the upper half of the energy plane ( above the real axis ) shows the [ @xmath125 riemann sheet , the third riemann sheet , which does not allow for @xmath57 quasibound interpretation of poles located therein . the pole trajectories shown in the figure were calculated from the free - space pole positions ( encircled dots ) up to the pole positions at full nuclear density @xmath126 . in addition to the two @xmath112 poles listed and discussed in table [ tab : models ] of the main text , each of the decoupled @xmath14 and @xmath57 channels also exhibits an @xmath127 pole , the one related to @xmath57 developing into a resonance residing on the [ @xmath125 riemann sheet and another one related to a @xmath14 state residing on the [ @xmath115 riemann sheet . while the @xmath127 pole related to @xmath14 lies too far from the real energy axis to affect any physical observable , the one related to @xmath57 is responsible for the peak structure in the real part of the @xmath128 amplitude near threshold . however , the riemann sheet location of this pole denies it of any quasibound interpretation . the @xmath127 poles persist also in the more involved nlo chiral models discussed in ref . @xcite . as expected , the nuclear medium has no significant impact on the position of poles related to the @xmath14 channel . on the other hand , both poles related to the @xmath57 channel move to considerably higher energies as the density increases . the @xmath112 @xmath57 pole that affects most the @xmath57 scattering amplitude moves as high as about 1475 mev , almost reaching the real energy axis . since the pole is relatively far from the physical region due to the @xmath57 branch cut , the scattering amplitude exhibits a cusp instead of a proper resonance structure ( see the dot - dashed line in fig . [ fig : akp1 ] of the main text ) . when kaon self energy is implemented the pole moves back below the @xmath57 threshold , residing now in the [ @xmath125 riemann sheet . since it remains relatively far from the physical region , one again gets a cusp structure as exhibited by the solid line in fig . [ fig : akp1 ] . j. schaffner - bielich , s. schramm , and h. stcker , in _ proc . school of physics enrico fermi " , course * clxvii * _ , eds . m. anselmino , _ et al . _ ( ios press , amsterdam , 2008 ) pp . 119144 ; f. zel , g. baym , and t. gver , phys . d * 82 * , 101301(r ) ( 2010 ) .

a self consistent scheme for constructing @xmath0 nuclear optical potentials from subthreshold in - medium @xmath1 @xmath2-wave scattering amplitudes is presented and applied to analysis of kaonic atoms data and to calculations of @xmath0 quasibound nuclear states . the amplitudes are taken from a chirally motivated meson - baryon coupled - channel model , both at the tomozawa - weinberg leading order and at the next to leading order . typical kaonic atoms potentials are characterized by a real part @xmath3 mev at nuclear matter density , in contrast to half this depth obtained in some derivations based on in - medium @xmath1 threshold amplitudes . the moderate agreement with data is much improved by adding complex @xmath4- and @xmath5dependent phenomenological terms , found to be dominated by @xmath5 contributions that could represent @xmath6 absorption and dispersion , outside the scope of meson - baryon chiral models . depths of the real potentials are then near 180 mev . the effects of @xmath7-wave interactions are studied and found secondary to those of the dominant @xmath2-wave contributions . the in - medium dynamics of the coupled - channel model is discussed and systematic studies of @xmath0 quasibound nuclear states are presented .

Donald Trump has said it’s imperative to unite the party — though he’s pushed back against complete unity. | Getty Trump camp suggests Ryan unfit to be speaker Donald Trump and his allies are lashing out at House Speaker Paul Ryan for his refusal to back — for now — the presumptive Republican nominee, with Trump’s spokeswoman even declaring Ryan unfit for his job. During a phone interview with Fox News on Friday, Trump said he was “very, very surprised” at Ryan’s comments. “It’s hard to believe,” he said, adding, “It doesn’t bother me at all.” His tweets, however, suggest otherwise. “So many great endorsements yesterday, except for Paul Ryan!” Trump tweeted. “We must put America first and MAKE AMERICA GREAT AGAIN!” Roughly 90 minutes later, Trump came back with a sharp critique of another comment Ryan made Thursday. “Paul Ryan said that I inherited something very special, the Republican Party. Wrong, I didn't inherit it, I won it with millions of voters!” Trump wrote on Twitter. The subtle difference Trump highlighted was a piercing remark that speaks to the rift between mainstream Republicans and the polarizing, unconventional candidate who has risen to become the face of the party. His proposal to ban Muslims from entering the U.S. and refusal to disavow David Duke and the Ku Klux Klan led to Ryan’s implicit rebuke of the candidate throughout the primary, but Trump’s rhetoric has resonated with millions of voters, who have come out in droves across the country to support his candidacy. Trump has said it’s imperative to unite the party — though he’s pushed back against complete unity, emphasizing that certain Republicans who have been critical of him should go their own way. During an interview with Sirius XM and “Breitbart News Daily,” Trump said on Friday morning that he liked Ryan but expressed some reservations about his most recent critic. “He’s doing it under the banner of unity, when in actuality that's the opposite of unity,” Trump said of Ryan’s remarks. “I've also had many people say that I'm better off, but I don't believe that. I think we should have unity. I think it would be better to have him. But it's just too bad. Many people think I'm better off. Who knows?” Trump spokeswoman Katrina Pierson went much further than her boss, suggesting that the Wisconsin Republican is unfit for his leadership role if he can’t support the party’s presumptive nominee. Asked plainly by CNN’s John Berman whether Ryan is fit to be speaker if he can’t come around to supporting Trump, Pierson responded, “No, because this is about the party.” Ryan suggested the onus was on Trump to show he can unite the different wings of the Republican Party, but Pierson disagreed, noting that since Trump has yet to clinch 1,237 delegates, he’s only the presumptive nominee. “We are a party. Paul Ryan needs to be a — he’s the leader right now,” Pierson said. “We’re told Donald Trump is only the presumptive nominee. He’s not the nominee until 1,237. So really it’s incumbent on Paul Ryan to help bring unity to the party.” The same sentiment was expressed Thursday evening by Fox News host Sean Hannity, who told viewers he is no longer “ready to support” Ryan as speaker. “I'm thinking maybe we need a new speaker,” Hannity said during his show. “Thoughts?” Trump convention manager Paul Manafort struck a more conciliatory tone, telling MSNBC’s Andrea Mitchell on Friday afternoon that the split among Republicans’ support for Trump will eventually subside. What’s most important, he continued, is that Ryan said he is prepared to support the nominee. “People are gonna be glad that he's at the top of the ticket,” Manafort said. “The reason he’s won overwhelmingly in the primaries is because he expanded the base of the Republican Party with thousands and thousands of people, you know, crossing over or in many cases changing their registration to participate in the Republican Party to vote for Donald Trump. That strength, those coattail of capabilities, are going to help the Republican ticket.” Ryan’s office confirmed that the two will meet in Washington on Thursday. “Having both said we need to unify the party, Speaker Ryan has invited Donald Trump to meet with members of the House Republican leadership in Washington on Thursday morning to begin a discussion about the kind of Republican principles and ideas that can win the support of the American people this November,” his office said in a statement. “The Speaker and Mr. Trump will also meet separately, along with RNC Chairman Reince Priebus.” In a statement to the Washington Post, Trump said Ryan’s comments were “totally inappropriate” and ominously said that the two may “go our separate ways.” “I told Reince that I thought it was totally inappropriate what Paul Ryan said and thought it was good for me politically,” he said. “But Reince feels, and I'm okay with that, that we should meet before we go our separate ways. So I guess the meeting will take place and who knows what will happen.” Pierson said the businessman is likely to tell Ryan that by refusing to support him, he’s also going against the will of the people. “Well, I think he’s gonna talk to Paul Ryan and just say look, you are not just against me. You are against a lot of your voters, and this is something that has been indicative,” Pierson said. “For the last couple of cycles you have had the leadership rejecting its own voters, silencing them, ignoring them, campaigning on one issue and not following through, and that’s why we have a nomination of Donald Trump.” Pierson said the last two Republican presidential nominees, John McCain and Mitt Romney, weren’t true conservatives, but conservatives “were told to hold our noses and vote for the sake of the party.” “These same people are now telling us that because their guy didn’t win, they want to hurt the party,” she said. “The issue here isn’t about Donald Trump. If you can’t hold yourself to the standard that you hold everyone else, the problem is with you.” Priebus, who declared Trump the presumptive nominee Tuesday following a decisive victory in Indiana that knocked Ted Cruz out of the race (and subsequently John Kasich), hopes to mitigate the brewing feud between the man who will top the GOP ticket in the fall and the man who will chair the Republican National Convention this summer. “My view is just relax and be gracious and I’ll talk to Paul and we’ll try to work on this,” Priebus said he told Trump. “I'm comfortable with the idea that it is going to take some time in some cases for people to work through differences,” he continued. “We talked about it and talked about it multiple times and they're very comfortable with sitting down with Donald Trump, and it may be at my office, it may be somewhere else but we're going to have that meeting to start the process of unifying.” Trump surrogate and former presidential candidate Ben Carson told MSNBC’s “Morning Joe” he was “very disappointed” by Ryan’s comments and suggested he was being immature. He added that a divided Republican Party ensures a Democratic president in 2017. “I hope Speaker Ryan and many others, as time goes on, will begin to understand that, realize that we have to work together,” Carson said. “You don’t have another choice, so you get behind the choice that you have, whether you like them or not.” YouTube vloggers and Trump supporters Lynnette Hardaway and Rochelle Richardson — better known as Diamond and Silk — called for Americans to vote out politicians who won’t respect the will of the voters, beginning with Ryan. “It's time to vote out these career politicians that don't want to honor who we the people voted for. Let's start with @SpeakerRyan #VoteOut,” they tweeted. President Barack Obama, meanwhile, seemed to revel in the GOP's identity crisis, telling reporters on Friday — with a smirk — that he couldn't begin to guess what will come of the civil war. "I think you have to ask Speaker Ryan what the implications of his comments are," Obama said. ||||| Donald Trump's modeling agency has profited from the very same visa program that the presidential candidate himself has slammed -- and appears to have violated federal law in the process, a CNNMoney investigation has found. Throughout his campaign, Trump has loudly opposed the practice of U.S. companies using foreign workers instead of Americans -- specifically the highly-skilled workers brought to the United States through the controversial H-1B visa program. "These are temporary foreign workers, imported from abroad, for the explicit purpose of substituting for American workers at lower pay. I remain totally committed to eliminating rampant, widespread H-1B abuse," Trump said in a statement on his website, though he backtracked on his position during a recent Republican debate. While this visa program is best known for bringing over technology workers like engineers and computer programmers, Trump's own modeling agency has used the program for years, federal data shows. That's because federal law surprisingly lumps in fashion models with these other specialized workers -- though it's the only job that doesn't require higher education. (Instead, models must have "distinguished merit and ability.") And now, the use of this visa by Trump Model Management, founded by Trump in 1999, is being questioned. Check out more CNNMoney investigations The agency is currently battling a proposed class action lawsuit filed by Jamaican model Alexia Palmer, who was brought to the country with an H-1B visa. The suit alleges that the agency recruits foreign models with promises of wages that never materialize and defrauds the U.S. government on visa applications. Palmer is currently the only plaintiff and the suit has not yet been approved as a class-action. In her case, Palmer says she was paid only a few thousand dollars over three years despite being lured with the promise of more than $200,000 in earnings in that same time period. That salary was also what was listed by Trump Model Management as part of the visa application. "Ms. Palmer will receive compensation of at least $75,000 per year," the agency's president Corinne Nicolas said in a letter to immigration officials. "She is a model whose services have been in great demand, and whose proposed temporary presence in the United States has stirred great anticipation by Trump Model Management and its clientele." (Nicolas did not respond to a request for comment). Government data analyzed by Howard University professor Ron Hira shows that since 2008, Trump's agency has successfully brought over around 30 foreign models -- from countries like Brazil, Latvia and China -- using the H-1B program. Almost half of these applications indicated the same $75,000 annual salary, while others went as high as $416,000. CNNMoney asked a dozen attorneys and other immigration experts to review facts and documents from the case, and the vast majority said Trump's agency appears to have violated immigration law. "It seems pretty clear to me that there was a violation... and a pretty egregious violation," said New York immigration attorney Jeffrey Feinbloom. Experts say that the U.S. government requires that full-time H-1B workers like Palmer be paid a high enough wage that they aren't being exploited or displacing American workers -- regardless of how much they end up working. Experts say that the firm was required by law to pay the amount stated on Palmer's visa -- in this case, $75,000 a year. Even more egregious, they say, was that the Trump agency didn't pay the "prevailing wage" determined by the U.S. government (which is based on the industry and location). The U.S. Citizenship and Immigration Services agency (USCIS) confirmed that a sponsoring company "must pay the actual wage or the prevailing wage, whichever is higher" -- meaning it was illegal to pay Palmer below either listed wage. "Employers may never pay below the prevailing wage," the agency said in a statement. For Palmer, the prevailing wage acknowledged by the Trump agency on the visa application was roughly $45,000 a year. Instead, she made less than $30,000 over three years from modeling jobs for clients ranging from Conde Nast to Saks Fifth Avenue. And she didn't even get to keep that full amount. It was almost entirely eaten up by taxes, a 20% commission to the Trump agency, administrative fees and modeling-related costs like $75 walking lessons and a $200 dermatology visit. In the end, Palmer netted $4,985 over three years (which included cash advances and a $3,880.75 check), a figure acknowledged by the Trump agency. It's unclear whether the U.S. government would look at the earnings she received before or after deductions like commissions and modeling expenses. But either way, experts say she earned far less than the amount required by law. "If someone isn't being paid what they are supposed to be paid, they are being exploited," said Neil Ruiz, executive director of the Center for Law, Economics and Finance at George Washington University and a national expert on H-1B visas. "This case shows that [Trump's] own company has benefited from exploiting his own H-1B visa holders." CNNMoney was unable to reach Palmer, but her attorney said it was a "no-brainer" that his client's rights had been violated. But the Trump agency said the 20% commission and reimbursements were clearly outlined in the contracts Palmer signed. "It is important to note that at no time while TMM was her model manager did Ms. Palmer EVER object to any of these deductions from her gross pay," Lawrence Rosen, the attorney representing the Trump agency, told CNNMoney. Rosen said that Palmer was paid for the jobs she booked and nothing more -- a practice that he described as standard throughout the modeling industry as a whole. The Trump campaign had a similar argument. "In regards to Ms. Palmer, this is standard practice in the modeling industry and the visa application form is inadequate to address the practice of the industry," a Trump spokesperson said in an email. Attorney Michael Wildes, whose law firm handled Palmer's visa application on behalf of Trump's agency, said that the H-1B visa gave Palmer the best chance of getting to the United States. He argued that it's not the agency's fault that U.S. immigration laws "are archaic." "Mr. Trump and his modeling agency decided they wanted to give this lady an opportunity to work," he said. "There is a disconnect in the world of agency law and immigration law." And Trump agency attorney Rosen argues that since the agency was hired by Palmer, she was never considered an employee of the firm, and thus has no claims for a certain wage. "She just didn't have a very successful modeling career," said Rosen. However, the U.S. Citizenship and Immigration Services agency was clear that the pay requirement applies to "an employer or an agent." Still, Rosen acknowledged that the agency should have been more clear in the initial visa application. He said that the $75,000 salary listed on official visa documents, which are filed under penalty of perjury, was nothing more than a "guesstimate." "In hindsight, now that he's running for president and all that, you look at it and say why doesn't it say 'estimate'? Well maybe it should have," he said. But immigration attorneys say that there is no such thing as a guesstimate when filing this kind of a federal visa application. "For them to promise the U.S. government to pay this employee this particular wage and not do it, it is a violation," said Virginia immigration attorney Hassan Ahmad. "It depresses wages. It is the underbelly of the industry." But even if it is determined that her wages were in violation of immigration laws, Rosen argued that the civil case has no merit because it's up to the Department of Labor to investigate a violation -- not the civil court system. CNNMoney asked the Department of Labor and the USCIS to weigh in, but neither would comment on the case specifically. Palmer's civil case has been pending since last year, awaiting a judge's decision on whether it should be thrown out (as requested by the Trump agency). A clerk for the judge said a ruling is expected by the end of the month. Whether or not it ends up being dismissed, many attorneys say Palmer would have a chance if she turned to the U.S. government instead. They also wonder just how far the alleged abuses go. "The real question," said New York immigration attorney Steve Maggi, "is if Trump does this in this case, how systematic is it?" ||||| Wage and Hour Division (WHD) H-1B Program Overview The H-1B program applies to employers seeking to hire nonimmigrant aliens as workers in specialty occupations or as fashion models of distinguished merit and ability. A specialty occupation is one that requires the application of a body of highly specialized knowledge and the attainment of at least a bachelor’s degree or its equivalent. The intent of the H-1B provisions is to help employers who cannot otherwise obtain needed business skills and abilities from the U.S. workforce by authorizing the temporary employment of qualified individuals who are not otherwise authorized to work in the United States. The law establishes certain standards in order to protect similarly employed U.S. workers from being adversely affected by the employment of the nonimmigrant workers, as well as to protect the H-1B nonimmigrant workers. Employers must attest to the Department of Labor that they will pay wages to the H-1B nonimmigrant workers that are at least equal to the actual wage paid by the employer to other workers with similar experience and qualifications for the job in question, or the prevailing wage for the occupation in the area of intended employment – whichever is greater. Key News DOL Announces Plans to Protect American Workers from H-1B Program Discrimination: On June 6, 2017, the Department of Labor announced actions to increase protections of American workers while more aggressively confronting entities committing visa program fraud and abuse. Read More General Guidance H-1B Outreach events H-1B Presentation Forms Fact Sheets Disqualified and Willful Violator Employers DOL maintains a list of individuals or corporations who, as a result of an H-1B investigation/final agency action, have been disqualified from approval of petitions to participate in the nonimmigrant program. In addition, willful violator employers are subject to random investigations by the Department of Labor for a period of up to five years from the date that the employer is determined to be a willful violator. H-1B Willful Violators List H-1B Debarred Employers List Applicable Regulations Nonimmigrant Worker Related Agency Links Civil Money Penalty Inflation Adjustments Starting in 2016, agencies across the federal government must adjust their penalties for inflation each year. Below is a table that reflects the adjustments that have occurred for penalties under this statute. For more information on the penalty adjustments, go here.

– Donald Trump admitted a business program he takes advantage of is "very, very bad for workers" and "shouldn't be allowed" during Thursday's Republican debate in Florida, the Hill reports. According to CNN, Trump's modeling agency uses the H-1B visa program. It's a program that allows US businesses to hire nonimmigrant aliens with special skills who otherwise wouldn't be allowed to work in the US. "I know the H-1B very well, it's something that I, frankly, use," Trump said during the debate. But after Marco Rubio defended H-1B visas, Trump condemned the program, Politico reports. He excused his use of a program he himself claims is bad for Americans by saying, "I'm a businessman, and I have to do what I have to do." In response, Rubio called Trump "clueless on so many issues."

testicular cancer is the most common malignancy among young men in north america and western european countries . there are several proposed risk factors for seminoma such as cryptorchidism , klinefelter syndrome , radiofrequency waves and etc . sporadic case reports and small series suggest that this type of radiation might lead to cancer or contribute to its evolution . the association between radiofrequency and testicular damage and cancer is unproved , but clinical and experimental data are suggestive of such possibility . there are some case series and case reports about this but this relation is not proved . in this paper we have reported three cases of seminoma in person who worked in the same place that exposed to radio frequency ( rf ) waves . he was a 31-year - old man who has worked in a radio station for 6 years while he was left that place 10 years before diagnosis of seminoma . initial evaluation revealed stage 1 seminoma and he was underwent radiotherapy after radical orchiectomy and his disease free until now . he was a 37-year - old man with seminoma diagnosis after radical orchiectomy on his 25 years after 6 years work in the same place . because of stage 1 disease he received radiotherapy and it made him disease free until now . he was a testicular cancer with the same pathology , seminoma , but with inguinal metastasis . he was worked in that place for 16 years and was diagnosed for seminoma at the last one year of his job . after radical orchiectomy radiotherapy is done his response was good and he is under follow up now . their workplace was a radio station that consist multiple receiver and transmitter antennas and the frequency of waves were in the radiofrequency spectrum . the staffs worked there for 24 hours , however in their resting time for 48 hours were in that enclosure too . rapid technological progress led to increase man - made sources for radiofrequency that some of these sources are mobile communication , microwave oven , wi - fi , television , antenna , detection equipment or radio stations . radiofrequency ( rf ) radiation is at the low - energy end of the electromagnetic spectrum and is a type of radiation that has enough energy to move atoms or cause them to vibrate but not enough to ionize them so called non - ionizing radiation . although rf radiation does not cause cancer by ionizing and damaging dna in cells , there has been concern that some forms of non - ionizing radiation might have biological effects that could result in cancer in some circumstances . increased incidence of cancer in the past decades made specialist to pay attention to some environmental risk factors and one of probable risks is radiofrequency exposure . sporadic case reports and small series suggest that this type of radiation might lead to cancer or contribute to its evolution . but the association between cancer and radiofrequency is still unproved and there are some controversies . most of exist studies are about the radiofrequency and brain tumor , however seminoma report just in some series . has evaluated the biological effect of radiofrequency in vivo , they found that reactive oxygen species concentration increased within the cell caused by rf / mw radiation seems to be a biologically relevant hypothesis to give clear insight into the rf / mw action at non - thermal level of radiation . in a population - based case - control study , baumgardt - elms et al . has examined the association of testicular cancer and electromagnetic fields ( emf ) in the workplace by standardized face to face interviews in case ( n=269 ) and control ( n=797 ) groups . they concluded environmental emf exposure in the workplace does not seem to be a relevant risk factor for testicular cancer as a result of their study . has reported the result of a study about all of previous publication about microwave exposure and radiofrequency effects . possible outcomes considered included blood count changes , evidence of somatic mutation , impairment of reproductive outcomes , especially spontaneous abortion , and increase in cancer incidence . the author presented evidence that sufficient microwave exposures are associated with all four of mentioned outcomes , concluding that the possible effects and their timings with respect to exposure are qualitatively similar to those on ionizing radiation . has investigated the association between occupation and testicular cancer risk , self - reported exposure to microwaves and other such waves was associated with an increased risk for both seminomas and other germinal cell tumors . however , an assessment of radio wave exposure based on job title did not support this finding . richter et al . has described results of a case - control study exposure - effect relationship in sentinel patients and their co - workers , who were technicians with high levels of exposure to rf / mw radiation . their calculations derived from a linear model of dose - response suggest the need to prevent exposures in the range of 10 - 100 w / cm2 . occupational exposure to extremely low - frequency magnetic fields ( mf ) was studied by stenlund et al . , in 144 subjects with testicular cancer , germ cell tumor , diagnosed in 1985 - 87 . the results for testicular cancer gave some support to the hypothesis of abnormal link between mfs and cancer , and should be further explored . studies about carcinogenic effect of radiofrequency waves and the mechanism of that are limited , and most of them are case series or case control retrospective studies , it seems that we need more in vivo surveys and prospective studies to evaluate this effect .

physical agents such as ultraviolet or ionizing radiation and repetitive trauma have been related to the causation of cancer in humans . much less clear is the association between exposure to radiofrequency , such as radar and microwave radiation to the development of cancer . sporadic case reports and small series suggest that this type of radiation might lead to cancer or contribute to its evolution . the association between radiofrequency and testicular damage and cancer is unproved , but clinical and experimental data are suggestive of such possibility . in this paper we have reported three cases of seminoma in person who worked in the same place that exposed to radio frequency ( rf ) waves .

arf was first discovered , purified , and functionally defined as the protein cofactor required for cholera toxin catalyzed adp ribosylation of the stimulatory regulatory subunit ( gs ) of adenylyl cyclase ( enomoto and gill , 1980 ; kahn and gilman , 1984 ) and , shortly thereafter , was shown to be a gtp - binding protein ( kahn and gilman , 1986 ) . use of the acronym arf is currently preferred to adp ribosylation factor , as only arf16 shares the cofactor activity for cholera toxin and because adp ribosylation does not appear to be involved in any aspect of the normal cellular actions of any member of the family . the use of all capital letters ( e.g. , arf1 ) refers specifically to the human gene or protein , whereas when only the first letter is capitalized ( e.g. , arf1 ) , it may refer to the protein from more than one species , an activity , or a group of proteins . since their discovery , they have been found to be ubiquitous regulators of membrane traffic and phospholipid metabolism in eukaryotic cells ( for reviews and discussion of arf actions see nie et al . arfs are soluble proteins that translocate onto membranes in concert with their activation , or gtp binding . the biological actions of arfs are thought to occur on membranes and to result from their specific interactions with a large number of effectors that include coat complexes ( copi , ap-1 , and ap-3 ) , adaptor proteins ( gga1 - 3 and mint1 - 3/x11-/apba1 - 3 ) , lipid - modifying enzymes ( pld1 , phosphatidylinositol ( 4,5)-kinase , and phosphatidylinositol ( 4)-kinase ) , and others . arf proteins are activated by guanosine diphosphate ( gdp ) to gtp exchange , which is stimulated by the sec7 domain of arf guanine nucleotide exchange factors , and their activity is terminated upon the hydrolysis of gtp , which is stimulated by interaction with an arf gtpase - activating protein . cloning and sequencing of the first arf family member ( sewell and kahn , 1988 ) led directly to the realization that arfs are closely related to both the ras and heterotrimeric g protein subunit families of gtpases , and all are thought to have arisen from a common ancestor . the very high degree of conservation of arf sequences in eukaryotes ( 74% between human and yeast ) was also noted early on and has allowed the ready identification of orthologues in every examined eukaryote , including giardia lamblia , which lack ras and g protein subunits ( murtagh et al . , 1992 ) . cloning by low stringency hybridization and chance led to the identification of additional members of the arf family in a wide array of eukaryotic species . , 1991 ) and were named in their order of discovery ( price et al . , 1988 ; bobak et al . , 1989 ; kahn et al . , 1991 ; lee et al . , the first confusion in the nomenclature was that the current human arf4 was originally published with the name arf2 ( kahn , et al . , 1991 ) . in fact , humans appear to have lost the arf2 orthologue , which is present in other mammals ( including rats , mice , and cows ) . the combination of protein sequence comparisons and intron / exon boundaries of arf genes led to further classification of the six mammalian arfs into classes : class i ( arf13 are > 96% identical ) , class ii ( arf4 and arf5 are 90% identical to each other and 80% identical to the other arfs ) , and class iii ( arf6 is 6469% identical to the other arfs ) . phylogenetic analyses support the conclusion that the three classes of arf diverged early , as flies and worms have single representatives of each of the three classes , and the number of genes / proteins in class i and ii were later expanded in vertebrates . the initial criteria for naming new arfs were functional , and only those proteins that could ( 1 ) serve as cofactors for cholera toxin , ( 2 ) rescue the lethal arf1arf2 deletion in saccharomyces cerevisiae , and ( 3 ) directly activate pld were given the name arf . thus , with the chance cloning of an essential gene in drosophila melanogaster that encoded a protein closely related to the arfs ( 5060% identity ) but lacking in these activities , it was named arflike ( tamkun et al . , 1991 ) . when orthologues were found in several other species , the name was changed to arf - like 1 ( arl1 ) in those species ( kahn et al . , 1992 ; breiner et al . note that although the name arf still denotes a protein with one or more specific functions or activities , the term arl does not . 1994 ) revealed the existence of a large number of mammalian cdnas encoding closely related proteins . the next to be cloned and sequenced were arl2 ( clark et al . , 1993 ) , arl3 ( cavenagh et al . , 1994 ) , arl4 ( schurmann et al . , each of the encoded proteins has a glycine at position 2 , the site of n - myristoylation in all arf proteins . note that although arl2 and arl3 have the nh2-terminal glycine , they appear not to be substrates for n - myristoyltransferases . around this time , a protein with similar percent identities to the arf and arls was found , but it lacked the nh2-terminal glycine , was membrane associated , and displayed distinctive nucleotide handling properties ( schurmann et al . thus , it was given the name arf - related protein 1 ( arfrp1 ) to distinguish it from the arls and arfs . we realize today that this was unfortunate , as several of the more recently identified arls also have functions and biochemical properties that are quite divergent from arfs . sar1 was among the earliest members of the arf family sequenced , and it came out of genetic screens in the yeast s. cerevisiae as a suppressor of sec12(ts ) ( nakano and muramatsu , 1989 ) . its name is derived from its identification as a secretion - associated and ras - related protein . cloning of the mammalian orthologues revealed the presence of two closely related ( 90% identity ) proteins / genes ( kuge et al . , 1994 ) . with < 30% identity to arfs or arls , the sar proteins are only slightly closer in sequence to arfs than to other families of gtpases , but they also share considerable functional relatedness to arfs in that they act through the recruitment of coat proteins or complexes to initiate vesicle budding . an interesting variation is found in ard1/tripartite motif 23 ( trim23 ) , a 64-kd protein that possesses a 20-kd domain at its cooh terminus with 60% identity to arfs ( mishima et al . , 1993 ) . originally named based on the presence of the arf domain , ard1 is also a member of the trim family , from which it obtained its current name , trim23 . a large extension is also seen in arl13b , a protein of 428 residues that contains an arl domain at its nh2 terminus ( chiang et al . , 2004 ; fan et al . , 2004 ) . although the nh2-terminal portion of trim23 may possess gtpase - activating protein activity toward its own arf domain ( vitale et al . , 1996 ) and e3 ubiquitin ligase activity ( vichi et al . , 2005 ) , the cooh - terminal portion of arl13b has no defined domains or functions to date . arf was first discovered , purified , and functionally defined as the protein cofactor required for cholera toxin catalyzed adp ribosylation of the stimulatory regulatory subunit ( gs ) of adenylyl cyclase ( enomoto and gill , 1980 ; kahn and gilman , 1984 ) and , shortly thereafter , was shown to be a gtp - binding protein ( kahn and gilman , 1986 ) . use of the acronym arf is currently preferred to adp ribosylation factor , as only arf16 shares the cofactor activity for cholera toxin and because adp ribosylation does not appear to be involved in any aspect of the normal cellular actions of any member of the family . the use of all capital letters ( e.g. , arf1 ) refers specifically to the human gene or protein , whereas when only the first letter is capitalized ( e.g. , arf1 ) , it may refer to the protein from more than one species , an activity , or a group of proteins . since their discovery , they have been found to be ubiquitous regulators of membrane traffic and phospholipid metabolism in eukaryotic cells ( for reviews and discussion of arf actions see nie et al . arfs are soluble proteins that translocate onto membranes in concert with their activation , or gtp binding . the biological actions of arfs are thought to occur on membranes and to result from their specific interactions with a large number of effectors that include coat complexes ( copi , ap-1 , and ap-3 ) , adaptor proteins ( gga1 - 3 and mint1 - 3/x11-/apba1 - 3 ) , lipid - modifying enzymes ( pld1 , phosphatidylinositol ( 4,5)-kinase , and phosphatidylinositol ( 4)-kinase ) , and others . arf proteins are activated by guanosine diphosphate ( gdp ) to gtp exchange , which is stimulated by the sec7 domain of arf guanine nucleotide exchange factors , and their activity is terminated upon the hydrolysis of gtp , which is stimulated by interaction with an arf gtpase - activating protein . cloning and sequencing of the first arf family member ( sewell and kahn , 1988 ) led directly to the realization that arfs are closely related to both the ras and heterotrimeric g protein subunit families of gtpases , and all are thought to have arisen from a common ancestor . the very high degree of conservation of arf sequences in eukaryotes ( 74% between human and yeast ) was also noted early on and has allowed the ready identification of orthologues in every examined eukaryote , including giardia lamblia , which lack ras and g protein subunits ( murtagh et al . , 1992 ) . cloning by low stringency hybridization and chance led to the identification of additional members of the arf family in a wide array of eukaryotic species . , 1991 ) and were named in their order of discovery ( price et al . , 1988 ; bobak et al . , 1989 ; kahn et al . , 1991 ; lee et al . , the first confusion in the nomenclature was that the current human arf4 was originally published with the name arf2 ( kahn , et al . , 1991 ) . in fact , humans appear to have lost the arf2 orthologue , which is present in other mammals ( including rats , mice , and cows ) . the combination of protein sequence comparisons and intron / exon boundaries of arf genes led to further classification of the six mammalian arfs into classes : class i ( arf13 are > 96% identical ) , class ii ( arf4 and arf5 are 90% identical to each other and 80% identical to the other arfs ) , and class iii ( arf6 is 6469% identical to the other arfs ) . phylogenetic analyses support the conclusion that the three classes of arf diverged early , as flies and worms have single representatives of each of the three classes , and the number of genes / proteins in class i and ii were later expanded in vertebrates . the initial criteria for naming new arfs were functional , and only those proteins that could ( 1 ) serve as cofactors for cholera toxin , ( 2 ) rescue the lethal arf1arf2 deletion in saccharomyces cerevisiae , and ( 3 ) directly activate pld were given the name arf . thus , with the chance cloning of an essential gene in drosophila melanogaster that encoded a protein closely related to the arfs ( 5060% identity ) but lacking in these activities , it was named arflike ( tamkun et al . , 1991 ) . when orthologues were found in several other species , the name was changed to arf - like 1 ( arl1 ) in those species ( kahn et al . , 1992 ; breiner et al . , 1996 ; lowe et al . , 1996 ) . note that although the name arf still denotes a protein with one or more specific functions or activities , the term arl does not . pcr amplification with degenerate oligonucleotide primers ( clark et al . , 1993 ; schurmann et al . , 1994 ) revealed the existence of a large number of mammalian cdnas encoding closely related proteins . the next to be cloned and sequenced were arl2 ( clark et al . , 1993 ) , arl3 ( cavenagh et al . , 1994 ) , arl4 ( schurmann et al . , 1994 ) , and arl5 ( breiner et al . , 1996 ) . each of the encoded proteins has a glycine at position 2 , the site of n - myristoylation in all arf proteins . note that although arl2 and arl3 have the nh2-terminal glycine , they appear not to be substrates for n - myristoyltransferases . around this time , a protein with similar percent identities to the arf and arls was found , but it lacked the nh2-terminal glycine , was membrane associated , and displayed distinctive nucleotide handling properties ( schurmann et al . , 1995 ) . thus , it was given the name arf - related protein 1 ( arfrp1 ) to distinguish it from the arls and arfs . we realize today that this was unfortunate , as several of the more recently identified arls also have functions and biochemical properties that are quite divergent from arfs . sar1 was among the earliest members of the arf family sequenced , and it came out of genetic screens in the yeast s. cerevisiae as a suppressor of sec12(ts ) ( nakano and muramatsu , 1989 ) . its name is derived from its identification as a secretion - associated and ras - related protein . cloning of the mammalian orthologues revealed the presence of two closely related ( 90% identity ) proteins / genes ( kuge et al . , 1994 ) . with < 30% identity to arfs or arls , the sar proteins are only slightly closer in sequence to arfs than to other families of gtpases , but they also share considerable functional relatedness to arfs in that they act through the recruitment of coat proteins or complexes to initiate vesicle budding . an interesting variation is found in ard1/tripartite motif 23 ( trim23 ) , a 64-kd protein that possesses a 20-kd domain at its cooh terminus with 60% identity to arfs ( mishima et al . , 1993 ) . originally named based on the presence of the arf domain , ard1 is also a member of the trim family , from which it obtained its current name , trim23 . a large extension is also seen in arl13b , a protein of 428 residues that contains an arl domain at its nh2 terminus ( chiang et al . , 2004 ; fan et al . , 2004 although the nh2-terminal portion of trim23 may possess gtpase - activating protein activity toward its own arf domain ( vitale et al . , 1996 ) and e3 ubiquitin ligase activity ( vichi et al . , 2005 ) , the cooh - terminal portion of arl13b has no defined domains or functions to date . as the discussion above suggests , there are no shared functions or activities that justify grouping arf , arl , and sar proteins into a family with a common nomenclature . similarities in protein sequences within the arf family were first identified by alignment and phylogenetic analyses and were shown to provide distinct signatures that allowed differentiation from ras , g protein subunits , and other gtpases . these include an nh2-terminal extension , a glycine acceptor for myristate at position 2 , an aspartate at position 26 ( in contrast to the glycine 12 of ras that carries oncogenic potential ) , and other residues that are very highly conserved within the family . these early observations were put on more solid functional footing when they were found to map to unique elements in their three - dimensional structures , which allow for the gdp / gtp switch to be coupled with interaction signals opposite to the nucleotide - binding site ( for review see pasqualato et al . , 2002 ) . the prominent feature of this unique nucleotide switch is a nonconventional gdp - bound form in which the two strands that connect the nucleotide - sensitive switch 1 and 2 regions ( also called the interswitch ) are retracted in the protein core and must undergo a two - residue shift to reach the active conformation ( fig . however , the interswitch can not do so unless the nh2-terminal helical extension , which caps the interswitch and locks it in the retracted conformation , has been displaced . in the case of arf1 , biochemical studies have established that this requires the interaction of the nh2 terminus with membranes , thus allowing the nucleotide - binding site to detect and respond to remote protein membrane interactions ( antonny et al . , , each sar has an nh2-terminal amphipathic helix that functions as a structural gdp / gtp switch to anchor the gtp - bound form to membranes of the endoplasmic reticulum ( huang et al . furthermore , membrane insertion of this nh2-terminal helix was recently shown to initiate membrane bending at the early stages of copii coat assembly and to be subsequently required for the completion of copii vesicle fission ( lee et al . , 2005 ) . in arfs , arls , and sar proteins , the interswitch toggles from an unusual retracted conformation in the gdp - bound form that is fastened by the nh2-terminal helix to an exposed conformation in the gtp - bound form that is stabilized by the w / gg / r signature ( shown here for arf6-gdp and arf6-gtp ) . this large conformational change , which involves a two - residue -strand register shift in the core of the g domain , allows the nucleotide - binding site to detect remote interactions taking place at the nh2 terminus ( reproduced from pasqualato et al . , 2001 with permission ) . structural analysis of arf1 and arf6 gdp / gtp cycles and their comparison with those of small gtp - binding proteins whose interswitch does not toggle identified three structural determinants for this movement : a helical nh2-terminal extension that fastens the retracted , gdp - bound interswitch ; a shorter interswitch that can retract completely ; and a sequence signature ( wdvggqxxxrxxw ) that provides both flexibility for the movement ( gg ) and hydrogen bonds for stabilization of the active conformation ( r / w ) . these characteristics are present in all arf and most arl sequences , which , therefore , are predicted to have the ability to undergo the interswitch toggle to detect interactions opposite to the nucleotide - binding site , whatever their nature , and propagate them to this site ( pasqualato et al . , 2002 ) . these structural criteria for unifying arf and arl proteins as a family have since been supported by various structures of gdp - bound arf and arl proteins ( table s1 , available at http://www.jcb.org/cgi/content/full/jcb.200512057/dc1 ) . it should be noted , however , that one subgroup , arl4 , has a long interswitch that may have lost the ability to toggle , whereas structures of nh2-terminally truncated arl8a and arl8b bound to gdp have a gtp - like conformation . this suggests that truncation of the nh2 terminus is sufficient in this family to destabilize the retracted interswitch or that these proteins have lost their ability to undergo the interswitch toggle . recent work on arl3 suggests that proteins interacting with the nh2 terminus could also work as the displacing factor as an alternative to membranes ( behnia et al . table i contains information on proposed and previous names as well as other information on the human arf family members . est and genomic sequencing resulted in the identification of subsequent arf - like proteins , and these proteins / genes were often misnamed or named multiple times by different research groups . some of these names suggest relationships that are misleading , and some are called arfs despite ( presumably ) lacking any arf activities . in many cases , one protein has been referred to by four different names , and some proteins / genes were named by curators of databases responding to specific requests in a manner that disagreed with common usage by researchers in the field . the confusion is magnified when species differences are considered ( e.g. , yeast arl3 is the orthologue of arfrp1 ) . the arf family gtpases : summary of names , identifiers , and nh2-terminal sequences because of previous usage and to avoid confusion , the new assignments result in there being no gene / protein named arl7 or arl12 . see table s2 for a list of earlier names and references in which earlier names were used ( available at http://www.jcb.org/cgi/content/full/jcb.200512057/dc1 ) . the sequence currently in the database is predicted to be incorrect , and our corrected information was used herein . the need for a generally agreed upon nomenclature for the arf family has become acute as a result of increasing confusion and interest in their study . it is not possible today to propose a completely consistent nomenclature , as there are simply too many studies with some of the earlier discovered proteins ( e.g. , arfrp1 should be an arl ) . the nomenclature developed and described in this article builds on previous efforts to describe phylogenetic relationships and bring consistency to nomenclature ( pasqualato et al . , 2002 ; li et al . , 2004 it is the result of many discussions between researchers in the field and with the hugo genome nomenclature committee ( hgnc ) and has been widely circulated to arf family researchers . we describe the presence in the human proteome of 29 members of the arf family and a system for naming newly identified proteins in human or other species . the use of letter suffixes is reserved for those groups of proteins within the family that share higher percent identities and are , therefore , likely to share some level of functional redundancy . one exception to this is the arl13a and arl13b proteins , which have been given a common number based upon phylogenetic evidence . the consensus nomenclature for the arf family is shown in table i along with previous names and unique gene / protein identifying information . note that in three cases ( arl5c , arl9 , and arl16 ) , the intron / exon boundary predictions in the database are thought to be incorrect ( based upon comparisons with sequences in other species ) , resulting in differences in the predicted protein sequences . in these cases , we use our corrected sequences for comparisons and provide the predicted protein sequences of the human proteins ( see supplemental material , available at http://www.jcb.org/cgi/content/full/jcb.200512057/dc1 ) . in addition , there is one case ( arl9 ) in which it appears that alternative splicing yields two different proteins , one of which is truncated and predicted to be unable to bind nucleotides , so both are provided in the supplemental protein sequence material . we also identify several gene sequences that have questionable est / mrna support and are likely pseudogenes derived from members of the arf family . these genes , which are annotated by the hgnc , are therefore not included as arf family members and are listed , along with their identifiers , in table ii . it is expected that additional pseudogenes will be found and added to this list over time . we also note some uncertainty as to whether arl5c in table i is a transcribed gene , as it may lack part of the consensus gtp - binding signature depending on which predicted protein sequence is used . pseudogenes of the arf family in the human genome this is a list of the hgnc - recognized pseudogenes from the arf family along with their locations in the genome , accession numbers , and gene identifiers . finally , we note that although the large majority of arf family members appear to have very broad and perhaps ubiquitous tissue expression patterns , a few are far more restricted in their expression . thus , it is expected that further additions and perhaps even deletions will be needed to keep the nomenclature of this family current and as consistent as possible . to ensure that new family members are assigned unique symbols , we strongly encourage authors to consult the hgnc before publishing any new names for members of this gene / protein family . this is a confidential service provided by the hgnc that will help prevent future confusion from arising . we also suggest that curators and researchers focusing on other organisms use the information provided in this article as much as possible to simplify and clarify the nomenclature across species . other researchers supporting the use of this nomenclature include : bruno antonny , bill balch , vytas bankaitis , gary bokoch , juan bonifacino , chris burd , jim casanova , tamara caspary , dany cassel , rick cerione , pierre chardin , philippe chavrier , shamshad cockcroft , peter cullen , ivan de curtis , maria antonella de matteis , julie donaldson , cryslin d'souza - schorey , john exton , victor faundez , jim goldenring , jean gruenberg , alan hall , fuchu he , wangjin hong , victor hsu , mary hunzicker - dunn , trevor jackson , cathy jackson , hans joost , toshi katada , fang - jen lee , michel leroux , jennifer lippincott - schwartz , john logsdon , alberto luini , vivek malhotra , ed manser , tobias meyer , paul melancon , joel moss , aki nakano , kazu nakayama , tommy nilsson , susanne pfeffer , richard premont , paul randazzo , anne ridley , scotty robinson , anne rosenwald , craig roy , hisataka sabe , randy schekman , nava segev , val sheffield , phil stahl , elizabeth sztul , chris turner , anne theibert , martha vaughan , kanamarlapudi venkateswarlu , fred wittinghofer , keqiang ye , and marino zerial .

the ras superfamily is comprised of at least four large families of regulatory guanosine triphosphate binding proteins , including the arfs . the arf family includes three different groups of proteins : the arfs , arf - like ( arls ) , and sars . several arf family members have been very highly conserved throughout eukaryotic evolution and have orthologues in evolutionally diverse species . the different means by which arf family members have been identified have resulted in an inconsistent and confusing array of names . this confusion is further compounded by differences in nomenclature between different species . we propose a more consistent nomenclature for the human members of the arf family that may also serve as a guide for nomenclature in other species .

spontaneous intracranial hypotension ( sih ) syndrome can be observed in patients with a postural headache because of low cerebrospinal fluid ( csf ) pressure and no previous history of head trauma or dural puncture . sih is caused by spontaneous csf leaks from the spinal meningeal diverticula or the dural rents along nerve sleeves . sih is characterized by spontaneous postural headache with nausea , neck stiffness , vomiting , tinnitus , and vertigo in patients with low csf pressure . brain magnetic resonance imaging ( mri ) has been used as the diagnostic study of choice for sih because of its ability to identify characteristic abnormalities such as subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain . when sih is suspected on a brain mri , radioisotope ( ri ) cisternography , and computed tomographic myelography can be used to identify the site of a csf leakage . indirect findings of ri cisternography , such as early visualization of bladder activity , may also be useful in the diagnosis and post - treatment follow - up of csf leakage . although many cases of sih resolve spontaneously with conservative treatment including bed rest , hydration , caffeine , and analgesics , others require the injection of autologous blood into the epidural space with csf leakage . various studies have demonstrated that an autologous epidural blood patch ( ebp ) is a very effective treatment modality for refractory cases of sih . although targeted autologous ebp seems to be effective , some patients require a repeat autologous ebp because of inadequate control of their postural headache . in our present study , we investigated whether autologous ebp responses correlate with surrogate markers of quantitative findings such as the early visualization of bladder activity in ri cisternography and subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain on mri . we aimed to identify factors affecting the therapeutic outcomes of autologous ebp in sih patients in order to help predict the response to autologous ebp . this retrospective study was approved by the institutional review board of asan medical center ( approval number : 20150886 ) , and the necessity for obtaining informed consent was waived as we were only reviewing recorded data . all cases of autologous ebp that were performed with the fluoroscopy - guided technique for sih from january 2006 to december 2014 were reviewed . patients who met all of the following criteria were included : ( 1 ) hospitalized by the neurology department because of symptomatic sih , ( 2 ) received autologous ebp under fluoroscopic guidance , ( 3 ) both ri cisternography and brain mri results were available , and ( 4 ) discharged with significant symptom improvement . the exclusion criteria were : ( 1 ) incomplete medical records such as an absence of preprocedural and postprocedural pain scores , and ( 2 ) absence of formal reports of ri cisternography and brain mri . among the 202 patients who underwent autologous ebp at our hospital , only 104 met the inclusion and exclusion criteria . the following data were collected and analyzed through a review of electronic medical records : demographic variables , number of ebps , pain scores ( vas ; visual analogue scale ) , early visualization of bladder activity by ri cisternography , and abnormal mri findings , including subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain . early visualization of bladder activity by ri cisternography was defined by the presence of radioactivity in the urinary bladder 1 to 3 hours after a lumbar intrathecal injection of a radioactive tracer . we evaluated the recorded ri activity in the urinary bladder at 30 minutes and 2 hours after lumbar intrathecal injection of the radioactive tracer for early visualization of bladder activity . patients were diagnosed with sih if they had at least 2 of the following 3 criteria : orthostatic headache , low csf pressure , and diffuse pachymeningeal gadolinium enhancement on brain mri . orthostatic headache was defined as a headache that occurs or worsens less than 15 minutes after assuming the upright position and disappears or improves less than 30 minutes after resuming the recumbent position . low csf pressure was defined as a csf opening pressure of less than 60 mmh2o in the sitting position . if these initial supportive treatments failed after 5 to 7 days , patients were referred to the pain clinic and treated with autologous ebp . when patients had orthostatic headache 4 to 5 days after autologous ebp , we performed repeat autologous ebp . the target level of autologous ebp was determined as the level of most increased paraspinal activity on ri cisternography . if additional autologous ebp was required in patients with multiple leakage sites , it was performed at another level that had not been targeted before . targeted autologous ebps were performed using a 21-gauge tuohy needle via a midline or paramedian approach under fluoroscopy c - arm system ( oec 9800 , general electric healthcare , little chalfont , united kingdom ) guidance with the patient in prone position . the epidural space was identified using the loss of resistance technique , and accurate localization was confirmed by ensuring the spread of the injected contrast medium over the targeted epidural space . thereafter , autologous blood was slowly injected until the patient began to complain of back pain or radicular pain . we divided the study subjects into two groups , one including patients in which autologous ebp was performed once ( ebp s ) , and another comprising cases in which autologous ebp was performed twice or more ( ebp m ) . correlation analysis was performed to identify relationships between the number of autologous ebps and radiologic findings , such as early visualization of bladder activity on ri cisternography , subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain on mri . for variables that correlated with the number of autologous ebps and pre- and post - ebp pain score differences , regression analysis was also conducted to evaluate the causal relationship . we divided the study subjects into two groups , one including patients in which autologous ebp was performed once ( ebp s ) , and another comprising cases in which autologous ebp was performed twice or more ( ebp m ) . correlation analysis was performed to identify relationships between the number of autologous ebps and radiologic findings , such as early visualization of bladder activity on ri cisternography , subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain on mri . for variables that correlated with the number of autologous ebps and pre- and post - ebp pain score differences , regression analysis was also conducted to evaluate the causal relationship . there were 39 men and 65 women subjects with a mean age ( interquartile range , ir ) of 39.2 years ( 2466 ) . the mean height ( ir ) and weight ( ir ) were 165.4 cm ( 146183 ) and 62.0 kg ( 4393 ) . the mean volume ( ir ) of injected blood was 14.7 ml ( 9.525 ) . the mean pain scores ( vas ) before and after the first ebp were 4.6 and 1.1 , respectively . incidences of subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain on mri examination occurred in 11 ( 10.6% ) , 61 ( 58.7% ) , 40 ( 38.5% ) , 14 ( 13.5% ) , and 22 ( 21.2% ) patients , respectively . the 104 study patients were divided into two groups , according to the number of autologous ebps performed , that is , only once ( ebp s , 37 patients ) , and twice or more ( ebp m , 67 patients ) . as indicated in table 1 , the demographic characteristics were not significantly different between these two groups . early bladder activity on ri cisternography showed a statistically significant correlation with the pain score difference between pre- and post - ebp ( p < 0.05 ; spearman rho : 0.240 ) . in addition , patients with early bladder activity on ri cisternography had a tendency to need a higher number of autologous ebps ( fisher exact test , p = 0.03 ) ( table 2 ) . by correlation analysis , only sagging of the brain and no other variables showed a statistically significant negative correlation with the number of autologous ebps ( p < 0.01 ; spearman rho : 0.259 ) . characteristics of spontaneous intracranial hypotension patients who receive single or multiple autologous epidural blood patch treatments proportions of the study patients with early bladder activity scahltenbrand initially introduced aliquorrhea in 1938 to describe a patient with sih , and also suggested that there were 3 possible causes of sih syndrome : increased csf absorption , reduced csf production , and csf leakage . csf leakage into the spinal epidural space causes several symptoms of sih such as spontaneous orthostatic headache with nausea , neck stiffness , vomiting , tinnitus , and vertigo . orthostatic headache due to sih syndrome usually resolves spontaneously , but autologous ebp should be considered to relieve symptoms in refractory cases . autologous ebp has been recommended as the treatment of choice in patients who have failed initial noninvasive treatments such as hydration and bed rest , a generous caffeine intake , and the use of an abdominal binder . the effect of autologous ebp is 2-fold : ( 1 ) an immediate effect related simply to volume replacement by compressing the dura mater ; and ( 2 ) a subsequent latent effect related to sealing of the leakage . in sih syndrome , the success rate with a first autologous ebp has been reported to be 30 to 87% . we have experienced cases in which 7 autologous ebps were needed to achieve lasting relief . we had aimed in a previous study to elucidate the relationship between autologous ebp responses and ri cisternographic findings , hypothesizing that the number of autologous ebps would be increased if the number of csf leakage levels on ri cisternography were increased . in our previous study , we found that the response to autologous ebp was related to the severity of symptoms but not to the number and location of csf leakages . one of the limitations of our previous study was that we only dealt with the number of leakage sites without any quantitative analysis of the amount of leakage because there are no proper tools to measure this . we , therefore , decided to use 6 surrogate markers of the quantitative evaluation of leakage based on previous studies . the first marker was derived from the study of morioka et al who evaluated four indirect findings of csf leakage on ri cisternography , such as the early visualization of bladder activity , no visualization of activity over the brain convexities , rapid disappearance of spinal activity , and abnormal visualization of the root sleeves . these authors demonstrated early visualization of bladder activity in ri cisternography in all patients with csf leakage . as the release of radioactive tracer into the systemic circulation by csf leakage increases , early bladder activity can be considered as a surrogate marker of csf leakage . severe intracranial hypotension is characterized by 5 mri findings described by schievink , which we used as the additional surrogate markers : ( 1 ) subdural fluid collections or hygromas , ( 2 ) pachymeningeal enhancement , ( 3 ) engorgement of venous structures , ( 4 ) pituitary hyperemia , and ( 5 ) sagging of the brain . we investigated in our current study whether autologous ebp responses correlate with these 6 surrogate markers of the quantitative levels of csf leakage . early bladder activity on ri cisternography showed a significant correlation with the pain score and with the number of autologous ebps in our current patient series . although there was no significant difference between these patients and the cases without early bladder activity on ri cisternography , multiple autologous ebp was often needed for patient with early bladder activity on ri cisternography . therefore , we suggest from our current findings that early bladder activity on ri cisternography is a predictive factor for the autologous ebp response . among the 5 mri surrogate markers we evaluated , only brain sagging showed a significant correlation with autologous ebp responses . although this was not significantly different in the cases without sagging of the brain on mri , the patients with sagging of the brain showed better autologous ebp responses . the better responses to autologous ebp treatments in patients with sagging of the brain were considered dependent on the fact that it is helpful to raises the csf pressure by preventing csf leakage sites . thus , we identified early bladder activity on ri cisternography and sagging of the brain as factors affecting the responsiveness to autologous ebp . these variables may , therefore , give some useful predictive information on the therapeutic effects of autologous ebp . first , we analyzed early visualization of bladder activity by ri cisternography because we could not analyze the actual ri activity . if we could get the raw data and analyze the actual ri activity in ri cisternography , this would give more reliable results . second , we considered the therapeutic effect of autologous ebp to be poor if the number of autologous ebps increased . however , the number of autologous ebps is not equivalent to the therapeutic effects of this treatment . this may introduce an error ; however , the patients were discharged after the symptoms of sih syndrome improved . if a postural headache worsened with ambulation or in a sitting position , autologous ebp was conducted again until the symptoms of sih improved . therefore , we decided to determine the treatment response by using the number of autologous ebps , and this modality of evaluation should have less influence on the results . in conclusion , autologous ebp is an effective treatment method for managing sih , and the response to it may be related to the radiologic findings of early bladder activity on ri cisternography and sagging of the brain on mri . however , the number of autologous ebps necessary to achieve symptomatic relief does not correlate with other mri abnormal findings , such as subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , and pituitary hyperemia . these results are meaningful because they reveal that the therapeutic effect of ebp on sih can be predicted .

abstractspontaneous intracranial hypotension ( sih ) is characterized by postural headache because of low cerebrospinal fluid ( csf ) pressure . brain magnetic resonance imaging ( mri ) and radioisotope ( ri ) cisternography can be used to identify the site of a csf leakage . although autologous epidural blood patch ( ebp ) is a very effective treatment modality , some patients require a repeat autologous ebp . we investigated whether autologous ebp responses correlate with surrogate markers of quantitative findings.all cases of autologous ebp for sih from january 2006 to december 2014 were enrolled . the demographic variables , number of ebps , pain scores , ri cisternography ( early visualization of bladder activity ) , and mri findings ( subdural fluid collections , pachymeningeal enhancement , engorgement of venous structures , pituitary hyperemia , and sagging of the brain ) were reviewed.patients with early bladder activity on ri cisternography had a tendency to need a higher number of autologous ebps . only sagging of the brain and no other variables showed a statistically significant negative correlation with the number of autologous ebps.the response to autologous ebp may be related to the radiologic findings of early bladder activity on ri cisternography and sagging of the brain on mri .

a plya urn is an urn which contains balls of two colors ( black and white ) , and which is coupled with an initial configuration and a set of evolution rules . a step then consists in randomly picking a ball from the urn , placing it back , and depending on its color , adding a fixed number of black and/or white balls . the question is : what does the urn look like after a large number of steps ? this simple process has turned out to be extremely versatile , and has been used to model many different phenomena , such as population growth , epidemics , tree structures in computer science ( bst , @xmath0-trees ) , electoral campaigns , etc . this paper analyzes a class of balanced additive urns . _ balanced _ urns are urns for which , at every step , the same constant number of balls is added . this property allows us to resort to a combinatorial treatment : enumerating all configurations using generating functions . such an approach , introduced by flajolet and his coauthors @xcite , is a departure from previous probabilistic methods . in _ additive _ urns , no ball is ever removed and the urn s size is strictly increasing . we specifically consider a class of balanced additive urns which has _ algebraic _ generating functions . through the use of analytic combinatorics @xcite , we obtain precise probability results , including a gaussian limit law with rate of convergence , a local limit law and large deviation bounds . our analysis makes use of a multiple coalescing saddle - point method , which is not classical . as previously thought , analytic combinatorial methods can provide a wealth of valuable information that seems to be new . in addition , our results seem to reinforce the idea of a general theory for additive balanced urns . this paper comes as the continuation of flajolet s work on urns @xcite and @xcite ; these two papers were on subtractive and triangular urn models . of course , this topic has been thoroughly addressed through probabilistic means . we can cite introductory books on urns @xcite @xcite and an article @xcite ; on the topic of limit distribution for urns , janson s papers are a reference @xcite @xcite @xcite as is smythe s @xcite ; and on the topic of large additive urns , @xcite . from an analytic point of view , hwang et al.s paper @xcite considers `` _ _ diminishing _ _ '' urn models . and in direct relation to the present paper , we have obtained similar results @xcite on a class of additive balanced urns which is linked to some family of @xmath1-trees @xcite . in sect . [ urn_system ] , we lay the ground work by introducing plya urn models as well as the main result of @xcite on the isomorphism between balanced urns and differential systems . then , in sect . [ note1 ] , we introduce our urn class , which can be viewed as a population growth model . we establish that the generating function is algebraic and provide our first results on mean and variance . section [ limit_th ] contains the main theorems of the paper regarding the limit distribution of our urn class . finally we state the propositions and lemmas required by the proof of the main theorems , and give some extensive details on the part involving multiple coalescing saddle - points . in plya s classical urn model , we have an urn containing balls of two different colors , black balls ( b type ) and white balls ( w type ) . this system evolves with regards to particular rules ( at each step , add and/or discard black and/or white balls ) , and these rules are specified by a @xmath2 matrix @xmath3 we start with an initial configuration @xmath4 . at step @xmath5 , the urn contains @xmath6 black balls and @xmath7 white balls . the evolution between steps @xmath8 and @xmath9 is now described . we uniformly draw a ball from the urn , we look at its color and _ we put it back into the urn_. if the color is black , then we add @xmath10 black balls and @xmath11 white balls ; if the color is white , we add @xmath12 black balls and @xmath13 white balls . [ def_balance ] the urn ( [ urne22 ] ) is said to be _ balanced _ if the sums of its rows are constant , that is if @xmath14 . this parameter is called the _ balance _ of the urn , and denoted by @xmath15 . at each step , we add @xmath15 balls in the urn . so , starting with @xmath16 balls in a balanced urn , we know that the total number of balls after @xmath8 steps will be @xmath17 . this balanced condition is the key requirement for using flajolet - dumas - puyhaubert differential systems . [ def_additive ] an urn is _ additive _ if all the coefficients in its rule matrix ( [ urne22 ] ) are strictly positive , i.e. , @xmath18 . no balls are ever removed from an additive urn . in our study , we focus on _ balanced additive _ urns . the papers @xcite and @xcite introduce a new analytical and combinatorial approach to the study of these balanced urn models . the crucial starting point is an isomorphism theorem between the rules of an urn and a differential system . we briefly recall these results . [ def_histoire ] a _ history _ of length @xmath8 is a sequence of @xmath8 steps , obtained by @xmath8 successive draws from the urn . the _ exponential generating function of histories _ of the urn ( [ urne22 ] ) is @xmath19 where @xmath20 is the number of histories of length @xmath8 starting at the configuration @xmath21 , and ending at a configuration @xmath22 . we will shorten this to @xmath23 when there is no ambiguity on the initial configuration @xmath21 . [ theo_fond ] we associate to the urn ( [ urne22 ] ) , with the balanced condition @xmath24 , the following differential system ( we denote @xmath25-differentiation by a point , @xmath26 ) : @xmath27 [ cols="^,^,^,^ " , ] let @xmath28 be the associated solution , then thanks to theorem [ theo_fond ] , and @xmath29 , @xmath30 , we get @xmath31 . rewriting the system , @xmath32 then , @xmath33 after a @xmath34-integration and naming the integration constant @xmath35 , @xmath36 we can set @xmath37 ( the variable is useless because of the balanced condition . indeed , in @xmath38 , the non - negative coefficients of @xmath39 appear when @xmath40 ) , then we get the result . thus , the generating function @xmath41 is algebraic , as solution of a polynomial of degree @xmath42 . from the polynomial equation ( [ eqn_algebric ] ) , we can directly extract some precise information concerning the expression of the mean and the variance of the urn composition . it is also possible to get all moments . [ moy_var ] let @xmath43 be the random variable counting the number of black balls b in the urn ( [ urne_note1 ] ) at step @xmath8 . then we can express mean and variance asymptotically : @xmath44 @xmath45 the following techniques are described in @xcite . we differentiate the equation ( [ eqn_algebric ] ) with regards to @xmath46 , then we set @xmath47 ; we use the asymptotic expansion form and normalize by the asymptotic expansion of @xmath48 . for variance , we differentiate twice and we use the same technique . it can be done for all moments . besides , it is possible to express any term in the asymptotic expansion , thanks to dr . salvy s maple package ` gfun ` . the aim of this section is to obtain properties on the limit distribution of the number of black balls in the urn . our combinatorial point of view implies the study of @xmath34-coefficients of the generating function @xmath49 . [ yn_exp ] the @xmath50-coefficient in the generating function of histories @xmath49 can by expressed by a contour integral ( with a contour around the origin ) : @xmath51 h(x , z ) = \frac{\sigma^{n+1}}{2 i \pi } \oint a_x(w ) h_x(w)^{n+1 } \text{\emph{d}}w \ , , \qquad\text{where}\ ] ] @xmath52^{-1 } , \\ a_x(w ) & = ( 1-w)^{\alpha + \beta -2 } \left ( x^{-\alpha } -1 + \left ( 1-w \right)^{\alpha } \right ) \ , .\end{aligned}\ ] ] we start with the polynomial ( [ eqn_algebric ] ) which cancels @xmath53 . we use a cauchy formula to express the @xmath50-coefficient , @xmath54 h(x , z ) = y_n(x ) = \frac{1}{2 i \pi } \oint \frac{y(x , z)}{z^{n+1}}\text{d}z \ , .\ ] ] then , by a lagrange inversion between @xmath34 and @xmath55 , using @xmath56 at this step , it is not yet possible to apply a saddle - point method , because the saddle - points are at @xmath57 . again , we change variables , and set @xmath58 to get the result . from this lemma , we have to evaluate this integral in order to have an expression of @xmath59 h(x , z)$ ] . it will be necessary for describing the limit probability distribution . indeed , our main goal is to understand the behavior of the probability generating function noted @xmath60 , @xmath61 h(x , z)}{[z^n ] h(1,z ) } \ , . \end{aligned}\ ] ] first , we focus on the evaluation of . in the special case @xmath47 , we can solve explicitly the equation ( [ eqn_algebric ] ) . thus , we know with classical analytic combinatorics that . for @xmath62 , we do nt have access to the explicit solution , therefore we use a saddle - point method for the general case . in the appendix [ saddle - point ] , the simple case @xmath63 is treated with this method . it is useful to guess the right normalization for the variables and the contour for the general case . for illustration , [ sadd3 ] shows the behavior of @xmath64 and how to choose the contour . for the urn @xmath65 . the three _ peaks _ correspond to zeros of the denominator of @xmath64 which are @xmath5 , @xmath66 and @xmath67 , where @xmath68 is the third - root of unity @xmath69 . _ right - _ diagram from a top view of the three poles and the double saddle - point in 1 , with the three - parts contour @xmath70 , @xmath71 , @xmath72.,title="fig:",height=226 ] for the urn @xmath65 . the three _ peaks _ correspond to zeros of the denominator of @xmath64 which are @xmath5 , @xmath66 and @xmath67 , where @xmath68 is the third - root of unity @xmath69 . _ right - _ diagram from a top view of the three poles and the double saddle - point in 1 , with the three - parts contour @xmath70 , @xmath71 , @xmath72.,title="fig:",height=151 ] here is the main result of the paper . it is described in the three following theorems which concerns the asymptotic distribution of the balls in the urn . proposition [ y_expr ] expresses the asymptotic expansion of the probability generating function @xmath60 . the refined saddle - point analysis is the core of the proof of this proposition . then , the proofs of the theorems are based on this proposition and on quasi - power theorems from h .- k.hwang , recalled in @xcite _ ( p . 645 , 696 , 700)_. let @xmath43 be the random variable counting the number of black balls in the urn @xmath73 after @xmath8 steps . [ th_loi_limite](gaussian limit law ) the random variable @xmath43 has mean @xmath74 and variance @xmath75 , and the normalized random variable @xmath76 converges in law to the standard normal law @xmath77 , with rate of convergence @xmath78 , @xmath79 @xmath80 with @xmath81 [ th_loi_locale](local limit law ) we denote @xmath82 . the distribution of @xmath43 satisfies a local limit law of gaussian type with rate of convergence @xmath78 , i.e. @xmath83 the last theorem concerns large deviation bounds . ( large deviations property ) let @xmath84 be a sequence tending to infinity . a sequence of random variables @xmath85 with mean @xmath86 , satisfies a _ large deviation property _ , relative to the interval @xmath87 $ ] containing @xmath88 , if there exists a function @xmath89 such as @xmath90 for @xmath91 , and for @xmath8 large enough , @xmath92 @xmath93 w(t ) is called the _ rate function _ , and @xmath94 is the _ scale factor_. [ grandes_deviations](large deviations ) for @xmath95 such as @xmath96 , the sequence of random variables @xmath85 satisfies a large deviation property relative to the interval @xmath87 $ ] , with a scale factor @xmath8 , and a rate @xmath89 , with @xmath97 @xmath98 @xmath99 } \ \log \left ( \frac{\chi(x)}{x^t } \right ) \ , , \text { where } \chi(x ) = x^{\mu } \ , e^ { \frac{\nu^2}{2 } \ln(x)^2 } \ , .\ ] ] the main proposition in the proof of the theorems is the asymptotic expression of the probability generating function @xmath60 , obtained by the division of @xmath100 by @xmath101 , where @xmath100 denotes the @xmath50-coefficient in @xmath49 . [ y_expr ] for @xmath102 , the expression of the probability generating function @xmath60 is , asymptotically when @xmath103 , @xmath104 with @xmath81 this expression ( [ pn_expr ] ) of @xmath60 is valid for @xmath46 in a neighborhood of @xmath105 , with the radius @xmath106 ( which will give the gaussian limit law ) ; for @xmath46 in a real segment centered in @xmath105 of length @xmath106 ( which will give large deviation ) ; for @xmath46 in the unit circle , @xmath107 ( which will give a local limit law ) . for all @xmath46 , @xmath108 has a simple pole in @xmath109 , and @xmath110 other simple poles . saddle - points are in @xmath111 with multiplicity @xmath112 , and in @xmath113 , with @xmath114 any @xmath115th - root of @xmath116 . in order to find saddle - points , we look at zeros of the derivative of @xmath117 , @xmath118 in our case , when @xmath62 , we have @xmath119 different saddle - points : one `` huge '' at @xmath111 , and @xmath115 secondary saddle - points depending on the @xmath46 value . when @xmath46 is in a neighborhood of @xmath105 , the @xmath115 saddle - points will merge at the point @xmath111 . we have to deal with @xmath119 coalescing saddle - points . it differs from usual saddle - points method because it is no longer possible to treat each saddle - point independently . we need to consider all saddle - points together in order to find the asymptotic expansion . for the urn @xmath120 . there are @xmath121 poles , and 4 saddle - points at point @xmath105 and at @xmath122 . _ right - _ multiple saddle - points for @xmath108 . the _ peaks _ ( poles ) corresponds to the zeros of the denominator of @xmath108 . the _ stars _ represent the different saddle - points . we illustrate _ in red _ the integration contour around 0.,title="fig:",height=207 ] for the urn @xmath120 . there are @xmath121 poles , and 4 saddle - points at point @xmath105 and at @xmath122 . _ right - _ multiple saddle - points for @xmath108 . the _ peaks _ ( poles ) corresponds to the zeros of the denominator of @xmath108 . the _ stars _ represent the different saddle - points . we illustrate _ in red _ the integration contour around 0.,title="fig:",height=151 ] we expect a gaussian law ( thanks to probabilistic results ) , so we use a renormalisation for @xmath46 of order @xmath106 . for the renormalisation of @xmath123 , we use the same scale as previously in the particular case @xmath47 ( see appendix [ saddle - point ] ) . so the normalizing factor is @xmath124 . the general idea for the choice of the contour is the same as in the previous simple case @xmath47 . we will use two segments beginning in the saddle - point area in @xmath111 and they have to follow the descents of the surface . this descent has to go between the pole @xmath5 and the first closest pole . the segment will make an angle of @xmath125 , as we can see on the right part of fig . [ sadd_multiple ] . the integration contour is described in three parts . we use the following parametrization for the segment @xmath70 . for @xmath126 $ ] , @xmath127 the same parametrization is used for the segment @xmath71 , with an angle of @xmath128 . the circle part @xmath72 completes the contour . [ hx_exp ] there is an asymptotic expansion in @xmath8 for @xmath129 : @xmath130 with @xmath131 notice that this expansion is valid for all @xmath25 and @xmath132 . besides , we obtain the same expansion using for @xmath46 the expression @xmath133 . then , it will be possible to use this expansion for all @xmath134 , then we will have an expression for @xmath135 uniformly , which is a necessary hypothesis for hwang s theorem on limit law . we will use @xmath46 real near from @xmath105 for large deviations theorem . the expression with @xmath136 implies @xmath137 for the local limit law theorem . [ tail_cut ] [ neglect the tails ] the @xmath70-contribution is asymptotically equivalent on both intervals , for @xmath138 $ ] and for @xmath139 $ ] . the error term is @xmath140 , so it is exponentially negligible . on the path @xmath70 , the function @xmath141 is strictly decreasing for . [ c1_part ] [ central approximation ] the @xmath70-contribution can be written @xmath142 we use lemma [ tail_cut ] to restrict the interval . then we can apply the asymptotic expansion of proposition [ hx_exp ] . besides , we have to know an asymptotic expansion for @xmath143 on this path , and we have @xmath144 [ tail_complete ] [ complete the tails ] the integral of @xmath145 on segment @xmath146 $ ] is equivalent to the same integral on interval @xmath147 . + the error term is @xmath140 , so it is exponentially negligible . [ 2-parts ] the @xmath70 and @xmath71 contribution can be written @xmath148 the work on segment @xmath70 is the same for segment @xmath71 . adding the two contribution , we get a @xmath149 factor . thanks to lemma [ tail_complete ] , the integral part of calculus reduces to the simple gamma factor @xmath150 . [ 3-part ] the circle part @xmath72 is exponentially negligible . adding all the contributions , thanks to lemmas [ 2-parts ] and [ 3-part ] , we obtain a global expression of @xmath100 , @xmath151 we can express @xmath60 with @xmath46 in a neighborhood of @xmath105 with radius @xmath106 , and we obtain an expression suited to quasi - power theorems , @xmath152 for the three main theorems , we use this expression which satisfies the hypothesis for applying h .- k.hwang theorems : quasi - power theorem , quasi - power limit theorem and quasi - power for large deviations ( in @xcite , _ p.645 , 696 , 700 _ ) . through the use of analytic combinatorics , we obtain precise probability results , including a gaussian limit law with its rate of convergence , a local limit law and large deviation bounds . for the first time , this kind of probabilistic results on additive balanced urns are obtained from an analytic point of view . as previously thought , analytic combinatorial methods can provide a wealth of valuable information . in addition , our results seem to reinforce the idea of a general theory for additive balanced urns . in this way , the work on urns linked to @xmath1-trees in @xcite use an other subclass of additive balanced urns , and similar probabilistic results were obtained . the natural next step is having a complete understanding of the whole class , following ideas of flajolet et al . in @xcite . i warmly thank my advisor and mentor , philippe flajolet , for guiding me and introducing me to research and especially to analytic combinatorics . this paper is dedicated to him . in addition , i m grateful to jrmie lumbroso for his helpful remarks . + this work was supported by the anr project 09 blan 0011 boole and the anr project 10 blan 0204 magnum . 11 bagchipal bagchi , a. , pal , a. asymptotic normality in the generalized plya - eggenberger urn model , with an application to computer data structures . _ siam journal on algebraic and discrete methods _ * 6 * , no . 3 , 394405 ( 1985 ) banflaschsor01 banderier , c. , flajolet , p. , schaeffer , g. , soria , m. random maps , coalescing saddles , singularity analysis , and airy phenomena . _ random structures & algorithms _ * 19 * , no . 3/4 , 194246 ( 2001 ) chaupousah09 chauvin , b. , pouyanne , n. , sahnoun , r. limit distributions for large plya urns . _ annals of applied probability _ * 21 * , no . 1 , 132 ( 2011 ) fladupuy06 flajolet , p. , dumas , p. , puyhaubert , v. some exactly solvable models of urn process theory . _ discrete mathematics & theoretical computer science proceedings _ * ag * , 59118 ( 2006 ) flagape05 flajolet , p. , gabarro , j. , pekari , h. analytic urns . _ annals of probability _ * 33 * , no . 3 , 12001233 ( 2005 ) flased09 flajolet , p. , sedgewick , r. _ analytic combinatorics . _ cambridge university press ( 2009 ) hwkupa07 hwang , h .- k . , kuba , m. , panholzer , a. analysis of some exactly solvable diminishing urn models . _ in : 19th formal power series and algebraic combinatorics , _ tianjin china ( 2007 ) jan04 janson , s. functional limit theorems for multitype branching processes and generalized plya urns . _ stochastic processes and their applications _ * 110 * , 177245 ( 2004 ) jan05 janson , s. limit theorems for triangular urn schemes . _ probability theory related fields _ * 134 * , no . 3 , 417452 ( 2005 ) jan08 janson , s. plane recursive trees , stirling permutations and an urn model . _ discrete mathematics & theoretical computer science proceedings _ * ai * , 541548 ( 2008 ) joko77 johnson , n. l. , kotz , s. _ urn models and their application . _ john wiley & sons ( 1977 ) mah03 mahmoud , h. plya urn models and connections to random trees : a review . _ journal of the iranian statistical society _ * 2 * , 53114 ( 2003 ) mah08 mahmoud . , h. _ plya urn models . _ chapman - hall / crc press ( 2008 ) morcrette10 morcrette , b. combinatoire analytique et modles durnes , _ master s thesis , mpri - cole normale suprieure de cachan , inria rocquencourt _ ( 2010 ) pansei10 panholzer , a. , seitz , g. ordered increasing @xmath1-trees : introduction and analysis of a preferential attachment network model . _ discrete mathematics & theoretical computer science proceedings _ * am * , 549564 ( 2010 ) smythe96 smythe , r. central limit theorems for urn models . _ stochastic processes and their applications _ * 65 * , 115137 ( 1996 ) we detail here the evaluation of the contour integral @xmath101 for the simple case @xmath47 , @xmath153 then , @xmath154 and @xmath155 . we have now to evaluate the integral . this is classical saddle - point method . the derivative @xmath156 becomes zero only for one value @xmath111 . there is only one saddle - point . we will use two segments starting at @xmath111 and descending along the surface , passing between the peaks ( singular points of @xmath157 ) . the third part of the contour is a circle to join the two ends of segments . figure [ sadd3 ] illustrates the three parts of the contour for the urn @xmath65 . the two cases are similar . for @xmath70 , the integral rewrites @xmath161 adding the two contributions of the two paths @xmath70 and @xmath71 , we get @xmath162 the expansion @xmath163 leads us to change variable with @xmath164 . thus , the integral rewrites @xmath165 we have to adjust the parameter @xmath166 which is the length of each segment . in order to use the expansion approximation , some conditions impose themselves : first , @xmath167 , and second , @xmath168 . we decide to fix @xmath169 . thus , @xmath170 and @xmath171 . in this case , we complete the tail of the gaussian approximation , @xmath172 to conclude with this illustration example , we need to deal with the third part of the contour , which is the circle part . we show that this part is exponentially small . indeed , it is possible to stretch the segments @xmath173 and @xmath174 . thus , the radius of the circle part will grow to infinity and this integral part will be negligible . besides , it is effectively possible to stretch the two segments because the function @xmath157 is strictly decreasing along the segments . its maximum is at the saddle - point . on @xmath175 $ ] , we have @xmath176 . so , the evaluation of the integral on the segment @xmath175 $ ] is the same order as the evaluation on @xmath177 $ ] . indeed , the majoration error is exponentially small . this error is about the order @xmath178 , which is negligible .

this paper introduces and analyzes a particular class of plya urns : balls are of two colors , can only be added ( the urns are said to be _ additive _ ) and at every step the same constant number of balls is added , thus only the color compositions varies ( the urns are said to be _ balanced _ ) . these properties make this class of urns ideally suited for analysis from an `` analytic combinatorics '' point - of - view , following in the footsteps of flajolet et al . @xcite . through an _ algebraic _ generating function to which we apply a multiple coalescing saddle - point method , we are able to give precise asymptotic results for the probability distribution of the composition of the urn , as well as local limit law and large deviation bounds . _ dedicated to the memory of philippe flajolet . _

our knowledge of the properties of cosmic rays produced by the star formation in the milky way galaxy is both precise and largely incomplete . it is precise because the details of the cosmic ray spectrum and elemental composition are measured with high precision @xcite . and it is incomplete because all the precision measurements refer to only single location within the galaxy : the position of the solar system . it is even not obvious what kind of information is contained in such single point measurements . deflections of cosmic rays by turbulent component of galactic magnetic field forces them into a random walk through the interstellar medium ( ism ) @xcite . as a result , cosmic rays arrive from random directions on the sky . it is clear that some information on the sources is encoded in the cosmic ray spectrum , mass composition and global anisotropy @xcite . however , it is not clear how the spectral slope @xmath2 and the break energies of the locally measured piecewise powerlaw cosmic ray spectrum @xmath3 are related to the properties of source population(s ) and their distribution in the galaxy . the diffusion through the ism and escape from the galactic disk modify the cosmic ray spectrum , in a model - dependent way . the locally measured properties of the spectrum are not necessarily representative for those of the global distribution of galactic cosmic rays . instead , they could be determined by the peculiarities of recent injection of particles in the local ism @xcite . an illustration of these uncertainties is found in the model of modification of the cosmic ray spectrum by the propagation effects encoded in an energy - dependent diffusion coefficient @xmath4 @xcite . the slope of the interstellar cosmic ray spectrum is determined by @xmath5 and by the slope @xmath6 of the injection spectrum , @xmath7 . the most commonly considered acceleration mechanism is diffusive shock acceleration ( dsa ) @xcite , which is expected to give a slope @xmath8 . comparison with the slope of the locally measured cosmic ray spectrum , @xmath9 , points to a value of @xmath10 . this is , however , in tension with the measurements of the ratio of abundances of primary and secondary nuclei which give @xmath11 @xcite and with the measurements of anisotropy of the cosmic ray flux @xcite . the value @xmath12 is also favoured by theoretical models of cosmic ray diffusion through the ism @xcite . recent the data on cosmic ray positrons and antiprotons and also the slope and anisotropy properties of the cosmic ray nuclei spectra suggest that the tev range cosmic ray spectrum has a strong contribution a supernova which exploded approximately two million years ago within several hundred parsec distance from the sun @xcite . the data on deposition of isotopes in the deep ocean crust provide information on the occurrence of such nearby supernova events @xcite indicate that only one such nearby supernova event has occurred over last 14 million years @xcite . the slope of the locally observed cosmic ray spectrum in the tev range might be largely determined by this recent supernova event . the information on the `` characteristic '' slope of the galactic cosmic ray spectrum is completely erased by this last supernova contribution . complementary information on the cosmic ray source and propagation parameters is provided by secondary s and neutrinos . contrary to the charged cosmic rays , neutral s and neutrinos go straight from their production sites to the earth . and neutrino signal from individual sources could provide information on the injection spectrum of cosmic rays , while diffuse and neutrino emission from the ism could provide the data on the propagation of cosmic rays in the galaxy . analysis of the signal from the galactic plane of the milky way galaxy and from the disk of the large magellanic cloud ( lmc ) galaxy suggest that the average slope of the cosmic ray spectra produced by the star formation in these two galaxies is @xmath0 , i.e. harder than that of the locally measured cosmic ray spectrum @xcite . the slope of the neutral pion decay spectrum produced by the interactions of cosmic rays with such hard slope is about @xmath13 . this slope is close to that of the slope of the spectrum of the isotropic diffuse background ( igrb)@xcite . this suggests that significant part of the igrb might originate from the cosmic ray interactions in the star forming galaxies@xcite which are not individually resolved by the fermi large area telescope ( lat ) . the normalisation of neutrino and flux in the gev energy range is fixed by the known relation between the far infrared and luminosity of galaxies , @xmath14 @xcite , and by the known level of extragalactic far infrared background , @xmath15 erg/(@xmath16 s sr ) @xcite . the most recent calculation of the and neutrino flux from star forming galaxies which takes into account this relation along with the details of cosmological evolution of different types of galaxies @xcite shows that they provide a significant contribution to the igrb . an independent verification of the result on the hard @xmath0 average cosmic ray spectrum resulting from the star formation in the milky way and other galaxies could be obtained through the neutrino channel . the slope of the spectrum of neutrino emission from the milky way and other star forming galaxies is expected be about @xmath17 , close to the slope of the spectrum . the icecube collaboration has recently reported the detection of astrophysical neutrino signal in the energy range from 10 tev to 2 pev @xcite . the signal forms a powerlaw spectrum @xmath18^{-p_\nu}$ ] , with @xmath19 @xcite . this slope and normalisation of the neutrino spectrum are obviously inconsistent with the possibility that the observed neutrino flux is produced by cosmic rays in the milky way and / or other star forming galaxies , if one assumes that the typical spectrum of the cosmic rays resulting from the star formation is about the locally observed cosmic ray spectrum slope , @xmath9 , and it has a knee feature exactly at the same energy as the knee of the locally measured cosmic ray spectrum @xcite , an assumption was explicitly adopted in most of the previous calculations of the galactic neutrino flux@xcite . different assumptions about the average galactic cosmic ray slope result in the estimates of the galactic contribution to the astrophysical neutrino flux which differ by orders of magnitude ( see e.g. @xcite for an example of calculation assuming @xmath20 ) . however , none of the assumptions about the slope and position of the knee of the galactic cosmic ray spectrum relying on local measurements is justified . the measured slope of the astrophysical neutrino spectrum is consistent with the neutral pion decay spectrum of the milky way and lmc disks @xcite , as expected if the typical slope of the cosmic ray spectrum resulting from the star formation is @xmath21 rather than @xmath9 . below we show that not only the slope , but also the normalisation of the neutrino flux is consistent with this hypothesis . we argue that this suggests the validity of a simple model in which the injection of cosmic rays with the spectrum with the slope suggested by the dsa , @xmath22 is followed by the softening by @xmath23 produced by the escape through the turbulent galactic magnetic fields with kolmogorov or iroshnikov - kraichnan turbulence spectrum . this simple model is valid for the spectrum of cosmic rays averaged over sufficiently large regions of galaxies . it is , however , not valid for the single point measurements of the cosmic ray spectrum , such as the measurements at the position of the solar system in the milky way . our analysis uses all publicly available fermi / large area telescope ( lat ) data @xcite collected over the period from august 2008 till june 2014 . we have processed the data using the _ _ fermi science tools v9r32p5 _ _ - a standard software package , provided by the fermi collaboration to reduce the data , obtained by the fermi / lat . we have used the pass 7 `` reprocessed '' event selection . we have filtered the event lists using the _ gtselect _ tool with parameter evclass=3 , which leaves the events and rejects most of the cosmic ray background events . to produce the all - sky spectrum shown in fig . 2 , we have used the aperture photometry method , applied to the full sky . an estimate of the exposure in each energy bin was done using the _ gtexposure _ tool with the option apcorr = no ( there is no need to correct the exposure for the point spread function for the full sky ) . to separate the diffuse emission from the point source contributions we subtract the flux in the circles of the radius @xmath24 around point sources from the four - year fermi catalogue @xcite . this is sufficient for the analysis of the diffuse emission in the energy band above 10 gev . in this energy band the point spread function of the lat is smaller than @xmath25 @xcite . we have verified that the aperture photometry approach gives the result which is consistent with the results obtained using the likelihood analysis . in particular , the spectrum of the @xmath26 part of the sky , calculated using the aperture photometry method is identical to that reported by @xcite over the entire energy range from 100 mev up to 1 tev . to produce the galactic latitude profiles for the neutrino data , we have binned the neutrino events reported by @xcite in galactic latitude and have estimated the icecube exposure in each galactic latitude bin . this was done via a monte - carlo simulation of the galactic latitude distribution of neutrino events driven from an isotropic sky distribution , with account of the declination dependence of the icecube effective area , derived from the information reported by @xcite . having estimated the exposure in each galactic latitude bin , we have multiplied the model fluxes of the galactic and isotropic components by the galactic latitude dependent exposure to estimate the expected number of neutrino counts in each latitude bin . [ fig : spectrum ] shows the combined and neutrino all - sky spectrum in a broad gev - pev energy range . the statistical errors of the signal are small in all energy bins up to @xmath27 gev . the uncertainty of the flux measurement is dominated by the systematic errors @xcite . the icecube neutrino spectrum is derived from the analysis of @xcite . the dark grey shaded band shows the 68% uncertainty of the flux and slope of the neutrino signal . . thin solid blue and dashed red curves show the estimates of possible and neutrino fluxes from star forming galaxies . ] from fig . [ fig : spectrum ] one could see that the neutrino spectrum lies at the high - energy extrapolation of the spectrum of the entire sky . thus , not only the slopes , but also the normalisation of the two spectra agree with each other . the uncertainty of the neutrino flux at 100 tev is just by a factor of @xmath28 . assuming a negligible uncertainty of the flux at @xmath29 gev , one could find that a powerlaw fit to the combined plus neutrino spectrum gives a very precise measurement of the slope of the powerlaw , @xmath30 , with an error @xmath31\simeq 0.05 $ ] . this is due to a very large dynamic range of the energy on which the powerlaw is observed and to the moderate uncertainty of the neutrino flux measurement . a more precise characterisation of consistency of the and neutrino spectra is given by the model calculation shown in fig . [ fig : spectrum ] . red and blue thin solid curves show a model of the neutrino and emission from interactions of cosmic rays with the ism . the cosmic rays have a powerlaw spectrum with the slope @xmath32 . the and neutrino spectra are calculated using the parametrizations of the pion production spectra by @xcite . the model does not fit the data in the energy band below @xmath33 gev . this is expected , because in this energy band significant contribution from electron bremsstrahlung is expected @xcite . consistency of the combined and neutrino signal with a straightforward model of and neutrino emission from a powerlaw distribution of the parent protons /nuclei suggests s simple model in which both the and neutrino signal are generated by the interactions of cosmic rays produced by the star formation process . from fig . [ fig : spectrum ] one could immediately conclude that in such a scenario contribution of the milky way galaxy in the neutrino flux could not be negligible . indeed , the neutrino flux from other star forming galaxies is constrained by the measurement of an upper limit on the flux of star forming galaxies , which is given by the measured igrb flux . assuming that the emission from cosmic ray interactions in star forming galaxies saturates the igrb measurement , one could estimate the neutrino flux from star forming galaxies via extrapolation of the igrb spectrum toward higher energies ( the red hatched range in fig . [ fig : spectrum ] . this gives an upper limit of @xmath34% of the contribution from star forming galaxies other than milky way . if a large part of the astrophysical neutrino signal is of galactic origin , one expects to find higher signal level at low galactic latitudes . the neutrino signal indeed shows a hint of anisotropy in the direction of the galactic plane @xcite , which is consistent with the neutrino signal correlation . the distribution of neutrinos along the galactic plane is consistent with the distribution of the s , with higher event statistics observed around the region of galactic ridge @xcite . to find the anisotropy properties of the galactic component of the neutrino flux , we use the observed galactic latitude profile of the emission in the energy band above 300 gev as a template this is possible because fig . [ fig : spectrum ] suggests that the and neutrino signals are both of hadronic origin and the neutrino signal above 10 tev could be directly calculated from the signal via s simple powerlaw extrapolation . in the energy band above 300 gev the signal is free from the extragalactic contribution which is suppressed by the effect of gamma - gamma pair production on the extragalactic background light @xcite . thus , the neutrino signal above 10 tev is a sum of the anisotropic galactic component which follows the anisotropy template plus an isotropic extragalactic component . [ fig : profile_gamma ] shows the galactic latitude profile of the signal compared to the `` template '' profiles of pion decay and inverse compton ( ic ) emission calculated via powerlaw extrapolation of the model of @xcite to the energy band above 100 gev . assuming that the emission from the galactic plane ( the first bin @xmath35 ) is dominated by the pion decay emission @xcite , one could find that the the pion decay component provides a good fit for the profile in the whole latitude range up to @xmath36 , without an additional contribution from the ic or isotropic flux . the sub - dominance of the ic contribution is also supported by the modelling of the diffuse emission in the 100 gev energy band in the galactic latitude range @xmath26 reported by @xcite . this analysis finds that the ic component is sub - dominant even compared to the pion decay component calculated assuming the slope @xmath37 of the cosmic ray spectrum . the dashed histogram in the two panels of fig . [ fig : profile_gamma ] shows the total flux in the latitude bins . one could see that the point source contribution to the all - sky flux is minor . thus , the observed galactic latitude profile of the flux above 300 gev could serve as a proxy for the galactic latitude profile of the galactic component of the neutrino flux . fig . [ fig : profile_neutrino ] shows the distribution of the neutrino events in galactic latitude . it is compared to the model calculation taking into account the dependence of the icecube exposure on the declination taken from the calculation of @xcite . one could see that a range of models with large galactic contribution to the neutrino flux ( assumed to follow the galactic latitude profile of the flux above 0.3 tev , shown in fig . [ fig : profile_gamma ] ) is consistent with the data . the statistics of the signal is currently not sufficient for the discrimination of the galactic and isotropic contributions . from fig . [ fig : profile_neutrino ] one could see that the reduced @xmath38 of the fits of both galactic latitude distribution models the with 50% and 90% galactic contribution is @xmath39 . the same would be true also for the isotropic models with 0% galactic contribution . discrimination between the dominant galactic or dominant extragalactic flux models will be possible already with icecube in its present configuration . fig . [ fig : profile_neutrino ] shows that a decrease of the size of the errorbars by a factor of @xmath40 is needed for this . this could be achieved with the increase of signal statistics by a factor of 4 , i.e. with a long exposure of icecube , @xmath41 yr ( compared to the available 3 yr ) . precision measurement of each component would , however , require a more powerful detector like icecube - gen2 @xcite or km3net @xcite . at the first sight , this result seems to be in tension with the analysis of @xcite who finds that the galactic diffuse emission could not contribute more than 50% of the observed neutrino signal . however , the discrepancy stems from model dependence of the results . one could notice that the result of @xcite depends on the choice of the spatial template for the hadronic component of the all - sky flux . it relies on a spatial template derived by the fermi collaboration @xcite assuming the reference cosmic ray spectrum with the slope 2.7 ( rather than 2.58 assumed by @xcite ) . the uncertainty of this template and its dependence on the assumed spectral shape of the template are difficult to estimate . in our analysis we assume that the galactic longitude profile of the galactic component of neutrino flux is identical to the profile of the emission in the energy band above 300 gev . this is motivated by the fact that the isotropic and the inverse compton components of the flux are suppressed at these energies . in such a way in our analysis we avoid using a model - dependent spatial template of the galactic component of neutrino flux . and inverse compton ( ic ) emission are taken from ref . @xcite . ] tev s ( thick grey histogram ) . upper and lower panels show two models in which the isotropic contribution the neutrino flux ( dotted histogram ) is at the level of 50% and 10% of the galactic neutrino flux , assumed to be proportional to the flux of @xmath42 tev s. ] detection of neutrino and emission from the galactic cosmic rays with @xmath32 powerlaw index provides an important clue for understanding of formation of galactic cosmic ray spectrum @xcite . it is consistent with the possibility that the cosmic rays are injected with the powerlaw spectrum with the slope @xmath43 predicted by the shock acceleration models @xcite , with the energy dependence of the diffusion coefficient @xmath44 as expected for the kolmogorov turbulence spectrum of the ism @xcite . although the slope and normalisation of the galactic neutrino spectrum are fixed by the data at lower energies , there is no certainty about its high - energy end . the galactic cosmic ray spectrum should have a knee like suppression at high energies produced by the escape from the galactic disk and / or high - energy cut - off due to the absence of sources capable of particle acceleration beyond certain energy range @xcite . similarly to the slope of the spectrum , the energy of the knee measured in the local galaxy is not necessary the same as the average knee energy for the galactic cosmic rays . the knee feature could be explained within the escape model of formation of cosmic ray spectrum as the energy at which the scattering length of cosmic rays becomes comparable to the correlation length of the galactic magnetic field @xcite . this model fits the shapes of the spectra of all elemental groups around the knee energy @xcite . within the escape model , the knee energy varies across the galaxy and from one galaxy to another in response to the variations of the properties of the galactic magnetic field . presence of the knee of the cosmic ray spectrum leads to a suppression of the neutrino flux at the energies @xmath45 of the knee energy . uncertainty of the average position of the knee in the galactic cosmic ray spectrum introduces an uncertainty in the shape of the spectra of galactic and neutrino emission in the pev energy band ( the dashed model line ranges in fig . [ fig : spectrum ] ) . the locally observed tev pev cosmic ray proton spectrum appears `` peculiar '' in the sense that its slope is different from the slope of the average galactic cosmic ray spectrum . this peculiarity could not be related to the specific of the propagation process in the local ism , because in this case also the spectra of atomic nuclei would be affected . it could also hardly be related to the process of injection from the galactic cosmic ray sources in general , because in this case the proton spectrum would be systematically softer than the nuclei spectrum everywhere in the galaxy and this would be visible in the softer / neutrino spectrum of the galaxy . the most probable reason for the peculiarity of the locally observed proton spectrum is in the change of the cosmic ray injection rate over the last @xmath46 yr @xcite . massive injection of cosmic rays in the local ism in a star formation episode @xmath1 yr ago could have resulted in an increase of the cosmic ray energy density at all energies . faster diffusion of higher energy particles should have led to faster `` wash out '' of the excess density at high - energies and , as a consequence , to a temporary softening of the local cosmic ray spectrum . several candidate past events in the local galaxy , like e.g. the event which produced an expanding ring of molecular clouds , the gould belt @xcite , could be considered . in a similar way , a nearby supernova explosion which occurred several million years ago could have produced an additional distortion in the cosmic ray spectrum . evidence for such an event could be found through the analysis of the secondary positrons and antiprotons in the cosmic ray spectrum @xcite and anisotropy @xcite . discreteness of the distribution of the cosmic ray sources and time variability of the star formation rate generically leads to a situation in which the locally measured cosmic ray spectrum is not identical to the average galactic cosmic ray spectrum @xcite . to summarise , we have shown that the the all - sky neutrino spectrum in the tev - pev energy range coincides with the high - energy extrapolation of the all - sky spectrum in the energy band below 1 tev . such a consistency of the and neutrino spectra is not unexpected in a simple model where both s and neutrinos originate in the decays of neutral and charged pions produced by interactions of cosmic rays in the milky way and other galaxies . noticing that the all - sky spectrum in the energy band just below 1 tev is dominated by the galactic contribution , we were able to estimate the flux and anisotropy properties of the galactic component of the neutrino spectrum . the isotropic neutrino flux from the cosmic ray interactions in star forming galaxies other than milky way is constrained by the level of the igrb and could not constitute more than @xmath34% of the observed neutrino flux . presence of significant galactic component of the neutrino flux ( at least 50% of the flux ) is also consistent with the anisotropy properties of the neutrino signal . combination of the and neutrino data suggests that the galactic cosmic ray spectrum is harder than previously thought , with the slope @xmath47 in the tev pev energy range . the discrepancy between the slopes of the average galactic cosmic ray spectrum and the locally measured cosmic ray spectrum is readily explained by the discreteness of the cosmic ray source distribution and time variability of the local star formation rate . 99 olive k.a . ( particle data group ) , chin . c , 38 , 090001 ( 2014 ) . berezinskii v.s . , bulanov s.v . , dogiel v.s . , ginzburg v.l . , ptuskin v. s. , _ the astrophysics of cosmic rays _ , nothr - holland , amsterdam ( 1990 ) . ptuskin v.s . , jones f.c . , , sina r. , ad.sp.res . 37 , 1909 ( 2006 ) . thoudam s. , hrandel j.r . , mnras , 421 , 1209 ( 2012 ) . sveshnikova l.g . , strelnikova o.n . , ptuskin v.s . , astropart.phys . 50 , 33 ( 2013 ) . ahn h.s . , et al . , ap.j . , 714 , l89 ( 2010 ) . neronov a. , semikoz d.v . d85 , 083008 ( 2012 ) . eicher d. , kumar r. , pohl m. , ap.j . , 769 , 138 ( 2013 ) . pohl m. , eichler d. , ap.j . , 766 , 4 ( 2013 ) . kachelriess m. , neronov a. , semikoz d. , arxiv:1504.06472 ( 2015 ) . savchenko v. , kachelriess m. , semikoz d.v . , arxiv:1505.02720 . krymskii g.f . , _ doklady akademii nauk sssr _ , 234 , 1306 ( 1977 ) . bell a.r . , _ royal astronomical society _ , 182 , 147 ( 1978 ) malkov m. , drury l.o.c 64 , 429 ( 2001 ) . oliva a. , _ proc . 33rd international cosmic ray conference _ , rio de janeiro , i d . 1266 ( 2013 ) . p.blasi , e.amato , jcap 01 11 ( 2012 ) . ellis j. , fields b.d . , schramm d.n . , ap.j . , 470 , 1227 ( 1996 ) . fields b.d . , hochmuth k.a . , ellis j. , ap.j . , 6210 , 902 ( 2005 ) . fry h.j , fields b.d . , ellis j. , ap.j . , 800 , 71 ( 2015 ) . neronov a. , malyshev d. , arxiv:1505.07601 ( 2015 ) . foreman g. , chu y .- h . , gruendl r. , hughes a. , fields , b. , ricker p. , arxiv:1502.04337 ( 2015 ) . abdo a.a . , et al . , phys . lett . , 104 , 101101 ( 2010 ) . the fermi lat collab . , ap.j . , 799 86 ( 2015 ) . ackermann m. et al . , ap.j . , 755 , 164 ( 2012 ) . murase , k. , ahlers , m. , lacki , b.c . , phys.rev . d88 , 121301 ( 2013 ) . tambora i. , ando s. , murase k. , jcap , 09 , 043 ( 2014 ) . hauser m.g . , dwek e. , ara&a , 39 , 249 ( 2001 ) . icecube collaboration , science , 342 , 947 ( 2013 ) . aartsen m.g . lett . , 111 , 021103 ( 2013 ) . aartsen m.g . _ et al . _ [ icecube collaboration ] , phys.rev.lett . , 113 , 101101 ( 2014 ) . aarsten m.g . _ et al . _ , arxiv:1410:1749 ( 2014 ) . m. kachelriess and s. ostapchenko , phys . d 90 , 083002 ( 2014 ) stecker f.w . , _ , 228 , 919 ( 1979 ) . berezinskii v.s . , gaisser t.k . , halzen f. , stanev t. , astropart.phys . , 1 , 281 ( 1993 ) . tchernin c. , aguilar j.a . , neronov a. , montaruli t. , a&a , 560 , a67 ( 2013 ) . neronov a. , semikoz d. , tchernin c. , phys.rev . , d89 , 103002 ( 2014 ) . ahlers , m. , murase k , phys.rev . d90 , 023010 ( 2014 ) . ahlers m. , et al . , arxiv:1505.03156 ( 2015 ) . atwood w.b . , et al . , ap.j . , 697 , 1071 ( 2009 ) . fermi collab . , arxiv:1501.02003 ( 2015 ) . ackermann m. et al . , ap.j.supp . 203 , 4 ( 2012a ) . kelner s.r . , aharonian f.a . , bugayov v.v . , phys.rev . , d74 , 034018 ( 2006 ) . kamae t. , karlsson n. , mizuno t. , abe , t. , koi t. , ap.j . , 647 , 692 ( 2006 ) . ackermann m. , et al . , 750 , 3 ( 2012 ) . aarsten m.g . , et al . , arxiv:1412.5106 ( 2014 ) . bagley p. et al . , km3net technical design report _ http://www.km3net.org/tdr/tdrkm3net.pdf _ ( 2009 ) . armstrong j.w . , rickett b.j . , spangler s.r . , 443 , 209 ( 1995 ) . giacinti g. , kachelriess m. , semikoz d.v . , phys.rev . d90 , 041302 ( 2014 ) . giacinti g. , kachelriess m. , semikoz d.v . , phys.rev . d91 , 083009 ( 2015 ) . ginzburg v.l . , syrovatskii s.i . , _ the origin of cosmic rays _ ( pergamon press , oxford , 1964 ) . gehlers n. , et al . , nature , 404 , 363 ( 2000 ) . neronov a. , semikoz d.v . , taylor a.m. , phys . , 108 , 051105 ( 2012 ) .

neutrino telescope icecube has recently discovered astrophysical neutrinos with energies in the tev pev range . we use the data of fermi telescope to demonstrate that the neutrino signal has significant contribution from the milky way galaxy . matching the and neutrino spectra we find that tev - pev galactic cosmic rays form a powerlaw spectrum with the slope @xmath0 . this spectral slope is consistent with the average cosmic ray spectrum in the disks of the milky way and large magellanic cloud galaxies . it is also consistent with the theoretical model of cosmic ray injection by diffusive shock acceleration followed by escape through the galactic magnetic field with kolmogorov turbulence . the locally observed tev - pev cosmic ray proton spectrum is softer than the average galactic cosmic ray spectrum . this could be readily explained by variability of injection of cosmic rays in the local interstellar medium over the past @xmath1 yr and discreetness of the cosmic ray source distribution .

in the absence of telomerase , telomere shortening limits the replicative lifespan of human cells thus providing a stringent tumor suppressive mechanism . however if dna damage checkpoints are compromised , cells can continue to divide until the telomeres lose their end - capping function and are subjected to dna double - strand break repair activity that results in telomere - telomere fusion events . the resulting dicentric chromosomes can initiate cycles of anaphase - bridging , breakage , and fusion that generate the large - scale genomic rearrangements common in human cancer . telomere - driven mutation is therefore a mechanism that generates variation in tumor cell populations , upon which clonal selection can operate and facilitate progression . we have developed high - resolution , single - molecule technologies to study telomere length and fusion in detail ; these methods have provided a level of clarity that was hitherto impossible to achieve in human cells . in colorectal cancer we showed that telomere erosion , dysfunction , and fusion not only precede the adenoma / carcinoma transition , but may also be pre - existent in the normal cells in which the initial mutation occurs . in chronic lymphocytic leukemia ( cll ) we observed extreme telomere erosion and fusion , consistent with cll b - cells undergoing a telomere - driven crisis . importantly , this was also detected in a subset of patients with early - stage disease prior to clinical progression . our recent large - scale analysis of telomere length and fusion in early - stage cll has allowed definition of the telomere length threshold below which telomere fusion is detected and revealed the prognostic value of stratifying patients according to this parameter . patients with telomeres below the telomere fusion threshold had a significantly shorter overall survival that was even more prognostic in early - stage disease patients ( p < 00001 , hr = 19.3 ) , and telomere dysfunction was the dominant variable in a multivariate analysis . based on these observations we hypothesize that short dysfunctional telomeres provide a mutator mechanism capable of driving genomic instability and disease progression . it is therefore important to understand the molecular basis of telomere fusion and how this drives mutation and clonal evolution . we have also investigated the process of fusion between short dysfunctional telomeres in human cells by the direct isolation and characterization of the dna sequence of telomere fusion events . irrespective of the tissue or cell model analyzed , we observed a consistent mutational profile with deletion into the subtelomeric dna and microhomology at the fusion junction ; this mutational profile is consistent with alternative non - homologous end - joining ( a - nhej ) processes . a - nhej involves the coordinated interaction of multiple proteins with nucleating , scaffolding , and resection activity , as well as those ultimately executing dna ligation . we therefore examined the contribution of dna ligase iii ( lig3)-dependent a - nhej and dna ligase iv ( lig4)-dependent classical - nhej ( c - nhej ) pathways in mediating fusion between short dysfunctional telomeres . using a dominant negative telomerase ( dn - htert ) we induced telomere erosion , fusion , and the onset of a telomere crisis in hct116 cells in which the lig3 or lig4 genes had been inactivated using recombinant adeno - associated virus - mediated gene targeting . both wild - type and lig4 clones displayed large - scale genomic rearrangements and telomere fusions , but readily escaped crisis following the re - establishment of telomerase activity . fusions were also detected in lig3 cells but strikingly no clones escaped crisis ; after 2 to 3 months no cells remained in these cultures . all lig3 clones escaped crisis following complementation with a wild - type lig3 cdna , but none escaped following complementation with cdnas containing either a deletion in the lig3 brca1 c - terminal domain or a a874d point mutation , both of which are required for the interaction of lig3 with x - ray repair cross - complementing protein 1 ( xrcc1 ) . these data demonstrate an absolute requirement for lig3 in mediating the escape from a telomere - driven crisis . in order to gain some insight into the underlying mechanisms by which lig3 facilitated the escape from crisis , we undertook a detailed molecular characterization of telomere fusion events mediated by lig3 or lig4 . sister chromatid telomere fusion events were detected in both lig3 and lig4cells , however there was a marked reduction in interchromosomal events in lig4 cells . sequencing of interchromosomal fusions from lig3 cells revealed a higher incidence of breakpoints within telomere repeats and a reduction in microhomology at the fusion junction . our data demonstrated the involvement of both lig3 and lig4 in the fusion of short dysfunctional telomeres , but also indicated that fusions involving lig3 provide a selective advantage to cells undergoing a telomere - driven crisis that facilitates clonal evolution and escape from crisis . the mechanism by which lig3 facilitates the escape from crisis is not clear ; our hypothesis is that interchromosomal fusions , which predominate in cells that can not escape crisis , are more mutagenic and detrimental to the cells in which they occur ; whereas fusion between sister chromatids resulting in localized amplification and deletion events may confer a selective advantage . we consider that the relative balance between these events dictates the ability of cells to escape crisis and that this is modulated by the activities of a - nhej and c - nhej at short dysfunctional telomeres ( fig . 1 ) . further work should elucidate the contributions of other components of the a - nhej pathway in telomere fusion and the escape from crisis , in addition to examining the mutational impact that these pathways have in the context of the evolving cancer genome . figure 1.schematic illustrating our hypothesis for how lig3 may affect the ability of cells to escape a telomere - driven crisis . cells with short dysfunctional telomeres undergo crisis , during which telomere fusion results in the creation of dicentric chromosomes and the initiation of anaphase - bridging , breakage , and fusion cycles ; the ensuing genomic instability leads to large - scale genomic rearrangements . clonal evolution results in cells that escape crisis ; these cells exhibit fewer interchromosomal fusion events compared to fusions between sister chromatids , whereas interchromosomal fusions predominate in cells that can not escape crisis . we consider that this is governed by the relative activities of ligase iii - dependent alternative non - homologous end - joining ( a - nhej ) compared to ligase iv - dependent classic non - homologous end - joining ( c - nhej ) pathways . schematic illustrating our hypothesis for how lig3 may affect the ability of cells to escape a telomere - driven crisis . cells with short dysfunctional telomeres undergo crisis , during which telomere fusion results in the creation of dicentric chromosomes and the initiation of anaphase - bridging , breakage , and fusion cycles ; the ensuing genomic instability leads to large - scale genomic rearrangements . clonal evolution results in cells that escape crisis ; these cells exhibit fewer interchromosomal fusion events compared to fusions between sister chromatids , whereas interchromosomal fusions predominate in cells that can not escape crisis . we consider that this is governed by the relative activities of ligase iii - dependent alternative non - homologous end - joining ( a - nhej ) compared to ligase iv - dependent classic non - homologous end - joining ( c - nhej ) pathways . telomere fusion during crisis is ultimately a cellular survival mechanism that provides short - term relief from telomere erosion , but importantly also facilitates genome instability that allows for the generation of the genomic rearrangements that can facilitate progression . our work identifies the a - nhej pathway as essential for the ability of cells to clonally evolve and escape a telomere crisis . this indicates that intervention(s ) in this pathway may sensitize cells with short dysfunctional telomeres and thus provide a potential therapeutic target in the subsets of tumors in which short dysfunctional telomeres confer such a poor prognosis . moreover , given that telomere dysfunction occurs early in tumorigenesis this may open up the possibility of therapeutic intervention prior to clinical progression . this work was supported by funding to the baird laboratory from cancer research uk , leukemia and lymphoma research and the national institute for social care and health research ; and to the hendrickson laboratory from the united states national institutes of health ( gm088351 ) and the national cancer institute ( ca15446 ) .

telomere dysfunction and fusion play key roles in driving genomic instability and clonal evolution in many tumor types . we have recently described a role for dna ligase iii ( lig3 ) in facilitating the escape of cells from crisis induced by telomere dysfunction . our data indicate that lig3-mediated telomere fusion is important in facilitating clonal evolution .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Every Child Counts Act''. SEC. 2. ALTERNATE STANDARDS AND ASSESSMENTS FOR STUDENTS WITH THE MOST SIGNIFICANT COGNITIVE DISABILITIES. Section 1111 of the Elementary and Secondary Education Act of 1965 (20 U.S.C. 6311) is amended-- (1) in subsection (b)-- (A) in paragraph (1)-- (i) in subparagraph (B), by striking ``The'' and inserting ``Except as provided in subparagraph (G), the''; and (ii) by adding at the end the following: ``(G) Alternate academic achievement standards for students with the most significant cognitive disabilities.-- ``(i) In general.--The State may, through a documented and validated standards-setting process, adopt alternate academic achievement standards in any subject included in the State's accountability system under paragraph (2) for students with the most significant cognitive disabilities, if such alternate academic achievement standards-- ``(I) are aligned with the State challenging academic content standards and challenging student academic achievement standards; ``(II) provide access to the general curriculum for the grade in which the student is enrolled; ``(III) are vertically aligned to ensure that a student who achieves at the on-target or advanced level under subclause (VI) signifies that the student is on track to access a postsecondary education or achieve competitive integrated employment, as defined under section 3 of the Workforce Innovation and Opportunity Act (Public Law 113-128; 128 Stat. 1425); ``(IV) are supported by evidence- based learning progressions to age and grade-level performance; ``(V) are designated in the individualized education program developed under section 614(d)(3) of the Individuals with Disabilities Education Act for each such student as the academic achievement standard that will be used for the student; and ``(VI) establish, at a minimum-- ``(aa) 2 levels of high achievement (on-target and advanced) that indicate that a student with the most significant cognitive disabilities meets or exceeds the State's proficient level of academic achievement under paragraph (2)(L) as measured by performance on alternate assessments under paragraph (3)(E); and ``(bb) a third level of achievement (catch-up) that provides information about the progress of a student with the most significant cognitive disabilities toward meeting the State's proficient level of academic achievement under paragraph (2)(L) as measured by performance on alternate assessments under paragraph (3)(E). ``(ii) Prohibition on any other alternate or modified standards.--A State shall not develop, or implement for use, under this part any alternate or modified academic achievement standards for students who are children with disabilities that are not alternate academic achievement standards that meet the requirements of clause (i).''; (B) in paragraph (2), by adding at the end the following: ``(L) Students with the most significant cognitive disabilities.--In determining the percentage of students meeting or exceeding the State's proficient level of academic achievement on the State assessments, a State educational agency may include, for all schools in the State, the performance of the State's students with the most significant cognitive disabilities on alternate assessments as described in paragraph (3)(E) in the subjects included in the State's accountability system, consistent with the 1 percent limitation of paragraph (3)(E)(i).''; (C) in paragraph (3), by adding at the end the following: ``(E) Alternate assessments for students with the most significant cognitive disabilities.--A State may provide alternate assessments that are aligned with alternate academic achievement standards described in paragraph (1)(G) for students with the most significant cognitive disabilities, if the State-- ``(i) ensures that for each subject, the total number of students in each grade level assessed in such subject using the alternate assessments does not exceed 1 percent of the total number of all students in such grade level in the State who are assessed in such subject; ``(ii) certifies, consistent with section 612(a)(16)(A) of the Individuals with Disabilities Education Act, that the State's regular academic assessments are universally designed to be accessible to students, including students with sensory, physical, and intellectual disabilities, through the provision of accommodations that produce valid results; and ``(iii) ensures that such alternate assessments are peer reviewed and based on the best available evidence.''; and (2) in subsection (h)(1)(C)-- (A) in clause (vii), by striking ``and'' after the semicolon; (B) in clause (viii), by striking the period at the end and inserting ``; and''; and (C) by adding at the end the following: ``(ix) the number and percentage of students with disabilities who take an alternate assessment under subsection (b)(3)(E), by grade, subject, and type of disability, as outlined in section 602(3) of the Individuals with Disabilities Education Act.''.

Every Child Counts Act Amends the school improvement program under part A of title I of the Elementary and Secondary Education Act of 1965 to allow states to establish alternate academic achievement standards and assessments for students who have the most significant cognitive disabilities. Requires the alternate standards to meet certain conditions, including that they: are aligned with the state's challenging academic content and achievement standards; provide access to the general curriculum for the grade in which the student is enrolled; and establish, at a minimum, two levels of achievement (on-target and advanced) that indicate that a student meets or exceeds the state's proficient level of academic achievement; and establish, at a minimum, a third level of achievement (catch-up) that provides information about a student's progress toward proficiency. Requires each state using alternate assessments to ensure that: (1) not more than 1% of the total number of all students in each grade level in the state who are assessed in a subject are assessed using the alternate assessments, (2) the state's regular academic assessments remain accessible to all students, and (3) the alternate assessments are peer reviewed and based on the best available evidence. Allows each state to count students who are determined to be proficient using such alternate assessments in its determination of the percentage of the state's students who are meeting or exceeding the state's academic content and achievement standards. Requires states' annual report cards to: (1) include the number and percentage of disabled students who take the alternate assessments; and (2) break that information down by grade, subject matter, and disability type.

elliptical and s0 galaxies show a striking rise in their spectra at @xmath1 . spectroscopy ( brown et al . 1997 ) and imaging ( brown et al . 2000b ) of local galaxies show this `` uv upturn '' arises from a minority population of hot horizontal branch ( hb ) stars . on energetic grounds , these evolved stars were long considered the best candidates for the uv emission ( greggio & renzini 1990 ) , with the implication that the uv - to - optical color could be the most rapidly evolving feature in the spectra of ellipticals . in theory , the uv upturn can fade by several magnitudes as the lookback time increases by a few gigayears , but the evolution is very model - dependent , and a strong uv upturn could appear at ages as early as @xmath2 gyr ( tantalo et al . 1996 ) or as late as @xmath315 gyr ( yi , demarque , & oemler 1998 ) . this evolution has motivated our ongoing survey to measure the uv upturn in clusters at intermediate redshifts . previously , we observed the rich clusters abell 370 at @xmath4 ( brown et al . 1998 ) and cl0016 + 16 at @xmath5 ( brown et al . 2000a ) ; those observations implied that there was little fading of the uv upturn out to @xmath6 with a significant decline at higher @xmath7 . however , further cluster measurements are clearly needed to explore the universality of this evolution . to that end , we have obtained far - uv images of zwcl1358.1 + 6245 with the space telescope imaging spectrograph ( stis ) on board the hubble space telescope ( hst ) . this is a rich , compact cluster of galaxies originally identified by zwicky & herwig ( 1968 ) and later rediscovered in the x- @xmath8based on observations made with the nasa / esa hubble space telescope , obtained at the space telescope science institute , which is operated by aura , inc . , under nasa contract nas 5 - 26555 . these observations are associated with proposal 8564 . ray observations of luppino et al . it lies at intermediate redshift ( @xmath0 ; fisher et al . 1998 ) with little foreground extinction ( @xmath9 mag ; schlegel , finkbeiner , & davis 1998 ) . when combined with archival images from the wide field planetary camera 2 ( wfpc2 ) on hst , our far - uv images provide a measurement of the uv upturn for 8 elliptical and s0 galaxies in the cluster core . seven of these galaxies are well - detected ( @xmath10 ) in the far - uv , and the central galaxy shows strong extended uv emission , likely associated with infalling matter . the weak uv upturn measured in these galaxies is in contrast to the strong uv upturn measured previously at @xmath4 , yet surprisingly similar to that at @xmath5 . we imaged zwcl1358.1 + 6245 for 68,291 s while the cluster was in the hst continuous viewing zone . the field was centered at an r.a . of @xmath11 and a dec . of @xmath12 ( j2000 ) with a position angle of 50@xmath13 , placing 8 s0 and elliptical galaxies within the stis @xmath14 field , including the brightest galaxy of the cluster ( see figure 1 ) . exposures were dithered by 12 pix to allow removal of hot pixels . we used the f25qtz filter ( 14501900 ) to minimize the background from geocoronal emission in @xmath15 and @xmath16 . note that the sensitivity of the far - uv camera has been slowly decreasing at the rate of @xmath171.5% yr@xmath18 ; we include this decline in our analysis ( at the time of our observations , a flat spectrum of @xmath19 erg@xmath18 s@xmath18 @xmath20 @xmath18 produced 1 count s@xmath18 in this bandpass ) . the stis far - uv detector has a very low dark rate when cold ( @xmath21 cts sec@xmath18 pix@xmath18 ) , but as observations progress , a dark count `` glow '' appears , centered in the upper left - hand quadrant of the detector . using the optical images to mask objects , we normalized and subtracted from each exposure a profile of this dark glow ( created from a sum of @xmath22 ks of dark exposures ) . we co - added the exposures using the iraf drizzle package , weighting the pixels in each frame by the ratio of the exposure time squared to the dark count variance , including a hot pixel mask . the algorithm weights the exposures by the square of the signal - to - noise ratio for sources fainter than the background . note that the stis uv detectors are photon counters that register less than 1 count per cosmic - ray hit , and thus the images do not require the cosmic - ray rejection required for processing ccd images . 0.1 in 0.5 in 0.1 in we used the drizzle package to co - add the archival wfpc2 images of this cluster , reject cosmic rays and hot pixels , and register the co - added optical data to the far - uv image . wfpc2 data in the f606w ( broad @xmath23 ) and f814w ( @xmath24 ) bandpasses were available for our entire field ; these data come from an impressive mosaic of the cluster by van dokkum et al . ( 1998 ) , who also provide morphological classifications for the galaxies in our sample ( table 1 ) . partial coverage of our field was also available in f450w ( @xmath25 ) . the uv upturn strength is usually measured by the rest - frame @xmath26 color , where the flux from 12501850 gives @xmath27 and @xmath23 is johnson @xmath23 . our far - uv bandpass corresponds to rest - frame 10901429 while the f814w bandpass corresponds roughly to johnson v in the rest - frame . in 2.5 , we will use the spectral energy distributions of local elliptical galaxies , redshifted to @xmath0 , to interpret the observed count rates in these bandpasses as @xmath26 colors . due to their low luminosity and sharp profile in the far - uv , elliptical galaxies usually appear point - like in images of distant clusters . what is striking about figure 1 is the appearance of the brightest cluster member , which shows extended tenuous emission that is not seen in the broad wfpc2 bandpasses at longer wavelengths . the cluster shows significant x - ray luminosity ( stocke et al . 1991 ) , and associated h-@xmath28 emission ( donahue , stocke , & giola 1992 ) . the h-@xmath28 contours extend outward from the nucleus in three prongs , and two of these trace the far - uv emission when the donahue et al . ( 1992 ) image is aligned to our own , strongly suggesting that the far - uv emission is due to lyman-@xmath28 redshifted into the stis far - uv bandpass . the x - ray and h-@xmath28 emission were historically taken as evidence of a `` cooling flow , '' although the presence of cooling gas is now controversial , and this term may be a misnomer . lyman-@xmath28 emission is expected to trace the h-@xmath28 emission in galaxy clusters , whether or not the infalling material is cooling in the historical sense , but it is rarely seen because this emission is lost in the geocoronal lyman-@xmath28 emission when observing local clusters . unfortunately , both the lyman-@xmath28 emission and the stellar light peak toward the center of this galaxy , so it is difficult to separately quantify the two . another , less likely , source would be star - formation from the infalling material . normalizing a model spectrum of constant star - formation to the far - uv emission , we find that such star formation would be difficult to detect in the optical images . in any case , the optical images show no evidence of the morphology seen in the far - uv . + we performed aperture photometry on the far - uv image using our own idl software , with a source aperture of radius 16 pixels ( 0.4@xmath29 ) and a sky annulus of radii 80 and 100 pixels , as done previously by brown et al . ( 2000a ) . each aperture was centered on the bright core of the galaxy , determined from the f814w wfpc2 data . statistical errors for the photometry include the poisson contribution from the source counts , the statistical uncertainties in the spatially - varying background , and the effects of the weighted co - addition of the frames ( see the previous section ) . using the daophot package in iraf , we measured the flux in the f814w data ( registered via drizzle to the far - uv frame ) using the same source and sky apertures . the optical and far - uv photometry are shown in table 1 . note that the aperture size does not contribute significant systematic errors in our analysis , whether we are considering measurements at different @xmath7 or in different bandpasses . except for galaxy 375 ( which has extended emission ) , there is little variation in our @xmath26 colors as we reduce the aperture size they remain uniformly red , with small variations consistent with the statistical uncertainties in table 1 . measurements of @xmath26 in local ellipticals ( burstein et al . 1988 ) were performed with a @xmath30 aperture , while our 0.8@xmath29 diameter aperture would subtend @xmath31 at the distance of virgo ( characteristic of the burstein et al . however , in local galaxies , there is almost no variation in the surface @xmath26 color out to a radius of @xmath32 ( ohl et al . 1998 ) , and the colors within any aperture are dominated by the core ( given the sharply peaked profiles ) . we also note that in the hst bandpasses , our aperture gives encircled energy agreement at the 5% level for point sources and better agreement for extended sources ( robinson 1997@xmath33 ; holtzman et al . 1995 ) . the uv upturn is traditionally characterized by the rest - frame @xmath26 color ( see burstein et al . we used the spectra of three local elliptical galaxies ( ngc1399 , m60 , and m49 ) to convert the observed stis and wfpc2 countrates to rest - frame @xmath26 , as done previously in brown et al . ( 1998 ) and brown et al . ( 2000a ) . our spectra of ngc1399 , m60 , and m49 have respective @xmath26 colors of 2.05 , 2.24 , and 3.42 mag ( burstein et al . 1988 ) ; despite the substantial range in uv upturn strength , the spectral shape within the far - uv range or within the optical range varies little from galaxy to galaxy . we redshifted these local templates to @xmath0 and then applied a foreground reddening of @xmath34 mag ( schlegel et al . we then used the iraf calcphot routine to calculate the relative countrates for these templates in the stis / far - uv and wfpc2/f814w bandpasses . the ratios of far - uv to f814w countrates observed in the zwcl1358.1 + 6245 galaxies ( @xmath35 ) were then compared to the ratios from the templates ( @xmath36 ) , and the template with the closest ratio was used to determine the rest - frame @xmath26 ( table 1 ) , using the relation + + @xmath37 . + + except for galaxy 375 , all of the galaxies show weak uv upturn emission . galaxy 375 is contaminated by the lyman-@xmath28 emission discussed previously , so the uv upturn emission is really an upper limit on the emission from the evolved hb population . note that in a much smaller aperture ( radius 5 pixels ) that excludes much of the lyman-@xmath28 emission , this galaxy has an even bluer @xmath26 of 1.6 mag . we show in figure 2 the @xmath26 colors measured in galaxy clusters to date . nearby quiescent ellipticals have been measured by burstein et al . ( 1988 ) in virgo , coma , and fornax . the galaxies at @xmath0 are from the present work ( excluding galaxy 375 ) . measurements at @xmath4 are from faint object camera ( foc ) observations of abell 370 ( brown et al . measurements at @xmath5 are from stis observations of cl0016 + 16 ( brown et al . at each redshift , the observed fluxes have been transformed to rest - frame @xmath26 using the spectra of local elliptical galaxies . before proceeding , it is worth noting that the @xmath4 data may have significant systematic errors the calibration on the foc was far less certain than it is with stis . the measurements at @xmath38 , @xmath0 , and @xmath5 were all done with distinct photometry in the far - uv and optical , whereas the foc measurements come from the ratio of two long - pass filters ( see brown et al . it would be prudent to verify the @xmath26 colors at @xmath4 with a true solar - blind instrument , such as stis or the far - uv channel on the advanced camera for surveys , to verify that the uv upturn is so strong in abell 370 . 0.1 in @xmath33r . robinson 1997 , examining the stis point - spread function , http://hires.gsfc.nasa.gov/stis/postcal/quick_reports.html to place our observations in context , we have plotted in figure 2 the models of tantalo et al . ( 1996 ) , which were constructed assuming gas infall for the chemical evolution , and under the assumption that massive ellipticals form by monolithic collapse . the onset of the uv upturn is very sensitive to the formation redshift ( @xmath39 ) assumed , and for the moment , we will consider this at face value . leaving aside the uncertain result at @xmath4 , figure 2 demonstrates that the uv upturn does indeed fade with increasing @xmath7 , but does so much more slowly than , for example , in the models of tantalo et al.(1996 ) . in fact , very little @xmath26 evolution appears to exist between @xmath0 and 0.55 . given the @xmath40 range observed at @xmath41 , correlated with metallicity , the trend is most apparent if one considers both the mean and the most blue @xmath26 in each epoch ; there are enough galaxies to imply that the uv upturn is systematically weaker at @xmath0 and 0.55 . the figure suggests that galaxies in the @xmath0 cluster formed at @xmath42 , while those in the @xmath4 and 0.55 clusters formed at @xmath43 . given the evidence for hierarchical merging , such variation may not be inconceivable . however , we have targeted the massive ellipticals in the centers of rich clusters , with no spectroscopic evidence of recent star formation . the uv upturn traces the age of the oldest stars in these populations , not necessarily the ages of the galaxies . if these galaxies formed via monolithic collapse , the age of the oldest stars reflects the age of the galaxies themselves , but if the galaxies formed via hierarchical merging , the oldest stars may predate the merger events and still comprise the bulk of the population . studies of clusters out to @xmath44 indicate that most of the star formation in ellipticals had to be completed at @xmath45 , followed by quiescent evolution ( stanford , eisenhardt , & dickinson 1998 ; kodama et al . 1998 ) . therefore , we expect little scatter in @xmath39 . in contrast , the strong distinction between the measurements at @xmath0 and 0.375 , and , more importantly , the similarity between the measurements at @xmath0 and 0.55 , implies a surprisingly large dispersion in the formation epochs between clusters ( @xmath46 ) . such variation in @xmath39 would be more plausible if the nonmonotonic evolution in @xmath26 implied by the foc measurements were independently confirmed . another ( less likely ) explanation for the variation in figure 2 is that there is a small dispersion in @xmath39 among the clusters , but the chemical evolution varied significantly from cluster to cluster . the onset of the uv upturn in the tantalo et al . ( 1996 ) models depends upon the details of the chemical evolution , and the uv upturn in local ellipticals correlates strongly with metallicity , and to a lesser extent , with luminosity ( burstein et al . 1988 ) . however , all of the galaxies in these programs are massive ellipticals in the centers of rich , massive clusters it seems unlikely that their populations would be chemically distinct from their analogs in the local universe . even so , it would be interesting to obtain metallicity measurements for our sample , to look for trends like those seen locally . models for the evolution of elliptical galaxies are sensitive not only to @xmath39 , but to other parameters , such as time of onset for galactic winds , accretion timescale , and efficiency of star formation . tantalo et al . ( 1996 ) tuned these parameters to reproduce the properties of low-@xmath7 ellipticals , and there is not much freedom to tune them further to match our observed uv evolution . it is therefore worth looking at the parameters that affect hb morphology in particular . hot hb stars have lost nearly all ( but not all ) of their envelope due to mass loss on the rgb . tantalo et al . ( 1996 ) make specific assumptions about the relation between mass loss and chemical abundance in order to approximate the uv upturn range at @xmath41 . in their models , hot hb stars do not exist at higher @xmath7 because their main sequence progenitors have larger masses ( resulting in redder hb stars ) . what if , instead , we imagine that at @xmath41 there is a reservoir of stars in ellipticals that have lost so much mass that they fail to ignite he ? see , e.g. , figure 9 in greggio & renzini ( 1990 ) . these stars could , for example , come from the high - metallicity tail of the metallicity distribution . at higher @xmath7 , the more massive stars in that metallicity range would become hot hb stars , providing the uv flux that would otherwise be missing . therefore , moving from zero to high redshift , the uv upturn would be produced by stars at progressively higher metallicity , until it disappears entirely when the very end of the metallicity distribution is reached . in more general terms , the same qualitative behavior is expected if the occurrence of hot hb stars is driven by a distribution of stellar ages , or a distribution of rgb mass loss , or a combination thereof . it is plausible that the details of the metallicity distribution , and the relation between mass loss and rgb parameters , could be tuned to reproduce the gradual @xmath26 evolution observed , with a common @xmath47 , without violating other constraints on stellar evolution . further alternatives are also possible . at @xmath41 , hot hb stars may be the dominant , but not the sole , contributor to the uv upturn . while the hot hb would rapidly disappear with redshift , the @xmath26 color would initially drop , but then hit a _ floor _ value as the role of dominant uv contributor is assumed by another class of uv - bright objects whose evolution with redshift is not as fast as that of the hot hb stars . possibilities include a low level of ongoing ( massive ) star formation , and various kinds of binaries such as , e.g. , post - rgb binary components and accreting white dwarfs ( greggio & renzini 1990 ) . if future observations can show that hb stars are not the sole contributor to the uv upturn at @xmath48 , the tantalo et al . ( 1996 ) models would imply @xmath49 ; however , given that kodama et al . ( 1998 ) and stanford et al . ( 1998 ) find the bulk of the stellar population formed at @xmath50 , such a finding would more likely tell us that the onset of the uv upturn takes place at an older age than the @xmath51 gyr given by the models of tantalo et al . . it would be difficult to rule out a low star formation rate ( sfr ) as the source of the @xmath26 floor . assuming constant star formation with a flat @xmath52 spectrum , the kennicutt ( 1998 ) relation gives sfr=1.4@xmath53 0.0050.02 @xmath54 yr@xmath18 for our @xmath0 sample ( excluding galaxies 375 and 357 ) . this is a lower limit , given that the real spectrum would likely have a far - uv downturn due to extinction . the rates in the galaxies at @xmath5 are similar ( 0.0080.015 @xmath54 yr@xmath18 ) . thus , from @xmath55 to @xmath56 ( a span of 2.4 gyr ) , this sfr would produce @xmath57 @xmath54 of stars , which would be at least 3.6 gyr old today if the star formation stopped at @xmath56 . a remnant intermediate - age population comprising a few percent of the total stellar mass in a normal elliptical galaxy would be difficult to detect . the same arguments apply if the star formation is episodic , because the number of @xmath58 detections at @xmath0 ( excluding galaxy 375 ) and @xmath5 implies a duty cycle of @xmath1780% . this hypothesis could be tested by searching for low levels of h-@xmath28 or emission . in summary , our findings are in broad agreement with the expectation of a fading uv upturn with redshift , due to a progressively smaller number of hot hb stars being produced in younger populations . however , the rate of this fading remains to be understood whether the whole trend can be attributed to the redshift evolution of the number of hot hb stars , or whether an additional class of hot stars is contributing a floor to the uv flux that is minor at @xmath41 but already dominant at @xmath59 . support for proposal 8564 was provided by nasa through a grant from the space telescope science institute , which is operated by aura , inc . , under nasa contract nas 5 - 26555 . we are grateful to a.v . sweigart for useful discussions .

we present far - ultraviolet ( far - uv ) images of the rich galaxy cluster zwcl1358.1 + 6245 , taken with the space telescope imaging spectrograph on board the hubble space telescope ( hst ) . when combined with archival hst observations , our data provide a measurement of the uv - to - optical flux ratio in 8 early - type galaxies at @xmath0 . because the uv flux originates in a population of evolved , hot , horizontal branch ( hb ) stars , this ratio is potentially one of the most sensitive tracers of age in old populations it is expected to fade rapidly with lookback time . we find that the uv emission in these galaxies , at a lookback time of 3.9 gyr , is significantly weaker than it is in the current epoch , yet similar to that in galaxies at a lookback time of 5.6 gyr . taken at face value , these measurements imply different formation epochs for the massive ellipticals in these clusters , but an alternative explanation is a `` floor '' in the uv emission due to a dispersion in the parameters that govern hb morphology . 0.1 in

ic 5063 is classified as a narrow line radio galaxy ( z=0.011 ) ( caldweel & phillips 1981 ) . ic 5063 was observed with the gas imaging spectrometer ( gis ) and solid state spectrometer ( sis ) on the asca satellite ( tanaka et al . 1994 ) in april 1994 and with the rosat pspc ( pfeffermann et al . 1987 ) from november 1991 to april 1992 . after applaying standard criteria to the data , about 19 ks of useful data for rosat and @xmath5 21(24 ) ks for each sis(gis ) detector were collected . + the combined analysis of asca and rosat data reveals a soft x - ray excess , a hard continuum and a reflection component . a double power law model plus a reflection component ( fixed to cover 2@xmath6 steradiants at the source ) provides a good fit to the rosat and asca data , but the spectral slope of the soft power law ( @xmath7=2.16@xmath8 , errors at 90% , @xmath9@xmath10=2.71 ) , steeper than the hard ( @xmath11=1.70@xmath12 ) , indicates a more complex soft x - ray emission . a @xmath13/@xmath14 @xmath51% ratio is obtained by a partial covering model . a bremsstrahlung model for the soft emission is equally good ( see table 1 ) . the broad h@xmath0 line in polarized flux ( fwzi@xmath56000 - 9000 km s@xmath3 , axon et al . 1994 ) and the anisotropy of the radiation field ( `` x '' geometry ) , with an opening angle of @xmath550@xmath15 ( colina et al . 1991 ) , suggest that the observed soft x - ray component may be emission scattered along the line of sight from ionized gas above an absorbing torus . the column density value , @xmath16=2.15@xmath17 @xmath1 10@xmath18 @xmath19 , and the dust lane across the galaxy , likely responsible for the ir emission ( axon et al . 1982 ) , agree with a nearly edge - on configuration . the 2 - 10 kev luminosity l@xmath52@xmath110@xmath2 ergs s@xmath3 indicates a sey1-like active nucleus for ic 5063 . strong evidence for the fek@xmath0 line is given only by the sis1 detector . the line parameters are given in table 2 . + axon , d.j . , et . al . : 1994 , 216 379 axon , d.j . , bailey , j. , hough , j.h . : 1982 , 299 234 caldwell , h. , phillips , m.m . : 1981 , 244 447 colina , l. , sparks , w.b . , macchetto , f. : 1991 , 370 102 fabbiano , g. , fassnacht , c. , trinchieri , g. : 1994 , 434 67 fabian , a.c . , rees , m.j . : 1995 , 277 l55 pfeffermann , e. , et al.:1987 , _ proc . spie _ * 733 * , 519 reichert , g.a . , et al . : 1992 , 387 536 tanaka , y. , inoue , h. , holt , s.s . : 1994 , 46 l37

the results of the 0.1 - 10 kev spectral analysis of ic 5063 ( narrow line radio galaxy ) and ngc 3998 ( liner ) are presented . in both cases there is evidence of a fek@xmath0 emission line , but its width is poorly constrained . the highly absorbed spectrum of ic 5063 is well described by a double power law model . the x - ray luminosity of a few @xmath1 10@xmath2 ergs s@xmath3 reveals a sey 1 nucleus seen nearly edge - on , as confirmed by optical and ir studies . ngc 3998 is well fitted by a power law model ( @[email protected] ) without reflection and weak absorption . the weak x - ray emission detected by asca and rosat suggests a low - luminosity agn or an active nucleus in a low - accretion period . # 1 # 2 _ mem . soc . astron . it . _ * # 1 * , # 2 # 1 # 2 _ the messenger _ * # 1 * , # 2 # 1 # 2 _ astron . nach . _ * # 1 * , # 2 # 1 # 2 _ astron . astrophys . _ * # 1 * , # 2 # 1 # 2 _ astron . astrophys . lett . _ * # 1 * , l#2 # 1 # 2 _ astron . astrophys . rev . _ * # 1 * , # 2 # 1 # 2 _ astron . astrophys . suppl . ser . _ * # 1 * , # 2 # 1 # 2 _ astron . j. _ * # 1 * , # 2 # 1 # 2 _ ann . rev . astron . astrophys . _ * # 1 * , # 2 # 1 # 2 _ astrophys . j. _ * # 1 * , # 2 # 1 # 2 _ astrophys . j. lett . _ * # 1 * , l#2 # 1 # 2 _ astrophys . j. suppl . _ * # 1 * , # 2 # 1 # 2 _ astrophys . space sci . _ * # 1 * , # 2 # 1 # 2 _ adv . space res . _ * # 1 * , # 2 # 1 # 2 _ bull . astron . inst . czechosl . _ * # 1 * , # 2 # 1 # 2 _ j. quant . spectrosc . . transfer _ * # 1 * , # 2 # 1 # 2 _ mon . not . r. astr . soc . _ * # 1 * , # 2 # 1 # 2 _ mem . r. astr . soc . _ * # 1 * , # 2 # 1 # 2 _ phys . lett . rev . _ * # 1 * , # 2 # 1 # 2 _ publ . astron . . japan _ * # 1 * , # 2 # 1 # 2 _ publ . astr . soc . pacific _ * # 1 * , # 2 # 1 # 2 _ nature _ * # 1 * , # 2 epsf.sty

we prospectively studied children < 16 years of age who came to the pediatric department at the vijayanagar institute of medical sciences , bellary , karnataka , southern india , with acute encephalitis syndrome during october 2005december 2007 . children with acute fever and symptoms with an onset < 14 days before coming to the hospital , a neurologic illness , and > 1 of the following signs ( change in mental status including confusion , disorientation , coma , or inability to talk ; new onset of seizures excluding simple febrile seizures ; photophobia , headache , or meningitis ) were recruited into the study . children with laboratory - confirmed plasmodium falciparum parasitemia or a history of neurologic conditions and those whose parents removed them from the hospital were excluded . the study protocol was reviewed and approved by the ethics committees of vijayanagar institute of medical sciences and the university of liverpool , uk . swabs were placed in sterile vials containing viral culture media ( dulbecco s modified eagle s medium ) . all samples were frozen at 20c , stored at 70c , and transferred to diagnostic laboratories . to detect enteroviruses , including ev75 , in throat swab extracts , rna was extracted by using the chemagic viral dna / rna kit ( chemagen ag , baesweiler , germany ) and a kingfisher ml magnetic extractor ( thermo fisher scientific inc . , pcr ( rt - pcr ) was then performed by using primers specific for the 5 untranslated region ( 5-att gtc acc ata agc agc ca-3 and 5-cct ccg gcc cct gaa tgc ggc taa t-3 ) ; these primers produced a 154-bp product ( 7 ) . enteroviruses identified by pan - enterovirus rt - pcr were typed by nucleotide sequencing of the viral protein 1 ( vp1 ) region ( 8,9 ) . to further type enteroviruses , phylogenetic analysis was performed on all nucleotide sequences ( from this study and others obtained from genbank ) by using mega4 software ( 10 ) ( www.megasoftware.net ) . the remaining swab transport medium was filtered , and 100 l of filtrate was aliquoted onto each of 3 tissue culture plates containing rhabdomyosarcoma , vero , and 293 t cell lines for virus isolation . cell lines were chosen to facilitate culturing of a range of viruses that may have been responsible for the clinical spectrum of illness seen . because csf volume for virus isolation was limited to a 100-l sample all csf and serum samples were tested by using an immunoglobulin m capture elisa to detect antibodies to japanese encephalitis virus ( jev ) and dengue virus , which circulate in the study region ( 11 ) . if a sufficient amount of csf remained , rna was extracted by using the viral rna mini extraction kit ( qiagen , hilden , germany ) according to the manufacturer s instructions for pan - enterovirus rt - pcr , as described above and for a jev rt - pcr ( 7,12 ) . plasma samples were also tested for chikungunya virus by using rt - pcr ( 13 ) . of 243 children recruited into the study , 3 died before diagnostic samples could be obtained and 8 left the hospital against medical advice before samples were obtained . among 232 children who satisfied the inclusion criteria , 166 csf samples were obtained from 152 children . we also obtained 108 throat swabs specimens from 106 children and 19 rectal swab specimens from 18 children from the 171 children recruited after december 2005 when swab sampling began . virus isolates from throat swabs of 5 ( 4.7% ) of 106 patients with a clinical signs of acute encephalitis syndrome were positive by pan - enterovirus rt - pcr for ev75 . sequencing indicated that vp1 regions of virus isolates obtained were similar to those of ev75 . the 5 ev75-positive children were admitted to hospital on days 16 ( median 4 days ) of illness ( table ) . these children had a median age of 8 years ( range 1.510 years ) , and 3 were girls . all 5 children had severe clinical disease ( drowsiness , irritability , and reduced consciousness ) at the time of admission , and 3 had seizures before admission . * ev75 , enterovirus 75 ; csf , cerebrospinal fluid ; gtc , generalized tonic clonic . laboratory values were within reference ranges for 2 children , leukocyte counts were increased for 3 children , and results were not available for 1 child . the child for whom no lumbar puncture was performed had neurologic deterioration , meningism , and bilateral papilloedema ; this child was treated empirically . sequencing showed that vp1 region homology for virus isolated in this study was similar to that observed for previously identified ev75 isolates ( figure ) . sufficient csf sample for pan - enterovirus rt - pcr was available for 162 samples from 162 patients , including 4 of the 5 ev75-positive patients ; all samples were negative for jev . these 162 samples were also negative for enteroviruses by pan - enterovirus rt - pcr ( 7,12 ) . serum samples from the 5 ev75-positive patients were negative for jev and dengue virus by immunoglobulin m capture elisa , for jev by rt - pcr , and for chikungunya virus by rt - pcr . eight patients showed positive results for chikungunya virus by rt - pcr , 48 showed positive results for jev by elisa , and 12 showed positive results for dengue virus by elisa ( 14 ) . the tree was constructed by using the neighbor - joining method and the maximum - composite likelihood - substitution model . closed circles indicate isolates from india ( this study ) and open circles previously reported ev75 sequences . all ev75 sequences are named by using the conventional genbank accession numbers ( published sequences ) or sample name ( sequences from this study ) , country of origin , and year of isolation ( where available ) . all prototype ev reference sequences are indicated by their genbank accession numbers preceding serotype identification . species b enteroviruses such as coxsackie virus a9 and echo viruses b16 are usually readily isolated from csf , unlike species a enteroviruses such as ev71 . although ev75 is a species b enterovirus , we were unable to isolate enterovirus from csf from any of the patients , although throat swabs specimens were positive . this finding is similar to that for ev71 , which has been isolated more frequently from throat swab specimens than from csf or vesicles ( 4 ) . in a study from spain , ev75 was isolated from the csf of 5 patients and nasopharyngeal swab specimens of 3 patients ( 3 ) . however , throat swab specimens are rarely obtained in rural hospital settings with limited diagnostic facilities . although ev75 infection may have been a coincidental finding for the patients , we believe that this possibility is unlikely because results for other common causes of encephalitis were negative . results of csf testing were negative for other circulating viruses , including jev , dengue virus , and herpes simplex virus , and patients also showed negative results for jev and dengue virus by elisa . our results illustrate the need to confirm diagnoses of ev75 in a range of specimens and by a range of laboratory investigations . this confirmation is required in india where encephalitis is often diagnosed clinically and recent outbreaks laboratory diagnosis is hampered by single samples and high cost and low reliability of diagnostic tests currently available . our study also shows that ev75 can cause encephalitis , in addition to aseptic meningitis and acute flaccid paralysis . thus , as for other enteroviruses , throat swab specimens may be especially useful for diagnosis of infection with ev75 .

recent outbreaks of enterovirus in southeast asia emphasize difficulties in diagnosis of this infection . to address this issue , we report 5 ( 4.7% ) children infected with enterovirus 75 among 106 children with acute encephalitis syndrome during 20052007 in southern india . throat swab specimens may be useful for diagnosis of enterovirus 75 infection .

Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period. ||||| Well-meaning adults decided a good prescription for schoolchildren with attention issues was a toy that promised to divert nervous energy. They called it the “fidget spinner.” What they never imagined is that these spinners would become hot items in American classrooms, and that all the fidgeting with them would someday create an epidemic of mass distraction. Bill... ||||| Florida-based creator Catherine Hettinger couldn’t afford the patent on the ubiquitous playground toy but insists she’s ‘pleased’ about its sudden popularity As the inventor of the original fidget spinner – the ubiquitous new toy that has quickly become a craze in playgrounds around the world – Catherine Hettinger should be enjoying the high life. Secret Teacher: Fidget cubes need kicking out of class Read more But the Florida-based creator is not making a penny off her genius invention, even as global sales of the gadget she envisioned two decades ago as a way to entertain her seven-year-old daughter soar into the tens of millions and suppliers struggle to meet massive demand. Hettinger held the patent on finger spinners for eight years, but surrendered it in 2005 because she could not afford the $400 (£310) renewal fee. “I just didn’t have the money. It’s very simple,” she said. The palm-sized spinners consist of a ball bearing which sits in a three-pronged plastic device which can then be flicked and spun round. Some schools in the UK and the US have banned the devices, but some teachers believe that they can help children concentrate – especially those with ADHD. Facebook Twitter Pinterest Catherine Hettinger, creator of the fidget spinner, with her granddaughter Chloe. Photograph: Richard Luscombe Now, while the manufacturers and retailers who are selling the modern-day versions of the toy rack up huge profits, Hettinger, 62, is downsizing from her tiny house to a cheaper condo, wondering whether to get her disconnected telephone line reinstated, and figuring out how to afford “a car that truly works”. “It’s challenging, being an inventor,” she told the Guardian during a coffee-shop interview near her home in Winter Park, a historic suburban city just east of Orlando. “Only about 3% of inventions make any money. I’ve watched other inventors mortgage their houses and lose a lot. You take roommates, you get help from friends and family. It is hard.” Hettinger accepts that had she been able to afford to keep the patent, she would now likely be sitting on a sizeable fortune. “I wouldn’t have any problem. That would have been good,” she said. But while she joins a notable list of others – including Tim Berners-Lee, founder of the world wide web, and hoverboard inventor Shane Chen, who by accident or design failed to cash in personally on their world-changing creations – Hettinger insists that she is not bitter over the lost opportunity, and is instead “encouraged” by the spinners’ sudden popularity. “Several people have asked me: ‘Aren’t you really mad?’ But for me I’m just pleased that something I designed is something that people understand and really works for them,” she said. “There’s just a lot of circumstances in modern life when you’re boxed in, you’re cramped in, and we need this kind of thing to de-stress. It’s also fun. That’s the thing about culture, once everybody starts doing it, it’s kind of OK.” The inventor of the hoverboard says he's made no money from it Read more Her views are not shared by increasing numbers of schools, who are banning children from bringing or using the spinners because they are seen as a distraction. But Hettinger said she was pleased that in other circumstances, schools were finding the devices helpful. “I know a special needs teacher who used it with autistic kids, and it really helped to calm them down,” she said. Hettinger says the origins of the spinner lie in “one horrible summer” back in the early 1990s when she was suffering from myasthenia gravis, an autoimmune disorder that causes muscle weakness, and was also caring for her daughter Sara, now 30. “I couldn’t pick up her toys or play with her much at all, so I started throwing things together with newspaper and tape then other stuff,” she said. “It wasn’t really even prototyping, it was some semblance of something, she’d start playing with it in a different way, I’d repurpose it.” After several redesigns, a basic, non-mechanical version of the spinner was born. “We kind of co-invented it – she could spin it and I could spin it, and that’s how it was designed,” she added. Hettinger, who spent her childhood in Tulsa, Oklahoma, spent the next few years exhibiting and selling upgraded versions of her design at arts and craft fairs around Florida. “The project was great, I essentially broke even, I sold units and tested it with a couple of thousand people,” she said. She also flew with her daughter to Washington DC for an appointment with the US patent and trademark office and secured a patent on her design in 1997. But just when it looked like her original spinner was on track for wider commercial success, Hettinger was hit by a disappointment. The toy manufacturing giant Hasbro, who had been testing the design, decided not to proceed to production – effectively leaving the project to wither and eventually die with the lapse of the patent in 2005. “I’m a techie, I’m not a person who closes multimillion-dollar deals,” Hettinger said. “If there had been money or I’d had a venture capitalist back then, it would have been different.” Undeterred, Hettinger is currently working contract engineering jobs to earn income while helping advise others at meetings of the inventors council of central Florida, and also has plans to manufacture and sell her original spinner design if a Kickstarter appeal can raise enough funds. It is not quite how things could have turned out had she retained the fidget spinner patent and secured her financial future, but Hettinger insists she has only one regret: “I would probably be doing more inventing,” she said. ||||| Catherine Hettinger has an inventor’s mind: When she notices a problem, she tries to imagine a toy or device that can remedy it. So when she heard about young boys throwing rocks at police officers and people walking past them while visiting her sister in Israel, her wheels started turning. She started brainstorming devices that could distract young children and provide them with a soothing toy to play with. First, she thought of a soft rock that kids could throw. But then she tossed that idea aside, still thinking about other options when she returned to her home in Orlando, Fla. It was there that she eventually developed the idea that would become the original fidget spinner — more than two decades before the wildly popular device became the must-have toy for both kids and adults this year. Buy now: Fidget Spinner, $26, Amazon “It started as a way of promoting peace, and then I went on to find something that was very calming,” Hettinger, now in her 60s, told MONEY of the fidget spinners, which she first began imagining back in the 1980s. The toys now come in different designs and have hit the mass market after the patent expired on Hettinger’s original product in 2005, meaning companies can sell the product independently from her. But Hettinger isn’t upset about the sudden popularity and capitalization of her invention. In fact, she’s excited about it. “Maybe if it was some kind of exploitative product — like a new style of cigarettes — and my only motivation was to make money, I’d have a different attitude,” Hettinger said. “But I am just thrilled.” Catherine Hettinger courtesy of Sara Hettinger READ MORE: Meet the Fidget Spinner, a New Toy Craze Entrancing Kids and Grownups Alike The modern iterations of the devices made out of metal or plastic and have a bearing in the middle that allows it to be spun. Some of the products have prongs on them, while others are circular. The spinners, which range in price from just a few dollars to hundreds, are intended to calm nerves and help with stress and anxiety. The handheld gadgets are now so popular that different versions of fidget spinners make up all of Amazon’s top 20 best sellers for toys and games as of May 2. “When you start seeing these things flying off the shelf at your local 7-11, you know things are heating up,” Hettinger joked. Hettinger grew up in Oklahoma and attended Rensselaer Polytechnic Institute in Troy, New York — a college known for its engineering and technology programs — before moving to Florida. The first fidget spinner debuted in 1993, and her patent approved four years later. But they didn’t take off — instead, she made rounds at fairs selling a couple thousand devices and frequently tried selling them to toy companies. Once she had her patent, she booked a meeting with Hasbro, the third-largest toy maker in the world, and even found herself using the fidget spinner to ease her nerves before the meeting with the company’s vice president. “That was one good thing about this product: If I walked into their headquarters spinning it, it totally calmed me down,” she recalled. “It’s not an easy thing for most people to walk in and close big deals.” Hasbro didn’t pick up the spinners, sending her a rejection letter after testing it on consumers. But now, Hasbro sells the fidget spinners — almost 20 years after it denied the original product. Chloe, Hettinger's granddaughter, plays with the original fidget spinner. Sara Hettinger– So why the sudden boom in popularity? Hettinger isn’t sure, but she speculates as a result of the recession in 2008, people may be looking for ways to calm their nerves and have fun. “That was always the concept — to help people,” she said. “I experienced it for myself.” “There’s a real need for this, ” she added. And given the device’s sudden popularity, Hettinger is working on a way to sell her original spinners, which have not been on the market throughout the current craze. She’s going to launch a a Kickstarter — called the Classic Spinner —soon and sell her version online. While she’s excited about the spinner’s newfound popularity, she’s still got an inventor’s mind and continues to observe her surroundings and think up products that can make life easier for people. Her latest project is a diet and fitness application for iPhones that she’s working on with the help of the Inventors Council of Central Florida, a Florida-based group that she is a member of that works on new ideas together. “The culture we live in now — the times now — everyone has a need for fun. People are realizing it — and it’s true,” she said. Correction: A previous version of this story misstated the year Hettinger’s patent expired. It expired in 2005, not 2017. Additionally, this story misstated what inspired her to create the fidget spinner. Hettinger was inspired after hearing about boys throwing rocks at people and police — she did not see it herself. ||||| A prototype is a preliminary model of something. Projects that offer physical products need to show backers documentation of a working prototype. This gallery features photos, videos, and other visual documentation that will give backers a sense of what’s been accomplished so far and what’s left to do. Though the development process can vary for each project, these are the stages we typically see: About Wikipedia credits Catherine Hettinger as the original inventor. This makes it a Classic. This has been a collaborative project with a three dimensional artist and an engineer. The first spinner is ready for primetime. The photo of the prototype becomes the original Classic Fidget Spinner, Fellow techies understand the need for movement. Not all of us can work in Silicon Valley and step out for a football throw. De- stress with a great spinner that is fun and enjoyable. This project allows for everyone to be able to enjoy this classic and truly original item that has been used and proven small scale. Be a part of the next big thing. If you are looking to get in as a supporter then meet the creators. Otherwise enjoy a wonderful talking point and de-stressor. Suddenly everyone understands the need today and let's help ourselves and help them fill that need. Kids are required to sit 7 solid hours in chairs and this is sparking a revolution to at least keep them from getting in trouble. No animal sits still for long and we can't either. Our times are seeing a surge in the need for fun. Be a part of that.

– It's hard to make money if you don't have any. That's the lesson from Catherine Hettinger, who is credited with inventing the original fidget spinner about three decades ago. In 2004, she says she could not afford the $400 patent renewal fee and thereby had to surrender it. "I just didn't have the money," she tells the Guardian. "It's that simple." Now, fidget spinners are all the rage—they brought in revenue of $2.6 million in April, reports the Wall Street Journal—but Hettinger hasn't made a dime. She says she's not bitter, however, and is hoping to cash in on a "classic" version of her design via Kickstarter. “Several people have asked me: ‘Aren’t you really mad?’" she says. "But for me I’m just pleased that something I designed is something that people understand and really works for them." Hettinger, now 62, says she concocted the device in the early 1990s to occupy her toddler daughter. She tells Time she was also inspired while on a trip to Israel when she saw young boys throwing rocks and wanted to give them an alternative. In any event, she got a patent in the 1990s and had a small measure of success at toy fairs. But toy-makers passed, including Hasbro, which now makes them today. "Maybe if it was some kind of exploitative product—like a new style of cigarettes—and my only motivation was to make money, I’d have a different attitude,” says Hettinger of the gizmo's popularity. “But I am just thrilled.”

the past decade has seen the discovery of over 150 exoplanets ( http://www.obspm.fr/planets ) . one statistical trend that has emerged from these data is that the probability of finding a gas giant planet around a star with current techniques increases with the host star s metallicity @xcite . as shown by @xcite , the high metal content of planet host stars seems to be primordial . therefore , this trend , if real @xcite , indicates that short - period gas giant planets are more likely to occur in metal - rich than in metal - poor protoplanetary disks . the two contending theories for gas giant formation are core accretion plus gas capture @xcite and disk instability @xcite . calculations show that the metallicity relation can be explained within the framework of core accretion ( e.g. , * ? ? ? * ; * ? ? ? * ) . for disk instability , @xcite finds that , in his three - dimensional hydrodynamics disk simulations with radiative cooling , clump formation by disk instability occurs for all metallicities over the range 0.1 to 10 z@xmath0 , due to rapid cooling by convection @xcite , and he attributes the abundance of short period gas giants around high metallicity stars to migration @xcite , a mechanism also invoked by @xcite to explain part of the metallicity correlation . by contrast , @xcite , who uses a somewhat more sophisticated treatment of radiative boundary conditions , finds much longer cooling times and no fragmentation into dense clumps in her disk instability simulations . here we report results of new disk calculations based on meja s methods in which the opacity is varied by using different metallicities and grain sizes . even over a much narrower range of metallicities than considered by @xcite , we find that the strength of the gi s does vary noticeably and that disk fragmentation is not seen for any metallicity or grain size tested . we conduct protoplanetary disk simulations using the indiana university hydrodynamics group code ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , which solves the equations of hydrodynamics in conservative form on a cylindrical grid @xmath1 to second order in space and time using an ideal gas equation of state . self - gravity and shock mediation by artificial bulk viscosity are included . reflection symmetry is assumed about the equatorial plane , and free outflow boundaries are used along the top , outer , and inner edges of the grid . we adopt the treatment of radiative physics detailed in @xcite with few modifications . let @xmath2 be the optical depth , defined by using the rosseland mean opacity measured vertically down from above . energy flow in cells with @xmath3 is calculated in all three directions using flux - limited diffusion @xcite . cells with @xmath4 2/3 , in the disk atmosphere and in the outer disk , cool radiatively using an optically thin lte emissivity . atmosphere heating by high - altitude shocks and upward moving photons from the photosphere are included . in this paper , we also assume that an external envelope heated by the star @xcite shines vertically down on the disk . this ir irradiation is characterized by a black body flux with a temperature @xmath5 . the optically thick and thin regions are coupled , over one or two cells , by an eddington - like grey atmosphere fit that defines the boundary flux for the diffusion approximation . the opacities and molecular weights for a solar composition are from @xcite , with a power - law grain size distribution of @xmath6 ranging from 0.005 @xmath7 m to a largest grain size @xmath8 that can be varied . to model variations in metallicity z , the mean opacities are multiplied by a factor @xmath9 z / z@xmath0 , as was done by @xcite . tests of our radiative scheme for a vertically stratified gas layer with a constant gravity , a constant input flux at the base , and a grey opacity show relaxation to an eddington - like solution with the correct flux from the photospheric layers . the initial axisymmetric model for all the calculations is the same as that used by @xcite . the central star is 0.5 @xmath10 , and the nearly keplerian disk of 0.07 @xmath10 has a surface density @xmath11 from 2.3 au to 40 au . the initial grid has ( 256 , 128 , 32 ) cells in ( @xmath12 ) above the midplane . when the disk expands at the onset of gi s , the grid is extended radially and vertically . the initial minimum value of the toomre stability parameter @xmath13 is about 1.5 , and so the disk is marginally unstable to gi s . the initial model is seeded with low - amplitude random density noise . we use @xmath14 k , which is lower than the 50 k assumed in @xcite because our larger and less massive disk is mostly stabilized by @xmath15 k. in this paper , we present simulations with four metallicities z = 1/4 z@xmath16 ( one - quarter solar metallicity ) , 1/2 z@xmath16 , z@xmath16 , and 2 z@xmath16 . the 1/4 z@xmath16 simulation was started from the 1/2 z@xmath16 disk after 13.0 outer rotation periods ( orps ) of evolution , to save computing resources . here 1 orp ( about 250 yrs ) is the initial rotation period at 33 au . the varied metallicity cases use a maximum grain size @xmath17 m in the dust opacities . an additional simulation with @xmath18 mm and z = z@xmath0 is conducted to explore the effects of grain growth . the current calculations resemble those presented in @xcite and @xcite . the disks remain fairly axisymmetric until a _ burst phase _ of rapid growth in nonaxisymmetric structure . subsequently , the disks gradually transition into a quasi - steady _ asymptotic phase _ , where heating and cooling are in rough balance , and average quantities change slowly ( see also * ? ? ? * ) . table [ comparetable ] summarizes some of the results . in the table , duration refers to the simulation length measured in orps , @xmath19 is the time in orps at which the burst phase begins , @xmath20 is the approximate time in orps when the simulation enters the asymptotic state , @xmath21 is a time - averaged integrated fourier amplitude for all nonaxisymmetric structure ( see below ) , @xmath22 is the final global cooling time obtained by dividing the final total internal energy of the disk by the final total luminosity , and thin@xmath23 is the percentage of disk volume that is optically thin during the asymptotic phase . one noticeable effect is that the onset of the burst phase ( @xmath19 ) is delayed for higher metallicity and larger grain size ( table [ comparetable ] ) , as expected due to higher opacity and therefore slower cooling . note that , over the bulk of our large cool disk , increasing @xmath8 increases the opacity . although the time to reach the asymptotic phase is relatively insensitive to grain size and metallicity , the overall final @xmath22 listed in table [ comparetable ] illustrates that the correlation between cooling time and opacity carries over to late times . during the asymptotic phase , in all cases , the toomre @xmath13 values remain roughly constant with time , with values ranging between 1.3 to 1.8 for @xmath24 10 to 40 au , and the mass inflow rates peak near 15 au at @xmath25/yr , with negligible difference between 1/2 z@xmath0 and 2 z@xmath0 to the accuracy that we can measure these inflows @xcite . although there are some regions of superadiabatic gradients , the rapid overall convective cooling reported by @xcite does not occur . we do see upward and downward motions , which we attribute to hydraulic jumps @xcite . whether or not some of these motions are actually thermal convection , they do not result in rapid cooling for our disks . in figure [ den ] , which shows midplane densities at 15 orps , the spiral structure appears stronger for 1/4 z@xmath16 than for 2 z@xmath16 . in order to quantify differences in gi strength , we compute integrated fourier amplitudes @xcite @xmath26 where @xmath27 is the axisymmetric component of the density and @xmath28 is the amplitude of the cos(@xmath29 ) component . although variable , after @xmath30 14 orps , the @xmath31 s for most @xmath32 s are greater for 1/4 z@xmath16 than for higher z s . to measure total nonaxisymmetry , we sum the @xmath31 s and average this sum over 14.5 to 15.5 orps . as shown in table [ comparetable ] , this global measure @xmath21 is greatest for 1/4 z@xmath16 and generally decreases with increasing metallicity and grain size . figure [ energy ] plots the cumulative energy loss due to cooling computed for only half the disk as a function of time . the upper curves show energy loss from the disk interior after compensating for energy input by residual irradiation and by the glowing disk upper atmosphere ; the lower curves show net energy loss from optically thin regions after accounting for heating due to envelope irradiation . due to our restricted vertical resolution and use of the eddington atmosphere fit over one or two vertical cells , the `` thick '' curves effectively include most of the photospheric layers for most columns through the disk . the `` thin '' curves tally additional cooling from extended layers above the photospheric cells , usually with @xmath33 , plus the parts of the outer disk that are optically thin all the way to the midplane . the initial cooling rates for the optically thick regions plus photosphere clearly differ . in fact , the initial slopes of the `` thick '' curves give @xmath34 z / z@xmath0 orps . however , the initial disks are far from radiatively relaxed , and so there are transients . remarkably , by the asymptotic phase , all the disk interior - plus - photosphere curves converge to similar energy loss rates . during these late times , the differences between the total cooling rates are dominated by the optically thin regions , which are larger for the lower metallicity cases , as indicated by the thin@xmath23 entry in table [ comparetable ] . the overall asymptotic phase @xmath22 s in table [ comparetable ] , based on summing the thick and thin loss rates , are longer for higher metallicity and larger grain size . altogether , the evidence in table [ comparetable ] and figures [ den ] and [ energy ] shows that higher opacity leads to slower cooling and that slower cooling produces lower gi amplitudes . we remind the reader that we detect these differences over a much narrower range of metallicities ( 1/4 to 2 z@xmath0 ) than considered by @xcite ( 0.1 to 10 z@xmath0 ) . as in @xcite , except for brief transients during the burst phases of some runs , these disks do not form dense clumps , in apparent disagreement with @xcite . to investigate whether the disk evolution depends on spatial resolution in the asymptotic phase @xcite , both the 1/4 z@xmath0 and 2 z@xmath0 simulations are extended for another 2 orp s with quadrupled azimuthal resolution ( 512 zones ) , and the disks do not fragment into dense clumps . this is consistent with the analytic arguments in @xcite that an unstable disk and fast radiative cooling are incompatible constraints for realistic disks at 10 au ( see boss 2005 for a different perspective ) . indeed , if @xmath22 listed in table [ comparetable ] is a good measure of local cooling times in these disks , we do not expect fragmentation . @xcite shows that fragmentation occurs only if the local @xmath22 is less than about half the local disk orbit period @xmath35 ( see also * ? ? ? * ; * ? ? ? * ) , except possibly near sharp opacity edges @xcite . we only find locallized cooling times shorter than 0.5 @xmath35 in the asymptotic phase of the 2 z@xmath0 case , and then only in the 30 to 40 au region , which is optically thin . this occurs because , even though @xmath36 z in optically thick regions ( higher optical depth ) , @xmath36 z@xmath37 in thin ones ( more emitters ) . as a result , this disk displays the steepest drop of local @xmath22 with @xmath38 . the short local @xmath22 s appear to be highly variable and transient . the continuation of this simulation for 2 orps at higher azimuthal resolution ( 512 zones ) does not show evidence for fragmentation into clumps . it could prove important to push our simulations to higher z in the future . our results show that gi strength decreases as metallicity increases and , contrary to @xcite , that global radiative cooling is too slow for fragmentation into dense clumps . in the asymptotic phase , cooling rates for the disk interior plus photospheric layers converge for all z , but the total cooling , including the optically thin regions , is higher for lower z. thus , the optically thin upper atmosphere and outer disk play a role in the cooling rate of an evolved disk . in fact , the fractional volume of the optically thin regions becomes very large at late times ( see thin@xmath23 in table [ comparetable ] ) . note also that the optically thick region fractional volume , @xmath39 , varies roughly as z. the greater surface area of the disk photosphere at higher z tends to compensate for the higher opacity and leads to convergence of the cooling rates for the parts of the disk contained within the photospheric layers . in this respect , we confirm boss s conclusion that the outcome of the radiative evolution is somewhat insensitive to metallicity . however , the important difference is that we do not see fragmentation into dense clumps , presumably because our cooling rates are much lower than in @xcite . for the 1 mm case , the optically thin regions have a much smaller volume ( table 1 ) and contribute little to cooling . outside the inner few au , bigger grains make the disk more opaque to longer wavelengths , and @xmath22 is thus considerably larger , even initially . our results argue against direct formation of gas giants by disk instability in two ways the global radiative cooling times seem too long for fragmentation to occur and gi s are stronger overall for _ lower _ metallicity . nevertheless , it is still possible that gi s play an important role in gas giant planet formation . @xcite suggest that dense gas rings produced by gi s will enhance the growth rate of solid cores by drawing solids toward their centers @xcite and thereby accelerating core accretion . such rings are indeed produced in the inner disks of all our calculations regardless of metallicity or grain size , and they appear to be still growing when the calculations end . in the weaker gi environments of high metallicity , there is less self - gravitating turbulence to interfere with the radial drift of solids @xcite . in this way , rings may provide a natural shelter and gathering place for growing embryos and cores . the apparent disagreement between our results and those of @xcite could be due to any number of differences in techniques and assumptions , such as artificial viscosity , opacities , equations of state , initial disk models and perturbations , grid shapes and resolution , and radiative boundary conditions , including the way that we handle irradiation . we are now collaborating with boss in an effort to pinpoint which of these is the principal cause ( k. cai et al . , in preparation ) . preliminary results suggest that it is the radiative boundary conditions . we are therefore developing alternative techniques for disk radiative transfer that we hope are more reliable and accurate . we thank a.p . boss and an anonymous referee for useful comments . this work was supported in part by nasa origins of solar systems grants nag5 - 11964 and nng05gn11 g , by nasa planetary geology and geophysics grant no . nag5 - 10262 , and by a shared university research grant from ibm , inc . to indiana university . sozzetti , a. , latham , d. w. , torres , g. , stefanik , r. p. , boss , a. p. , carney , b. w. , & laird , j. b. , in proceedings of the gaia symposium `` the three - dimensional universe with gaia '' ( esa sp-576 ) . editors : c. turon , k.s . oflaherty , m.a.c . , 309 @xmath8 & duration & @xmath19 & @xmath20 & @xmath21 & @xmath22 & thin% + 1/4 z@xmath16 & 1/4 & 1 @xmath40 m & 3.8 & n / a & n / a & 1.29 & 2.1 & 99% + 1/2 z@xmath16 & 1/2 & 1 @xmath40 m & 15.6 & 4.0 & 10 & 1.09 & 2.9 & 98% + z@xmath16 & 1.0 & 1 @xmath40 m & 15.7 & 5.0 & 10 & 1.10 & 3.2 & 94% + 2 z@xmath16 & 2.0 & 1 @xmath40 m & 16.5 & 5.0 & 10 & 0.72 & 3.7 & 86% + 1 mm & 1.0 & 1 mm & 17.2 & 7.0 & 11 & 0.88 & 4.5 & 44% +

observational studies show that the probability of finding gas giant planets around a star increases with the star s metallicity . our latest simulations of disks undergoing gravitational instabilities ( gi s ) with realistic radiative cooling indicate that protoplanetary disks with lower metallicity generally cool faster and thus show stronger overall gi - activity . more importantly , the global cooling times in our simulations are too long for disk fragmentation to occur , and the disks do not fragment into dense protoplanetary clumps . our results suggest that direct gas giant planet formation via disk instabilities is unlikely to be the mechanism that produced most observed planets . nevertheless , gi s may still play an important role in a hybrid scenario , compatible with the observed metallicity trend , where structure created by gi s accelerates planet formation by core accretion .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Secure Fence Restoration Act of 2015''. SEC. 2. FENCING ALONG AND OPERATIONAL CONTROL OF THE SOUTHWEST BORDER. (a) Fencing.--Paragraph (1) of section 102(b) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (8 U.S.C. 1103 note) is amended-- (1) in subparagraph (A), by inserting ``, not later than December 31, 2017,'' before ``construct''; (2) in subparagraph (B)-- (A) in clause (i), by striking ``370 miles, or other mileage determined by the Secretary, whose authority to determine other mileage shall expire on December 31, 2008,'' and inserting ``areas''; and (B) in clause (ii), by striking ``2008'' and inserting ``2017''; and (3) by striking subparagraph (D). (b) Operational Control.--Subsection (a) of section 2 of the Secure Fence Act of 2006 (8 U.S.C. 1701 note; Public Law 109-367) is amended, in the matter preceding paragraph (1)-- (1) by striking ``18 months after the date of the enactment of this Act,'' and inserting ``December 31, 2017,''; and (2) by inserting ``, in consultation with State and local officials along the international border between the United States and Mexico, including governors of border States, mayors of border towns and cities, and border sheriffs,'' before ``shall''. SEC. 3. PROHIBITION ON ACTIONS THAT IMPEDE BORDER SECURITY ON CERTAIN FEDERAL LAND. (a) Short Title.--This section may be cited as the ``National Security and Federal Lands Protection Act''. (b) Prohibition on Secretaries of the Interior and Agriculture.-- Neither the Secretary of the Interior or the Secretary of Agriculture may impede, prohibit, or restrict activities of U.S. Customs and Border Protection on Federal land located within 100 miles of an international land border that is under the jurisdiction of the Secretary of the Interior or the Secretary of Agriculture, as the case may be, to execute search and rescue operations and to prevent all unlawful entries into the United States, including entries by terrorists, other unlawful aliens, instruments of terrorism, narcotics, and other contraband through such border. (c) Authorized Activities of U.S. Customs and Border Protection.-- U.S. Customs and Border Protection shall have immediate access to Federal land within 100 miles of the international land border under the jurisdiction of the Secretary of the Interior or the Secretary of Agriculture for purposes of conducting the following activities on such land that prevent all unlawful entries into the United States, including entries by terrorists, other unlawful aliens, instruments of terrorism, narcotics, or other contraband through such border: (1) Construction and maintenance of roads. (2) Construction and maintenance of barriers. (3) Use of vehicles to patrol, apprehend, or rescue. (4) Installation, maintenance, and operation of communications and surveillance equipment and sensors. (5) Deployment of temporary tactical infrastructure. (d) Clarification Relating to Waiver Authority.-- (1) In general.--Notwithstanding any other provision of law (including any termination date relating to the waiver referred to in this subsection), the waiver by the Secretary of Homeland Security on April 1, 2008, under section 102(c)(1) of the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 (8 U.S.C. 1103 note; Public Law 104-208) of the laws referred to in paragraph (2) of this subsection with respect to certain sections of the international border between the United States and Mexico and between the United States and Canada shall be considered to apply to all Federal land under the jurisdiction of the Secretary of the Interior or the Secretary of Agriculture within 100 miles of the international land borders of the United States for the activities of U.S. Customs and Border Protection specified in subsection (c) of this section. (2) Description of laws waived.--The laws referred to in paragraph (1) are the Wilderness Act (16 U.S.C. 1131 et seq.), the National Environmental Policy Act of 1969 (42 U.S.C. 4321 et seq.), the Endangered Species Act of 1973 (16 U.S.C. 1531 et seq.), the National Historic Preservation Act (16 U.S.C. 470 et seq.), Public Law 86-523 (16 U.S.C. 469 et seq.), the Act of June 8, 1906 (commonly known as the ``Antiquities Act of 1906''; 16 U.S.C. 431 et seq.), the Wild and Scenic Rivers Act (16 U.S.C. 1271 et seq.), the Federal Land Policy and Management Act of 1976 (43 U.S.C. 1701 et seq.), the National Wildlife Refuge System Administration Act of 1966 (16 U.S.C. 668dd et seq.), the Fish and Wildlife Act of 1956 (16 U.S.C. 742a et seq.), the Fish and Wildlife Coordination Act (16 U.S.C. 661 et seq.), subchapter II of chapter 5, and chapter 7, of title 5, United States Code (commonly known as the ``Administrative Procedure Act''), the National Park Service Organic Act (16 U.S.C. 1 et seq.), the General Authorities Act of 1970 (Public Law 91-383) (16 U.S.C. 1a-1 et seq.), sections 401(7), 403, and 404 of the National Parks and Recreation Act of 1978 (Public Law 95-625, 92 Stat. 3467), and the Arizona Desert Wilderness Act of 1990 (16 U.S.C. 1132 note; Public Law 101-628). (e) Protection of Legal Uses.--This section may not be construed to provide-- (1) authority to restrict legal uses, such as grazing, hunting, mining, or public-use recreational and backcountry airstrips on land under the jurisdiction of the Secretary of the Interior or the Secretary of Agriculture; or (2) any additional authority to restrict legal access to such land. (f) Effect on State and Private Land.--This Act shall-- (1) have no force or effect on State or private lands; and (2) not provide authority on or access to State or private lands. (g) Tribal Sovereignty.--Nothing in this section supersedes, replaces, negates, or diminishes treaties or other agreements between the United States and Indian tribes.

Secure Fence Restoration Act of 2015 This bill amends the Illegal Immigration Reform and Immigrant Responsibility Act of 1996 with respect to construction of border fencing and road improvements to direct the Department of Homeland Security (DHS) to complete the required 700-mile southwest border fencing and priority-area fencing by December 31, 2017. The Secure Fence Act of 2006 is amended to direct DHS, in consultation with state and local officials along the U.S.-Mexico border, to achieve operational control over U.S. international land and maritime borders by December 31, 2017. National Security and Federal Lands Protection Act Neither the Department of the Interior nor the Department of Agriculture may prohibit or restrict U.S. Customs and Border Protection (CBP) activities on federal land under their respective jurisdictions within 100 miles of an international land border to: execute search and rescue operations; and prevent unlawful entries into the United States, including entries by terrorists, other unlawful aliens, instruments of terrorism, narcotics, and other contraband through such border. CBP shall have access to such lands to conduct: (1) road and barrier construction and maintenance, (2) vehicular patrols, (3) surveillance activities, and (4) deployment of temporary tactical infrastructure.

a solar disturbance propagating away from the sun affects the pre - existing population of galactic cosmic rays ( gcrs ) in a number of ways . most well - known is the `` forbush decrease '' ( fd ) , a region of suppressed cosmic - ray density located downstream of an interplanetary coronal mass ejection ( icme ) shock . some particles from this region of suppressed density leak into the upstream region and , traveling nearly at the speed of light , they race ahead of the approaching shock and are observable as a precursory loss cone ( lc ) anisotropy far into the upstream region @xcite @xcite . lcs are characterized by intensity deficits confined to a narrow pitch - angle region around the sunward direction along the interplanetary magnetic field ( imf ) and are typically visible 4 - 8 hours ahead of shock arrival associated with major geomagnetic storms @xcite . on the basis of numerical simulations of the high - energy particle transport across the shock , @xcite[hereafter referred to as paper 1 ] derived the theoretical constraints for the lc anisotropy . in particular , they presented the quantitative relationship between the angular width of the pitch - angle distribution and the interplanetary parameters which include the angle between the shock normal and the upstream imf and the mean free path of the pitch - angle scattering of gcrs in the turbulent magnetic field . by analyzing the `` two - dimensional map '' of the cosmic ray intensity observed with a large single muon hodoscope during a lc precursor period in october , 2003 , @xcite reported a lead time of 4.9 hours for the lc precursor indicating a mean free path of the pitch - angle scattering shorter than the theoretical expectation based on the numerical simulation . this implies that the imf was more turbulent in the event analyzed by them , than a typical power spectrum of the imf turbulence assumed in paper 1 . they also reported , on the other hand , a rather broad pitch - angle distribution for the event , which implies a `` quasi - parallel '' shock according to the numerical simulation . although this seemed to be conflicting with in - situ imf and plasma data suggesting a `` quasi - perpendicular '' shock , it was discussed that this apparent conflict can be resolved by taking account of a pair of shocks formed by icmes successively ejected from the sun . the `` alaska model '' simulation of the event indicated that a large shock responsible for the ssc at the earth was overtaking another smaller shock westward of the earth . during the loss cone period , therefore , it was possible that the earth may have been connected with the westward shock which was more consistent with a quasi - parallel geometry . thus , the situation of this event was rather complicated introducing an additional ambiguity in the comparison of the observation with theoretical predictions . in this paper , we analyze another simpler lc event associated with a single shock . cosmic ray precursors observed with a long lead time is of particular importance for the possible space weather forecast using cosmic ray measurements . an accurate measurement of such a precursor , however , requires detectors in a global network for continuous monitoring over a long time period more than a day prior to the ssc onset @xcite . such a network has been realized only recently by the global muon detector network ( gmdn ) @xcite . for accurate analyses of lc events , it is also necessary to properly remove the contribution from the diurnal anisotropy , which always exists in space with an amplitude comparable to the intensity deficit due to the lc anisotropy . the gmdn can also measure precisely the diurnal anisotropy utilizing the global sky coverage of the network @xcite . in this paper , we develop new analysis methods for removing the influence of the diurnal anisotropy and apply the `` two - dimensional map '' analysis by @xcite to the cosmic - ray precursors observed with the gmdn in december 2006 for better visualization of the signatures of cosmic ray precursors . the outline of this paper is as follows . in 2 , we briefly summarize the features of the event which we analyze in this paper . in 3 , we apply a new analysis method to the data observed by the gmdn and present the best - fit analyses of a model based on the theoretical prediction by paper 1 . our conclusions and discussions based on the comparison with the theoretical prediction are given in 4 . an x3.4 flare was first observed at 02:14 ut on december 13 , 2006 and was followed by a halo coronal mass ejection ( cme ) eruption shortly after at 02:54 ut . this cme was accompanied by a strong interplanetary ( ip ) shock , which traveled interplanetary space with an average velocity of 1160 km / s and arrived at the earth causing the storm sudden commencement ( ssc ) onset at 14:14 ut on december 14 @xcite . the shock speed at 1 au was 1030 km / s as calculated from the conservation of the plasma mass across the shock . it was also derived from the rankine - hugoniot relations @xcite that the shock normal makes an angle of about 56@xmath1 with the upstream magnetic field indicating the quasi - perpendicular shock . an intense geomagnetic storm followed the ssc with peak kp index of 8 + . there was no other ssc and interplanetary disturbances recorded at the earth between 02:14 ut on december 13 and 14:14 ut on december 14 . from the data recorded by the gmdn , we routinely derive the anisotropy vector ( or the first order anisotropy ) by fitting the function @xmath2 given by @xmath3 to the pressure - corrected hourly count rate @xmath4 at universal time @xmath5 in the @xmath6-th directional channel of the @xmath7-th muon detector in the gmdn . in this equation , @xmath8 denotes the contribution from the cosmic ray density @xmath9 and @xmath10 , @xmath11 , @xmath12 are the best - fit parameters denoting three components of the anisotropy vector in the local geographical coordinate system ( geo ) , @xmath13 , @xmath14 and @xmath15 are the coupling coefficients calculated by assuming a rigidity independent anisotropy , @xmath16 is the local time at the location of the @xmath7-th detector and @xmath17 ( for more detail of our analyses , see * ? ? ? figs.1a-1b display the hourly data of the solar wind velocity and the imf magnitude measured by the _ ace _ satellite over three day period between december 13 and 15 , each as a function of time in the day of year ( doy ) on the horizontal axis . the left and right vertical solid lines indicate the flare onset and the ssc onset , respectively . a clear signature of the ip shock is seen in abrupt increases of the solar wind velocity and the imf magnitude following the ssc onset . the imf data observed during the period between the flare and ssc onsets show no signature of the imf sector boundary and indicate that the earth was in the `` toward '' sector throughout the period . figure 1c shows hourly values of the derived cosmic ray density ( @xmath9 ) , whereas figs.1d-1f display three anisotropy components ( @xmath18 , @xmath19 , @xmath20 ) transformed to the geocentric solar ecliptic ( gse ) coordinate system . the anisotropy components shown in figs.1d-1f are corrected for both the solar wind convection anisotropy and the compton - getting anisotropy arising from the earth s 30 km / s orbital motion around the sun . in figure 1c , a fd is clearly observed with a @xmath03 % maximum depression of the cosmic ray density following the onset of the ssc as indicated by the vertical solid line . the average feature of the anisotropy components over the period preceding the ssc in figs.1d-1f indicates @xmath21 , @xmath22 and @xmath23 , which is in a qualitative agreement with the drift model prediction for the anisotropy in the `` toward '' imf sector during the @xmath24 epoch of the solar polar magnetic field @xcite . also plotted by black points in figure 1 g is the pressure - corrected count rate recorded in the vertical channel of the so martinho da serra detector in brazil ( hereafter so martinho ) . it is evident in this panel that so martinho observed a sharp intensity decrease around doy 348.4 a few hours prior to the ssc onset indicating the lc precursor . we note in this figure that @xmath9 , @xmath18 , @xmath19 and @xmath20 are all changing in response to the lc precursor recorded by the so martinho detector . as shown later , the residual of the best - fitting is larger in two periods of 347.563- 347.771 and doys 348.271 - 348.563 , with the second period containing the lc signature in so martinho data in figure 1 g . this shows that the simple model in eq . ( [ eq01 ] ) can not properly describe the lc anisotropy . in the next section , we improve this model by taking account of the contribution from the lc anisotropy . by using the _ ace _ imf data , we first examine the asymptotic viewing direction along the sunward imf in 24 hours prior to the ssc onset in december 14 , together with viewing directions ( after correction for geomagnetic bending ) available in the gmdn . although there is a large fluctuation in the imf orientation observed by _ ace _ , we find that the majority of the imf orientation is in the southern hemisphere , as expected for the sunward direction along the nominal parker field in the ecliptic plane viewed from the earth in december . the lc precursor , therefore , is expected to be observed in the directional channels viewing around the equator or a little south of the equator . this is consistent with the lc signature observed by so martinho in the bottom panel of figure 1 . our detailed analysis in the next section will show the lc precursor also observed by a small detector at hobart viewing the mid - latitude in the southern hemisphere . in the following analysis , we use for calculating the pitch - angle of each viewing direction in the gmdn the nominal parker field calculated from the solar wind velocity by _ ace _ @xcite , instead of using the _ ace _ imf , to avoid effects of the large fluctuation in the _ ace _ imf orientation . the anisotropy of @xmath030 gev gcr intensity observed with muon detectors is rather stable , changing only gradually even when the _ ace _ imf shows a large fluctuation . muon detectors measure high - energy gcrs by detecting secondary muons produced from the hadronic interactions of primary gcrs ( mostly protons ) with atmospheric nuclei . since relativistic muons have relatively long lifetimes ( the proper half - life being 2.2 @xmath25s ) and can reach the ground preserving the incident direction of the initiating primary particles , we can measure the gcr intensity in various directions with a multi - directional detector at a single location . the typical energy of primary gcrs modulated by fds is @xmath030 gev for muon detectors . the global muon detector network ( gmdn ) originally started with three detectors at nagoya ( japan ) , hobart ( australia ) and so martinho da serra ( brazil ) , each of which is multi - directional , thus allowing us to simultaneously record the muon intensities in various directions of viewing . these detectors have identical design , except for their detection area which is 36 m@xmath26 for nagoya , 9 m@xmath26 for hobart and 28 m@xmath26 for so martinho , consisting of two horizontal layers of plastic scintillators , vertically separated by 1.73 m , with an intermediate 5 cm layer of lead to absorb the soft component radiation in the air . each layer consists of an array of 1 m@xmath26 unit detectors , each with a 1 m@xmath271 m plastic scintillator viewed by a photomultiplier tube of 12.7 cm diameter . by counting pulses of the 2-fold coincidences between a pair of detectors on the upper and lower layers , we can record the rate of muons from the corresponding incident direction . the multi - directional muon telescope comprises various combinations between the upper and lower detectors . the field of view ( fov ) of the vertical channel has a broad geometrical aperture of @xmath28 ( @xmath29 ) . a precise measurement of lcs using muon detectors became possible only recently , when the gmdn capable of continuously monitoring the sunward imf direction was completed in march 2006 by adding another 9 m@xmath26 detector at kuwait university . unlike the other three detectors , the kuwait muon telescope ( hereafter kuwait ) consists of four horizontal layers of 30 proportional counter tubes ( pcts ) . each pct is a 5 m long cylinder with a 10 cm diameter having a 50-micron thick tungsten anode along the cylinder axis . a 5 cm layer of lead is installed above the detector to absorb the soft component radiation . the pct axes are aligned geographic east - west ( x ) in the top and third layers and north - south ( y ) in the second and bottom layers . the top and second layers form an upper pair , while the third and bottom layers form a lower pair . the two pairs are separated vertically by 80 cm . muon recording is triggered by the fourfold coincidence of pulses from all layers and the incident direction is identified from x - y locations of the upper and lower pct pairs . this is approximately equivalent to recording muons with two 30@xmath2730 square arrays of 10 cm@xmath2710 cm detectors separated vertically by 80 cm . the geometrical aperture of the fov in this detector is @xmath31 ( @xmath32 ) for the vertical channel . the muon count is recorded in each of 23@xmath2723=529 directional channels which cover 360@xmath1 of azimuth angle and 0@xmath1 to 60@xmath1 zenith ( for more detail of gmdn , see * ? ? ? the number of viewing directions available from the gmdn was drastically increased from the conventional one by installing a new recording system using the field programmable gate arrays ( fpgas ) , with which we can count muons for all possible coincidences between a pair of unit detectors on the upper and lower layers @xcite . if we have a square @xmath33 array of unit detectors aligned to the north - south ( or east - west ) direction in the @xmath7-th muon detector , it is possible to analyze the pressure corrected muon rates @xmath34 in total @xmath35 directional channels at the time @xmath5 , where positive ( negative ) @xmath36 and @xmath37 represent eastern ( western ) and northern ( southern ) incidence , respectively , with @xmath38 corresponding to the vertical incident . in order to visualize the directional distribution of gcr intensity , we plot @xmath39 as a function of @xmath36 and @xmath37 in a color - coded format , which we call the `` 2d map '' ( two dimensional map of the cosmic ray intensity ) . the number of directional channels used in this paper is 25 ( 5@xmath275 ) from hobart , 121 ( 11@xmath2711 ) from kuwait and 49 ( 7@xmath277 ) from so martinho , respectively . we can not apply this technique to nagoya data in this paper , as the fpga recording system was installed in the nagoya detector only in may , 2007 and not available for the fd event in december 2006 . in this paper , therefore , we analyze only the conventional 17 direction data from nagoya ( for the conventional directional channels in the gmdn , see * ? ? ? * ) . thus , the total number of the directional channels analyzed in this paper is 212 from four detector systems in the gmdn . as stated in 1 , we need to accurately remove from the data the contribution from the diurnal anisotropy ( da ) for precise analysis of the lc precursor . this was not possible for us before completing the gmdn with which we can precisely measure the da utilizing the global sky coverage of the network . by using the 24-hour trailing moving averages ( tmas ) of @xmath40 , @xmath41 , @xmath42 and @xmath43 in eq . ( [ eq01 ] ) , we calculate the contribution from the da to @xmath44 at a universal time _ t _ as @xmath45 where @xmath46 is the 24-hour tma of the contribution from the cosmic ray density ( @xmath9 ) and @xmath47 , @xmath48 , @xmath49 and @xmath50 are the 24-hour tmas of the best - fit parameters in eq . ( [ eq01 ] ) calculated as @xmath51 by subtracting @xmath52 in eq . ( [ eq02 ] ) from the observed @xmath39 , we get the directional intensity distribution @xmath53 free from the da as @xmath54 we can not use @xmath40 , @xmath41 , @xmath42 , @xmath43 in eq . ( [ eq02 ] ) instead of @xmath47 , @xmath48 , @xmath49 , @xmath50 , respectively , because the lc signature recorded in a large detector like so martinho makes the best - fit @xmath44 too close to the observed value and consequently leads to too small @xmath53 in eq . ( [ eq07 ] ) . in figure 1 g , @xmath39 , @xmath52 and @xmath53 for the vertical channel of so martinho are displayed by solid circles , a gray curve and open circles , respectively . it is seen that the gradual variation of @xmath39 due to the da ( @xmath55 ) is successfully removed in @xmath53 . we have calculated using 8-hour and 12-hour tmas for @xmath52 instead of 24-hour tma and have confirmed that the results remain essentially unchanged . note that @xmath53 in eq . ( [ eq07 ] ) is derived using the `` trailing '' average and is not affected by the variation occurring after @xmath5 . this is an important issue for possible real time forecasting . to visualize the lc signature more clearly by suppressing statistical fluctuation which is larger in the inclined channels , we also use , instead of @xmath53 , the `` significance '' @xmath56 defined as @xmath57 where @xmath58 is the count rate error for the @xmath59 directional channel in the @xmath7-th detector . figure 2a shows the 2d maps of @xmath60 in eq . ( [ eq08 ] ) for so martinho on december 13 and 14 during 36 hours preceding the ssc onset at 14:14 ut on december 14 ( doy 348.593 ) , whereas figure 2c shows @xmath60 for hobart in the same period . each small square panel in these figures displays @xmath60 observed in one hour in a color - coded format as a function of @xmath36 and @xmath37 on the horizontal and vertical axes denoting the east - west and north - south inclinations of the viewing direction , respectively . red color denotes the excess intensity in each ( @xmath61 ) pixel relative to the ominidirectional intensity in an entire fov , while blue color denotes the deficit intensity . in these figures , we set color scales ranging @xmath62 5 for so martinho and @xmath62 3 for hobart taking account of larger statistical error in hobart due to its smaller detection area . also shown by the white curve in each panel is the contour line of the pitch - angle measured from the sunward imf direction and calculated for cosmic rays incident to each ( @xmath61 ) pixel with the median primary energy appropriate to that pixel ( we assume @xmath63 rigidity spectrum for the lc anisotropy throughout this paper ) . it is seen that the zero pitch - angle region is first captured in the fov by so martinho in doys 347.354 - 347.563 ( 08:00 - 13:00 ut , december 13 ) , and then by hobart in doys 347.771 - 347.979 ( 18:00 - 23:00 ut , december 13 ) and by so martinho again in doys 348.354 - 348.563 ( 08:00 - 13:00 ut , december 14 ) according to the earth s spin . hereafter , these three 6-hour periods are referred to as the lc periods . in figure 2a for so martinho , there is a clear lc precursor seen as a deficit intensity at around @xmath64 pitch - angle with the minimum intensity about -0.8 % in doys [email protected] ( 09:00@xmath012:00 ut on december 14 ) during one of the lc periods . a striking feature of this event is that a weaker lc signature is also seen one day earlier in doys [email protected] ( 10:00@xmath012:00 ut on december 13 ) during another lc period . this suggests that the lc precursor already existed only 7 hours after the cme eruption at 02:54 ut on december 13 , when the ip shock driven by an icme located at 0.4 au from the sun @xcite . if this is the case , the signature also should have been observed during a period in between these two lc periods by other detectors viewing the eastern sky neighboring the fov of so martinho . this is actually seen in @xmath60 for hobart in figure 2c in doys [email protected] ( 18:00 , december 13@xmath000:00 ut , december 14 ) . in doys [email protected] ( 04:00@xmath007:00 ut on december 14 ) , a weak lc signature is also seen in figure 2e for kuwait viewing the sky in between the fovs of so martinho and hobart . it is rather surprising that the lc signature passing along the southern edge of the fov of kuwait can be seen even with such a small detector ( thanks to a better directional resolution of the muon hodoscope ) . we add to note that a large muon hodoscope grapes-3 in operation at ooty in southern india also recorded a clear lc precursor on @xmath009:00 lt ( 03:30 ut ) in december 14 , just before the signature recorded in kuwait in figure 2e @xcite[dr . h. kojima , private communication ] . these all give observational supports for the picture that the lc signature was continuously existing and was successively observed with the multiple detectors in the gmdn according to the earth s spin . there is also a clear intensity excess ( ex ) seen with the maximum intensity about + 0.5 % at @xmath65-@xmath66 pitch - angle particularly in doys 348.188 - 348.563 ( 04:00 - 13:00 ut on december 14 ) in figs . 2a and 2c , partly overlapping the lc signature in figure 2a for so martinho . such an intensity excess is expected from the ground based measurement of gcrs reflected by the ip shock approaching the earth @xcite . the numerical model for gcr transport across the shock also predicts such an ex anisotropy superposed on the lc distribution ( paper 1 ) . the fractional energy gain for a gcr traveling along the imf with an energy @xmath67 after the reflection by the ip shock approaching with a velocity @xmath68 is calculated as @xmath69 where @xmath70 is the angle between the shock normal and the upstream imf and @xmath71 is the speed of light . the intensity excess expected from this energy gain is estimated as @xmath72 where @xmath73 is the power - law index of the gcr energy spectrum , which we set to 2.7 . by using the ip shock velocity ( 1030 km / s ) at 1 au @xcite for @xmath68 and by tentatively assuming @xmath74 , we get @xmath0 + 0.9 % ( + 1.6 % ) for @xmath75 . we confirm that there is no notable excess or deficit intensity in @xmath60 except that in the periods mentioned above . in the following subsection , we will present detailed comparisons between the observation and the theoretical model for the lc and ex anisotropies . figure 3 shows the pitch - angle distribution of the gcr intensity . open circles in this figure display a sample numerical pitch - angle distribution near an oblique interplanetary shock taken from fig.5 of paper 1 . in this figure , the gcr intensity is plotted as a function of the pitch - angle cosine ( @xmath25 ) . a sharp lc around @xmath76 ( zero pitch - angle ) and a broad excess intensity around @xmath77 ( @xmath78 pitch - angle ) are both evident in this figure . we model this distribution by a superposition of the lc and ex anisotropies , shown by plus signs and crosses in figure 3 , respectively , as given by @xmath79 where @xmath80 and @xmath81 is the pitch - angle measured from the sunward imf direction , @xmath82 is the rigidity of gcrs in gv , @xmath83 ( @xmath84 ) and @xmath85 ( @xmath86 ) are amplitudes of the lc and ex anisotropies , respectively , and @xmath87 is the angle parameter denoting the width of the lc anisotropy . the @xmath63 dependence of the lc amplitude on @xmath82 is assumed to follow the average @xmath82-dependence of the size of the fd . it is seen in figure 3 that the model anisotropy shown by a solid curve reproduces well the numerical pitch - angle distribution by paper 1 . by using @xmath88 defined in eq . ( [ eq11 ] ) , we calculate the expected intensity @xmath89 for the @xmath59 pixel in the @xmath7-th detector , as @xmath90 where @xmath91 , representing the number of muons produced by primary particles with rigidity @xmath82 and recorded in the @xmath59 pixel in the @xmath7-th detector , is calculated by utilizing the response function of muons in the atmosphere to primary particles @xcite and @xmath92 represents the minimum ( cut - off ) rigidity of primary cosmic rays to produce muons recorded in the @xmath59 pixel . for detectors ( nagoya , hobart and so martinho ) in which each @xmath59 pixel has a wide fov resulting from the 2-fold coincidence between 1 m@xmath26 unit detectors , we perform the integration in the last term for each combination of the virtual [email protected] m@xmath26 sub - detectors and then sum all values to get an integration . we perform only one integration for each @xmath59 pixel in kuwait . the angular resolution of this integration is , therefore , 3.3@xmath1 for nagoya , hobart and so martinho and 7.1@xmath1 for kuwait . note that the ex anisotropy , which is essentially the first order anisotropy along the imf as described in eq . ( [ eq11 ] ) , is included in @xmath93 , @xmath94 and @xmath95 , while the lc amplitude @xmath83 explicitly appears in the model intensity in eq . ( [ eq13 ] ) . we will derive later @xmath85 , therefore , by calculating the component of @xmath96 parallel to the imf . we repeat the calculation of @xmath89 in eq . ( [ eq13 ] ) changing @xmath87 in every @xmath97 step and determine the best - fit parameters @xmath83 , @xmath98 , @xmath96 which minimize @xmath99 defined as @xmath100 where @xmath101 is the hourly residual of the best - fitting at the time @xmath102 and @xmath103 and @xmath104 are the total number of directional channels and hours used for the best - fit calculations , respectively . note that all the best - fit parameters @xmath83 , @xmath98 , @xmath96 at each time @xmath5 are uniquely determined by the linear least - square method for each value of @xmath87 . we carry out this best - fit calculation for a total of 36 hours ( doys [email protected] ) preceding the ssc onset and obtain the best - fit parameters with the minimum residual of @xmath105 and @xmath106 . as we did for deriving @xmath60 in eq . ( [ eq08 ] ) , we subtract @xmath52 in eq . ( [ eq02 ] ) from @xmath89 and get the reproduced intensity distribution @xmath107 , as @xmath108 the 2d maps ( @xmath109 ) reproduced from the best - fit parameters are shown in figs.2b , 2d and 2f for so martinho , hobart and kuwait , respectively . it is seen that both the lc and ex features are successfully reproduced with the best - fit parameters , although we do nt see such a clear resemblance for kuwait in figure 2f due to the poor statistical significance of the data from this small muon hodoscope . figure 4 displays the best - fit parameters , each as a function of time measured from the ssc . in figure 4a , the hourly residual @xmath101 is shown by black circles , together with the residual in the conventional best - fit analyses in figure 1 shown by gray circles . it is seen that the best - fitting is improved by the new model in eq . ( [ eq13 ] ) as indicated by the reduced residual , particularly when the best - fitting in figure 1 fails with large residual due to the lc signatures observed by the gmdn . black circles in figure 4b display the lc amplitude ( @xmath83 ) obtained for the lc periods when the zero pitch - angle is monitored by the gmdn , while gray circles display the amplitude obtained when the zero pitch - angle is out of the fov of the gmdn . there is a large fluctuation seen in @xmath83 in this figure because we can not make accurate best - fitting when the lc is out of the fov . it is clear , however , that the lc amplitude ( @xmath83 ) gradually decreases toward @xmath110 % at the ssc onset . this lc amplitude is almost twice the fd size of @xmath0 - 3 % ( see figure 1c ) , indicating that the maximum intensity depression behind the ip shock is much larger than the fd size recorded at the earth . also shown in the remaining panels are the best - fit parameters @xmath98 and @xmath96 transformed to the gse coordinate system . in figs.4d-4f , we plot parameters ( @xmath111 , @xmath112 , @xmath113 , @xmath114 ) respectively calculated , as @xmath115 after subtracting the 24 hour tmas of the conventional best - fit parameters representing the contribution from the diurnal anisotropy . we note @xmath112 and @xmath113 in figs.4d and 4e showing positive and negative deviations from zero , respectively , during @xmath010 hours preceding the ssc . this is consistent with the enhancement of the excess intensity from the sunward imf direction , as expected from the measurement of the shock reflected particles . this is confirmed in figure 4 g showing the anisotropy from the sunward imf direction . this parallel anisotropy shows the maximum deviation of @xmath01 % at the ssc onset which is consistent with the expectation from the measurement of the shock reflected particles as discussed in eq . ( [ eq10 ] ) . we finally note the density ( @xmath111 ) also showing a positive deviation similar to the parallel anisotropy . the maximum deviation is @xmath01 % at 0 hour from the ssc and is almost the same as the maximum deviation of the parallel anisotropy , giving a support to our model function of the ex anisotropy in eq . ( [ eq11 ] ) , wherein the second term of the right hand side contains two terms independent and dependent on the pitch - angle ( @xmath81 ) with the same amplitude at @xmath116 . in the next section , we will compare these best - fit parameters with the theoretical predictions by paper 1 and discuss their physical implications . we have analyzed cosmic ray precursors of a forbush decrease ( fd ) observed on december 2006 with the gmdn monitoring the directional intensity of @xmath050 gev galactic cosmic rays . this forbush decrease was caused by an ip shock associated with a cme which erupted from the sun shortly after an x3.4 flare on december 13 and arrived at the earth in december 14 . an intense geomagnetic storm was also recorded during this fd with the peak kp index of 8 + . there was no other ssc and/or interplanetary disturbances recorded at the earth during a period between the onsets of the flare and the ssc , which is analyzed in this paper . by using the 2d maps of the cosmic ray intensity produced by removing the contribution from the diurnal anisotropy , we found a clear signature of the lc anisotropy which was observed as a deficit intensity from the sunward imf direction . the significant lc signature was first recorded by hobart at @xmath117 hours before the ssc and then by so martinho with a larger amplitude at @xmath110 hours . a weak lc signature was also seen in kuwait viewing the sky in between fovs of hobart and so martinho . the `` half - width '' opening angle @xmath118 of the lc is defined in paper 1 as the pitch - angle at which the intensity decrease ( relative to the omnidirectional intensity ) has reached half its maximum value . according to this definition , @xmath118 is calculated to be @xmath119 using @xmath106 obtained in 3.2 . by linearly interpolating the numerical relationship between the loss - cone width ( @xmath118 ) and the angle between the shock normal and the upstream magnetic field ( @xmath70 ) given by paper 1 ( see table 2 in paper 1 ) , we find @xmath120 corresponding to @xmath121 assuming the `` local '' slope of the power spectrum of the imf turbulence ( @xmath122 ) appropriate for the muon detector . this @xmath70 is less than half of @xmath123 obtained by @xcite(see 2 ) . one possible source of this discrepancy is that a large error might associate with the non - linear best - fit parameter @xmath87 obtained in 3.2 . if we evaluate the error by calculating @xmath87 with which @xmath124 reaches at @xmath125 , that is , + 1.0 more than @xmath124 with minimum @xmath99 , @xmath87 with the error is estimated to be @xmath126 which corresponds to @xmath127 . this @xmath70 with a large error is not inconsistent with @xmath123 by @xcite . we are not sure whether this error estimation is appropriate or not , but we also carried out the best - fit calculation in 3.2 with @xmath87 fixed at 23@xmath1 corresponding to @xmath123 and confirmed that the minimum residual @xmath99 and the best - fit parameters except @xmath87 are almost unchanged from those in figure 4 . the reproduced 2d maps were also very similar to those in figs.2b , 2d and 2f . this implies that @xmath70 can not be determined accurately by the present analysis method for the gmdn data . one reason for such a large error in @xmath70 ( or @xmath87 ) is the poor angular resolution of the observed incident direction in detectors ( hobart and so martinho ) with which the lc anisotropy was recorded . this is different from another lc event on october 2003 which was observed with a large muon hodoscope with the better angular resolution @xcite . it is also noted that the dependence of @xmath118 ( i.e. @xmath87 ) on @xmath70 becomes very small for @xmath70 above @xmath128 according to paper 1 . this means that one has to measure @xmath87 very accurately for precisely determining @xmath70 particularly when @xmath70 is large in case of the quasi - perpendicular shock . a striking feature of this event is that a weak lc signature was also recorded by so martinho more than a day earlier on december 13 at @xmath129 hours . to examine the lead time of this lc precursor , we fit to @xmath83 in figure 4b an exponential function of time @xmath5 ( measured from the ssc ) defined as , @xmath130 and obtain @xmath131 % and @xmath132 hours . for this fitting , we used only @xmath83 obtained when the zero pitch - angle is monitored by the gmdn ( as displayed by solid circles in figure 4b ) . this lead time @xmath133 for 30 gev particles corresponds to the `` decay length '' @xmath37 of the lc , as @xmath134 with @xmath135 and @xmath136 km / s @xcite . by using a ratio @xmath137 derived for @xmath122 and @xmath138 from interpolating table 2 in paper 1 , we estimate the parallel mean free path for the pitch - angle scattering ( @xmath139 ) to be @xmath02.6 au , which is almost two times longer than 1.5 au estimated by paper 1 for the muon detector . this indicates that the imf was more quiet in this event than a typical power spectrum assumed for the imf turbulence by paper 1 . these conclusions with @xmath122 remain unchanged even if we choose @xmath140 , with which we get @xmath141 , @xmath142 au and @xmath143 au . we have also found the excess intensity from the sunward imf direction clearly observed during @xmath010 hours preceding the ssc . we have shown that this excess intensity is consistent with the measurement of the particles accelerated by the head - on collisions with the approaching shock . this is the first detailed observation of the precursor due to the shock reflected particles with muon detectors . it is interesting to note that there is also an enhancement seen in the anisotropy perpendicular to the imf in figure 4h . we think that this perpendicular anisotropy is probably arising from the drift anisotropy expressed by the vector product between the imf and the spatial gradient of the cosmic ray density , which directs toward the shock due to the higher population of the reflected particles at the shock . by using the observed perpendicular anisotropy together with the imf data , therefore , we can deduce the temporal variation of the cosmic - ray density gradient and infer the geometry of the ip shock . in our separate papers , we actually succeeded in deriving the geometry of the magnetic flux rope in icmes by this method @xcite . the precursor observed with the long lead time , like the event analyzed in this paper , is of particular importance for the possible space weather forecast using cosmic ray measurements . for the accurate observation of such event , however , we need further improvement of the gmdn . first , the incomplete sky - coverage of the gmdn allowed us to analyze the best - fit parameters during only half a period in figure 4 , when the sunward imf direction was in the fov of the gmdn . second , the insufficient detection areas of hobart and kuwait increased the statistical error and introduced a non - uniformity into the response of the gmdn to the lc precursor . we believe that such a non - uniform response also contributes to the large fluctuations in the best - fit parameters in figure 4 . we are now planning to overcome these technical problems by expanding the detection areas of hobart and kuwait and also by installing new detector(s ) to expand the fov of the gmdn preparing for the next solar maximum expected at around the year 2013 . this work is supported in part by nasa grant nnx 08aq01 g , and in part by grants - in - aid for scientific research from the ministry of education , culture , sports , science and technology in japan and by the joint research programs of the solar - terrestrial environment laboratory , nagoya university . the observations with the kuwait muon telescope are supported by the kuwait university grant sp03/03 . we thank n. f. ness for providing _ ace _ magnetic field data via the _ ace _ science center . barnden , l. r. 1971 , , 18 , 165 - 171 belov , a. v. et al . 1995 , proc . 24th internat . cosmic ray conf . , 4 , 888 - 891 belov , a. v. et al . 2001 , proc . 27th internat . cosmic ray conf . , 9 , 3507 - 3510 dorman , l. i. et al . 1995 , proc . 24th internat . cosmic ray conf . , 2 , 425 - 428 fushishita , a. et al . 2010 , advances in geosciences , in press ( arxiv0912.4859 ) kuwabara , t. et al . 2004 , , 31 , l19803 - 1@xmath05 kuwabara , t. et al . 2009 , , 114 , a05109 - 1@xmath010 leerungnavarat , k. , ruffolo , d. , & bieber , j. w. 2003 , , 593 , 587 - 596 liu , y. , et al . 2008 , , 689 , 563 - 571 munakata , k. , et al . 2000 , , 105 , 27457 - 27468 munakata , k. et al . 2005 , , 32 , l02s04 - 1@xmath04 murakami , k. et al . 1979 , nuovo cim . , 2c , 635 - 651 nahashima , k. , et al . 1992 , , 40 , 1109 - 1137 nonaka , t. et al . 2006 , , 74 , 052003 - 1@xmath015 okazaki , y. , et al . 2008 , , 681 , 693 - 707 parker , e. n. 1958 , , 128 , 664 - 676 vins , a. f. , & scudder , j. d. 1986 , , 91 , 39 - 58 yasue , s. , et al . 2003 , proc . 28th internat . cosmic ray conf . , 6 , 3461 - 3464

we analyze the precursor of a forbush decrease ( fd ) observed with the global muon detector network on december 14 , 2006 . an intense geomagnetic storm is also recorded during this fd with the peak kp index of 8 + . by using the `` two - dimensional map '' of the cosmic ray intensity produced after removing the contribution from the diurnal anisotropy , we succeed in extracting clear signatures of the precursor . a striking feature of this event is that a weak loss - cone signature is first recorded more than a day prior to the storm sudden commencement ( ssc ) onset . this suggests that the loss - cone precursor appeared only 7 hours after the coronal mass ejection ( cme ) eruption from the sun , when the interplanetary ( ip ) shock driven by the interplanetary coronal mass ejection ( icme ) located at 0.4 au from the sun . we find the precursor being successively observed with multiple detectors in the network according to the earth s spin and confirmed that the precursor continuously exists in space . the long lead time ( 15.6 hours ) of this precursor which is almost twice the typical value indicates that the imf was more quiet in this event than a typical power spectrum assumed for the imf turbulence . the amplitude ( -6.45 % ) of the loss - cone anisotropy at the ssc onset is more than twice the fd size , indicating that the maximum intensity depression behind the ip shock is much larger than the fd size recorded at the earth in this event . we also find the excess intensity from the sunward imf direction clearly observed during @xmath010 hours preceding the ssc onset . it is shown that this excess intensity is consistent with the measurement of the particles accelerated by the head - on collisions with the approaching shock . this is the first detailed observation of the precursor due to the shock reflected particles with muon detectors .

the genus dirofilaria consists of at least 2 species of epidemiologically important human pathogens , dirofilaria immitis ( leidy , 1856 ) and dirofilaria ( nochtiella ) repens ( railliet and henry , 1911 ) . these worms commonly cause dirofilariasis in dogs , cats , and wild carnivores and are globally recognized as etiological agents of zoonotic infections in humans , transmitted by vectors / mosquitoes ( mosquito - borne zoonosis ) , including anopheles , culex , and aedes . d. immitis , that causes dirofilariasis in dogs , cats , and humans , tends to distribute in temperate and tropical regions of the world , while d. repens infections are limited in asia and europe , including vietnam . however , to our knowledge , no previous report of human infection on the posterior thoracic region due to d. repens has been reported . here , we report a rare case of subcutaneous posterior thoracic infection caused by d. repens diagnosed by morphology and molecular analysis . on 14 march 2011 , a 34-year old woman , visited a surgeon at a clinic in a suburban area of hanoi , vietnam with a painful swelling and itchy and palpable nodule on her posterior thoracic wall . she lived in an area where dogs and cats were outdoors allowed and several times exposed to mosquito bites . three weeks before , on 26 february 2011 , she suddenly noticed a swollen , tangible , subcutaneous nodule of the similar appearance as the current one at the same site but it has spontaneously disappeared days after . during the physical examination , a smooth , tangible , slightly movable , painful nodule of 12 cm in size was touchable under the skin on the posterior part of the thoracic wall , correlative with the vertebrae d11 . the overlying skin was normal without any overt signs of inflammation and axillary lymph nodes were not enlarged . routine laboratory test showed red blood cells of 3.910/mm , white blood cells of 6.110/mm ( the percentage of neutrophils , lymphocytes , and eosinophils were 60% , 20.7% , and 11.5% , respectively ) . no microfilaraemia was detected at this time in her blood samples by microscopy . by local excision under anesthesia , after opening the capsule , a thin thread - like worm was noted and captured in 3 fragments which then were fixed in 10% formalin for morphological examinations and a piece was preserved in 70% ethanol for molecular identification . a long , slender , whitish worm ( fig . 1a , b ) excised from the nodule was approximately 10.5 cm in length and about 400 m in its largest width , typical of the description of a female d. repens . microscopy revealed a thick laminated cuticle with the characteristic longitudinal ridges and cross - striations ( fig . the anterior end was bluntly rounded and was of greater diameter than the posterior end ( fig . 1a ) . the body cavity contained a female reproductive system , with the bulbous vulva of about 1 mm from the anterior end , and ended in a uterine bifurcation . following the surgical removal , symptoms were quickly resolved , and the patient was recovered without any consequences after a long - time followed up . total genomic dna was extracted from an ethanol - fixed fragment of the excised worm by qiaamp dna mini kit ( qiagen , hilden , germany ) . pcr of a portion of the mitochondrial cytochrome c oxidase i ( cox1 ) gene was performed using the primer pairs ( forward dimref , 5 gatgttgcctttgatattggg 3 ; and reverse dimrer , 5 accagcwgtwyacatatgatgacc 3 ) designed based on the alignment of cox1 sequences of both dirofilaria repens and d. immitis available in genbank . the pcr , of 50 l containing 25 l pcr master mix from promega , 2 l of each primer ( 10 pmol/l ) , 2.5 l dmso , 16.5 l pure water , and 1 l template ( 100 ng/l ) , was carried out in a mj thermal cycler ptc-100 ( mj research , watertown , massachusetts , usa ) with initiation at 94c for 4 min , then 35 cycles including denaturation at 94c for 30 sec , annealing at 55c for 30 sec , extension at 72c for 1 min ; and a final cycle of 7 min at 72c to obtain a pcr product of 643 bp , and a 576 bp portion was used for alignment for taxonomic identification . to support the identification , the presence of 16s rrna sequence of wolbachia sp . was obtained by pcr with the primer pairs designed hereby in this study , based on 16s ribosomal sequence of wolbachia pipientis available in genbank ( wp16f : 5-ccacactggaactgagatacg-3 and wp16r : 5-tgtagccaccattgtagcac-3 ) . the parasite recovered from the subcutaneous tissue of our patient was identified as d. repens on the basis of the morphology and molecular methods . the external longitudinal cuticular ridges differentiate d. repens from d. immitis , the other important human pathogens of the genus dirofilaria . however , identification of dirofilaria spp . based only on the morphology is difficult ; therefore , molecular methods supported to determine the species . molecular identification was carried out by using primers of cox1 and of nuclear internal transcribed spacer 2 ( its2 ) , and additionally 16s rrna identification of the endosymbiont w. pipientis commonly co - existing with dirofilaria spp . . nucleotide cox1 sequence determination of the vietnamese dirofilarial nematode revealed 96% identity to those of the italian / albanian d. repens strains ( genbank no . am749230-am749234 ; dq358814 ; aj271614 ; jf461458 ) ; and 89% to d. immitis ( genbank : am749226 ; am749227 ; am749229 ; aj537512 ; eu159111 ; eu163945 ; kc107805 ; aj271613 ; dq358815 ; fn391553 ) of different geographic origins . the cox1 amino acid sequence showed 99 - 100% similarity to all of the d. repens samples , while only 96% to d. immitis . high intraspecific variability was observed in d. repens cox1 sequences , while those of d. immitis species samples were identical ( 100% identity to each other ) , regardless of geographical distribution . phylogenetic tree inferred from the 576 bp mitochondrial cox1 sequence of 20 strains including d. repens collected from the subcutaneous posterior thoracic nodule in this study , and 8 other d. repens , 10 d. immitis , and a nematode species o. lupi ( as an out - group ) indicated that the vietnamese filarial sample clustered with cox1 sequences of d. repens , in a group , that was completely separated from the d. immitis and from o. lupi out - group sequences ( fig . the genetic distances among the newly identified d. repens of vietnamese patient and reference strains were calculated based on the kimura 2-parameter model using mega5.2 software ( table 1 ) . the genetic distances among the dirofilaria strains within each of d. repens or d. immitis , respectively , were very low , ranging from 0.000 to 0.039 for d. repens ( table 1 , no . 1 - 9 ) and no variation ( 0.000 ) for d. immitis ( table 1 , no . there was relatively high taxonomic genetic distance , ranging from 0.103 to 0.117 between d. repens and d. immitis ( table 1 , no . 1 - 9 10 - 19 ) ; and 0.109 to 0.125 between dirofilaria spp . and a nematode o. lupi , used for an out - group ( table 1 , no . 20 ) . by amplification with the primer pairs based on 16s ribosome , a sequence of 918 nucleotides was obtained and compared with those of the previously known w. pipientis 16s rrna sequences , i.e. , one amplified from a d. repens ( italian strain , genbank : aj276500 ) and several from d. immitis strains ( z49261 , af088187 , and af487892 ) , available in genbank . the comparative sequence analysis revealed 96 - 97% identity among the endosymbionts and accurately confirmed the presence of the endosymbiont w. pipientis in the vietnamese d. repens . the species identification of this vietnamese d. repens , thus , was completely accurate using both the mitochondrial and nuclear nucleotide analysis and distance - based / phylogenetic approaches . to date , of 3,192 human dirofilariasis cases reported worldwide , 372 pulmonary and 1,410 subcutaneous / ocular infections were documented ; and due to aberrant migration of the microfilariae , dirofilaria spp . lesions caused by d. immitis are focused mainly in the heart ( dogs and cats ) and in the lungs and skin ( in humans , presented as pulmonary and subcutaneous forms ) , whilst d. repens tends to localize in multiple organs , mainly in the subconjunctiva , lungs and coronary artery [ 11 - 13 ] , soft tissues as the breast , penis , spermatic cord , epididymis , and scrotum [ 14 - 17 ] , brain , liver , lymph nodes , muscles , and anterolaterial neck [ 5,18 - 21 ] , and rare places , i.e. , causing intravitreous infection in humans . to our knowledge , this is the first case of human infection on subcutaneous posterior thoracic region due to d. repens reported . in humans , normally a single subcutaneous nodule and lesions have been developed during weeks and described as little granulomatous inflammatory lesions . in the case reported here , the time and the means of transmission by which the patient caught d. repens infection is unclear , probably by mosquitoes bites ( infected by larvae from the outdoor dogs / cats wandering in the suburb ) . unfortunately , no surveys of microfilariae in dogs / cats have been conducted yet . to date , 12 dirofilaria infections of the conjunctiva ( eye subcutaneous and subconjuctiva ) have been detected in vietnam . the case of posterior thoracic localization hereby presented is a rare record and all of the vietnamese infections documented are autochthonous , caused by solitary d. repens . in our case , molecular classification of the causal agent confirmed it to be d. repens using complex approaches , including morphological , historic , mitochondrial cox1 , nuclear its-2 , distance - based / phylogenetic analysis , and supported by the endobiosymbiont , w. pipientis , 16s - rrna based identification . regarding high risk of human dirofilariasis ( imported dirofilaria is not exclusive ) in vietnam , detailed national surveys involving pathological , epidemiological and etiological information on dirofilaria species , animal / host reservoirs , vectors / mosquitoes , provincial distribution and improvement of routine laboratory diagnostic approaches , including molecular identification / discrimination of zoonotic dirofilaria are needed for early control of the emerging dirofilarial infections .

the emergence of dirofilarial infections in asia including vietnam is a clinically significant threat to the community . we here report a rare case of subcutaneous dirofilaria repens infection on the posterior thoracic wall in a young woman presenting a painful , itchy , and palpable nodule . the adult worm was identified by mitochondrial cox1 and nuclear its-2 sequence determination . the diagnosis was additionally confirmed by 16s rrna sequencing of the endosymbiont wolbachia pipientis commonly co - existing with d. repens . this is a rare case of subcutaneous human infection on the posterior thoracic region caused by d. repens .

the notion of lyapunov function plays a very important role in design and verification of dynamical systems , in particular , in performance analysis , stability analysis and controller synthesis of complex dynamical and controlled systems @xcite . in recent years , people realized that the notion is quite helpful to safety verification of hybrid and cyber - physical systems as well @xcite . however , the following two issues hinder the application of lyapunov functions in practice . firstly , it is actually not necessary for the first - order lie derivative of a lyapunov function to be strictly negative to guarantee asymptotic stability , which is shown by _ lasalle s invariance principle _ @xcite . such a condition could limit to scale up the method . secondly , in general there is no effective way so far to find lyapunov functions , although many methods have been proposed by different experts using their field expertise . to address the above two issues , in this paper , we first generalize the standard concept of lyapunov function to _ relaxed lyapunov function _ ( rlf ) for asymptotic stability analysis . compared with the conventional definition of lyapunov function , the first non - zero higher order lie derivative of rlf is required to be negative , rather than its first - order lie derivative . such a relaxation extends the set of admissible functions that can be used to prove asymptotic stability . another contribution of this paper is that we present a complete method to automatically discovering polynomial rlfs for polynomial dynamical systems ( pdss ) . the basic idea of our method is to predefine a parametric polynomial as a template of rlf first , and then utilize the lie derivatives of the template at different orders to generate constraint on the parameters , and finally solve the resulting constraint . our method is complete in the sense that it is able to generate all polynomial rlfs by enumerating all polynomial templates for any pds . * related work . * in @xcite , the same terminology relaxed lyapunov function " is used , with a different definition . the idea of applying higher order lie derivatives to analyze asymptotic stability is not new . for example , in @xcite the authors resorted to certain linear combinations of higher order lie derivatives with non - negative coefficients such that the combination is always negative . this method could be included in the framework of vector lyapunov functions method @xcite . our method is essentially different from theirs because an rlf only requires its first non - zero higher order lie derivative to be negative . in the literature , there is a lot of work on constructing lyapunov functions . for instance , in @xcite , methods for constructing common quadratic lyapunov functions for linear systems were proposed , which were generalized in @xcite and @xcite for nonlinear systems wherein the generated lyapunov functions are not necessarily quadratic . another useful technique is the linear matrix inequality ( lmi ) method introduced in @xcite and @xcite , which enables us to utilize the results of numerical optimization for discovering piecewise quadratic lyapunov functions . based on sums - of - squares ( sos ) decomposition and semi - definite programmng ( sdp ) @xcite , a method for constructing piecewise high - degree polynomial and piecewise non - polynomial lyapunov functions was proposed in @xcite and @xcite . the sos and sdp based method was also used in @xcite to search for control lyapunov functions for polynomial systems . in @xcite , the authors proposed a new method for computing lypunov functions for polynomial systems by solving semi - algebraic constraint using their tool discoverer @xcite . approaches to constructing lyapunov functions beyond polynomials using radial basis functions were proposed in @xcite . our method has the following features compared to the related work . firstly , it generates relaxed lyapunov functions rather than conventional lyapunov functions . secondly , it is able to discover all polynomial rlfs by enumerating all polynomial templates for any pds , whereas the krasovskii s method @xcite and zubov s method @xcite can only produce lyapunov functions of special forms . thirdly , the lmi method and sos method are numerical , while our method is symbolic , which means it could provide a mathematically rigorous framework for the stability analysis of polynomial dynamical systems . * structure : * the rest of this paper is organized as follows . in section [ sec : foundations ] , the theoretical foundations are presented . section [ sec : rlf ] shows a new criterion for asymptotic stability using the notion of relaxed lyapunov functions . in section [ sec : main - result ] we present a sound and complete method and a corresponding algorithm for automatically discovering polynomial rlfs on polynomial dynamical systems . the method is illustrated by an example in section [ sec : example ] . finally , we conclude this paper and discuss possible future work in section [ sec : conclusion ] . in this section , we present the fundamental materials based on which we develop our method . let @xmath0 be an algebraic field , and @xmath1 $ ] denote the polynomial ring over @xmath0 . customarily , let @xmath2 denote the @xmath3-tuple @xmath4 . then @xmath5 $ ] can be written as @xmath6 $ ] for short , and a polynomial in @xmath7 $ ] can simply be written as @xmath8 or @xmath9 . particularly , @xmath0 will be taken as the real field @xmath10 in this paper , and @xmath2 takes value from the @xmath3-dimensional euclidean space @xmath11 . in our method we will use polynomials with undetermined coefficients , called parametric polynomials or _ templates_. such polynomials are denoted by @xmath12 , where @xmath13 is a @xmath14-tuple of parameters . a parametric polynomial @xmath12 in @xmath15 $ ] with real parameters can be seen equivalently as a regular polynomial in @xmath16 $ ] . given @xmath17 , we call the polynomial @xmath18 resulted by substituting @xmath19 for @xmath20 in @xmath12 an _ instantiation _ of @xmath12 . the following are some fundamental results relative to polynomial ideals , which can be found in @xcite . a subset @xmath21 $ ] is called an ideal iff 1 . @xmath22 ; 2 . if @xmath23 , then @xmath24 ; 3 . if @xmath25 , then @xmath26 for any @xmath27 $ ] . it is easy to check that if @xmath28 $ ] , then @xmath29.\ , h_i \in \mathbb{k}[{\mathbf{x}}]\}\ ] ] is an ideal . in general , we say an ideal @xmath30 is _ generated _ by polynomials @xmath31 $ ] if @xmath32 where all @xmath33 for @xmath34 $ ] are called _ generators _ of @xmath30 . in fact , we have [ basis ] every ideal @xmath30 @xmath35 $ ] has a finite generating set . that is , @xmath36 for some @xmath37 $ ] . from this result , it is easy to see that [ acc ] for any ascending chain @xmath38 of ideals in polynomial ring @xmath6 $ ] , there must be an @xmath39 such that for all @xmath40 , @xmath41 . we summarize some fundamental theories of dynamical systems here . for details please refer to @xcite . we consider autonomous dynamical systems modeled by first - order ordinary differential equations @xmath42 where @xmath43 and @xmath44 is a vector function from @xmath45 to @xmath45 , which is also called a vector field in @xmath45 . in this paper , we focus on special nonlinear dynamical systems whose vector fields are defined by polynomials . [ dfn : ads ] suppose @xmath46 in ( [ eq : ode ] ) . then ( [ eq : ode ] ) is called a _ polynomial dynamical system _ ( pds for short ) if for every @xmath47 , @xmath48 is a polynomial in @xmath49 $ ] . if @xmath44 satisfies the local lipschitz condition , then given @xmath50 , there exists a unique solution @xmath51 of ( [ eq : ode ] ) defined on @xmath52 with @xmath53 s.t . @xmath54 we call @xmath51 on @xmath55 the _ trajectory _ of ( [ eq : ode ] ) starting from initial point @xmath56 . let @xmath57 be a function from @xmath45 to @xmath58 . suppose both @xmath59 and @xmath44 are differentiable in @xmath2 at any order @xmath60 . then we can inductively define the _ lie derivatives _ of @xmath59 along @xmath44 , i.e. @xmath61 for @xmath62 , as follows : * @xmath63 , * @xmath64 , for @xmath65 , where @xmath66 is the inner product of two vectors , i.e. @xmath67 polynomial functions are sufficiently smooth , so given a pds @xmath68 and a polynomial @xmath9 , the vector field @xmath44 of @xmath68 satisfies the local lipschitz condition , and the higher order lie derivatives of @xmath9 along @xmath44 are well defined and are all polynomials . for a parameterized polynomial @xmath12 , we can define @xmath69 by seeing @xmath20 as undetermined constants rather than variables . in the sequel we will implicitly employ these facts . [ eg : lie - derv ] suppose @xmath70 and @xmath71 . then @xmath72 , @xmath73 , @xmath74 , @xmath75 . the following are classic results of stability of dynamical systems in the sense of lyapunov . a point @xmath76 is called an _ equilibrium or critical point _ of ( [ eq : ode ] ) if @xmath77 . we assume @xmath78 w.l.o.g from now on . suppose @xmath79 is an equilibrium of ( [ eq : ode ] ) . then * @xmath79 is called lyapunov stable if for any @xmath80 , there exists a @xmath81 such that if @xmath82 , then for the corresponding solution @xmath51 of ( [ eq : ode ] ) , @xmath83 for all @xmath84 . * @xmath79 is called asymptotically stable if it is lyapunov stable and there exists a @xmath81 such that for any @xmath82 , the corresponding solution @xmath51 of ( [ eq : ode ] ) can be extended to infinity and @xmath85 . lyapunov first provided a sufficient condition , using so - called _ lyapunov function _ , for the lyapunov stability as follows . [ lya]suppose @xmath86 is an equilibrium point of ( [ eq : ode ] ) . if there is an open set @xmath87 with @xmath88 and a continuous differentiable function @xmath89 such that 1 . @xmath90 , 2 . @xmath91 for all @xmath92 and 3 . @xmath93 for all @xmath94 , then @xmath79 is a stable equilibrium of ( [ eq : ode ] ) . moreover , if condition ( c ) is replaced by 1 . @xmath95 for all @xmath96 , then @xmath79 is an asymptotically stable equilibrium of ( [ eq : ode ] ) . such @xmath97 is called a _ lyapunov function_. for asymptotic stability , we have barbashin - krasovskii - lasalle ( bkls ) principle which relaxes condition @xmath98 in theorem [ lya ] . [ bkls ] suppose there exists @xmath97 satisfying the conditions ( a ) , ( b ) and ( c ) in theorem [ lya ] . if the set @xmath99 does not contain any trajectory of the system besides the trivial trajectory @xmath100 , then @xmath79 is asymptotically stable . inspired by theorem [ bkls ] , we will define _ relaxed lyapunov function _ ( rlf for short ) in the subsequent section , which guarantees the asymptotic stability of an equilibrium of a dynamical system . intuitively , a lyapunov function requires that any trajectory starting from @xmath101 can not leave the region @xmath102 . while , in the asymptotic stability case , the corresponding @xmath97 forces any trajectory starting from @xmath101 to transect the boundary @xmath103 towards the set @xmath104 . it is clear that @xmath105 is only a sufficient condition to guarantee asymptotic stability . when a point @xmath2 satisfies @xmath106 , the transection requirement may still be met if the first non - zero higher order lie derivative of @xmath97 at @xmath2 is negative . to formalize this idea , we give the following definition . [ dfn : point - rank ] let @xmath107 be the set of positive natural numbers . given sufficiently smooth function @xmath59 and vector filed @xmath44 , the _ pointwise rank _ of @xmath59 w.r.t . @xmath44 is defined as the function @xmath108 given by @xmath109 [ eg : point - rank ] for @xmath70 and @xmath71 , by example [ eg : lie - derv ] , we have @xmath110 , @xmath111 , @xmath112 . [ dfn : transet]given sufficiently smooth function @xmath59 and vector field @xmath44 , the _ transverse set _ of @xmath59 w.r.t @xmath44 is defined as @xmath113 intuitively , @xmath114 consists of those points at which the first non - zero high order lie derivative of @xmath59 along @xmath44 is negative . now we can relax condition @xmath98 in theorem [ lya ] and get a stronger result for asymptotic stability . [ lyasta]suppose @xmath115 is an equilibrium point of ( [ eq : ode ] ) . if there is an open set @xmath87 with @xmath116 and a sufficiently smooth function @xmath89 s.t . 1 . @xmath90 , 2 . @xmath91 for all @xmath117 and 3 . @xmath118 for all @xmath117 , then @xmath79 is an asymptotically stable equilibrium point of ( [ eq : ode ] ) . first notice that condition ( c ) implies @xmath93 for all @xmath96 . in order to show the asymptotic stability of @xmath86 , according to theorem [ bkls ] , it is sufficient to show that @xmath99 contains no nontrivial trajectory of the dynamical system . if not , let @xmath51 , @xmath84 be such a trajectory contained in @xmath119 other than @xmath120 . then @xmath121 for all @xmath84 . noting that @xmath122 , we can get the taylor expansion of @xmath123 at @xmath124 : @xmath125 by definition [ dfn : transet ] , there exists an @xmath80 s.t . @xmath126 which contradicts the assumption . we refer to the function @xmath97 in theorem [ lyasta ] as a _ relaxed lyapunov function _ , denoted by rlf . in the next section , we will explore how to discover polynomial rlfs automatically for pdss . given a pds , the process of automatically discovering polynomial rlfs is as follows : * a template , i.e. a parametric polynomial @xmath12 , is predefined as a potential rlf ; * the conditions for @xmath12 to be an rlf are translated into an equivalent formula @xmath127 of the decidable _ first - order theory of reals _ @xcite ; * constraint @xmath128 on parameters @xmath20 , or equivalently a set @xmath129 of all @xmath14-tuples subject to @xmath130 , is obtained by applying _ quantifier elimination _ ( qe for short . see @xcite ) to @xmath127 , and any instantiation of @xmath20 by @xmath131 yields an rlf @xmath18 . correct translation of the three conditions in theorem [ lyasta ] is crucial to our method . in particular , we have to show that for any polynomial @xmath8 and polynomial vector field @xmath44 , the transverse set @xmath132 can be represented by first order polynomial formulas . to this end , we first give several theorems by exploring the properties of lie derivatives and polynomial ideas . in what follows , given a parameterized polynomial @xmath12 , all lie derivatives @xmath133 are seen as polynomials in @xmath134 $ ] . besides , we will use the convention that @xmath135 and @xmath136 , where @xmath137 is logical formula . [ git]given @xmath138 , if @xmath139 @xmath140 , then for all @xmath141 , @xmath142 we prove this fact by induction . assume @xmath143 @xmath140 for @xmath144 . then there are @xmath145 $ ] s.t . @xmath146 . by the definition of lie derivative it follows that @xmath147 by induction hypothesis , @xmath148 , so @xmath149 . by induction , the fact follows immediately . [ thm : upper]given @xmath138 , the number @xmath150 is well defined and computable . first it is easy to show that @xmath151 has an equivalent expression @xmath152 , where @xmath153 $ ] . notice that @xmath154 forms an ascending chain of ideals . by theorem [ acc ] , @xmath151 is well - defined . computation of @xmath151 is actually an _ ideal membership _ problem , which can be solved by computation of _ grbner basis _ @xcite . for @xmath70 and @xmath71 , by example [ eg : lie - derv ] , we have @xmath155 and @xmath156 , so @xmath157 . [ para - dir - rank ] suppose that @xmath158 . then for all @xmath159 and all @xmath17 , @xmath160 implies @xmath161 if the conclusion is not true , then there exist @xmath162 and @xmath163 s.t . @xmath164 by definition [ dfn : point - rank ] , @xmath56 satisfies @xmath165 then by theorem [ thm : upper ] and [ git ] , for all @xmath166 , we have @xmath167 . in particular , @xmath168 , which contradicts @xmath169 . now we are able to show the computability of @xmath132 . [ thm : comput - trans]given a parameterized polynomial @xmath138 and polynomial vector field @xmath44 , for any @xmath17 and any @xmath43 , @xmath170 if and only if @xmath19 and @xmath2 satisfy @xmath171 , where @xmath172 @xmath173 ( @xmath174 ) suppose @xmath170 . by definition [ dfn : transet ] @xmath2 satisfies @xmath175 by theorem [ para - dir - rank ] , @xmath176 . then it is easy to check that ( [ eq : trans2 ] ) implies ( [ eq : varphi ] ) when @xmath177 . ( @xmath174 ) if @xmath19 and @xmath2 satisfy @xmath171 , then from definition [ dfn : transet ] we can see that @xmath170 holds trivially . based on the results established in section [ sec : auxiliary ] , we can give a sound and complete method for automatically generating polynomial rlfs on pdss . given @xmath178 , let @xmath179 denote the euclidean norm of @xmath2 . let @xmath180 for any @xmath181 . then our main result can be stated as follows . [ thm : main ] given a pds @xmath182 with @xmath183 and a parametric polynomial @xmath138 . let @xmath184 and @xmath185 . then @xmath186 is an rlf in @xmath187 if and only if @xmath188 where @xmath189 @xmath190 @xmath191 @xmath192 first , in theorem [ lyasta ] , the existence of an open set @xmath193 is equivalent to the existence of an open set @xmath194 . then according to theorem [ thm : comput - trans ] , it is easy to check that ( [ eq : phi-1 ] ) , ( [ eq : phi-2 ] ) and ( [ eq : phi-3 ] ) are direct translations of conditions @xmath195 , @xmath196 and @xmath197 in theorem [ lyasta ] . according to theorem [ thm : main ] , we can follow the three steps at the beginning of section [ sec : main - result ] to discover polynomial rlfs on pdss . this method is complete " because we can discover all possible polynomial rlfs by enumerating all polynomial templates . to construct @xmath198 in theorem [ thm : main ] , we need to compute @xmath151 in advance , which is time - consuming . what is worse , when @xmath151 is a large number the resulting @xmath198 can be a huge formula , for which qe is difficult . for analysis of asymptotic stability , one rlf is enough . therefore if an rlf can be obtained by solving constraint involving merely lower order lie derivatives , there s no need to resort to higher order ones . regarding this , we give an incomplete but more efficient implementation of theorem [ thm : main ] , by constructing @xmath198 and searching for rlfs in a stepwise manner . let @xmath199 @xmath200 and @xmath201 intuitively , for @xmath2 satisfying @xmath202 , we have to impose constraints @xmath203 or @xmath204 on the @xmath205-th higher order lie derivative of @xmath9 along @xmath44 . now the rlf generation algorithm ( rlfg for short ) can be formally stated as follows . [ alg : lfg ] input : @xmath206^n$ ] with @xmath183 , + @xmath207 $ ] + output : @xmath208 + @xmath209 ; @xmath210 ; @xmath211 ; + @xmath212 ; + return @xmath213 ; formula @xmath214 and @xmath215 in line 5 are defined in ( [ eq : phi-1 ] ) and ( [ eq : phi-2 ] ) ; qe in line 5 , 10 and 14 is done in a computer algebra tool like redlog @xcite or qepcad @xcite ; in line 20 the loop test can be done by calling the _ idealmembership _ command in maple@xmath216 @xcite . the idea of algorithm [ alg : lfg ] is : at the @xmath205-th step , we search for an rlf using constraint constructed from lie derivatives with order no larger than @xmath205 . if this fails to produce a solution , then we add the @xmath217-th order lie derivative to the constraint . this process continues until either we succeed in finding a solution , or we can conclude that there is no rlf with the predefined template , or we get to the @xmath151-th iteration , which means no solution exists at all . correctness of the algorithm rlfg is guaranteed by the following theorem . [ thm : crrct ] for algorithm [ alg : lfg ] , we have 1 ) termination . : : rlfg terminates for any valid input . 2 ) soundness . : : if @xmath218 , then @xmath219 is an rlf in @xmath220 . 3 ) weak completeness . : : if @xmath221 then there does not exist an rlf in the form of @xmath12 . * the loop condition is @xmath222 @xmath223 . by theorem [ thm : upper ] , rlfg can run at most @xmath151 many iterations . * suppose @xmath224 is the longest sequence generated by rlfg when it terminates . we can inductively prove that this sequence satisfies the following properties . * * @xmath225 . * * @xmath226 , for @xmath227 , where @xmath228 * * @xmath229 for @xmath230 , where @xmath231 * * @xmath232 if and only if either @xmath233 or @xmath234 ; otherwise @xmath235 . + suppose @xmath236 , then by ( p1 ) , ( p4 ) and ( [ eqn : phi ] ) we can get @xmath237 . thus @xmath238 and @xmath219 is an rlf according to theorem [ thm : main ] . * suppose @xmath221 , then by ( p4 ) we have either @xmath234 or @xmath233 . if @xmath239 , then by ( p3 ) and ( [ eqn : phi ] ) we get @xmath240 ; if @xmath233 , from ( p1 ) , ( p2 ) , ( [ eqn : phi ] ) as well as the validity of @xmath241 we have @xmath242 . so far we have proved @xmath243 implies @xmath244 . again by applying theorem [ thm : main ] we get the final conclusion . we illustrate our method for rlf generation using the following example . [ eg : smpl ] consider the nonlinear dynamical system @xmath245 with a unique equilibrium point @xmath246 . we want to establish the asymptotic stability of @xmath247 . first , the linearization of ( [ eqn : eg1 ] ) at @xmath247 has the coefficient matrix @xmath248 with eigenvalues @xmath249 and @xmath250 , so none of the principles of stability for linear systems apply . besides , a homogeneous quadratic lyapunov function @xmath251 for verifying asymptotic stability of ( [ eqn : eg1 ] ) does not exist in @xmath252 , because @xmath253 is @xmath254 . however , if we try to find an rlf in @xmath252 using the simple template @xmath255 , then algorithm [ alg : lfg ] returns @xmath256 at the third iteration . this means ( [ eqn : eg1 ] ) has an rlf @xmath257 , and @xmath247 is asymptotically stable . from this example , we can see that rlfs really extend the class of functions that can be used for asymptotic stability analysis , and our method for automatically discovering rlfs can save us a lot of effort in finding conventional lyapunov functions in some cases . in this paper , we first generalize the notion of lyapunov functions to _ relaxed lyapunov functions _ by considering the higher order lie derivatives of a smooth function along a vector field . the main advantage of rlf is that it provides us more probability of certifying asymptotic stability . we also propose a method for automatically discovering polynomial rlfs for polynomial dynamical systems . our method is complete in the sense that we can enumerate all potential polynomial rlfs by enumerating all polynomial templates for a given pds . we believe that our methodology could serve as a mathematically rigorous framework for the asymptotic stability analysis . the main disadvantage of our approach is the high computational complexity : the complexity of the first - order quantifier elimination over the closed fields of reals is doubly exponential @xcite . currently we are considering improving the efficiency qe on first order polynomial formulas in special forms , and it will be the main focus of our future work . the authors thank professors c. zhou , l. yang , b. xia and w. yu for their helpful discussions on the topic .

the notion of lyapunov function plays a key role in design and verification of dynamical systems , as well as hybrid and cyber - physical systems . in this paper , to analyze the asymptotic stability of a dynamical system , we generalize standard lyapunov functions to _ relaxed lyapunov functions _ ( rlfs ) , by considering higher order lie derivatives of certain functions along the system s vector field . furthermore , we present a complete method to automatically discovering polynomial rlfs for polynomial dynamical systems ( pdss ) . our method is complete in the sense that it is able to discover all polynomial rlfs by enumerating all polynomial templates for any pds .

SECTION 1. SHORT TITLE. This Act may be cited as the ``Consistency, Accuracy, Responsibility, and Excellence in Medical Imaging and Radiation Therapy Act of 2009''. SEC. 2. PURPOSE. The purpose of this Act is to improve the quality and value of health care by increasing the safety and accuracy of medical imaging examinations and radiation therapy procedures, thereby reducing duplication of services and decreasing costs. SEC. 3. QUALITY OF MEDICAL IMAGING AND RADIATION THERAPY. Part F of title III of the Public Health Service Act (42 U.S.C. 262 et seq.) is amended by adding at the end the following: ``Subpart 4--Medical Imaging and Radiation Therapy ``SEC. 355. QUALITY OF MEDICAL IMAGING AND RADIATION THERAPY. ``(a) Qualified Personnel.-- ``(1) In general.--Effective January 1, 2013, personnel who perform or plan the technical component of either medical imaging examinations or radiation therapy procedures for medical purposes must be qualified under this section to perform or plan such services. ``(2) Qualification.--Individuals qualified to perform or plan the technical component of medical imaging examinations or radiation therapy procedures must-- ``(A) possess current certification in each medical imaging or radiation therapy modality and service provided from a certification organization designated by the Secretary pursuant to subsection (c); or ``(B) possess current State licensure, or certification, where-- ``(i) such services and modalities are within the scope of practice as defined by the State for such profession; and ``(ii) the requirements for licensure, certification, or registration meet or exceed the standards established by the Secretary pursuant to this section. ``(3) State licensure, certification, or registration.-- ``(A) Nothing in this section diminishes the authority of a State to define requirements for licensure, certification, or registration, the requirements for practice, or the scope of practice of personnel. ``(B) The Secretary shall not take any action under this section that would require licensure by a State of those who perform or plan the technical component of medical imaging examinations or radiation therapy procedures. ``(4) Exemptions.--The qualification standards described in this subsection shall not apply to physicians (as defined in section 1861(r) of the Social Security Act (42 U.S.C. 1395x(r))) or to nurse practitioners and physician assistants (each as defined in section 1861(aa)(5) of the Social Security Act (42 U.S.C. 1395x(aa)(5))). ``(b) Establishment of Standards.-- ``(1) In general.--For the purposes of determining compliance with subsection (a), the Secretary, in consultation with recognized experts in the technical provision of medical imaging or radiation therapy services, shall establish minimum standards for personnel who perform, plan, evaluate, or verify patient dose for medical imaging examinations or radiation therapy procedures. Such standards shall not apply to the equipment used. ``(2) Experts.--For the purposes of this subsection, the Secretary shall select expert advisers to reflect a broad and balanced input from all sectors of the health care community that are involved in the provision of such services to avoid undue influence from any single sector of practice on the content of such standards. ``(3) Minimum standards.--Minimum standards may vary in form for each of the covered disciplines, reflecting the unique or specialized nature of the technical services provided, and shall represent expert consensus from those practicing in each of the covered disciplines as to what constitutes excellence in practice and be appropriate to the particular scope of care involved. ``(4) Allowance for additional standards.--Nothing in this subsection shall be construed to prohibit a State or certification organization from requiring compliance with higher standards than the minimum standards specified by the Secretary pursuant to this subsection. ``(5) Timeline.--The Secretary shall promulgate regulations for the purposes of carrying out this subsection no later than 18 months after the date on which this section is enacted. ``(c) Designation of Certification Organizations.-- ``(1) In general.--The Secretary shall establish a program for designating certification organizations that the Secretary determines have established appropriate procedures and programs for certifying personnel as qualified to furnish medical imaging or radiation therapy services. ``(2) Factors.--When designating certification organizations, and when reviewing or modifying the list of designated organizations for the purposes of paragraph (4)(B), the Secretary shall consider-- ``(A) whether the certification organization has established certification requirements for individuals that are consistent with or exceed the minimum standards established in subsection (b); ``(B) whether the certification organization has established a process for the timely integration of new medical imaging or radiation therapy services into the organization's certification program; ``(C) whether the certification organization has established education and continuing education requirements for individuals certified by the organization; ``(D) whether the organization has established reasonable fees to be charged to those applying for certification; ``(E) whether the examinations leading to certification by the certification organization are accredited by an appropriate accrediting body as defined in subsection (d); ``(F) the ability of the certification organization to review applications for certification in a timely manner; and ``(G) such other factors as the Secretary determines appropriate. ``(3) Equivalent education, training, and experience.-- ``(A) In general.--For purposes of this section, the Secretary shall, through regulation, provide a method for the recognition of individuals whose training or experience are determined to be equal to, or in excess of, those of a graduate of an accredited educational program in that specialty. Such authority shall expire seven years after the enactment of this section. ``(B) Eligibility.--The Secretary shall not recognize any individual pursuant to the authority of subparagraph (A) unless such individual-- ``(i) was performing or planning the technical component of medical imaging examinations or radiation therapy treatments prior to enactment of this section; and ``(ii) is ineligible to take the licensure or certification examination for that discipline. ``(4) Process.-- ``(A) Regulations.--The Secretary shall, by July 1, 2012, promulgate regulations for designating certification organizations pursuant to this paragraph. ``(B) Designations and list.--The Secretary shall, by January 1, 2013, make determinations regarding all certification organizations that have applied for designation pursuant to the regulations promulgated under subparagraph (A), and shall publish a list of all certification organizations that have received designation. ``(C) Periodic review and revision.--The Secretary shall periodically review the list, taking into account the factors established under paragraph (2). After such review, the Secretary may, by regulation, modify the list of certification organizations that have received designation. ``(D) Certifications prior to removal from list.-- If the Secretary removes a certification organization from the list of certification organizations designated under subparagraph (B), any individual who was certified by the certification organization during or before the period beginning on the date on which the certification organization was designated as a certification organization under subparagraph (B) and ending on the date on which the certification organization is removed from such list shall be considered to have been certified by a certification organization designated by the Secretary under subparagraph (B) for the remaining period that such certification is in effect. ``(d) Approved Accrediting Bodies.-- ``(1) In general.--The Secretary shall publish a list of entities that are approved accrediting bodies for certification organizations for purposes of subsection (c)(2)(E). The Secretary shall publish the list no later than 24 months after enactment of this section and shall revise the list as appropriate. ``(2) Requirements for approval.--The Secretary shall not approve an accrediting body for certification organizations unless the Secretary determines that such accrediting body-- ``(A) is a nonprofit organization; ``(B) is a national or international organization with accreditation programs for examinations leading to certification by certification organizations; ``(C) has established standards for recordkeeping and to minimize the possibility of conflicts of interest; and ``(D) demonstrates compliance with any other requirements established by the Secretary. ``(3) Withdrawal of approval.--The Secretary may withdraw the approval of an accrediting body if the Secretary determines that the body does not meet the standards defined in paragraph (2). ``(e) Alternative Standards for Rural and Underserved Areas.-- ``(1) In general.--The Secretary shall determine whether the standards established under subsection (a) must be met in their entirety for medical imaging examinations or radiation therapy procedures that are performed and planned in a geographic area that is determined by the Medicare Geographic Classification Review Board to be a `rural area' or that is designated as a health professional shortage area. If the Secretary determines that alternative standards for such rural areas or health professional shortage areas are appropriate to assure access to quality medical imaging examinations or radiation therapy procedures, the Secretary is authorized to develop such alternative standards. ``(2) State discretion.--The chief executive officer of a State may submit to the Secretary a statement declaring that an alternative standard developed under paragraph (1) is inappropriate for application to such State, and such alternative standard shall not apply in such submitting State. The chief executive officer of a State may rescind a statement described in this paragraph following the provision of appropriate notice to the Secretary. ``(f) Rule of Construction.--Notwithstanding any other provision of this section, individuals who provide medical imaging examinations relating to mammograms shall continue to meet the regulations applicable under the Mammography Quality Standards Act of 1992, as amended. ``(g) Definitions.--As used in this section-- ``(1) Medical imaging.--The term `medical imaging' means any examination or procedure used to visualize tissues, organs, or physiologic processes in humans for the purpose of detecting, diagnosing, treating or impacting the progression of disease or illness. For purposes of this section, such term does not include routine dental diagnostic procedures or advanced imaging procedures as defined in section 1834(e)(1)(B) of the Social Security Act. ``(2) Perform.--The term `perform', with respect to medical imaging or radiation therapy, means-- ``(A) the act of directly exposing a patient to radiation including ionizing or radio frequency radiation, to ultrasound, or to a magnetic field for purposes of medical imaging or for purposes of radiation therapy; and ``(B) the act of positioning a patient to receive such an exposure. ``(3) Plan.--The term `plan', with respect to medical imaging or radiation therapy, means the act of preparing for the performance of such a procedure to a patient by evaluating site-specific information, based on measurement and verification of radiation dose distribution, computer analysis, or direct measurement of dose, in order to customize the procedure for the patient. ``(4) Radiation therapy.--The term `radiation therapy' means any procedure or article intended for use in the cure, mitigation, treatment, or prevention of disease in humans that achieves its intended purpose through the emission of ionizing or non-ionizing radiation.''. SEC. 4. PAYMENT AND STANDARDS FOR MEDICAL IMAGING AND RADIATION THERAPY. Section 1848(b)(4) of the Social Security Act (42 U.S.C. 1395w- 4(b)(4)) is amended-- (1) in subparagraph (A), by striking the ``imaging'' and inserting ``medical imaging and radiation therapy'' and; (2) by adding at the end the following new subparagraph: ``(C) Payment for medical imaging and radiation therapy services.--With respect to expenses incurred for the planning and performing of the technical component of medical imaging examinations or radiation therapy procedures furnished on or after January 1, 2013, payment shall be made under this section only if the examination or procedure is planned or performed by an individual who meets the requirements established by the Secretary under section 355 of the Public Health Service Act.''. SEC. 5. REPORT ON THE EFFECTS OF THIS ACT. (a) In General.--The Secretary of Health and Human Services, acting through the Director of the Agency for Healthcare Research and Quality, shall submit to the Committee on Health, Education, Labor, and Pensions of the Senate, the Committee on Finance of the Senate, and the Committee on Energy and Commerce of the House of Representatives, a report on the effects of this Act no later than 5 years after the date of the enactment of this Act. (b) Requirements.--Such report shall include the types and numbers of individuals qualified to perform or plan the technical component of medical imaging or radiation therapy services for whom standards have been developed, the impact of such standards on diagnostic accuracy and patient safety, and the availability and cost of services. Entities reimbursed for technical services through programs operating under the authority of the Secretary of Health and Human Services shall be required to contribute data to such report.

Consistency, Accuracy, Responsibility, and Excellence in Medical Imaging and Radiation Therapy Act of 2009 - Amends the Public Health Service Act to require personnel who perform or plan the technical component of either medical imaging examinations or radiation therapy procedures for medical purposes to possess, effective January 1, 2013: (1) certification in each medical imaging or radiation therapy modality and service provided from a certification organization designated by the Secretary of Health and Human Services (HHS); or (2) state licensure or certification where such services and modalities are within the scope of practice as defined by the state for such profession and where the requirements for licensure, certification, or registration meet or exceed the standards established by the Secretary. Exempts physicians, nurse practitioners, and physician assistants. Directs the Secretary to: (1) establish minimum standards for personnel who perform, plan, evaluate, or verify patient dose for medical imaging examinations or radiation therapy procedures; (2) establish a program for designating certification organizations after consideration of specified criteria; (3) provide a method for the recognition of individuals whose training or experience are determined to be equal to, or in excess of, those of a graduate of an accredited educational program in that specialty; and (4) approve and publish a list of accrediting bodies for such certification organizations. Authorizes the Secretary to develop alternative standards for rural or health professional shortage areas as appropriate to assure access to quality medical imaging. Amends the Social Security Act to allow Medicare payment for medical imaging and radiation therapy services furnished on or after January 1, 2013, only if the examination or procedure is planned or performed by an individual who meets this Act's requirements.

it is characterised by a rapidly progressive glomerulonephritis due to circulating anti - glomerular basement membrane ( anti - gbm ) antibodies . the subject of this report developed acute pulmonary aspergillosis following exposure to fungal spores in mouldy tree bark whilst gardening and this led to goodpasture 's syndrome . we believe that this is the first presentation of aspergillosis induced goodpasture 's syndrome to be reported in the medical literature . a 69 year old retired man with no significant medical history was admitted to hospital with a 5 week history of increasing dyspnoea and intermittent haemoptysis . antibiotics in the community had not improved his symptoms . he was a lifelong smoker of 30 cigarettes per day . on admission ( day 0 ) , his temperature was 37.2 c , his pulse was 72 , his respiratory rate 22 per minute and his blood pressure was 120/69 mmhg . initial blood tests revealed raised inflammatory markers ( crp 225 mg / l and leucocyte count 19.510/l with a neutrophilia ) . spirometry on day+5 was as follows : fev1 1.69 l ( 55% predicted ) ; forced vital capacity 2.59 l ( 65% predicted ) : fev1/fvc ratio 65% . on day+6 , a high resolution ct of his thorax revealed widespread fine nodularity , maximal in the midzones and ill - defined peribronchial inflammatory shadowing . there was bronchiectasis ( which had improved on a follow - up scan 2 months later ) and patchy tree - in - bud change , but no radiological features of pulmonary haemorrhage . at bronchoscopy on day+7 , endobronchial biopsies showed non - specific inflammatory changes , with no granulomata seen . transbronchial biopsy was not possible as the patient 's oxygen levels fell and so the procedure was abandoned . serum ana was weakly positive at 1/100 ( speckled pattern ) with negative ena and anca . he had elevated igg to aspergillus fumigatus of 47 mga / l ( reference range up to 40 a diagnosis of acute invasive pulmonary aspergillosis ( ipa ) was made and he was discharged home on day+13 , on oral itraconazole , 200 mg twice daily . his discharge creatinine was 80 mol / l . at clinic on day+27 , his respiratory symptoms had improved substantially following treatment . he was able to climb 20 steps and the saturation did not fall below 90% . spirometry was greatly improved at 2.4/3.9 ( fev1 78% predicted , vital capacity 90% predicted , fev1/fvc ratio 61% ) . direct questioning revealed that his symptoms had developed about 2 weeks after spreading eight , 40 l bags of foul smelling mouldy tree bark on the garden . this material was subsequently cultured in the national aspergillosis centre and it grew a. fumigatus , rhizopus spp . , sporobolomyces spp . and bacteria ( fig . a renal immunology screen showed positive anti - glomerular basement membrane ( anti - gbm ) antibodies with a titre of 111 u / ml ( elisa assay ) ( reference range<15 u / ml ) . retrospective analysis of a blood sample from day 3 of his first hospital admission showed an anti - gbm titre of 67 u / ml at that time . renal biopsy demonstrated necrotising crescentic glomerulonephritis with linear deposition of igg along the basement membrane , consistent with anti - gbm disease . on day+28 , he was commenced on haemodialysis , pulsed methylprednisolone 500 mg once daily for 3 days , cyclophosphamide 750 mg ( once monthly dose ) and plasma exchange . subsequent anti - gbm antibody titres were significantly lower ( 20 u / ml 6 weeks post - presentation , 8 u / ml at 8 weeks and < 7 u / ml at 5 months post - presentation ) . aspergillus igg 6 weeks after his acute respiratory presentation had fallen to 7 mga / l , and after 3 months total ige was normal . unfortunately the patient remained frail and housebound despite haemodialysis and he died from severe sepsis and acute pneumonia 10 months after his first presentation . invasive pulmonary aspergillosis has specifically been reported in healthy individuals after spreading rotting tree bark whilst gardening [ 13 ] . in previous cases , massive inhalation of spores there is diagnostic difficulty in these cases and diagnosis is often made at post - mortem , because blood and sputum cultures have poor sensitivity . serological testing for aspergillus igg antibodies can be used in the diagnosis of ipa . in a study of patients developing ipa following bone marrow transplant , an igg response to acute infection was noted . anti - gbm antibody disease is characterised by a rapidly progressive glomerulonephritis due to circulating anti - gbm antibodies . the target of these antibodies is the non - collagenous domain of the 3 chain of type iv collagen . there is a body of evidence to suggest that certain human leucocyte antigen ( hla ) molecules , notably hla - dr 15 and hla - dr 4 , are associated with the development of anti - gbm disease . subsequent analysis of our patient 's hla type revealed hla - dr 17 and dr 4 . hypothetically certain epitopes that are normally immunologically privileged can become exposed and perceived as foreign , leading to antibody development . a. fumigatus conidia bind to type iv collagen ( and fibrinogen ) , a process inhibited by free sialic acid and in particular n - acetylneuraminic acid . whether the binding of a. fumigatus to collagen iv in the lung altered the allergenicity of this major structural protein , allowing auto - antibodies to be formed , remains conjecture . it has been hypothesised that exposure to certain environmental factors may affect the molecular structure of 3nc1 domain , making antibody binding more likely . development of goodpasture 's syndrome has been reported following exposure to inhaled chemicals , drugs and in association with infectious disease . we hypothesise that our patient contracted invasive pulmonary aspergillosis due to heavy exposure to fungal spores whilst gardening . this led to epitope exposure in the alveoli with subsequent development of gbm auto - antibodies and acute renal failure , in an individual with pre - existing genetic risk factors . we have no conflicts of interest in the publication of this article , including financial ones to declare .

a non - immunocompromised man developed acute aspergillus pneumonia after spreading mouldy tree bark mulch . despite normal renal function at presentation , he developed rapidly progressive glomerulonephritis with acute kidney injury due to anti - glomerular basement membrane antibodies ( anti - gbm ) 4 weeks later . he remained dialysis dependent and died of sepsis 10 months later . we hypothesise that he contracted invasive pulmonary aspergillosis from heavy exposure to fungal spores , leading to epitope exposure in the alveoli with subsequent development of gbm auto - antibodies .

hippocampal networks can display sequences of neuronal activation at the temporal resolution of behavior , or compressed within the period of network oscillations ( buzski , 2010 ) . the occurrence and organization of these sequences are thought to underlie numerous fundamental operations of the hippocampus , from the sensing of sensory cues and building a cognitive map of the environment , to mnemonic and planning functions ( dragoi and tonegawa , 2011 ; skaggs and mcnaughton , 1996 ; wilson and mcnaughton , 1994 ) . at the behavioral timescale , these sequences were first shown to occur in the presence of external landmarks that provide successive cues organizing neuronal activity through exteroception . for example , hippocampal place cells are sequentially activated at consecutive positions in space when a rodent explores an environment naturally delivering serially ordered external landmarks ( dragoi and buzski , 2006 ) , even when only tactile and visual cues are provided ( royer et al . , 2012 ) . however , the sequential activation of hippocampal neurons at the behavioral timescale can also be disengaged from external landmarks and instead occur in the absence of changing sensory or feedback cues . this involves self - organized internal mechanisms but happens within a behaviorally relevant context for example , during the delay period of a memory task ( itskov et al . , 2011 ; , 2013 ; pastalkova et al . , 2008 ; wang et al . , 2014 ) . to some extent , the reward that guides an animal s behavior within a defined task also provides an external drive on hippocampal dynamics . hence , so far it remains unknown whether hippocampal activity can also be organized at population level in the absence of any driving external goal . it is also unknown whether the span of hippocampal sequences is intrinsically predetermined in time or space in the absence of any temporal and spatial boundary . indeed , both externally and internally triggered sequences observed until now at the timescale of behavior always cover a finite spatial and temporal extent that is constrained by external factors such as the temporal organization of the task ( pastalkova et al . , 2008 ) or the size of the environment explored in space ( ravassard et al . , 2013 ) . this is an important issue , since it defines the intrinsic determinants and behavioral reach of hippocampal population coding . here , large - scale two - photon calcium imaging was used to capture population dynamics while resolving single - cell behavior in the ca1 region of awake mice . a simple experimental paradigm was implemented to record spontaneous dynamics while minimizing the influence of external spatiotemporal landmarks or limits , which allows separating the contributions of time , distance , and external motivation to neuronal firing . in these conditions , we show that hippocampal dynamics self - organize into sequences of neuronal activation recurring one after another within discrete run epochs and each spanning accross a fixed traveled distance . these recurring sequences translate into a behavioral correlate , since spontaneous run epochs display some stereotypy : they distribute as multiple integers of the distance unit represented in the sequences . we propose that such sequences could be a default internal dynamic template for spatiotemporal processing in the hippocampus . to observe hippocampal dynamics , we examined the spatiotemporal distribution of neuronal activity in the ca1 pyramidal layer using two - photon calcium imaging of awake head - restrained mice allowed to self - regulate their motion in the dark on a nonmotorized treadmill ( royer et al . , 2012 ) in contrast to previous studies , we chose not to deprive mice of water or food so that their behavior was not guided toward receiving any reward . in this way , during each daily imaging session , mice spontaneously traveled on the track through the alternation of run epochs ( interquartile range 410 s ; see figure s1 available online ) and rest epochs ( from 10 to 74 s ; figure 1a ) . within run epochs , mice moved at various speeds ( average 10.4 cm / s , range : 520 cm / s ) and displayed short periods of immobility ( < 2 s ; figures 1d and s1 ; see experimental procedures ) . to map neuronal activity across consecutive days , we used a viral vector ( aav2/1.syn - gcamp5 g ) that makes gabaergic and glutamatergic ca1 neurons express the calcium indicator gcamp5 ( akerboom et al . , 2012 ) . in order to image from a large population of neurons ( 1,000 cells , figure 1 ) , we used a low - magnification objective that allows for imaging a 400 400 m field of view centered on the stratum pyramidale ( figure 1b ) after surgical implantation of a chronic glass window on the hippocampus ( dombeck et al . , this surgical procedure was previously shown to allow for the reliable recording of place cell activity ( dombeck et al . , 2010 ) , and we show it has no impact on exploratory activity ( figure s2 ) . after three to five habituation sessions , mice running on an empty self - paced treadmill in the dark were imaged ( figure 1a ) , an experimental configuration that allows studying ca1 dynamics under the sole influence of self - motion cues . spontaneous behavior remained highly variable and did not display any significant repetition pattern from one day to the next ( figures s1c s1f ) . this lack of behavioral stereotypy enabled disentangling the relative contributions of time and distance to the firing of neurons . unexpectedly ( kentros et al . , 2004 ; pastalkova et al . , g ) , we found that ca1 dynamics displayed recurring sequences of neuronal firing exclusively during run epochs in 28 imaging sessions ( five mice ; figure 1c ; movie s1 ) . statistical analysis using data reshuffling established that sequences were not occurring by chance ( p < 0.001 , see experimental procedures ) . these sequences repeatedly engaged a sparse and scattered neuronal population that represented about 5% of all imaged neurons and 36% of the total fraction of active cells during run ( figure 1b ) . cells engaged in these sequences were spatially intermingled with other run active cells that displayed variable activity patterns ( figures 1b and 1c ) , including sustained firing ( 25% of active cells , figure 1c ) , or uncorrelated and sparse activation onsets ( 39% of active cells , figure s3 ) . recent studies have addressed the relative influence of external sensory cues or behavioral context on the patterning of hippocampal dynamics , and it is now well established that , at the single - cell level , these can be controlled by absolute or relative location and time depending on the available and relevant stimulus for the task at hand ( aghajan et al . , 2014 ; chen et al . , 2013 ; itskov et al . , 2011 ; kraus et al . , 2013 ; ravassard et al . , 2013 ) . we thus asked whether the sequences of neuronal activation observed here were driven by absolute location or time . we can exclude a modulation of neuronal firing by the absolute position on the treadmill ( as could occur if an undetected cue was left on the track ) since ( 1 ) sequence recurrence never matched the length of the treadmill ( 180 cm , figure 2d ) and ( 2 ) as expected from a 0.05 statistical cutoff , less than 5% of the cells recruited in sequences displayed significantly location - modulated activation ( 1,048 cells out of 28 sessions , p < 0.05 , kolmogorov - smirnoff uniformity test on firing onset distribution along the treadmill , figure 2e ) . similarly , sequences could not be integrating absolute elapsed time because ( 1 ) sequences could repeat one after another either within the same run epoch ( defined as periods where speed exceeds 2 cm / s , figure 3a ) or separated by rest periods of variable duration ( figures 1a and s1 ) ; and ( 2 ) sequences could be transiently perturbed during short immobility gaps ( figure s1 ) and then resumed when running restarted , since the slope during the pause was significantly different from that before and after it ( figure 1d ) . analysis was therefore next restricted only to run epochs in order to determine whether neuronal sequences were constrained by the integration of time or distance during mouse travel . to test whether sequences integrated travel duration or distance , we analyzed , for each imaging session , the correlation between the slopes of the sequences ( in the temporal or spatial domain ) and the median mouse speed of the corresponding run epochs . if the progress of neuronal activation was set by the run distance , then the temporal slope of the sequences ( expressed as cell / s ) should correlate with speed while the spatial slope ( in cm / cell ) should be constant and thus independent from speed ( figures 2a and 2b ) . for each imaging session , we calculated the spearman correlation coefficient between the temporal or spatial slope and the speed ( figure 2b ) ; this analysis is a robust way to assess distance or time representation in noisy data ( see data simulation in figures s3b , sequences could be modulated by time and distance ( 28 imaging sessions , n = 5 mice , figures 2b and s1 ) . however , in many cases they were principally modulated by distance alone ( 14 out of 28 sessions , spearman p < 0.05 ; table s1 ) . in the intermediate cases , both time and distance representations seemed to intermingle ( 11 out of 28 ) , whereas time alone was organizing neuronal activation in a minority of the sessions ( 3 out of 28 ) . this demonstrates that , as previously described at single - cell level , hippocampal dynamics capture both spatial and temporal information at the population level ( kraus et al . , 2013 ) . however , when integrating information at the population level over each imaging session , we observe that on average distance is more likely to be represented in our experimental conditions ( figures 2b and s1 ) . as distance - modulated sequences were frequent , analysis was next restricted to the imaging sessions in which these were observed ( n = 14 sessions , 5 mice , 493 sequences , experimental procedures , and figure s1 g ) . such distance - modulated sequences ( ds ) repetitively engaged the same neurons within an imaging session ( figures 1c and 2c , on average 70% ) . a period of travel could therefore sometimes not be represented within neuronal dynamics ( a nonencoded travel distance , this indicated that dss do not provide a metric integrating the total distance covered by the mouse but instead display a finite size that is intrinsically set . this nonencoded travel distance did not involve the coordinated firing of another group of cells , as only one recurring pattern of neuronal activation was detected per session . also , as expected , the onsets of the calcium transients of the neurons engaged in the ds ( ds neurons ) were not locked to the treadmill lap in contrast to those of the neurons displaying location - dependent firing after a few days of spontaneous run in the presence of serial tactile cues ( i.e. , place cells , n = 3 mice , figure 2d ) . neither were these onsets periodic , given the occurrence of nonencoded traveled distances between sequences . nor were the dss triggered by a undetectable cue on the track ( figure 2e ) . therefore , in conditions dominated by idiothetic cues , some fixed distance metric can be represented in the hippocampus in the form of recurring sequences of neuronal activation . we next asked whether the finite size of the ds was due to experimental limitations , or instead could represent an intrinsic metric for distance . to this aim , we first analyzed the topographical arrangement of ds neurons . the spatial distribution of ds neurons within the pyramidal layer did not display any remarkable pattern since these were not more clustered than expected by chance , even when taking into account their time of recruitment within the sequence ( figure s4 ) . this indicates that our imaging field of view sampled from a random representative subset of ds neurons and that the distance span covered by each sequence was unlikely to be truncated . thus , the distance encoded at population level in the ds could be set by the mouse behavior or conversely , spontaneous runs could be internally predetermined by the spatial extent of the ds . in order to address the former hypothesis , we have plotted the distribution of the mouse speed centered on the time of ds start or stop . we first used the first ds of each run epoch as a reference ( figure 3b ) . in this case , ds onsets were time - locked to the start of the run ( figure 3b1 ) whereas ds offsets occurred before its end ( figure 3b2 ) . ds could also repeat in the middle of a run epoch one after another ( figure 3a ) , and this repetition is expected to be triggered by an external drive , such as a short pause in mouse run or a cue on the track . to test the first possibility , the onsets and offsets of these ds were specifically used as a reference for the mouse speed distribution plots ( figures 3b3 and 3b4 ) . surprisingly , no significant pause or deceleration were observed . however , speed significantly increased by about 20% ( figure 3b3 ) . this is a potentially interesting finding that may relate to the mechanisms of sequence initiation given that the firing frequency of ca1 pyramidal neurons increases with speed ( hirase et al . , 1999 ; in addition , ds repetition was not linked to a cue on the track ( uniformity kolmogorov - smirnov test figure 3c , p > 0.1 ) . hence , both the onset and offset of a ds could be uncorrelated to the start and end of the run , in contrast to previous reports where the span of neuronal activation sequences was constrained by the underlying task ( kraus et al . , 2013 ; , 2008 ; ravassard et al . , 2013 ; royer et al . , this shows the intrinsic finite extent of sequences of neural activation in ca1 that encode traveled distance without being locked to behavior . we thus refer to such discrete span of the ds as the distance unit ( du ) encoded at population level within the imaging session . quantification of the du for each imaging session revealed that these spanned across a wide range ( 12112 cm , figure 4a ) , even for the same mouse across imaging days , indicating that this value is not preset . we took advantage of this variability to test if , as for place cells where the size of place fields scales with that of the explored environment ( diba and buzski , 2008 ; muller and kubie , 1987 ; okeefe and burgess , 1996 ) , the average distance field width ( experimental procedures ) linearly scaled with the du . such a relationship could be observed ( figure 4e , pearson , r = 0,94 , p < 0.001 ) , indicating a shared property between distance and place fields . since the du could considerably vary across days , we compared the set of neurons involved within the ds from one imaging session to the next . almost one - third of the cells involved within a ds one day were still recruited the next ( 28% 8% , three sessions paired , two mice , figures 4b and 4c ) . in addition , although no serial external cues were provided to support and recall the sequence organization , the relative order of the neurons within the sequences was also maintained ( figures 4c and s4b ) . last , we asked whether the template metric provided by the du shaped spontaneous mouse runs . to this aim , analysis was focused on the distribution of the distance traveled within single run epochs ( that comprised a detected ds ) , expressed in du ( rather than cm ) . the median value of this normalized distance , calculated per imaging session , segregated into two groups ( group 1 , 12 du , 235 run epochs , 10 sessions ; group 2 , 2.53.2 du , 90 run epochs , 4 sessions ; figure s4c ; table s1 ) . when pooling together group 1 , we noticed that the distribution was significantly bimodal with peaks at 1.1 and 2.1 du ( figures 4d and s4 ; p < 0.001 , see experimental procedures ) , whereas it was log - normal without normalization . regarding group 2 distribution bimodality , the occurrence of imaging sessions displaying a majority of run epochs with more than 2ds was too infrequent to draw any significant conclusion . thus , spontaneous run epochs tended to distribute as integer multiples of the distance intrinsically integrated in the respective ds . this further supports the idea that dss are a representation of distance encoded in the hippocampal network . this study shows that sparse and stereotyped chains of neuronal activation , integrating spatiotemporal components of behavior , spontaneously recur one after another , without any external drive , in the hippocampus under the influence of self - motion . we show that the distance unit associated to these intrinsically finite sequences provides a population metric for distance encoded in ca1 dynamics . this du is not entirely engraved , as it could vary on a daily basis . however , the partial replay of sequences from one day to the next strongly suggests the existence of internally prewired networks ( dragoi and tonegawa , 2014 ) . animals were more likely to travel spontaneously once or twice the distance unit , suggesting that linear path integration may use dead reckoning cycles and that this internal representation is limited . in natural environments , this function is complemented by landmark recognition ( mcnaughton et al . , 1991 ) . in contrast , in the absence of external cues , integer multiples of the du operate as attractor states for spontaneous behavior . this finding was made possible by a combination of factors that were not gathered before ( chen et al . , 2013 ; kraus et al . , 2013 ; pastalkova et al . , 2008 ; poucet et al . , 2014 ; ravassard et al . , 2013 ) and that include ( 1 ) the absence of sensory or cognitive external drive , ( 2 ) the absence of reward , ( 3 ) the absence of temporal or spatial borders ( solstad et al . , 2008 ) , ( 4 ) the sampling of activity from a large number of neurons , ( 5 ) a large range of running speeds to allow disentangling elapsed time from distance even for short travels , and ( 6 ) the use of a one dimensional environment . last , we can not exclude that keeping head direction signals constant also contributed in revealing such stereotyped dynamics ( cowen and nitz , 2014 ; sargolini et al . , 2006 ) . it is also possible that the filtering of neuronal spiking , an experimental limitation of the use of calcium indicators , is here providing a first integration step of hippocampal dynamics . besides spatial cognition and memory , sequences of neuronal activation have been previously reported in different brain regions and species where they have been associated with a variety of brain computations , including song generation ( long et al . , 2010 ) , odor encoding ( wehr and laurent , 1996 ) , choice decision ( harvey et al . , 2012 ; , 2008 ) , associative learning ( modi et al . , 2014 ) , or brain - state transitions ( luczak et al . , 2007 ) . here they can repeat one after another within a continuous behavioral episode , sometimes following a spatiotemporal gap lacking any significant neuronal activity pattern . interestingly , spontaneous repetition of neuronal activation has been reported at the single - cell level for example for cells displaying multiple place fields when large environments are explored ( rich et al . , 2014 ) , and at the population level when identical repeating environments are successively explored ( mizuseki et al . , 2012 ) . the same way that cells with multiple place fields somehow provide a natural segmentation of large environments , it is possible that the repetition of finite sequences reflects a similar phenomenon where an infinite environment is divided into discrete cognitive chunks ( gupta et al . , 2012 ) . this activity repetition may reflect a self - generated behavioral strategy ( cabral et al . , 2014 ) or the limit of the internal representation of the world , the latter being more likely for hence , for a given imaging session , we observed that mice could run once or twice the du , with no strategical preference for either one of these options . therefore , ds may represent the full capacity of the available working memory for a given experience . when animals are trained for a particular task , sequential neuronal activation covers the entire length of the task at hand ( in time or space ) ( dragoi and buzski , 2006 ; itskov et al . , 2011 ; 2014 ) . as a consequence of the intrinsic finite size , sequences scale to match the experienced episode , which implies that the coding resolution is inversely proportional to the size of the task hence , we observed that average distance field width linearly scaled with the du . absolute distance from a fixed starting point has recently been reported to be represented in hippocampal firing at single - cell level ( kraus et al . , 2013 ) and to contribute to place coding in the absence of visual cues ( chen et al . , 2013 ) or in virtual environments ( ravassard et al . , 2013 ) . the critical implication of self - body cues in the distance representation within place fields has recently been demonstrated in virtual environments ( chen et al . , 2013 ) . from that , it was thus expected , in our particular conditions where self - motion cues are prominent , that sequential neuronal firing integrates traveled distance . however , the single - cell activity recorded here can not provide a measure of run distance since run epochs comprise periods of non - encoded distance . in addition , in the case of the ds described here , as reported before for single - cell hippocampal activity ( kraus et al . , 2013 ) , it is very likely that time is also contributing to single - cell firing . probably best supporting that point is the fact that the organization of sequences was not affected by short rest periods , indicating that some cells are bridging the temporal gap between two diconstinuous runs within a single sequence . alternatively , information may be transiently stored and hidden for example in the decaying synaptic weights over time accross short temporal gaps ( less than one second long ) ( buonomano and maass , 2009 ) . distance was known to be represented within hippocampal dynamics at a shorter timescale , in the form of the sequential firing of place cells sharing overlapping place fields within a theta cycle ( dragoi and buzski , 2006 ) . interestingly , theta phase precession is preserved after stimulation - induced perturbation of hippocampal activity ( zugaro et al . , 2005 ) , the same way sequences described here resumed after a short immobility period . in addition , theta sequences were recently shown to be critically related to internally generated hippocampal sequences formed during an episodic memory task ( wang et al . , 2014 ) . it will thus be important to examine the link between these two temporal scales of distance representation , which may ultimately require determining the translation of distance sequences in a two - dimensional environment . sequences were also shown to occur at an even more compressed timescale , during sharp wave activity and quiet wakefulness . these sequences reflect previous sensory experience ( buzski et al . , 1992 ; karlsson and frank , 2009 ) . in the same way , distance sequences may recapitulate a recent experience thus supporting the view of the hippocampus as a relational processing system ( eichenbaum and cohen , 2014 ) , linking sequential body movements to an existing distance template supported by internally preconfigured networks . in this way , these may contribute to the generation of place fields in the absence of proximal sensory cues as likely occurs in the dark ( poucet et al . , 2014 ) , or when large environments are explored ( wang et al . , 2014 ) . these may also contribute to temporal integration when time becomes a more prominent component ( macdonald et al . future studies are needed to address the cellular mechanisms of sequence generation , in particular their link to entorhinal inputs from grid cells , the standard metric for space in the brain ( moser and moser , 2008 ) , or to medial septum inputs that pace the internal hippocampal clock at theta frequency . the preconfigured character of hippocampal dynamics , dominated by a small minority of active cells in many states and contexts ( mizuseki and buzski , 2013 ) , may provide a cellular substrate by which hippocampal dynamics spontaneously collapse into these default sequences , based on the preferential activation of a highly excitable subset of neurons triggering a chain of pre - existing functional links . interestingly , sequences of neuronal activation lacking spatial specificity ( cheng and ji , 2013 ) have been recently observed in an alzheimer disease model , suggesting that these may represent the minimum default operational mode of the hippocampus when sensory perception is reduced . all protocols were performed under the guidelines of the french national ethic committee for sciences and health report on ethical principles for animal experimentation in agreement with the european community directive 86/609/eec under agreement # 01413 . male adult wild type swiss mice ( n = 8 , 2540 g body weight ) were used for experiments . all mice were housed in standard conditions ( 12 hr light / dark cycles light off at 7:30 a.m. , housed one per cage , water and food ad libitum ) . mice were handled before recording sessions to limit head restraint associated stress and experiments were performed during the dark cycle . in order to perform large - scale calcium imaging , mice were injected with a viral solution ( titer , 10 genomes copy / ml ; penn vector core ) of aav2/1.syn.gcamp5g.wpre.sv40 . mice were first anesthetized ( 100 mg / kg ketamine , 10 mg / kg xylazine ) , and 500 nl of viral solution was injected at a rate of 100 nl / min into the left dorsal hippocampus at following coordinates : ap , 2 and 2.5 ; ml , 1.6 and 2.1 relative to bregma ; dv , 1.3 relative to brain surface . the constrained tissue was allowed to recover for 1 min prior and 3 min after injections to prevent injection backwash . after 4 days of water deprivation to transiently modify hemodynamics to help for the surgery ( 1.5 ml/24 hr ; < 20% loss of initial body weight ) , mice were anesthetized with ketamine ( 100 mg / kg ) and xylazine ( 10 mg / kg ) , and a 3 mm diameter craniotomy centered over virus injection sites was performed . the dura was gently cut and a portion of the overlying cortex was aspirated to allow optical access to the hippocampus . similarly to the original method , the external capsule was exposed and allowed to dry until tacky , upon which a stainless steel canula ( microgroup ) attached to a glass coverslip was placed in the hole , sealed with uncured kwik sil ( wpi ) , and fixed to the skull using super - bond ( dsm dentaire ) . mice were allowed to recover for 46 days and then handled for 2 days in order to limit head restraint - associated stress . mice were head - fixed on a nonmotorized treadmill ( adapted from royer et al . , 2012 ) allowing them self - paced locomotion , and all experiments after three to five habituation sessions , mice were watchful but calm and alternated between periods of moving and resting activity during recordings . the treadmill was made from a 180 cm black velvet seamless belt for the experiments done in the absence of external cue ( n = 5 mice ) . in the experiments aiming at imaging place cell firing ( n = 3 mice ) , the belt was enriched in tactile cues as follows : we delineated four zones of 45 cm displaying the following items : ( 1 ) 2 cm wide disks of white velcro ; ( 2 ) small white pressure buttons ; ( 3 ) gray diamond shaped textured plastic fabric ; ( 4 ) no cue . for all experiments , extra sound , odor , touch , and light were minimized during the imaging session ( in preliminary experiments where the seam was too prominent we observed cue - related firing ; data not shown ) . the mouse speed and instantaneous position were tracked using a graded wheel , as previously described ( royer et al . , 2012 ) imaging was performed with a single beam multiphoton pulsed laser scanning system coupled to a microscope ( trim scope ii , lavision biotech ) . the ti : sapphire excitation laser ( chameleon ultra ii , coherent ) was operated at 920 nm . images were acquired through a gasp pmt ( h7422 - 40 , hamamatsu ) using a 16 immersion objective ( nikon , na 0.8 ) . using imspector software ( lavision biotech ) , the fluorescence activity from a 400 m field of view was acquired at 9.62 hz with a 1.85 s dwell time per pixel ( 2 m / pixel ) . imaging fields were selected to sample the dorsal ca1 area and maximize the number of imaged neurons in the stratum pyramidale . speed , position , and image triggers were synchronously acquired and digitized using a 1440a digidata ( axon instrument , 2 khz sampling ) and the axoscope 10 software ( axon instrument ) . a typical imaging session occurred as follows : ( 1 ) the mouse was handled then fixed on the treadmill ; ( 2 ) five consecutive 3,000 frames movies were acquired ; ( 3 ) the mouse returned to its homecage . run epochs were defined as continuous periods of time during which the average mouse speed exceeded 2 cm / s . a custom - made algorithm based on pca / ica was used and combined to morphological identification . movement correction was first performed for each frame using the cross - correlation with a reference image . the offset pca method was next applied ( kaifosh et al . , 2013 ) . principal components displaying a variance greater than noise were fed to an iterative ica algorithm ( mukamel et al . , 2009 ) . cells were identified in the output of the ica using 2d - spatial wavelet filtering matching the expected cell size ( 715 m diameter ) . the obtained roi were finally smoothed using a closing algorithm thus defining the active cell population . gcamp fluorescence traces were smoothed in time ( gaussian filtering , s=5s ) before fed to the offset pca algorithm ( kaifosh et al . , 2013 ) . the smoothing adds correlation between neighbouring time points in order to gather the activity of cells that fire successively . the principal component which displayed recurring fluorescence patterns during each run epoch ( among the five with the highest variance ) the reason for manual selection was ( 1 ) the need to select a principal component that contained information about population activity during run epochs ( i.e. , displaying transients at each run ) ; and ( 2 ) among the five extracted principal components , it also often happened that traces reflecting for example high activity of a single neuron outside from run epochs or movement artifacts , were considered as holding the most information by the pca . the derivative of that principal component ( figure s3 , green ) was then cross - correlated with the activity of each individual cell . the use of the derivative preferentially select cells with short calcium transient and thus remove cells that fire during the entire run epoch which are not part of a sequence . the correlation coefficients thus obtained were used as a metric to determine the participation of each cell to recurring activity : a threshold was calculated applying otsu 's method ( otsu , 1979 ) to the distribution of this metric in the cell population ( figure s3 ) . cells whose correlation was higher than the threshold were considered as involved in such recurring activity . note that in several instances ( 37 out of 65 imaging sessions from five mice , see figure s1 g ) , no recurring pattern was detected . to identify another group of cells that would display another recurring pattern , we reiterate this procedure with the previously identified cells removed . after reshuffling between active cells independently in each run epoch , i.e. , the fluorescence trace is divided in different time interval inside which cells activity is permuted ( e.g. , cell 1 gets the activity of cell 5 during the first run epoch and of cell 3 during the second one , etc . ) , no recurring activity ( at least two sequences of five cells ) was detected which validated our detection method ( 0 occurrence out of 1,000 reshufflings ) . for each recurring activity pattern , cell activation onset was defined by the maximum of the first derivative of the smoothed trace ( gaussian filtering , s = 2s ) . cells were then ordered in a sequence according to their median onset delay in each run epoch . the sequences that involved at least half of the cells were linearly fitted using a regression algorithm that ignores outliers ( matlab function robustfit ) . the fits displaying a robust root mean square error exceeding 20% of the duration of the sequence were discarded . the remaining sequences were used for all quantitative analysis ( n = 389 fitted sequences , 79% of all sequences ) . this linear fit provided the slope ( in cell / s ) of each sequence . to assess whether the dynamics of these sequences depended on run distance , we analyzed the correlation between the slope and the corresponding median speed . in the case of a statistically significant correlation ( p < 0.05 , spearman , n = 14 out of 28 sessions ) , a distance unit du that links the speed v , the slope s , and the number of cells n could be defined as follows : du is the spatial extent of the run distance from the first to the last cell of the sequence . the same analysis was performed in the spatial domain by converting activation onsets in time to onsets in space using the measured mouse position . a few sessions ( 3 out of 28 ) displayed a significant correlation , which indicated that run time could also modulate sequence dynamics . short pauses were defined as the periods when the speed was lower than 2 cm / s for more than 500 ms and less than 2 s. to analyze whether the occurrence of short pauses affected the dynamics of ds , the distribution of neuronal activation onsets centered on each pause start was computed . the five sessions that displayed more than ten pauses ( n = 3 mice ) were kept for further analysis . in addition , only pauses which roughly occurred in the middle of a sequence ( 20%80% of sequence completion , n = 91 pauses ) could be analyzed , since information was needed about cell activation before and after the pause . we next used the onset of the last cell before the pause as a reference to center all sequences on the pause . in that way , the arrangement of the sequences around the pauses could be pooled across sessions . the evolution of the normalized temporal slope was measured using a linear fit over a sliding window of six cells ; the 95% confidence interval was calculated using the distribution of these slopes before the pause ( n = 8 slope values , gaussian approximation ) . in order to reveal a potential link between the animal 's speed and the dynamics of the ds , speed was normalized across sessions and pooled using a 20 s time window centered either on the onsets or the offsets of ds . these were calculated using the median activation onsets of the first or last five cells in the sequence , respectively . the 95% confidence interval was calculated using the speed distribution before the pause ( from the time when speed plateaus to pause onset , gaussian approximation ) . in order to assess whether a second peak in an apparently uniform distribution was significant , first , the distribution histogram was fitted using an ad hoc uniform function ( log - normal in our case ) and a least - squares fit algorithm ( lsqcurvefit function in matlab ) . second , the probability distribution for the value of each bin was calculated by computing random samples ( n = 10 samples ) using the fitted distribution . third , a significance curve was defined by applying the same percentile to all bins ( equiprobability ) . the value of the percentile was chosen so that the probability of having at least one peak bigger than the significance curve was 5% ( see figure s4 ) . this statistical test was robust against binning phase and size as long as the peak was not split between two bins ( see figures s4f we detected the onset and offset of its mean fluorescence transient over all sequences ; the onset being the time when the fluorescence transient reached 10% of its maximum value and the offset the time when the trace derivative reached its minimum value . this gave an estimate of the firing duration for each cell ; the distance field was defined as the product of the median speed and the firing duration thus calculated .

summarythe hippocampus is essential for spatiotemporal cognition . sequences of neuronal activation provide a substrate for this fundamental function . at the behavioral timescale , these sequences have been shown to occur either in the presence of successive external landmarks or through internal mechanisms within an episodic memory task . in both cases , activity is externally constrained by the organization of the task and by the size of the environment explored . therefore , it remains unknown whether hippocampal activity can self - organize into a default mode in the absence of any external memory demand or spatiotemporal boundary . here we show that , in the presence of self - motion cues , a population code integrating distance naturally emerges in the hippocampus in the form of recurring sequences . these internal dynamics clamp spontaneous travel since run distance distributes into integer multiples of the span of these sequences . these sequences may thus guide navigation when external landmarks are reduced .

photoacoustic tomography ( pat ) is a recently developed medical imaging paradigm that combines the high spatial resolution of ultrasound imaging with the high contrast of optical imaging @xcite . suppose a semitransparent sample is illuminated with a short pulse of electromagnetic energy near the visible range . then parts of the optical energy will be absorbed inside the sample which causes a rapid , non - uniform increase of temperature . the increase of temperature yields a spatially varying thermoelastic expansion which in turn induces an acoustic pressure wave ( see figure [ fig : pat ] ) . the induced acoustic pressure wave is measured outside of the object of interest , and mathematical algorithms are used to recover an image of the interior . basic principle of pat . a semitransparent sample is illuminated with a short optical pulse . due to optical absorption and subsequent thermal expansion within the sample an acoustic pressure wave is induced . the acoustic pressure wave is measured outside of the sample and used to reconstruct an image of the interior.,scaledwidth=85.0% ] original ( and also a lot of recent ) work in pat has been concentrated on the problem of reconstructing the initial pressure distribution , which has been considered as final image ( see , for example , @xcite ) . however , the recovered pressure distribution only provides indirect information about the investigated object . this is due to the fact , that the initial pressure distribution is the product of the optical absorption coefficient and the spatially varying optical intensity which again indirectly depends on the tissue parameters . as a consequence , the initial pressure distribution only provides qualitative information about the tissue - relevant parameters . quantitative photoacoustic tomography ( qpat ) addresses exactly this issue and aims at quantitatively estimating the tissue parameters by supplementing the wave inversion with an inverse problem for the light propagation in tissue ( see , for example , @xcite ) . to the best of our knowledge , apart from the very recent work @xcite , all existing reconstruction algorithms for qpat are currently performed via the following two - stage procedure : first , the measured pressure values are used to recover the initial pressure distribution caused by the thermal heating . in a second step , based on an appropriate light propagation model , the spatially varying tissue parameters are estimated from the initial pressure distribution recovered in the first step . however , any algorithm for solving an inverse problem requires prior knowledge about the parameters to be recovered as well as partial knowledge about the noise . if one solves qpat via a two - stage approach , appropriate prior information for the acoustic inverse problem is difficult to model , because the initial pressure depends on parameters not yet recovered . this is particularly relevant for the case that the acoustic data can only be measured on parts of the boundary ( limited - angle scenario ) , in which case the acoustic inverse problems is known to be severely ill - posed . further , using a two - stage approach , only limited information about the noise for the optical problem is available . in view of such shortcomings of the two - stage approach , in this paper we propose to recover the optical parameters directly from the measured acoustical data via a single - stage procedure . we work with the stationary radiative transfer equation ( rte ) as model for light propagation . our simulations show improved reconstruction quality of the proposed single - stage algorithm at a computational cost similar to the one of existing two - stage algorithms . obviously our single - stage strategy can alternatively be combined with the diffusion approximation , which has also frequently been used in qpat . in the present work we use the stationary rte since it is the more realistic model for light propagation in tissue . in combination with the two - stage approach , the rte has previously been used for qpat , for example , in @xcite . throughout this paper , let @xmath0 denote a convex bounded domain with lipschitz - boundary @xmath1 , where @xmath2 denotes the spatial dimension . we model the optical radiation by a function @xmath3 , where @xmath4 is the density of photons at location @xmath5 propagating in direction @xmath6 . the photon density is supposed to satisfy the rte , which reads @xmath7 here @xmath8 is the scattering coefficient , @xmath9 is the absorption coefficient , and @xmath10 is the photon source density . the scattering kernel @xmath11 describes the redistribution of velocity directions of scattered photons due to interaction with the background . the stationary rte is commonly considered as a very accurate model for light transport in tissue ( see , for example , @xcite ) . in order to obtain a well - posed problem one has to impose appropriate boundary conditions . for that purpose it is convenient to split the boundary @xmath12 into inflow and outflow boundaries , @xmath13 with @xmath14 denoting the outward pointing unit normal at @xmath15 . we then augment by the inflow boundary conditions @xmath16 under physically reasonable assumptions it can be shown that the stationary rte together with the inflow boundary conditions is a well - posed problem . in section [ sec : transport ] we apply a recent result of @xcite that guarantees the well - posedness of , even in the presence of voids ( parts of the domain under consideration , where @xmath17 and @xmath18 vanish ) . the absorption of photons causes a non - uniform heating of the tissue proportional to the total amount of absorbed photons , @xmath19 the heating in turn induces an acoustic pressure wave @xmath20 . the initial pressure distribution is given by @xmath21 , where @xmath22 is the grneissen parameter describing the efficiency of conversion of heat into acoustic pressure . for the sake of simplicity we consider the grneissen parameter to be constant , known and rescaled to one . we further assume the speed of sound to be constant and also rescaled to one . the photoacoustic pressure then satisfies the following initial value problem for the standard wave equation , @xmath23 the goal of qpat is to reconstruct the parameters @xmath17 and @xmath18 from measurements of the acoustic pressure @xmath24 outside @xmath25 . pressure measurements are usually taken as a function of time on parts of the boundary @xmath26 . in the following we assume that acoustic measurements are available for multiple optical source distributions ( illuminations ) . for that purpose , let @xmath27 for @xmath28 be given pairs of source patterns and boundary light sources . we use @xmath29 to denote the operator that takes the pair @xmath30 to the solution of the stationary rte , with @xmath31 and @xmath32 in place of @xmath33 and @xmath34 , and denote by @xmath35 the operator describing the corresponding thermal heating . further , we write @xmath36 for the operator that maps the initial data @xmath37 to the solution @xmath38 of the wave equation restricted to the boundary @xmath1 . appropriate functional analytic frameworks for @xmath29 , @xmath39 and @xmath40 will be given in section [ sec : forward ] , where we also study properties of these mapping . the reconstruction problem of qpat with multiple illuminations can be written in the form of a nonlinear inverse problem , @xmath41 here @xmath42 are the measured noisy data , the operators @xmath43 model the forward problem of qpat , @xmath44 are the noise in the data , and @xmath45 are the true parameters . the aim is to estimate the parameter pair @xmath46 from given data @xmath42 , and hence solving the inverse problem . in this paper we address the inverse problem by tikhonov regularization , @xmath47 where @xmath48 is a convex penalty and @xmath49 is the regularization parameter . we show that tikhonov regularization applied to single - stage qpat is well - posed and convergent ; see theorem [ thm : tik ] . for that purpose we derive regularity results for the heating operators @xmath39 in section [ sec : forward ] . to establish such properties we use results for the stationary rte derived recently in @xcite . for numerically minimizing the tikhonov functional we apply the proximal gradient algorithm ( also named forward backward splitting ) ; see section [ sec : min ] . the proximal gradient algorithm , is an iterative scheme for minimizing functionals that can be written as the sum of a smooth and a convex part @xcite . for the classical two - stage approach in qpat in combination with the diffusion approximation , the proximal gradient algorithm has recently been applied in @xcite . numerical results using the proximal gradient algorithm applied to our single - stage approach are presented in section [ sec : num ] , where we also include a comparison with the two - stage approach . of course , our single - stage approach can be combined with classical gradient or newton - type schemes . the proximal gradient algorithm is our method of choice , since its is very flexible and fast , and can be applied for a large class of smooth or non - smooth penalties . before actually studying the inverse problem of qpat we first make sure that the forward problem is well - posed in suitable spaces and that the data depend continuously on the parameters we intend to reconstruct . for that purpose we review a recent existence and uniqueness result for the stationary rte allowing for voids in the domain of interest @xcite . the use of a - priori estimates will lead to differentiability results for the operators @xmath29 and @xmath39 . the stationary rte has been studied in various contexts . the most prominent , apart from the transport of radiation in a scattering media , is reactor physics , where the equation is used in the group velocity approximation of the neutron transport problem . an extensive collection of results regarding applications as well as existence and uniqueness of solutions can be found in @xcite . the analysis of the rte becomes considerably more involved if internal voids , i.e. regions where scattering and absorption coefficient become zero , are allowed . suppose @xmath50 , and denote by @xmath51 the space of all measurable functions @xmath34 defined on @xmath52 for which @xmath53{\int_{\gamma_- } { \left\vert\nu(x ) \cdot \theta\right\vert } { \left\vertf(x,\theta)\right\vert}^p { \mathrm d}(x,\theta ) } & \text{if $ p < \infty$ } \\ \operatorname*{ess\,sup}_{(x,\theta ) \in \gamma_- } { \left\{{\left\vert\nu(x ) \cdot \theta\right\vert } { \left\vertf(x,\theta)\right\vert } \right\ } } & \text{if $ p = \infty$ } \end{cases}\ ] ] is finite . we write @xmath54 for the space of all measurable functions defined on @xmath55 such that @xmath56 is well defined and finite ( with the usual modification for @xmath57 ) . the subspace of all @xmath58 with @xmath59 will be denoted by @xmath60 . further , for a given scattering kernel @xmath61 we write @xmath62 for the corresponding scattering operator , @xmath63 throughout this article , the scattering kernel @xmath64 is supposed to be symmetric and nonnegative , and to satisfy @xmath65 for all @xmath6 . this reflects the fact that @xmath66 is a probability distribution describing the redistributions of velocity directions due to interaction of the photons with the background . under these assumption , the scattering operator @xmath67 is easily seen to be linear and bounded . using the notation just introduced , the stationary rte , can be written in the compact form @xmath68 by definition , a solution of the stationary rte , in @xmath69 is any function @xmath70 satisfying . the following theorem , which has been derived very recently in @xcite , states that under physically reasonable assumptions there exists exactly one such solution , that further continuously depends on the source pattern and the boundary light source . [ thm : exist ] let @xmath71 denote positive constants , let @xmath72 be measurable functions satisfying @xmath73 and @xmath74 , and let @xmath75 . then , for any source pattern @xmath76 and any boundary light source @xmath77 , the stationary rte , admits a unique solution @xmath78 . moreover , there exists a constant @xmath79 only depending on @xmath24 , @xmath80 and @xmath81 , such that the following a - priori estimate holds @xmath82 see @xcite . throughout this subsection , let @xmath50 , and let @xmath84 and @xmath85 be given source pattern and boundary light source , respectively . further , for fixed positive numbers @xmath86 we denote @xmath87 then @xmath88 is a closed , bounded and convex subset of @xmath89 , that has empty interior in the case that @xmath90 . the parameter - to - solution operator for the stationary rte is defined by @xmath91 where @xmath92 denotes the unique solution of , . according to theorem [ thm : exist ] the operator @xmath83 is well defined . note further , that @xmath83 depends on @xmath24 , @xmath33 , @xmath34 , @xmath80 and @xmath81 . since these parameters will be fixed in the following and in order to keep the notation simple we will not indicate the dependence of @xmath83 on these parameter explicitly . now we are in the position to state continuity properties of @xmath83 derived in @xcite . we include a short proof of these results as its understanding is very useful for the derivation of similar properties of the operator describing the heating that we investigate in the following subsection . [ thm : contf ] 1 . [ it : contf - a ] the operator @xmath83 is lipschitz - continuous . [ it : contf - b ] if @xmath93 , then @xmath83 is sequentially weakly continuous . [ it : contf - a ] let @xmath94 be two given pairs of absorption and scattering coefficients and denote by @xmath95 and @xmath96 the corresponding solutions of the stationary rte . since @xmath97 and @xmath98 , theorem [ thm : exist ] implies that the difference @xmath99 is an element of @xmath100 . further , this difference is easily seen to satisfy @xmath101 because @xmath67 is a bounded linear operator on @xmath102 , the right hand side in the above equation is actually contained in @xmath102 . therefore , a further application of theorem [ thm : exist ] yields @xmath103 where @xmath104 denotes the identity and @xmath105 the operator norm on @xmath106 . since @xmath107 is bounded independently of @xmath108 , this implies the lipschitz continuity of @xmath83 . [ it : contf - b ] let @xmath109 be a sequence in @xmath88 that converges weakly to the pair @xmath110 , and denote by @xmath111 and @xmath112 the corresponding solutions of the stationary rte . as in [ it : contf - a ] , one argues that the difference @xmath113 is contained in @xmath100 and satisfies @xmath114 now , from theorem [ thm : exist ] it follows that @xmath115 is invertible as an operator from @xmath116 to @xmath106 . consequently , the inverse mapping @xmath117 is linear and bounded and in particular weakly continuous . it therefore remains to show that @xmath118 weakly converges to zero in @xmath106 . to see this , denote by @xmath119 the dual index and let @xmath120 be any element in the dual of @xmath121 . by fubini s theorem we have @xmath122 the averaging lemma ( see , for example , @xcite ) implies that the averaging operator @xmath123 is compact for @xmath124 . since @xmath125 is bounded in @xmath126 , this implies that @xmath127 converges to @xmath128 with respect to @xmath129 . as @xmath130 we can conclude that @xmath131 converges to zero weakly . in the same manner one shows @xmath132 . finally , the equality @xmath133 and the use of similar arguments show that @xmath134 . for the solution of the inverse problem of qpat we will make use the derivative of @xmath83 that we compute next . for that purpose we call @xmath135 a feasible direction at @xmath136 if there exists some @xmath137 such that @xmath138 . due to the convexity of @xmath88 we have @xmath139 for all @xmath140 . the set of all feasible directions at @xmath141 will be denoted by @xmath142 . one immediately sees that @xmath143 for @xmath136 and any feasible direction @xmath144 we denote the one - sided directional derivative of @xmath83 at @xmath145 in direction @xmath37 by @xmath146 provided that the limit on the right hand side of exists . if both limits @xmath147 and @xmath148 exist and @xmath149 is bounded and linear , we say that @xmath83 is gtaux differentiable at @xmath150 and call @xmath151 the gtaux derivative of @xmath83 at @xmath145 . [ thm : fdiff ] for any @xmath136 , the one - sided directional derivative of @xmath83 at @xmath145 in direction @xmath152 exists . further , we have @xmath153 , where @xmath154 is the unique solution of @xmath155 if @xmath156 and @xmath157 , then @xmath83 is gteaux differentiable at @xmath150 . suppose @xmath158 and let @xmath159 be any feasible direction . for sufficiently small @xmath160 write @xmath161 and @xmath95 . as in the proof of theorem [ thm : contf ] one shows that @xmath162 is contained in @xmath163 and solves the equation @xmath164 . consequently the difference @xmath165 solves @xmath166 application of the a - priori estimate of theorem [ thm : exist ] shows the inequality @xmath167 together with the continuity of @xmath83 this implies that the one - sided directional derivative @xmath168 exists and is given by @xmath169 . finally , if @xmath156 and @xmath157 , then @xmath170 is bounded and linear and therefore @xmath83 is gteaux differentiable at @xmath150 . note that for any parameter pair @xmath171 , the solution of depends linearly and continuously on @xmath172 . as a consequence , the one - sided directional derivative can be extended to a bounded linear operator @xmath173 where @xmath154 is the unique solution of . we refer to this extension as the derivative of @xmath83 at @xmath145 . throughout this subsection , let @xmath84 and @xmath85 be given source pattern and boundary light source , respectively . as already mentioned in the introduction , photoacoustic signal generation due to the absorption of light is described by the operator @xmath175 to shorten the notation , in the following we will make use of the averaging operator @xmath176 defined by @xmath177 . by hlders inequality the averaging operator is well defined , linear and bounded . using the averaging operator we can write @xmath178 . [ thm : heating ] 1 . [ it : heating - a ] the operator @xmath174 is lipschitz continuous . [ it : heating - b ] if @xmath179 , then @xmath174 is sequentially weakly continuous . [ it : heating - a ] suppose that @xmath94 are two pairs of admissible absorption and scattering coefficients . the decomposition @xmath178 and the triangle inequality imply @xmath180 according to theorem [ thm : contf ] , the operator @xmath83 is lipschitz continuous . because @xmath181 is linear and bounded , also the composition @xmath182 is lipschitz . noting that @xmath183 and @xmath184 are bounded by constants independent of @xmath185 and @xmath186 , this implies the lipschitz continuity of @xmath174 . [ it : heating - b ] let @xmath109 be a sequence in @xmath88 that converges weakly to @xmath187 . since @xmath83 is weakly continuous and @xmath181 is linear and bounded , @xmath188 converges weakly to @xmath189 . further , for any function @xmath190 , the dual space of @xmath191 , we have @xmath192 the weak convergence of @xmath193 and @xmath188 therefore implies the weak convergence of @xmath194 to @xmath195 and shows the weak continuity of @xmath174 . note that for the case @xmath93 , the averaging operator @xmath181 is even compact ( see @xcite ) which implies the compactness of the composition @xmath182 . as a consequence , for any given @xmath17 , the partial mapping @xmath196 is compact . it seems unlikely , however , that the full operator @xmath174 is compact , too . [ thm : hdiff ] for any @xmath136 , the one - sided directional derivative of @xmath174 at @xmath145 in any feasible direction @xmath197 exists . further , we have @xmath198 where @xmath199 denotes the one - sides directional derivative of @xmath83 at @xmath145 in direction @xmath200 and can be computed as the solution of . finally , if @xmath156 and @xmath157 , then @xmath174 is gteaux differentiable at @xmath150 . let @xmath201 and let @xmath197 be a feasible direction . for sufficiently small @xmath160 , we have @xmath202 according to theorem [ thm : contf ] , the operator @xmath83 is continuous and therefore the first term converges to @xmath203 as @xmath204 . because @xmath83 is one - sided differentiable , see theorem [ thm : fdiff ] , the second term converges to @xmath205 . finally , if @xmath156 and @xmath157 , then @xmath206 is linear and bounded in the argument @xmath37 which implies the gteaux differentiability of @xmath174 at @xmath150 . recall that for any @xmath171 , the derivative @xmath207 is bounded and linear . therefore , the right hand side of depends linearly and continuously on @xmath172 . as a consequence , the one - sided directional derivative of @xmath174 at @xmath208 can be extended to a bounded linear operator @xmath209 . we will refer to this extension as the derivative of @xmath174 at @xmath145 . the derivative of @xmath174 can be written in the form @xmath210 . let @xmath211 be a bounded and convex domain with smooth boundary . we assume that @xmath212 and write @xmath213 for the space of all square integrable functions defined on @xmath214 that are supported in @xmath215 . likewise we denote by @xmath216 the space of all infinitely differentiable functions defined on @xmath214 having support in @xmath217 . further , let @xmath218 be a relatively open subset of @xmath219 , and denote by @xmath220 the maximal diameter of @xmath221 and by @xmath222 the distance between @xmath223 and the observation surface @xmath224 . [ def : w ] let @xmath225 be a smooth , nonnegative , compactly supported function with @xmath226 for all @xmath227 . we then define the wave operator by @xmath228 where @xmath24 denotes the unique solution of . the operator @xmath40 maps the initial data of the wave equation to its solution restricted to @xmath229 and models the acoustic part of the forward problem of pat . the cutoff function @xmath230 accounts for the fact , that in the two dimensional case the solution of the wave equation has unbounded support in time but measurements can only be made over a finite time interval . in the following we use a result from @xcite to show that @xmath40 is a bounded linear and densely defined operator , and therefore can be extended to a bounded linear operator on @xmath213 in a unique manner . [ thm : wave ] there exists some constant @xmath231 such that @xmath232 for all @xmath233 . consequently , there exists a unique bounded linear extension @xmath234 with some abuse of notation we again write @xmath40 for @xmath235 in the sequel . it is sufficient to consider the case when the data are measured on the whole boundary @xmath236 . the well known explicit formulas for the solution of in two and three spatial dimensions ( see , for example , @xcite ) imply that for every @xmath237 we have @xmath238 we define the spherical mean radon transform @xmath239 by @xmath240 for @xmath241 . with the spherical mean radon transform , the wave operator can be written as @xmath242 in the case of two spatial dimensions and @xmath243 in the three dimensional case . next we use a sobolev estimate derived in @xcite , which states that for every @xmath244 there exists a constant @xmath245 such that @xmath246 for any @xmath233 . application of this identity with @xmath247 and using the smoothing properties of the abel transform by degree @xmath248 for the case of two spatial dimensions yields the continuity of @xmath40 with respect to the @xmath249 topologies . in particular , @xmath40 has a unique bounded linear extension to @xmath213 . for solving the inverse problem of qpat we will further utilize an explicit expression for the adjoint of @xmath40 , that we compute next . for @xmath250 , and every @xmath251 , we have @xmath252 this is a simple application of fubini s theorem and the explicit expression for @xmath253 given in . in this section we solve the inverse problem of qpat by a single - stage approach . our setting allows acoustic measurement for multiple sources . such a strategy has been called multi - source qpat or multiple illumination qpat ( see @xcite ) . for that purpose , throughout this section @xmath254 and @xmath255 , for @xmath256 , denote given source patterns and boundary light sources , respectively . recall that @xmath0 denotes a bounded convex domain with lipschitz boundary and @xmath52 denotes the inflow boundary consisting of all pairs @xmath257 with @xmath258 . [ ] . the absorption of photons induces an initial pressure wave proportional to the heating @xmath259 . further , @xmath217 is supposed to be contained in another domain @xmath221 , and the pressure waves are measured with acoustic detectors located on a open subset @xmath229 of the boundary of @xmath221.,title="fig:",scaledwidth=35.0% ] to indicate the dependence of the solution of the stationary rte on the pair @xmath260 we write @xmath261 for the solution operator of the stationary rte , with sources @xmath260 . here @xmath262 is the set of all admissible pairs @xmath263 defined in . further , we use @xmath264 to denote the corresponding operator describing the heating . for the coupling to the acoustic problem , it will be convenient to consider @xmath265 as an element of @xmath266 , by extending it to a function defined on @xmath214 that is equal to zero on @xmath267 . further , recall the definition [ def : w ] of the wave operator @xmath40 modeling the acoustic problem , that maps the initial pressure @xmath37 in the wave equation to its solution restricted to @xmath229 . here @xmath221 is a convex domain with smooth boundary that contains the support of @xmath34 . to apply the results of section [ sec : forward ] , in the following we assume that @xmath212 . then , according to the section [ sec : forward ] , the operators @xmath39 are lipschitz continuous , weakly continuous and one - sided directional differentiable , and @xmath40 is linear and bounded . a practical representation of these domains is illustrated in figure [ fig : geometry ] . in order to apply standard techniques for the solution of inverse problems we write the reconstruction problem of ( multiple - source ) qpat as a single operator equation . for that propose we denote by @xmath268 the operator describing the entire forward problem of qpat . further we denote by @xmath269 the squared norm on @xmath270 . [ thm : prop ] 1 . the operator @xmath271 is sequentially weakly continuous . the operator @xmath271 is lipschitz continuous . 3 . for any @xmath272 , the one - sided directional derivative in any feasible direction @xmath273 exists . further , @xmath274 where @xmath275 is given by with @xmath83 replaced by @xmath29 . 4 . if @xmath276 and @xmath157 , then @xmath271 is gteaux differentiable at @xmath145 . all claims follow from the corresponding properties of the operators @xmath277 ( see theorems [ thm : heating ] and [ thm : hdiff ] ) and the boundedness of @xmath40 discussed in theorem [ thm : wave ] . the inverse problem of qpat with multiple illuminations consists in solving the nonlinear equation @xmath278 where @xmath279 is the unknown , @xmath280 are the given noisy data , @xmath281 is the forward operator , and @xmath282 is the noise in the data . our single - stage approach for qpat consists in estimating the parameter pair @xmath279 directly from . in contrast , existing two - stage approaches for qpat first construct estimates @xmath283 for the heating functions @xmath284 from data @xmath42 by numerically inverting @xmath40 , and subsequently solve @xmath285 for @xmath286 . there are at least two common methods for tackling an inverse problem of the form : tikhonov type regularization methods on the one and iterative regularization methods on the other hand . in the following we apply tikhonov regularization to the inverse problem of qpat . we address the inverse problem by tikhonov regularization with general convex penalty . for that purpose , let @xmath287 be a convex , and lower semicontinuous functional with domain @xmath288 . we assume that @xmath48 is chosen such that @xmath289 is non - empty . tikhonov regularization with penalty @xmath48 consists in computing a minimizer of the generalized tikhonov functional @xmath290 here @xmath49 is the so called regularization parameter which has to be chosen accordingly , to balance between stability with respect to noise and accuracy in the case of exact data . the data - fidelity term @xmath291 guarantees that any minimizer of predicts the given data sufficiently well . the regularization term @xmath292 on the other hand avoids over - fitting of the data and makes the reconstruction process well - defined and stable . note that tikhonov regularization with penalty @xmath48 is designed to stably approximate a solution of the constrained optimization problem @xmath293 here @xmath294 is an element in the range of @xmath271 and is referred to as exact data . any solution of is called @xmath48-minimizing solution of the equation @xmath295 . under the given assumptions there exists at least one @xmath48-minimizing solution , which however is not necessarily unique , see @xcite . the properties of the operator @xmath271 derived above and the use of general results from regularization theory yield the following result . [ thm : tik ] 1 . for data @xmath296 and every @xmath297 , the tikhonov functional @xmath298 has at least one minimizer . 2 . let @xmath297 , @xmath299 , and let @xmath300 be a sequence in @xmath270 with @xmath301 . then every sequence of minimizers @xmath302 has a weakly convergent subsequence . further , the limit @xmath303 of every weekly convergent subsequence @xmath304 is a minimizer @xmath145 of @xmath305 and satisfies @xmath306 for @xmath307 . 3 . let @xmath294 , let @xmath308 be a sequence converging to zero , and let @xmath309 be a sequence of data with @xmath310 . suppose further that @xmath311 satisfies @xmath312 and @xmath313 as @xmath307 . then the following hold : * every sequence @xmath314 has a weakly converging subsequence . * the limit of every weakly convergent subsequence @xmath315 of @xmath109 is an @xmath48-minimizing solution @xmath316 of @xmath295 and satisfies @xmath317 . * if the @xmath48-minimizing solution of @xmath295 is unique , then @xmath318 . since @xmath271 is sequentially weakly continuous ( see theorem [ thm : prop ] ) and @xmath262 is closed and convex , this follows from general results of tikhonov regularization with convex penalties , see for example , ( * ? ? ? 3.3 , thm . 3.4 , thm . 3.5 ) . for numerically minimizing the tikhonov functional we will use the gradient of the data - fidelity term @xmath319 recall that @xmath320 are the given data , @xmath29 is the solution operator for the stationary rte with source patterns @xmath31 and boundary light sources @xmath32 , @xmath181 is the averaging operator , and @xmath40 is the solution operator for the wave equation . let @xmath321 be some admissible pair of parameters and let @xmath322 denote the one - sided directional derivative of @xmath323 at @xmath263 . we define the gradient @xmath324 of @xmath323 at @xmath263 to be any element in @xmath325 satisfying @xmath326 from theorem [ thm : prop ] and the chain rule , it follows that @xmath327 exists for any feasible direction @xmath328 . further , in the case that @xmath17 and @xmath18 are strictly positive , we have @xmath329 , which implies that @xmath324 is uniquely defined by . in order to compute the gradient we derive a more explicit expression for the one - sided directional derivative . [ prop : gradient ] let @xmath272 be an admissible pair of parameters and let @xmath330 be a feasible direction . then we have @xmath331- { \mathbf a}(\phi_i{\phi^*}_i),{h_\mu}\right\rangle}_{l^2({\omega } ) } \\ + \sum_{i=1}^n { \left\langle- \phi_i { \phi^*}_i + ( { \mathbf k}\phi_i ) { \phi^*}_i,{h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \,,\end{gathered}\ ] ] where @xmath332 , and @xmath333 is the unique solution of the adjoint equation @xmath334 \quad\text { in } { \omega}\times { \mathbb s}^{d-1}\ ] ] satisfying the zero outflow boundary condition @xmath335 . obviously it is sufficient to consider the case @xmath336 , where we write @xmath337 , @xmath83 , @xmath92 and @xmath338 in place of @xmath42 , @xmath29 , @xmath339 and @xmath333 . by we have @xmath340,{h_\mu}\right\rangle}_{l^2({\omega } ) } \\ & \label{eq : term12}\hspace{3cm}+ { \left\langle{\mathbf a}^\ast\mu{\mathbf w}_{{\omega},{\lambda}}^*\left[{\mathbf w}_{{\omega},{\lambda } } \mu{\mathbf a}\phi - v\right],{\mathbf t}'(\mu,\sigma)({h_\mu},{h_\sigma})\right\rangle}_{l^2({\omega}\times { \mathbb s}^{d-1})}\,.\end{aligned}\ ] ] recall that @xmath338 is the solution of with source term @xmath341 $ ] and zero outflow boundary conditions @xmath335 . further , according to theorem [ thm : fdiff ] , the one - sided directional derivative of @xmath83 is given by @xmath153 , where @xmath154 is the unique solution of @xmath342 with inflow boundary conditions @xmath343 . the zero outflow and zero inflow boundary conditions of @xmath338 and @xmath154 , respectively , and one integration by parts , show @xmath344 . further , notice that the averaging operator @xmath181 has adjoint @xmath345 , @xmath346 , and that the scattering operator @xmath67 is self - adjoint . using these considerations , the second term in can be written as @xmath347,{\mathbf t}'(\mu,\sigma)({h_\mu},{h_\sigma})\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1})}\\ \begin{aligned } & = { \left\langle { \left ( -\theta \cdot \nabla_x + { \left(\mu + \sigma - \sigma{\mathbf k}\right ) } \right ) } { \phi^*},\psi\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \\&= { \left\langle{\phi^*},{\left ( \theta \cdot \nabla_x + { \left(\mu + \sigma - \sigma{\mathbf k}\right ) } \right ) } \psi\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \\&= { \left\langle{\phi^*},-\left({h_\mu}+{h_\sigma}-{h_\sigma}{\mathbf k}\right)\phi\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \\&= -{\left\langle\phi{\phi^*},{h_\mu}+{h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } + { \left\langle({\mathbf k}\phi ) { \phi^*},{h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \\&= -{\left\langle\phi{\phi^*},{\mathbf a}^\ast({h_\mu})+{h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } + { \left\langle({\mathbf k}\phi ) { \phi^ * } , { h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \\&= { \left\langle -{\mathbf a}(\phi{\phi^*}),{h_\mu}\right\rangle}_{l^2({\omega } ) } + { \left\langle-\phi{\phi^*}+ ( { \mathbf k}\phi ) { \phi^*},{h_\sigma}\right\rangle}_{l^2({\omega}\times\mathbb{s}^{d-1 } ) } \ , . \end{aligned } \end{gathered}\ ] ] together with this yields the desired identity . let @xmath272 be an admissible pair of absorption and scattering coefficient . if @xmath185 are both strictly positive , then one concludes from proposition [ prop : gradient ] that the gradient of @xmath323 at @xmath145 is uniquely defined and given by @xmath348 with @xmath349- { \mathbf a}(\phi_i{\phi^*}_i)\right ) } \\ \label{eq : gradient3 } \nabla_\sigma { \mathcal f}(\mu,\sigma ) & = \sum_{i=1}^n { \left(- \phi_i { \phi^*}_i + ( { \mathbf k}\phi_i ) { \phi^*}_i\right ) } \,.\end{aligned}\ ] ] here @xmath332 , and @xmath333 is the solution of the adjoint equation with zero outflow boundary condition . in the case that @xmath185 are not both strictly positive , the gradient is not uniquely defined by . however , proposition [ prop : gradient ] implies that the vector @xmath324 defined by , still satisfies . we therefore take , as gradient of @xmath323 at any @xmath272 . in order to minimize the tikhonov functional we apply the proximal gradient ( or forward backward splitting ) algorithm , which is an iterative algorithm for minimizing functionals that can be written as a sum @xmath350 , where @xmath323 is smooth and @xmath351 is convex @xcite . the proximal gradient algorithm computes a sequence of iterates by alternating application of explicit gradient steps for the first functional @xmath323 and implicit proximal steps for the second functional @xmath351 . to apply the proximal gradient algorithm for minimizing the tikhonov functional we take @xmath352 for the first and @xmath353 for the second functional . the proximal gradient algorithm then generates a sequence @xmath354 of iterates defined by @xmath355 here @xmath356 is an initial guess , @xmath357 is the step size in the @xmath358-th iteration , @xmath348 is the gradient of @xmath323 given by , , and @xmath359 is the proximity operator corresponding to the functional @xmath360 . note that the gradient @xmath361 of the data - fidelity term is easily shown to be lipschitz continuous . this either can be deduced from the explicit expressions , or by using @xmath362 . in any case , the lipschitz continuity of @xmath363 follows from similar arguments as in the proofs of the lipschitz - continuity of @xmath83 and @xmath174 , given in section [ sec : f ] and section [ sec : h ] , respectively . convergence of the proximal gradient algorithm is well known for the case that @xmath323 is convex with @xmath364-lipschitz continuous gradient and step sizes satisfying @xmath365 $ ] for some constant @xmath137 , see @xcite . these results are also valid for infinite dimensional hilbert spaces . because our forward operator @xmath271 is nonlinear , the data - fidelity term @xmath323 is non - convex and these results are not directly applicable to qpat . note however recently , the converge analysis of the proximal gradient analysis has been extended to the case of non - convex functionals ; see @xcite . our numerical simulations are carried out in @xmath366 spatial dimensions . the stationary rte is solved on a square domain @xmath367 ^ 2}$ ] . for the scattering kernel we choose the two dimensional version of the henyey - greenstein kernel , @xmath368 where @xmath369 is the anisotropy factor . before we present results of our numerical simulations we first outline how we numerically solve the stationary rte in two spatial dimensions . this step is required for evaluating both , the forward operator @xmath271 and the gradient @xmath361 of the data - fidelity term . for the numerical solution of the stationary rte , we employ a finite element method . for that purpose one calculates the weak form of equation , by integrating the equation against a test function @xmath370 . integrating by parts in the transport term yields @xmath371 here we dropped all dependencies on the variables to shorten notation and @xmath372 denotes the usual surface measure on @xmath373 . the numerical scheme replaces the exact solution by a linear combination in the finite element space @xmath374 where any @xmath375 is the product of a basis function in space and a basis function in velocity and the sum ranges over all possible combinations . the spatial domain is triangulated uniformly with mesh size @xmath37 as illustrated in figure [ fig : triangulation ] . the velocity direction on the circle is divided into @xmath376 equal subintervals . we use @xmath377 lagrangian elements , i.e. piecewise affine functions , in the two dimensional spatial domain as well as for the angle . [ ] ^2}$ ] is divided into @xmath378 triangles . to any of the @xmath379 grid points @xmath380 a piecewise affine basis function is associated , that takes the value one at one grid point and the value zero on all other grid points , and is affine on every triangle.,title="fig:",scaledwidth=25.0% ] to increase stability in low scattering areas we add some artificial diffusion in the transport direction . this is called the streamline diffusion method , see for example @xcite and the references therein . in the streamline diffusion method the solution @xmath92 is approximated in the usual way by . however , the test functions take the form @xmath381 where the additional term introduces some artificial diffusion . in our experiments , the stabilization parameter is taken as @xmath382 for @xmath383 and zero otherwise . note that the streamline diffusion method provides a fully consistent stabilization of the original problem . making the ansatz for the numerical solution and using test functions of the form , equation yields a system of linear equations @xmath384 for the coefficient vector of the numerical solution . the entries of @xmath385 and @xmath386 can be calculated by setting @xmath387 and @xmath388 . for simplicity we only consider the case @xmath389 corresponding to zero sources of internal illumination . then , similar to we obtain @xmath390 the entries of the matrix @xmath385 now can be calculated by evaluating the integrals on the left hand side of . the right hand side of together with the prescribed boundary light sources on @xmath52 yields the entries of @xmath386 . for the following numerical results , the stationary rte is solved by the finite element method outlined in subsection [ sec : fe ] . for that purpose the domain @xmath391 ^ 2}$ ] is discretized by a mesh of triangular elements ( compare figure [ fig : triangulation ] ) . the angular domain is divided into @xmath376 subintervals of equal length . the anisotropy factor is taken as @xmath392 and the scattering coefficient is taken as @xmath393 . we use a single boundary source distribution @xmath34 representing a planar illumination along the lower edge @xmath394 \times { \left\{-1\right\}}}$ ] , where all photons enter the domain vertically . for solving the inverse problem we used a mesh containing @xmath395 triangular elements . in order to avoid performing inverse crime , for simulating the data we used a finer mesh containing @xmath396 triangular elements . the solution of the two - dimensional wave equation is computed by numerically evaluating the solution formula , where the detection curve @xmath397 is a half - circle on the boundary of @xmath398 . the adjoint @xmath399 is evaluated by numerically implementing . this can be done efficiently by a filtered backprojection algorithm as described in @xcite . the geometry of @xmath223 and @xmath224 is similar to the one illustrated in figure [ fig : geometry ] . for our initial experiments we assume the scattering coefficient @xmath18 to be known . in such a situation , the proximal gradient algorithm outlined in the subsection [ sec : min ] reads @xmath400 where @xmath357 is the step size , @xmath401 is the gradient of @xmath323 in the first component , given by , and @xmath402 is the proximity operator similar as in . in the presented numerical examples the regularization term is taken as a quadratic functional @xmath403 . in order to speed up the iterative scheme we compute the proximity operator only approximately by projecting the unconstrained minimizer @xmath404 on @xmath262 . therefore the main numerical cost in the proximal step is the solution of a linear equation , which is relatively cheap compared to the evaluation of the gradient @xmath405 . in figures [ fig : sim1 ] and [ fig : sim ] we present results of our numerical experiments . figure [ fig : sim1 ] shows the true absorption coefficient as well as the heating function and the simulated pressure data . the left image in figure [ fig : sim ] shows the numerical reconstruction with the proposed single - stage approach using 40 iterations of the proximal gradient algorithm . we observed empirically , that the proximal gradient algorithm stagnated after 20 to 40 iterations and therefore we used 40 as a stopping index . for comparison purpose , the right image in figure [ fig : sim ] shows reconstruction results using the classical two - stage approach . for that purpose we apply tikhonov regularization and the proximal gradient algorithm to the inverse problem @xmath406 . again the iteration has been stopped after 40 iteration , where the iteration has been stagnated . the approximate heating @xmath37 is computed numerically by applying the two dimensional universal backprojection formula @xcite to the acoustic data @xmath407 . all computations have been performed in matlab on a notebook with @xmath408{ghz}$ ] intel core i7 processor . the total computation times have been 26 minutes for the two - stage approach and 38 minutes for the single - stage approach . one notices that in both reconstructions some boundaries in the upper half are blurred . such artifacts are expected and arise from the ill - posedness of the acoustical problem when using limited - angle data ; see @xcite . however these artifacts are less severe for the single - stage algorithm than for the classical two - stage algorithm . further , in this example , the single - stage algorithm also yields a better quantitative estimation of the values of the absorption coefficient . added noise ( left ; detector location varies in the horizontal and time in the vertical direction ) , reconstructed absorption coefficient using our single - stage approach ( middle ) the classical two - stage approach ( right).,title="fig:",scaledwidth=31.0% ] added noise ( left ; detector location varies in the horizontal and time in the vertical direction ) , reconstructed absorption coefficient using our single - stage approach ( middle ) the classical two - stage approach ( right).,title="fig:",scaledwidth=30.0% ] added noise ( left ; detector location varies in the horizontal and time in the vertical direction ) , reconstructed absorption coefficient using our single - stage approach ( middle ) the classical two - stage approach ( right).,title="fig:",scaledwidth=30.0% ] finally , in order to investigate the stability of the derived algorithms with respect to noise , we applied the single - stage and the two - stage algorithm after adding gaussian white noise to the data with standard deviation equal to @xmath409 of the maximal absolute data values . note that for both , the single - stage and the two - stage algorithm , noise has only been added to the acoustic data . the reconstruction results for noisy data are shown in figure [ fig : sim - noisy ] . as can be seen both algorithms are quite stable with respect to data perturbations . however , again , the single - stage approach yields better results and less artifacts than the two - stage algorithm . in this paper we proposed a single - stage approach for quantitative pat . for that purpose we derive algorithms that directly recover the optical parameters from the measured acoustical data . this is in contrast to the usual two - stage approach , where the absorbed energy distribution is estimated in a first step , and the optical parameters are reconstructed from the estimated energy distribution in a second step . our single - stage algorithm is based on generalized tikhonov regularization and minimization of the tikhonov functional by the proximal gradient algorithm . in order to show that tikhonov regularization is well - posed and convergent we analyzed the stationary radiative transfer equation , in a functional analytic framework . for that purpose we used recent results of @xcite that guarantees the well - posedness even in the case of voids . we presented results of our initial numerical studies using a simple limited angle scenario , where the scattering coefficient is assumed to be known . in this situation our single - stage algorithms has led to less artifacts than the two - stage procedure . more detailed numerical studies will be presented in future work . in that context , we will also investigate the use of multiple illuminations and multiple wavelength , which allows to also reconstruct the in general unknown scattering coefficient and grneissen parameter . we further plan to investigate the use of more general regularization functionals such as the total variation in combination with the single - stage approach . this work has been supported by the tyrolean science fund ( tiroler wissenschaftsfonds ) , project number 153722 . we want to thank the referees for useful comments which helped to improve our manuscript , and for bringing reference @xcite to our attention . m. agranovsky , p. kuchment , and l. kunyansky . on reconstruction formulas and algorithms for the thermoacoustic tomography . in l. v. wang , editor , _ photoacoustic imaging and spectroscopy _ , chapter 8 , pages 89101 . crc press , 2009 . h. attouch , j. bolte , and b. f. svaiter . convergence of descent methods for semi - algebraic and tame problems : proximal algorithms , forward backward splitting , and regularized gauss seidel methods . , 137(1 - 2):91129 , 2013 . b. t. cox , s. r. arridge , p. kstli , and p. c. beard . two - dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method . , 45(8):18661875 , 2006 . b. t. cox , t. tarvainen , and s. r. arridge . multiple illumination quantitative photoacoustic tomography using transport and diffusion models . in g. bal , d. finch , p. kuchment , j. schotland , p. stefanov , and g. uhlmann , editors , _ tomography and inverse transport theory _ , volume 559 of _ contemporary mathematics _ , pages 112 . ams , 2011 .

the development of efficient and accurate image reconstruction algorithms is one of the cornerstones of computed tomography . existing algorithms for quantitative photoacoustic tomography currently operate in a two - stage procedure : first an inverse source problem for the acoustic wave propagation is solved , whereas in a second step the optical parameters are estimated from the result of the first step . such an approach has several drawbacks . in this paper we therefore propose the use of single - stage reconstruction algorithms for quantitative photoacoustic tomography , where the optical parameters are directly reconstructed from the observed acoustical data . in that context we formulate the image reconstruction problem of quantitative photoacoustic tomography as a single nonlinear inverse problem by coupling the radiative transfer equation with the acoustic wave equation . the inverse problem is approached by tikhonov regularization with a convex penalty in combination with the proximal gradient iteration for minimizing the tikhonov functional . we present numerical results , where the proposed single - stage algorithm shows an improved reconstruction quality at a similar computational cost . * keywords . * quantitative photoacoustic tomography , stationary radiative transfer equation , wave equation , single - stage algorithm , inverse problem , parameter identification * ams classification numbers . * 44a12 , 45q05 , 92c55 .

crystal growth by molecular beam epitaxy ( mbe ) involves processes on quite different physical scales , from atomic to micrometer scales . to capture the large scale features it may be appropriate to represent the surface as a continuous height field @xmath0 above a set of so called base points @xmath1 where @xmath2 . the surface dynamics is then modelled by a parabolic pde for @xmath0 , which often is a starting point interesting mathematical problems , and in some cases for rigorous results @xcite , which were an important part of this workshop . their mathematical tractability somehow contrasts with the lack of rigour in their derivations , as we shall see below . it would be nice to `` prove '' a certain pde to be the appropriate large scale model for some underlying more elementary model , typically a stochastic model of the solid on solid type . this would connect the result for large scales with the microscopic model which is much closer to physical reality . nevertheless , often this chain can be closed in a heuristic sense , and this lecture presents some examples . it is organised as follows : first , the heuristic procedure of deriving a continuum model is motivated and its structure is explained . then , two examples of applications are presented , covering in some sense extreme cases of applicability of continuum models ; ( i ) coarsening of mound patterns in homoepitaxy and ( ii ) damping of width oscillations in the transition from layer by layer to rough growth . last , the general applicability of continuum models to mbe growth is discussed , in particular those features of discreteness of the underlying process which can only be covered incompletely by a continuum model . open questions in the derivation which have not been addressed so far , but appear to be solvable , are mentioned here . the main purpose of this introductory lecture is to recollect the physical motivation of the class of models which deal with the largest spatial and temporal scales involved in mbe growth , and to give some intuition to other more mathematical approaches . continuum models for surface growth are comparable to the hydrodynamic limit of microscopic models of fluid dynamics . behind the continuous macroscopic height field @xmath0 one has to imagine an ensemble of microscopic configurations which are locally in a steady state . figure [ fig : ensemble ] illustrates this relationship . the local state is subject to changes on time scales , ideally longer than the relaxation times into those states , which leads to the dynamics of the height field . as a representation.,width=302 ] the structure of the pde governing the dynamics of @xmath0 reflects different elementary processes and their symmetries . in growth from molecular beam epitaxy there is * a deposition flux @xmath3 , i.e. , the deposited volume per time and surface area , * possibly an evaporation loss @xmath4 , again volume per time and area , * a surface current @xmath5 on terraces and along steps , transported volume per time and length , i.e. , cross section on the surface . multiplied with a volume density @xmath6 these quantities become mass fluxes and currents . all three depend on the actual surface configuration @xmath7 , e.g. , on local slopes , their orientations and curvatures . elastic interactions and terrace adatom detachment with subsequent redeposition couple the dynamics at a surface point _ nonlocally _ to surface configurations at other places . there may also be an _ explicit _ space dependence beyond the influence of the height configuration , e.g. , for a non uniform deposition with pulsed flux . deposition , evaporation , and surface current are combined into a _ continuity equation _ @xmath8 note that small local slopes are assumed , such that any geometric prefactors to the divergence of the surface current typically are neglected . a full derivation from local steady states in the sense postulated above is of course impossible in almost any case , apart from some one - dimensional examples @xcite . one therefore has to rely on heuristically justified ( _ reasonable _ ) assumptions for the dynamic quantities involved . the connection to the more detailed models on smaller scales is given by length scales which influence the surface morphology and become visible . explained more precisely in the other introductory lectures of this conference @xcite they are * @xmath9 , the lattice spacing of the crystal . * @xmath10 , the diffusion length , i.e. , the `` typical '' distance of nucleation sites on a terrace , with a non trivial dependence on the deposition rate @xmath11 and adatom diffusivity @xmath12 . * @xmath13 , the ehrlich schwoebel length , i.e. , a measure for the reflectivity of the barrier at a downward step . roughly speaking , an adatom located right at a downward step is equally likely to hop downward as it is to reach the next upward step , if it lies at a distance @xmath13 . * @xmath14 , the average distance between two truly ascending at a vicinal surface of slope @xmath15 without counting islands between them . * ehrlich schwoebel effect on terraces * + as was realised quite early the most important ingredient of eq . ( [ eq : surfdyn ] ) is a non equilibrium current on surface terraces induced by ehrlich schwoebel ( es ) barriers @xcite . for small average slopes @xmath16 with @xmath17 or @xmath18 , the es barrier induces a net uphill current @xmath19 . inserted into the surface current in eq . ( [ eq : surfdyn ] ) this results in a _ destabilising _ term for the height equation @xmath20 . of course one would like to know the functional dependence of the surface current @xmath21 beyond this approximation for small slopes . following an argument of siegert for @xmath22 dimensions @xcite there must also be surface orientations with stabilising surface current : think of @xmath23 as a vector field on the tangent bundle of the unit sphere of possible surface orientations . by the es instability all high symmetry orientations have @xmath21 pointing outward around a zero . by continuity of @xmath21 as a function of the orientation there must be zeroes with the current field pointing inward to the zero , i.e. , orientations stabilised by the surface current . these qualitatively fundamental properties , the existence of unstable and stable surface orientations , can be cast into a heuristically postulated function @xmath24 . . left : in plane isotropy , @xmath25 , continuous set of stable slopes @xmath26 . right : anisotropy , four fold symmetry , @xmath27 with @xmath28 , discrete set of stable slopes at @xmath29.,title="fig:",width=188 ] . left : in plane isotropy , @xmath25 , continuous set of stable slopes @xmath26 . right : anisotropy , four fold symmetry , @xmath27 with @xmath28 , discrete set of stable slopes at @xmath29.,title="fig:",width=188 ] figure [ fig : es ] shows two such examples , one isotropic within the crystal terrace a somewhat artificial but nevertheless theoretically interesting case , one isotropic , with four fold ( @xmath30 ) rotational symmetry . * ehrlich schwoebel effect at steps * + the ehrlich schwoebel effect also has an influence on adatom diffusion along steps , allowing for attachment of atoms to kinks preferentially from one side , as is sketched in fig . [ fig : ess ] . it is one important mechanism causing a step meandering instability on growing vicinal surfaces @xcite . politi and krug derived the contribution @xmath31 of non equilibrium current along steps to the total surface current for a surface with given average slope which is assumed to be constant on a sufficiently large region such that steps have a well defined average density and orientation with respect to the underlying crystal lattice @xcite . * curvature relaxation * + clearly on small scales the destabilising es effects encountered in this section so far are balanced . too thin protrusions are forbidden by their cost in surface free energy . for thermal relaxation towards equilibrium the corresponding continuum dynamics are straightforward to derive . the surface free energy @xmath32 weights each surface element by its orientation dependent contribution @xmath33 . the gradient in chemical potential @xmath34 drives the relaxational surface current which is also proportional to the ( tensorial and orientation dependent ) adatom mobility @xmath35@xmath36 . a linear expansion around a surface of constant slope @xmath37 small enough to again neglect geometric effects @xcite yields @xmath38 \ ! \cdot \ ! \nabla h. \label{eq : mullins}\ ] ] the expression in square brackets is generally called the surface _ @xmath39 where @xmath40 denotes derivation with respect to the slope dependence of @xmath41 and @xmath42 is the unity matrix . strictly speaking this derivation applies only to _ equilibrium relaxation_. for a far from equilibrium process like mbe growth it does not make sense to define a surface free energy per area @xmath33 , although the `` true '' contribution of the surface current due to relaxation by curvature most likely has a functional form of that type . the identification of these contributions and the correct derivation of the corresponding continuum form remains an open question . for most applications it will be correct to assume a _ deposition _ intensity @xmath11 constant in time and space . interesting cases with _ explicit _ space and time dependence are ( i ) pulsed molecular beams , used to decrease the second layer island nucleation rate , and ( ii ) geometric inhomogeneities if the beam does not reach every part of the surface under the same angle . the most important mechanism for _ implicit _ deposition heterogeneity is steering , where the incident atoms are deflected by attractive interaction with surface features such as islands and mounds , and effect which is of course most prominent under grazing incidence @xcite . at sufficiently high temperatures _ desorption _ may become an important effect . terrace adatoms then will be most susceptible to desorption at a rate @xmath43 , during their diffusion time before they reach the stronger binding steps . to a first approximation the desorption rate depends on the average distance to the next reachable step and therefore on the surface slope : the higher the slope , the more steps are present and the lower the desorption loss . within an ansatz la burton frank @xcite one can relate the desorption length @xmath44 , diffusion length @xmath10 , and slope @xmath45 @xcite to an expression for the desorption loss in volume per time and surface area @xmath46 \approx f \ ; \frac{(\ell_{\rm d}/x_{\rm s})^2/3}{1+(\nabla h)^2}.\ ] ] there are three sources for _ noise _ in mbe growth @xcite : ( i ) deposition is a stochastic process of single events , so @xmath11 has to be complemented by a `` shot noise '' term @xmath47 with statistics @xmath48 ( ii ) adatom diffusion also consists of single events , and to a first approximation surface currents are blurred by a `` diffusion noise '' term @xmath49@xmath50 with statistics @xmath51 ( iii ) nucleations also occur at random but the precise form of this contribution remains an open question . there are nontrivial correlations in time , as new islands tend to nucleate close to centres of previously nucleated islands . the space dependence of the nucleation noise correlator @xmath52 is expected to have the form @xmath53 @xcite . heuristic surface currents as in the example in fig . [ fig : es ] lead to a symmetry in the resulting dynamical equation which can be used for evaluation , but is too strong a restriction compared to the `` real '' dynamics and may lead to erroneous results . if @xmath21 uniquely depends on the slope @xmath54 and not on derivative of its functions then crystal symmetry imposes @xmath55 . the resulting term of surface dynamics is invariant under the transformation @xmath56 and so will be the surface configurations obtained from that . breaking of this symmetry , e.g. , by terms as @xmath57 in @xmath58 or an evaporation term @xmath59 do in fact change the characteristics of the dynamics substantially @xcite one can take advantage of this simple slope dependence if there is a scalar function @xmath60 such that @xmath61 . stable zeroes of @xmath21 then are minima of @xmath60 . if additionally the curvature relaxation is of a simple `` scalar '' form @xmath62 @xmath63 @xmath64 there is a lyapunov functional of the dynamics @xmath65 \ ; d^2x\ ] ] and the surface dynamics eq . ( [ eq : surfdyn ] ) can be written for the field of slopes @xmath16 as @xmath66 if @xmath54 is interpreted as a two dimensional magnetic order parameter this from compares to conserved ( model b ) relaxational dynamics , with the only restriction that it remains a conservative field at all times , @xmath67 . facets in the surface are regions of constant slope , and appear as domains of constant `` magnetisation '' , edges between them are domain walls . as compared to its magnetic analogon , here the parallel component of @xmath54 remains constant across a domain wall , which in the case of discrete stable zeroes of the current function ( right panel of fig . [ fig : es ] ) restricts the possible domain wall orientations and imposing constraints on the relaxational dynamics @xcite . ( c.f . left panel in fig . [ fig : es]).,title="fig:",width=188 ] ( c.f . left panel in fig . [ fig : es]).,title="fig:",width=188 ] ( c.f . left panel in fig . [ fig : es]).,title="fig:",width=188 ] ( c.f . left panel in fig . [ fig : es]).,title="fig:",width=188 ] [ fig : coarse ] continuum equations are now applied in two examples of very basic choices in eq . ( [ eq : surfdyn ] ) . in some sense they highlight two opposite regimes , ( i ) on very long length and time scales coarsening of mounds in homoepitaxy , and ( ii ) on short scales resolving the lattice structure in the transition from layer by layer to rough growth . in some sense the simplest example of a surface dynamics equation is the analogon to the classical xy model in the sense of eq . ( [ eq : modelb ] ) @xmath68 , \label{eq : siegert}\ ] ] i.e. , with the current function depicted in the left panel of fig . [ fig : es ] . an initially flat surface @xmath69 is linearly unstable to fluctuations of wave lengths @xmath70 which therefore initially grow exponentially . once slopes of @xmath71 are reached the surface organises itself into a pattern of regular mounds and troughs which keep the symmetry @xmath72 of eq . ( [ eq : siegert ] ) . plane isotropy of ( [ eq : siegert ] ) is locally broken by the need to arrange the mounds and troughs into a regular pattern and facets with sharp wedges form @xcite . subsequently the pattern of mounds and troughs coarsens keeping a single typical length scale and a statistically self similar pattern at every time . the average mound size is found to increase with time as @xmath73 @xcite . in a weak sense this can be proved as an upper bound for an appropriate time average of the length scales @xmath74 observed up to a give time @xmath75 @xcite . here only a quick handwaving argument is given following @xcite : . the only macroscopic length scale is the domain size @xmath74.,width=302 ] [ fig : csketch ] the spatial average of the interface width @xmath76 ( where @xmath77 ) increases due to eq . ( [ eq : siegert ] ) as @xmath78 by the sketch of fig . [ fig : csketch ] the contributions of these terms are estimated to be of order @xmath79 : the facets are flat and the curvature is restricted to narrow strips of with @xmath71 at the domain boundaries , which have a relative weight of @xmath79 . also , here the slopes are smaller than the stable value @xmath80 attained at the facets . so all terms give a contribution of @xmath81 and because of the stable slope @xmath82 the increase in width leads to the estimate @xmath83 the same rough heuristic argument holds for anisotropic surface currents with discrete minima , i.e. , a discrete set of preferential surface orientations , but the four fold symmetry ( right panel of fig . [ fig : es ] ) plays a special role because two kinds of edges occur , such that in general the assumption of a single length scale @xmath74 in the system is wrong @xcite . layer by layer growth is technologically interesting because one can monitor the subsequent deposition of layers by oscillations in the surface width . it is nearly flat around integer fillings and the roughness takes maxima at half integer fillings . during growth the interface roughens and the width oscillations decay @xcite . the ehrlich schwoebel barrier and mounding instability is one prominent mechanism destroying layer by layer growth , and so can be any inhomogeneity in the deposition intensity @xmath84 . although weaker , even the fluctuations of shot noise have this effect , and it can be captured by a simple renormalisation group calculation . the simplest way to implement layer lattice effects into an continuum surface equation like eq . ( [ eq : surfdyn ] ) is pursued by the conserved _ sine gordon_equation @xmath85 among other the surface current is driven to regions of incomplete fillings such that @xmath86 is favoured to take integer values @xcite . the notation distinguishes between the lattice constant normal ( @xmath87 ) and parallel ( @xmath88 ) to the surface terraces which will be used in the following analysis . in a momentum shell renormalisation one can average over the fluctuations caused by the short wavelength components of the noise , @xmath89 , where @xmath90 only contains modes of wavenumber smaller than some cutoff @xmath91 and @xmath92 the others . one now tries to approximate the dynamic equation for the averaged height field @xmath93 by an equation like ( [ eq : csg ] ) with suitably adjusted parameters . after rescaling , an effective _ renormalised _ equation is obtained . three important physical interpretations can be obtained from the renormalised parameters of eq . ( [ eq : csg ] ) . \(i ) by the interplay of the diving force @xmath11 and the lattice potential the up down symmetry ( @xmath94 ) is broken and a term @xmath95 is created . \(ii ) the strength of the lattice potential @xmath96 is damped out decays exponentially with coverage @xmath97 like @xmath98 \(iii ) in a finite size sample smaller than the so called _ layer coherence _ length @xmath99 renormalisation has to stop before the lattice potential has decayed . shot noise fluctuations can not accumulate to the point where width oscillations are completely blurred . in presenting the model derivations and examples of their application it becomes clear that continuum models are a good tool for questions where the inherent _ simplifications _ are justified . the insight gained from partial differential equations is different from results of more microscopic model . last not least continuum equations can handle larger systems and longer times than monte carlo simulations or even molecular dynamics . in many cases the phenomena of particular technological interest can not be captured by continuum equations of the type described in this lecture . magic island shapes , surface reconstruction , step bunching , formation of quantum dots and wires are just a few examples . even if one is nt interested in these inherently discrete phenomena themselves they nevertheless carry over to the behaviour on larger scales and a naive straightforward derivation of large scale continuum models may be wrong . the implementation of noise for some questions , such as roughening , is one such example . also , the effective `` large scale '' ehrlich schwoebel barrier of a step is influenced by kinks along the step which may serve as channels for downward incorporation of a terrace adatom . obtaining the correct effective barrier , dependent on orientation and curvature of the step certainly is a nontrivial task . an important part of the surface current @xmath58 flows along steps , as has become clear in the above derivation . in ref . @xcite the step current due to kink es barriers is derived as a function of the surface orientation or slope . an open question is the role of step curvature and therefore of surface curvature on the step current . also on the surface itself , the regularising term as it is derived in eq . ( [ eq : mullins ] ) , should be derived from true nonequilibrium arguments . to do so , one would have to incorporate island nucleations , the creation and annihilation of steps . one possible approach is to introduce fields for the densities of adatoms , advacancies , steps , kinks , and for their orientations . locally they could be treated as mean field densities with certain effective `` reaction '' rates , but in their spatial interaction , by diffusion and advective transport , one could obtain a conceptually more fundamental continuum model for surface growth . in this lecture an overview of continuum models for mbe surface growth has been given which includes * the conceptual foundation of continuum models as a limit of more detailed small scale approaches , * heuristic derivations due to lack of rigorous or even exact ways to obtain them , * the structure and the symmetry of the equations obtained in that way , * two examples emphasising two opposite time limits in the growth process with the application of two contrary methods , * criticism of weak points in continuum modelling , open questions and some speculations about answers to them . the main purpose was to highlight the physical background and give some intuition of possible approaches to it as a basis for mathematical treatments , both rigorous and numerical . it should be seen as a complement of the lectures @xcite and @xcite which give a similar introduction to lattice and burton cabrera frank models respectively . although continuum models seem to fail in some important physical aspects they nevertheless are a good tool and subject for mathematical approaches . 99 m. biehl ( 2004 ) this volume . w.k . burton , n. cabrera , f.c . frank , _ the growth of crystals and the equilibrium of their surfaces _ london a * 243 * ( 1951 ) 299358 . b. derrida , e. domany , and d. mukamel , _ an exact solution of the one dimensional asymmetric exclusion model with open boundaries _ , j. stat . * 69 * ( 1992 ) 667687 ; g. schtz and e. domany , _ phase transitions in an exactly soluble one - dimensional asymmetric exclusion model _ , j. stat . * 72 * ( 1993 ) 277296 . s. van dijken , l.c . jorritsma , and b. poelsema , _ steering - enhanced roughening during metal deposition at grazing incidence _ , phys . * 82 * ( 1999 ) 40384041 . g. ehrlich and f.g . hudda , _ atomic view of surface diffusion : tungsten on tungsten _ , j. chem . * 44 * ( 1966 ) 10361099 . h. kallabis , l. brendel , j. krug , j. , and d.e . wolf , _ damping of oscillations in layer - by - layer growth _ , int . j. mod . b * 31 * ( 1997 ) 36213634 . j. kallunki , j. krug , m. kotrla , _ competing mechanisms for step meandering in unstable growth _ , b * 65 * ( 2002 ) 205411 . r.v . kohn and f. otto , _ upper bounds on coarsening rates _ , comm . math . * 229 * ( 2002 ) 375395 . kohn , x.d . yan , _ upper bound on the coarsening rate for an epitaxial growth model _ , comm . pure appl . * 56 * ( 2003 ) 15491564 . j. krug ( 2004 ) this volume . d. moldovan and l. golubovic , _ interfacial coarsening dynamics in epitaxial growth with slope selection _ , phys . e * 61 * ( 2000 ) 61906214 . mullins , _ flattening of a nearly planar solid surface due to capillarity _ , j. appl . phys . * 30 * ( 1959 ) 77 ? ? . o. pierre - louis , m.r . dorsogna , and t.l . einstein , _ edge diffusion during growth : the kink ehrlich - schwoebel effect and resulting instabilities _ , phys . * 82 * ( 1999 ) 36613664 . p. politi , g. grenet , a. marty , a. ponchet , and j. villain , _ instabilities in crystal growth by atomic or molecular beams _ , physics reports * 324 * ( 2000 ) 271404 . p. politi and j. krug , _ crystal symmetry , step edge diffusion , and unstable growth _ , surface science * 446 * ( 2000 ) 8997 . m. rost and j. krug _ coarsening of surface structures in unstable epitaxial growth _ , phys . e * 55 * ( 1997 ) 39523957 . m. rost and j. krug , _ damping of growth oscillations in molecular beam epitaxy : a renormalization group approach _ , j. de physique i * 7 * ( 1997 ) 16271638 . l. schwoebel and e.j . shipsey , _ step motion on crystal surfaces _ , j. appl . * 37 * ( 1966 ) 36823686 . m. siegert , _ ordering dynamics of surfaces in molecular beam epitaxy _ , physica a * 239 * ( 1997 ) 420427 . m. siegert , _ coarsening dynamics of crystalline thin films _ , phys . * 81 * ( 1998 ) 54815484 . p. milauer , m. rost , and j. krug , _ fast coarsening in unstable epitaxy with desorption _ , e * 59 * ( 1999 ) r6263r6266 . e. somfai , d.e . wolf , and j. kertsz , _ correlated island nucleation in layer - by - layer growth _ , j. de physique i * 6 * ( 1996 ) 393401 . j. villain , _ continuum models of crystal growth form atomistic beams with and without desorption _ , j. de physique i * 1 * ( 1991 ) 1942 . wolf , _ computer simulation of molecular beam epitaxy _ , in _ scale invariance , interfaces and non equilibrium dynamics _ , eds . mckane , m. droz , j. vannimenus , and d.e . wolf , plenum press , new york ( 1995 ) . j. yu , j.g . amar , and a. bogicevic , _ first - principles calculations of steering forces in epitaxial growth _ , phys . b * 69 * ( 2004 ) 113406 .

as an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations ( pdes ) . their _ heuristic derivation _ makes use of inherent symmetries in the physical process ( mass conservation , crystal symmetry , ) which determines their _ structure_. two examples of applications are given , one for large scale properties , one including crystal lattice discreteness . these are : ( i ) a simplified model for _ mound coarsening _ and ( ii ) for the transition from _ layer - by - layer _ to _ rough growth_. virtues and shortcomings of this approach is discussed in a concluding section .

understanding the connection between galaxies and dark matter halos is one of the most important goals of astrophysics and cosmology . the framework of the halo occupation distribution ( hod ) provides a powerful means of studying the relation of galaxy distributions with underlying dark matter distributions @xcite . the hod characterizes the galaxy bias in terms of the halo occupation number , the average number of galaxies within individual dark halos as a function of halo masses , @xmath1 , and is very successful in explaining clustering properties of galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the idea of the hod has also been applied to rarer cosmological objects such as quasars @xcite . the hod model tells us how galaxies are connected to dark matter halos _ statistically_. a natural extension is then to consider how well we can connect galaxies to dark matter halos for _ individual _ galaxies . naively we can infer the host halo property of individual galaxies by examining number densities of galaxies around the target galaxies , since a higher number density suggests that the target galaxy is more likely to reside in a group- or cluster - scale dark matter halo . however it is also possible that the galaxy actually resides in a low - mass halo which appears to be associated with a massive halo because of chance projection along the line - of - sight . the redshift information is usually not sufficient to remove the chance projection , particularly because the observed spatial distributions of galaxies in massive halos are significantly elongated in the redshift direction due to peculiar motions of the galaxies ( the so - called fingers of god effect ) . in this paper , we develop a theoretical framework to compute the probability distribution function ( pdf ) of host halo masses of individual galaxies given number counts of nearby galaxies , assuming that the true hod is known a priori . we employ the hod formalism to predict , for each galaxy , the expected number of neighboring galaxies within a cylinder of redshift interval @xmath2 and transverse comoving distance within @xmath3 . we include contributions from both galaxies within the same host halo and those residing in different halos . the result is used to derive the conditional pdf of host halo masses of a galaxy given the neighboring galaxy counts within the cylinder ( see also * ? ? ? * for a similar study using a semi - analytic model of galaxy formation ) . we compare our results with those from a mock galaxy catalog constructed from the millennium run simulation @xcite . neighboring galaxy counts , or sometimes referred as counts - in - cylinders , have also been used to constrain the hod from observations . for instance , @xcite directly counted number of galaxies within massive clusters to constrain the hod at high mass end . @xcite counted the number of quasars in galaxy clusters to try to break degeneracies in the quasar hod . @xcite conducted a counts - in - cylinders analysis to study the hod of luminous red galaxies ( see also * ? ? ? in the previous studies , however , connecting galaxies to dark halos , including the estimate of chance projection , has been attempted rather empirically , e.g. , using mock galaxy catalogs . the new theoretical framework developed in this paper provides a more rigorous means of connecting neighboring galaxy counts and the underlying hod . the structure of this paper is as follows . in section [ sec : nc ] , we present our analytic model to compute neighboring galaxy counts within the hod framework . using the result , in section [ sec : pdf ] we derive conditional pdfs of the host halo mass given neighboring galaxy counts . we compare our analytic model predictions with results from the mock galaxy catalog in section [ sec : mock ] . we discuss possible extensions and applications of our model in section [ sec : ext ] , and give a summary in section [ sec : summary ] . where necessary we use the @xmath4-dominated cold dark matter cosmology model employed by the millennium run simulation , where @xmath5 , @xmath6 , @xmath7 with @xmath8 , @xmath9 , and @xmath10 . the hod model specifies the mean halo occupation number @xmath1 as a function of halo mass @xmath11 . given the mass function and clustering properties of dark matter halos calibrated by @xmath12-body simulations , the hod modeling enables us to analytically compute clustering properties of galaxies . following @xcite , we consider central and satellite galaxies separately @xmath13 where @xmath14 and @xmath15 describe the central and satellite components , respectively . we parametrize both components as ( e.g. , * ? ? ? * ; * ? ? ? * ) @xmath16 , \label{eq : hod_cen}\ ] ] @xmath17 here @xmath18 is the characteristic minimum mass that can host central galaxies , @xmath19 is the characteristic transition width , @xmath20 is the cutoff mass for satellites , and @xmath21 and @xmath22 determine how the mean number of satellite galaxies within halos grows as a function of halo masses ( also see table [ tab : hod ] below ) . this functional form is motivated by cosmological galaxy formation simulations and is known to explain various observational data very well . in the following , the galaxies for which we wish to infer host dark matter halo masses are referred to as _ target _ galaxies , while the galaxies surrounding them ( as seen in projection on the sky ) are called _ neighboring _ galaxies . quantities associated with target ( neighboring ) galaxies are denoted with a subscript or superscript t ( n ) . the subscript p serves as a reminder when a quantity is evaluated in projection . our primary goal is to compute number counts of neighboring galaxies around a target galaxy . throughout the paper we count the number of neighboring galaxies within a cylinder defined by a redshift interval @xmath23 and transverse comoving distance @xmath24 . we denote these neighboring galaxy counts as @xmath25 . for a galaxy at redshift @xmath26 , the volume integral of the cylinder is explicitly written as @xmath27 it is convenient to derive an explicit expression for the volume integral of the two - point correlation function @xmath28 over the cylinder . suppose the redshift interval is large enough to include correlated structures , we have @xmath29 the projected correlation function @xmath30 is related to the power spectrum @xmath31 via @xmath32 with @xmath33 being the bessel functions of the first kind . using the relation @xmath34 we then obtain @xmath35 we first consider the so - called 1-halo term , i.e. , number counts of neighboring galaxies that reside in the same dark halo . neighboring galaxy counts should depend on where in the halo the target galaxy is located . we can include this effect by computing neighboring galaxy counts for central and satellite galaxies separately . using the expression given in equation ( [ eq : xi_pk ] ) , we can derive the average number of neighboring galaxies within the cylinder around a central galaxy as @xmath36 where @xmath37 is the fourier transform of the normalized number density profile of satellite galaxies , @xmath38 @xmath39 with @xmath40 being the spherical bessel function . in this paper , we define the halo mass @xmath11 by the total mass within a sphere of @xmath41 , within which the mean density is 200 times the critical density of the universe . we use this overdensity in order to compare our results with those from the mock galaxy catalog of ( * ? ? ? * see section [ sec : mock ] ) . we make the simplifying assumption that the satellite number density profile follows the matter density profile of dark matter ( * ? ? ? * hereafter nfw ) @xmath42 and is truncated at @xmath41 . an important parameter to characterize the nfw profile is concentration @xmath43 . we use the mass - concentration relation from @xcite @xmath44 similarly , the 1-halo term of the average number of neighboring galaxies around a satellite galaxy at distance @xmath45 from the halo center is derived as @xmath46j_0(kr).\end{aligned}\ ] ] in each halo with mass @xmath11 , we can also define the probability of a member galaxy being a central or a satellite galaxy at @xmath45 as @xmath47 @xmath48 the average neighboring galaxy counts within the same halo are then computed as @xmath49 . \label{eq : ngc_ave_1h}\end{aligned}\ ] ] on the other hand , the probability distribution of the host dark halo mass is given by @xmath50 where @xmath51 is the mass function of dark matter halos , for which we adopt the fitting function of @xcite , and @xmath52 is the average number density of the target / neighboring galaxy population defined by @xmath53 hence the average neighboring galaxy counts from galaxies residing in halos of all masses reduce to @xmath54 where @xmath55 is the standard 1-halo term of galaxy power spectrum @xmath56.\end{aligned}\ ] ] next we consider the 2-halo term , i.e. , contributions to neighboring galaxy counts from different halos . we shall include contributions from both the spatially correlated halos and uncorrelated structures along the line - of - sight . we start by describing neighboring galaxy counts formally as @xmath57 where @xmath58 is the number density of the target galaxy . the number density of neighboring galaxies is written using the density fluctuation @xmath59 as @xmath60 . since we are interested in a single target galaxy , @xmath58 is written as @xmath61 where @xmath62 denotes the dirac delta function , @xmath63 is the location of that galaxy , and @xmath64 where the integral is performed over a sufficiently large volume . the average 2-halo neighboring galaxy counts for the target galaxy in a halo of mass @xmath11 , including the background contribution , are obtained from equation ( [ eq : np_formal ] ) as @xmath65 the first term describes the background contribution ( or random chance projection ) , while the second term describes the enhancement of neighboring galaxy counts due to clustering of the underlying matter density field . each term is explicitly written as @xmath66 @xmath67 in practice , there are additional terms originating from higher order correlation functions ( see sec . 39 of * ? ? ? in this paper we ignore those higher order contributions for simplicity . as we will see below , this is a reasonably good approximation in our case where we study number counts projected over redshift ranges that is much larger than typical correlating lengths ( @xmath68 mpc ) . the 2-halo term of the power spectrum is simply given by @xmath69 where @xmath70 is the halo bias for which we adopt a fitting function of @xcite , @xmath71 is the linear matter power spectrum ( computed using the fitting formulae of @xcite ) , and @xmath72 is the average galaxy bias computed by @xmath73 again by averaging @xmath74 over @xmath75 ( equation [ eq : pm ] ) we deduce an expression similar to equation ( [ eq : np_1h_all ] ) @xmath76 where @xmath77 is the fourier transform of the two - halo galaxy power spectrum @xmath78 . based on this formalism we can also derive the variance of neighboring galaxy counts in the limit of @xmath79 as @xmath80 where @xmath81 ^ 2,\end{aligned}\ ] ] with @xmath82 . again , we have ignored contributions from higher order correlations . we start by deriving the pdf of neighboring galaxy counts around a target galaxy that resides in a dark halo with mass @xmath11 . for this purpose , we adopt the following assumptions : ( 1 ) the pdf of 1-halo neighboring galaxy counts follows the poisson distribution , which is a reasonable assumption at least for massive halos where @xmath83 is large ( e.g. , * ? ? ? * ; * ? ? ? * ) , ( 2 ) the pdf of 2-halo plus background neighboring galaxy counts follows the log - normal distribution , given that the probability distribution function of cosmological density fields is accurately described by the log - normal distribution ( e.g. , * ? ? ? * ) , and ( 3 ) the 1-halo and 2-halo pdfs are uncorrelated with each other . for the expected value of @xmath84 , the poisson distribution gives the pdf of observed number @xmath12 as @xmath85 we include the position dependence of the galaxy in the calculation of the pdf of 1-halo neighboring galaxy counts . using the results given in section [ sec:1h ] , we obtain @xmath86 we assume that the pdf of 2-halo neighboring galaxy counts follows the log - normal distribution @xmath87 detailed discussions on the validity of this assumption are given in appendix . we then obtain @xmath88 where the parameters @xmath89 and @xmath90 are related to the mean @xmath91 and variance @xmath92 as @xmath93 @xmath94.\ ] ] finally we combine these two pdfs to obtain the pdf of total neighboring galaxy counts @xmath95 we now turn the problem around and ask how well we can infer the host halo mass of a single target galaxy from observed neighboring galaxy counts . this is obtained by using the bayes theorem @xmath96 where @xmath97 and @xmath75 are given in equations ( [ eq : pofnp ] ) and ( [ eq : pm ] ) , respectively . we use the all - sky light - cone mock catalog from @xcite to test our analytic predictions . this mock is based on the semi - analytic model of @xcite , and is constructed by replicating the millennium run simulation box ( @xmath98mpc on a side ) without transformations such as rotation , translation , or inversion . @xcite showed that their model can reproduce important statistical properties of nearby galaxies such as the stellar mass function and two - point correlation function . for each galaxy in the mock , information such as the sky position , redshift , apparent and absolute magnitudes , host dark matter halo mass , and central / satellite designation , is available . the catalog is flux limited to @xmath99 . in this paper , we generate a volume - limited galaxy subsample of @xmath100 to about @xmath101 and use the subsample for our analysis . cc @xmath102 $ ] & @xmath103 + @xmath19 & 0.207 + @xmath104 $ ] & @xmath105 + @xmath106 $ ] & @xmath107 + @xmath22 & 0.960 [ tab : hod ] an essential ingredient in our formalism is the halo occupation number @xmath1 . in the mock galaxy catalog , we know host halo properties of individual galaxies , which allows us to derive the mean halo occupation number directly without ambiguity . we fit the halo occupation number obtained directly from the mock catalog to the parametrized form in equations ( [ eq : hod_cen ] ) and ( [ eq : hod_sat ] ) , which contains five free parameters in total . we show the fitting result in figure [ fig : hod ] , and summarize best - fit parameters in table [ tab : hod ] . we find that the hod model adopted in this paper reproduces the mean occupation number in the mock galaxy catalog very well . before comparing the pdf of the halo mass , we first check whether our analytic model reproduces neighboring galaxy counts in the mock galaxy catalog . the average ( projected ) neighboring galaxy counts around a galaxy inside a halo with mass @xmath11 is given by @xmath108 where @xmath109 and @xmath110 are given in equations ( [ eq : ngc_ave_1h ] ) and ( [ eq : ngc_ave_2h ] ) , respectively . we compute neighboring galaxy counts as a function of the maximum comoving transverse distance @xmath3 . the redshift of target galaxies for which neighboring galaxy counts are considered is arbitrarily fixed at @xmath111 . in the mock galaxy catalog , we actually use galaxies in the small redshift range of @xmath112 . throughout the paper we consider the redshift range of neighboring galaxies of @xmath113 , which is sufficiently large to include the correlated structure . figure [ fig : nc ] ( upper panel ) compares the average neighboring galaxy counts from the mock galaxy catalog with the analytic calculation ( equation [ eq : ngc_ave ] ) . we consider target galaxies living in halos of three masses , @xmath114 , @xmath115 , and @xmath116 , and find that our model agrees well with the mock result , both at small and large @xmath3 where 1-halo and 2-halo contributions are dominated , respectively . as expected , neighboring galaxy counts are higher for galaxies in more massive host halos . we also check the variance of the average neighboring galaxy counts , @xmath117 . again , the variance is given by the sum of 1-halo and 2-halo contributions @xmath118 where @xmath119 is derived in equation ( [ eq : ngc_var_2h ] ) . given the pdf of 1-halo neighboring galaxy counts ( equation [ eq : pdf_ngc_1h ] ) , we can compute @xmath120 as @xmath121 the comparison shown in figure [ fig : nc ] ( lower panel ) indicates that the analytic model reproduces the variance as well , in both 1-halo and 2-halo regimes . however there is relatively large deviation of the analytic model at @xmath122 for the host halo mass of @xmath123 . this might be explained by the non - gaussian error of the 2-halo term at very small scale . another possible explanation of the discrepancy is the presence of satellite galaxies outside @xmath41 ; we find that the mock galaxy catalog contains satellite galaxies that are located outside @xmath41 ( @xmath124 % ) , whereas we have assumed that all satellite galaxies are located within @xmath41 . we now compare our model of pdfs of the host halo masses given neighboring galaxy counts , @xmath125 ( equation [ eq : pofm ] ) , with those obtained directly from the mock galaxy catalog . figure [ fig : pofm ] compares the pdfs from the mock galaxy catalog with our analytic model . we find that our analytic models are in reasonably good agreement with the simulation result . in particular the analytic model nicely captures the complex behaviors of the pdfs . we find the pdf exhibits two peaks when the number of neighboring galaxies @xmath126 is large . the higher mass peak corresponds to the case that the galaxy resides in massive halos with about the peak mass . on the other hand , the lower mass peak is due to the chance projection , i.e. , the low - mass host halo of the galaxy is superposed on a massive halo or a dense structure on the sky , which boosts the neighboring galaxy counts . our analytic model reproduces this behavior . we find that the dependence of the pdfs on neighboring galaxy counts is weak for the large cylinder radius of @xmath127 for which the contribution is dominated by the 2-halo term . although neighboring galaxy counts depend on the host halo mass due to the halo mass dependence of the halo bias , neighboring galaxy counts also involves the large scatter originating from clustering of neighboring galaxies ( see figure [ fig : nc ] ) . thus , in order to infer the host halo mass of individual galaxies , small cylinder radii of @xmath128 should be used for neighboring galaxy counts . with the analytic model of pdfs of the host halo masses , we can easily explore how different choices of neighboring counts provide tighter constraints on halo masses . in addition to @xmath3 discussed above , we can also adjust the redshift range @xmath129 . here we demonstrate how we can optimize @xmath3 and @xmath129 from the pdfs . as a specific example , we consider an input halo mass of @xmath123 . we first compute the average neighboring number @xmath130 ( equation [ eq : ngc_ave ] ) for given values of @xmath3 and @xmath129 , and compute the conditional pdf @xmath125 ( equation [ eq : pofm ] ) given the number count @xmath131 equal to the average neighboring number . we quantify the tightness of the halo mass inference by computing the variance of the halo mass @xmath132 , @xmath133 , using the computed pdf . smaller @xmath133 indicates a narrower peak of the pdf and therefore tighter constraints on the halo mass . the contours shown in figure [ fig : wpm ] confirm that cylinder radii of @xmath134 provide tightest constraints on the halo masses . we find that the dependence on @xmath129 is not very strong , but smaller @xmath129 generally produces tighter constraints , because of the smaller number of projected galaxies . we note that the best choice of the parameters depends also on other factors such as halo masses and underlying hod models . in section [ sec : mock ] we have used a mock galaxy catalog to demonstrate that our analytic model can robustly predict the pdf of halo mass for a _ single _ galaxy , given its neighboring counts . although the example we have considered is somewhat idealized ( i.e. , with 100% spectroscopic sampling and redshift success rate ) , we note that these conditions are not required . in principle , for a given galaxy sample , as long as we can accurately model its hod , our model can be used to predict the host halo mass pdf for the galaxies _ in _ the sample . here we briefly discuss various ways to extend the scope and capabilities of our model , including the possibility to distinguish central galaxies from satellites , the situation when the target and neighboring galaxies are from two different galaxy samples , the potential of improving the pdf with neighboring counts within multiple apertures , constraints on the hod itself , the application to galaxy samples selected with photometric redshifts , and the prospect of applying the same principle to inferring masses of galaxy clusters . in many of hod studies , central and satellite components are treated separately . therefore it is of great interest to know whether each galaxy corresponds to the central or satellite type . this can be obtained easily in this theoretical framework . from equation ( [ eq : pdf_ngc_1h ] ) , we derive the joint probability of being a central galaxy and having a 1-halo neighboring galaxy count of @xmath135 as @xmath136 by replacing @xmath137 in equation ( [ eq : pofnp ] ) with @xmath138 and inserting the result to equation ( [ eq : pofm ] ) , we obtain the joint pdf of @xmath139 . the probability of being central given the host halo mass @xmath11 and neighboring galaxy count @xmath126 is then obtained as @xmath140 figure [ fig : cent ] shows some examples of @xmath141 for the cylinder of radius @xmath142 . the probability is generally higher for smaller halo masses , simply because there are fewer satellite galaxies in lower mass halos ( see figure [ fig : hod ] ) . on the other hand , the probabilities shown in figure [ fig : cent ] exhibit dependences on neighboring galaxy counts @xmath126 , suggesting that neighboring galaxy counts do provide information when determining whether a galaxy is central or not . while we have assumed that the target galaxy for which we infer the host halo mass and neighboring galaxies are the same population and they share the same hod , in principle we can use populations with different hods for neighboring galaxy counts ( e.g. , red and blue galaxies , galaxies of different luminosity / stellar mass , or groups / clusters instead of galaxies ) . the extension of our theoretical framework to this situation is straightforward . suppose the halo occupation number of the target galaxy @xmath143 differs from that of neighboring galaxies @xmath144 , the 1-halo neighboring galaxy counts are modified as @xmath145 @xmath146j_0(kr),\end{aligned}\ ] ] @xmath147 @xmath148 where @xmath149 and @xmath150 are spatial distributions of satellite components of target and neighboring galaxies , respectively , and the pdf of the host halo mass becomes @xmath151 and the average bias for the 2-halo calculation becomes @xmath152 where @xmath153 and @xmath154 are average number densities ( see equation [ eq : n3dave ] ) of target and neighboring galaxies , respectively . also note that @xmath52 in @xmath155 should be interpreted as @xmath154 . since different galaxy populations probe different halo masses , the use of different galaxy populations for neighboring galaxy counts can help improve the inference of the host halo mass . the inference of the host halo mass may be improved further by considering multiple apertures , i.e. , combining neighboring galaxy counts with different cylinder radii . in this case , we need to take account of the covariance of neighboring galaxy counts carefully . we leave the exploration of this possibility for future work . there is also room for the improvement of our analytic model . for instance , attempts to improve the halo model have been made by including the halo exclusion effect and non - linearity of the 2-halo power spectrum ( e.g. , * ? ? ? * ) . the evaluation of non - gaussian error may be necessary to improve the estimate of the variance of 2-halo neighboring galaxy counts , @xmath92 ( see figure [ fig : nc ] ) . we have also ignored the complexity of the halo properties , such as the scatter in the concentration parameter and the halo triaxiality . the hod model itself is also subject to possible improvements , e.g. , by including assembly bias @xcite and relative velocities of central galaxies @xcite . neighboring galaxy counts depend on the underlying hod model , and therefore in principle they can be used to constrain the hod itself . for this application , it is crucial to estimate and remove the chance projection . one can infer the effect of pure chance projection by estimating the average number density , but the 2-halo contribution is not homogeneous but clustered around the target galaxy . the theoretical framework developed in this paper may be used to estimate the 2-halo contribution and its variance to derive more rigorous constraints on hod with counts - in - cylinders . although our formalism is readily applicable to several spectroscopic surveys such as sloan digital sky survey ( sdss ; * ? ? ? * ) , galaxy and mass assembly ( gama ; * ? ? ? * ) , prism multi - object survey ( primus ; * ? ? ? * ) , vimos public extragalactic redshift survey ( vipers ; * ? ? ? * ) , and eventually dark energy spectroscopic instrument ( desi ; * ? ? ? * ) , and subaru prime focus spectrograph ( pfs ; * ? ? ? * ) , it is highly desirable to extend our model to incorporate samples selected with photometric redshifts , so that we could fully exploit the potential offered by large imaging surveys such as subaru hyper suprime - cam ( hsc ; * ? ? ? * ) survey , dark energy survey , and large synoptic survey telescope ( lsst ; * ? ? ? we plan to address this extension in a future paper . galaxy clusters have long been regarded as a powerful cosmological probe , as their abundance is sensitively dependent on parameters such as @xmath156 and @xmath157 . accurate knowledge of cluster mass is required , however , before any useful cosmological constraints can be deduced @xcite . our formalism could be straightforwardly applied to galaxy clusters , especially samples detected in optical / near - ir imaging surveys , for which it has typically been difficult to deduce mass reliably for individual clusters . with the knowledge of pdf of cluster mass , it should be possible to obtain tighter constraints from cluster abundance . in the highly successful hod framework , the dark matter halo mass is the sole factor controlling the galaxy formation process . it is thus critically important to be able to estimate the halo mass of galaxies . traditionally , this is achieved by techniques such as strong gravitational lensing ( e.g. , * ? ? ? * ) , galaxy - galaxy lensing ( e.g. , * ? ? ? * ) , satellite kinematics ( e.g. , * ? ? ? * ) , and large scale clustering ( e.g , . * ? ? ? except for the first method , all the others work in a statistical sense , that is , they can not be applied to a single galaxy . an alternative method is developed by @xcite , where the concept of abundance matching is employed to a large group catalog which includes groups with only one member . under the assumption of one - to - one correspondence between halo mass and stellar mass / luminosity content of the group members , a halo mass is _ assigned _ to each of the groups . however , with this approach , little or no information on the pdf of the halo mass is provided . furthermore , given the difficulties in constructing group group catalogs at low mass halo regime and the associated uncertainties , the one - to - one correspondence between these groups and dark halos is likely to break down , rendering halo mass assignment unreliable . we have developed a theoretical framework to compute the pdf of the host halo mass for a single galaxy , given its neighboring galaxy counts . we have derived explicit expression for the number of neighboring galaxies within the cylinder of redshift interval @xmath23 and transverse comoving distance @xmath158 in terms of the hod model . we include both 1-halo contribution from the same host halo and 2-halo contribution including chance projection for the neighboring galaxy counts . we have used the result to obtain the conditional pdf of the host halo mass given neighboring galaxy counts . we compare our analytic model with results from the mock galaxy catalog , finding reasonable agreements . the pdf of the host halo mass exhibits complex behavior , with generally two peaks at low- and high - mass regimes for the case of large neighboring galaxy counts . this is understood as the effect of chance projection along the line - of - sight , which can boost neighboring galaxy counts even if the host halo is a low - mass halo . we find that cylinder radii of @xmath0 are optimal for the inference of the host halo mass , at least for the case of the hod examined in this paper . this paper serves as a proof - of - concept for our theoretical framework , and we expect our new approach to have many applications . we thank an anonymous referee for useful comments and suggestions . this work was supported in part by world premier international research center initiative ( wpi initiative ) , mext , japan , and grant - in - aid for scientific research from the jsps ( 26800093 ) . mo acknowledges the hospitality of asiaa where this work was partly done . ytl acknowledges support from the ministry of science and technology grant nsc 102 - 2112-m-001 - 001-my3 and the hospitality of kavli ipmu where this work was initiated . bolton , a. s. , burles , s. , koopmans , l. v. e. , et al . 2008 , , 682 , 964 chatterjee , s. , nguyen , m. l. , myers , a. d. , & zheng , z. 2013 , , 779 , 147 coil , a. l. , blanton , m. r. , burles , s. m. , et al . 2011 , , 741 , 8 cooray , a. , & sheth , r. 2002 , , 372 , 1 coupon , j. , kilbinger , m. , mccracken , h. j. , et al . 2012 , , 542 , a5 driver , s. p. , hill , d. t. , kelvin , l. s. , et al . 2011 , , 413 , 971 duffy , a. r. , schaye , j. , kay , s. t. , & dalla vecchia , c. 2008 , , 390 , l64 eisenstein , d. j. , & hu , w. 1999 , , 511 , 5 guo , q. , white , s. , boylan - kolchin , m. , et al . 2011 , , 413 , 101 guzzo , l. , scodeggio , m. , garilli , b. , et al . 2014 , , 566 , a108 haas , m. r. , schaye , j. , & jeeson - daniel , a. 2012 , , 419 , 2133 hamana , t. , ouchi , m. , shimasaku , k. , kayo , i. , & suto , y. 2004 , , 347 , 813 henriques , b. m. b. , white , s. d. m. , lemson , g. , et al . 2012 , , 421 , 2904 hikage , c. 2014 , , 441 , l21 ho , s. , lin , y .- t . , spergel , d. , & hirata , c. m. 2009 , , 697 , 1358 kayo , i. , & oguri , m. 2012 , , 424 , 1363 kayo , i. , taruya , a. , & suto y. 2001 , , 561 , 22 kravtsov , a. v. , berlind , a. a. , wechsler , r. h. , klypin , a. a. , gottlber , s. , allgood , b. , & primack j. r. 2004 , , 609 , 35 lacerna , i. , padilla , n. , & stasyszyn , f. 2014 , , 443 , 3107 leauthaud , a. , tinker , j. , bundy , k. , et al . 2012 , , 744 , 159 levi , m. , bebek , c. , beers , t. , et al . 2013 , arxiv:1308.0847 lin , y .- t . , mohr , j. j. , & stanford , s. a. 2004 , , 610 , 745 lsst science collaboration , abell , p. a. , allison , j. , et al . 2009 , arxiv:0912.0201 mandelbaum , r. , seljak , u. , kauffmann , g. , hirata , c. m. , & brinkmann , j. 2006 , , 368 , 715 miyazaki , s. , komiyama , y. , nakaya , h. , et al . 2012 , , 8446 , 84460z more , s. , van den bosch , f. c. , cacciato , m. , et al . 2009 , , 392 , 801 more , s. , miyatake , h. , mandelbaum , r. , takada , m. , spergel , d. , brownstein , j. , & schneider d. p. 2014 , arxiv:1407.1856 navarro , j. f. , frenk , c. s. , & white s. d. m. 1997 , , 490 , 493 peacock , j. a. , & smith , r. e. 2000 , , 318 , 1144 peebles , p. j. e. 1980 , the large - scale structure of the universe ( princeton , nj : princeton univ . press ) reid , b. a. , & spergel , d. n. 2009 , , 698 , 143 richardson , j. , zheng , z. , chatterjee , s. , nagai , d. , & shen , y. 2012 , , 755 , 30 scoccimarro , r. , sheth , r. k. , hui , l. , & jain , b. 2001 , , 546 , 20 seljak , u. 2000 , , 318 , 203 shen , y. , mcbride , c. k. , white , m. , et al . 2013 , , 778 , 98 skibba , r. a. , van den bosch , f. c. , yang , x. , et al . 2011 , , 410 , 417 springel , v. , white , s. d. m. , jenkins , a. , et al . 2005 , , 435 , 629 takada , m. , ellis , r. s. , chiba , m. , et al . 2014 , , 66 , 1 tinker , j. l. , weinberg , d. h. , zheng , z. , & zehavi , i. 2005 , , 631 , 41 tinker , j. , kravtsov , a. v. , klypin , a. , abazajian , k. , warren , m. , yepes , g. , gottlber , s. , & holz , d. e. 2008 , , 688 , 709 tinker , j. l. , robertson , b. e. , kravtsov , a. v. , klypin , a. , warren , m. s. , yepes , g. , & gottlber , s. 2010 , , 724 , 878 wake , d. a. , whitaker , k. e. , labb , i. , et al . 2011 , , 728 , 46 wang , l. , weinmann , s. m. , de lucia , g. , & yang , x. 2013 , , 433 , 515 weinberg , d. h. , mortonson , m. j. , eisenstein , d. j. , et al . 2013 , , 530 , 87 white , m. , blanton , m. , bolton , a. , et al . 2011 , , 728 , 126 yang , x. , mo , h. j. , van den bosch , f. c. , & jing , y. p. 2005 , , 356 , 1293 york , d. g. , adelman , j. , anderson , j. e. , jr . , et al . 2000 , , 120 , 1579 zehavi , i. , zheng , z. , weinberg , d. h. , et al . 2011 , , 736 , 59 zentner , a. r. , hearin , a. p. , & van den bosch , f. c. 2014 , , 443 , 3044 zheng , z. , berlind , a. a. , weinberg , d. h. , et al . 2005 , , 633 , 791 we assumed that the pdf of 2-halo neighboring galaxy counts follows the log - normal distribution ( equation [ eq : logn ] ) based on the fact that the pdf of underlying cosmological density fields is well described by the log - normal distribution @xcite . it is not clear whether the log - normal distribution can also describe the pdf of halo number densities which is more closely related to neighboring galaxy counts . here we adopt the mock galaxy catalog used in section [ sec : mock ] to check this log - normal assumption more directly . we consider halo catalogs with masses of @xmath159 and @xmath116 . for each halo sample , we count the number of neighboring halos within the maximum transverse distance @xmath160 and the redshift interval @xmath161 , as in the case for our neighboring galaxy counts . we consider all halos with the masses higher than @xmath162 which correspond roughly to the resolution limit of the millennium run simulation . figure [ fig : pdf ] shows the pdfs of the number of neighboring halos around @xmath159 and @xmath116 halos , for the maximum transverse separations of @xmath163 , @xmath164 , and @xmath165 . we find that the log - normal distribution generally fits very well . a possible exception is the case for small @xmath166 and the halo mass of @xmath123 for which effects of halo exclusion and non - gaussian error are most prominent , but even in this case the log - normal distribution provides a reasonably good approximation . given the log - normal pdf of halo number counts , we expect neighboring galaxy counts also obey the long - normal distribution .

how well can we infer host dark matter halo masses of individual galaxies ? based on the halo occupation distribution ( hod ) framework , we analytically compute the number of neighboring galaxies within a cylinder of some redshift interval and radius in transverse comoving distance . the result is used to derive the conditional probability distribution function ( pdf ) of the host halo mass of a galaxy , given the neighboring galaxy counts . we compare our analytic results with those obtained using a realistic mock galaxy catalog , finding reasonable agreements . we find the optimal cylinder radius to be @xmath0 for the inference of halo masses . the pdf is generally broad , and sometimes has two peaks at low- and high - mass regimes , because of the effect of chance projection along the line - of - sight . potential applications and extensions of the new theoretical framework developed herein are also discussed .

the concept of correlation , i.e. , information of one system about another , is a key element in many - body physics . indeed , the properties of a many - body system are strongly affected by changes in the correlations among its constituents . these changes are responsible for the occurrence of remarkable phenomena such as a quantum phase transition ( qpt ) , which is a critical change in the ground state of a quantum system due to level crossings in its energy spectrum . qpts occur at low temperatures @xmath1 where the de broglie wavelength is greater than the correlation length of the thermal fluctuations ( effectively @xmath2 ) @xcite . striking examples of qpts include metal - insulator transitions in strongly correlated electronic materials , magnetic transitions in quantum spin lattices , superfluid - mott insulator transitions in atomic gases induced by a bose - einstein condensation , among others . correlations can be both from classical and quantum sources . the existence of genuinely quantum correlations can be usually inferred by the presence of entanglement among parts of a system . indeed , entanglement displays a rather interesting behavior at qpts @xcite , being able to indicate a quantum critical point ( qcp ) through nonanalyticities inherited from the ground state energy @xcite . moreover , for one - dimensional critical systems , ground state entanglement entropy exhibits a universal logarithmic scaling governed by the central charge of the virasoro algebra associated with the underlying conformal field theory @xcite . remarkably , the logarithmic scaling is robust against disorder @xcite . in higher dimensions , entanglement usually scales following an area law for noncritical systems ( see , e.g. , ref . @xcite ) . for critical models , violations of the area law have been found @xcite , with logarithmic - type corrections appearing . more recently , it has been observed that an area law is generally implied by a finite correlation length when measured in terms of the mutual information @xcite . this remarkable behavior of entanglement at criticality is indeed a consequence of the correlation pattern exhibited by the ground state of the system . nevertheless , although entanglement provides a route to find out the existence of quantum correlations , it can be shown that they can appear even when entanglement is absent @xcite . quantum correlations , which can be measured by the _ quantum discord _ @xcite , often arise as a consequence of coherence in a quantum system , being present even for separable states . moreover , entangled states commonly involve more than only quantum correlations , i.e. , they usually carry classical correlations among their parts . in a multiparty mixed - state scenario , the possibility of nonseparable states with purely quantum correlations ( with no supporting background of classical correlations ) have also been investigated @xcite , but genuine indicators of multiparticle classical correlations are still under debate @xcite . by focusing on condensed - matter systems , the aim of this work is , starting from an arbitrary @xmath0-symmetric model , to investigate pairwise correlations , explicitly splitting up their classical and quantum contributions and analyzing their behavior at qpts . as an illustration , ground states of both xxz and transverse field ising spin chains will be shown to share quantum as well as classical correlations for nearest - neighbor spin pairs , with both of them signalling the critical behavior of the system . an analysis of such correlations for the thermodynamic limit of xxz and ising chains has recently appeared in ref . @xcite . here , we generalize this analysis by providing analytical expressions for the correlations in each model and also by discussing their finite - size behavior . as a further illustration , we describe the correlations in the hartree - fock ground state of many - body systems , taking the lipkin - meshkov - glick ( lmg ) model as an example . the paper is organized as follows . in sec . [ sec - qd ] we review the evaluation of correlations from the point of view of information theory , describing in particular the concept of quantum discord . in sec . [ sec - sl ] , we discuss the computation of classical and quantum correlations for general models displaying @xmath0 symmetry . sec . [ sec - xxz ] , sec . [ sec - ib ] , and sec . [ sec - lip ] are devoted to illustrating our results for the xxz chain , the transverse field ising chain , and the lmg model , respectively . conclusions are then presented in sec . [ sec - con ] . in classical information theory , the information obtained , on average , after knowing the value of a random variable @xmath3 , which takes values within a set of probabilities @xmath4 , can be quantified by its shannon entropy @xmath5 . we use the symbol @xmath6 as denoting logarithm at base 2 throughout the text . by taking two such random variables @xmath3 and @xmath7 , we can measure the correlation between them by their mutual information @xmath8 where @xmath9 is the joint entropy for @xmath3 and @xmath7 . by introducing the conditional entropy @xmath10 which quantifies the ignorance ( on average ) about the value of x given y is known , we can rewrite eq . ( [ mi1 ] ) as @xmath11 in order to generalize the above equations to the quantum domain , we replace classical probability distributions by density matrices . denoting by @xmath12 the density matrix of a composite system @xmath13 and by @xmath14 and @xmath15 the density matrices of parts @xmath16 and @xmath17 , respectively , the quantum mutual information can be defined as @xmath18 where @xmath19 is the von neumann entropy for subsystem @xmath16 and @xmath20 is a quantum generalization of the conditional entropy for @xmath16 and @xmath17 . a remarkable observation realized in ref . @xcite is that the conditional entropy can be introduced by a different approach which , although classically equivalent to eq . ( [ cce1 ] ) , yields a result in the quantum case that differs from eq . ( [ qce1 ] ) . indeed , let us consider a measurement performed locally only on part @xmath17 . this measurement can be described by a set of projectors @xmath21 . the state of the quantum system , conditioned on the measurement of the outcome labelled by @xmath22 , becomes @xmath23 where @xmath24 $ ] denotes the probability of obtaining the outcome @xmath22 and @xmath25 denotes the identity operator for the subsystem @xmath16 . the conditional density operator given by eq . ( [ rhok ] ) allows for the following alternative definition of the quantum conditional entropy : @xmath26 therefore , following eq . ( [ mi2 ] ) , the quantum mutual information can also be alternatively defined by @xmath27 eqs . ( [ qmi1 ] ) and ( [ qmi2 ] ) are classically equivalent but they are different in the quantum case . the difference between them is due to quantum effects on the correlation between parts @xmath16 and @xmath17 and provides a measure for the quantumness of the correlation , which has been called _ quantum discord _ @xcite . in fact , following refs . @xcite , we can define the classical correlation between parts @xmath16 and @xmath17 as @xmath28 with the quantum correlation accounted by the quantum discord , which is then given by @xmath29 we will consider here an interacting pair of spins-1/2 in a spin lattice , which is governed by a hamiltonian @xmath30 that is both real and exhibits @xmath0 symmetry , i.e. invariance under @xmath31-rotation around a given spin axis . by taking this spin axis as the @xmath32 direction , this implies the commutation of @xmath30 with the parity operator @xmath33 , where @xmath34 denotes the total number of spins and @xmath35 is the pauli operator along the @xmath32-axis at site @xmath36 . note that a number of spin models are enclosed within these requirements as , for instance , the xxz spin chain and the transverse field ising model . disregarding spontaneous symmetry breaking ( see , e.g. , refs . @xcite for a treatment of spontaneously broken ground states ) , the two - spin reduced density matrix at sites labelled by @xmath36 and @xmath37 in the basis @xmath38 , with @xmath39 and @xmath40 denoting the eigenstates of @xmath41 , will be given by @xmath42 in terms of spin correlation functions , these elements can be written as @xmath43 where @xmath44 @xmath45 is the magnetization density at site @xmath22 and @xmath46 ( @xmath47 ) denote two - point spin - spin functions at sites @xmath36 and @xmath37 , with the expectation value taken over the quantum state of the system . note that , in case of translation invariance , we will have that @xmath48 ( @xmath49 ) and , therefore , @xmath50 . moreover , observe also that the density operator given in eq . ( [ rhoab ] ) can be decomposed as @xmath51,\ ] ] with @xmath52 in particular , for translation invariant systems , we have that @xmath53 . in order to determine classical and quantum correlations , we first evaluate the mutual information as given by eq . ( [ qmi1 ] ) . the eigenvalues of @xmath12 read @xmath54 , \nonumber \\ \lambda_1 & = & \frac{1}{4 } \left [ \left(1+c_3\right ) - \sqrt{\left(c_4+c_5\right)^2 + \left(c_1-c_2\right)^2}\right ] , \nonumber \\ \lambda_2 & = & \frac{1}{4 } \left [ \left(1-c_3\right ) + \sqrt{\left(c_4-c_5\right)^2 + \left(c_1+c_2\right)^2}\right ] , \nonumber \\ \lambda_3 & = & \frac{1}{4 } \left [ \left(1-c_3\right ) - \sqrt{\left(c_4-c_5\right)^2 + \left(c_1+c_2\right)^2}\right ] . \label{qmi - ev}\end{aligned}\ ] ] therefore , the mutual information is given by @xmath55 where @xmath56 with @xmath57 , @xmath58 , @xmath59 , and @xmath60 . classical correlations can be obtained by following a procedure that is similar to those of refs . @xcite , but applying it now for the case of the general density matrix given by eq . ( [ rhoab ] ) . we first introduce a set of projectors for a local measurement on part @xmath17 given by @xmath61 , where @xmath62 is the set of projectors on the computational basis ( @xmath63 and @xmath64 ) and @xmath65 . note that the projectors @xmath66 represent therefore an arbitrary local measurement on @xmath17 . we parametrize @xmath67 as @xmath68 where @xmath69 and @xmath70 . note that @xmath71 and @xmath72 can be interpreted as the azimuthal and polar angles , respectively , of a qubit over the bloch sphere . by using eq . ( [ rhok ] ) and the equation @xmath73 , with @xmath74 denoting the kronecker symbol , we can show that the state of the system after measurement @xmath21 will change to one of the states @xmath75 where @xmath76 , \nonumber \\ q_{k2 } & = & ( -1)^k \ , c_2 \left [ \frac{w_2}{1+(-1)^k c_4w_3 } \right ] , \nonumber \\ q_{k3 } & = & ( -1)^k \ , \left [ \frac{c_3 w_3 + ( -1)^k c_5}{1 + ( -1)^k c_4w_3}\right ] , \end{aligned}\ ] ] with @xmath77 and @xmath78 then , by evaluating von neumann entropy from eqs . ( [ rho0 ] ) and ( [ rho1 ] ) and using that @xmath79 , we obtain @xmath80 with @xmath81 therefore , the classical correlation for the spin pair at sites @xmath36 and @xmath37 will be given by @xmath82 where @xmath83 . for some cases , the maximization in eq . ( [ cc - final ] ) can be worked out and an expression purely in terms of the spin correlation functions can be obtained ( e.g. , the xxz and ising chains below ) . in general , however , @xmath84 has to be numerically evaluated by optimizing over the angles @xmath71 and @xmath72 . once classical correlation is obtained , insertion of eqs . ( [ qmi - final ] ) and ( [ cc - final ] ) into eq . ( [ qcorrel ] ) can be used to determine the quantum discord . let us illustrate the discussion of classical and quantum correlations between two spins by considering the xxz spin chain , whose hamiltonian is given by @xmath85 where periodic boundary conditions are assumed , ensuring therefore translation symmetry . we will set the energy scale such that @xmath86 and will be interested in a nearest - neighbor spin pair at sites @xmath36 and @xmath87 . concerning its symmetries , the xxz chain exhibits @xmath88 invariance , namely , @xmath89=0 $ ] , which provides a stronger constraint over the elements of the density matrix than the @xmath0 symmetry . indeed , @xmath88 invariance ensures that the element @xmath90 of the reduced density matrix given by eq . ( [ rhoab ] ) vanishes . moreover , the ground state has magnetization density @xmath91 ( @xmath92 ) , which implies that @xmath93 where , due to translation invariance , we write @xmath94 ( @xmath95 ) . due to the fact that @xmath96 , we will have that @xmath97 , which considerably simplifies the computation of classical and quantum correlations . moreover , we will have that @xmath98 and @xmath99 . then , the maximization procedure in eq . ( [ cc - final ] ) can be analytically worked out @xcite , yielding @xmath100 with @xmath101 . for the mutual information @xmath102 we obtain @xmath103 where @xmath104 in order to compute @xmath84 and @xmath105 we write @xmath106 , @xmath107 , and @xmath108 in terms of the ground state energy density . by using the hellmann - feynman theorem @xcite for the xxz hamiltonian ( [ hxxz ] ) , we obtain @xmath109 where @xmath110 is the ground state energy density @xmath111 with @xmath112 denoting the ground state of @xmath113 . eqs . ( [ c - xxz ] ) and ( [ aux - xxz ] ) hold for a chain with an arbitrary number of sites , allowing the discussion of correlations either for finite or infinite chains . indeed , ground state energy as well as its derivatives can be exactly determined by bethe ansatz technique @xcite , which allows us to obtain the correlation functions @xmath106 , @xmath107 , and @xmath108 . in fig . [ f1 ] , we plot classical and quantum correlations between nearest - neighbor pairs for an infinite xxz spin chain . note that , in the classical ising limit @xmath114 , we have a fully polarized ferromagnet . the ground state is then a doublet given by the vectors @xmath115 and @xmath116 , yielding the mixed state @xmath117 indeed , this is simply a classical probability mixing , with @xmath118 and @xmath119 . the same applies for the antiferromagnetic ising limit @xmath120 , where a doubly degenerate ground state arises . moreover , observe that the classical ( quantum ) correlation is a minimum ( maximum ) at the infinite order qcp @xmath121 . on the other hand , both correlations are discontinuous at the first - order qcp @xmath122 . this is indeed in agreement with the usual behavior of entanglement both at infinite and first - order qpts . for an infinite - order qcp , entanglement commonly display a maximum at the qcp @xcite , while for a first - order qcp , entanglement usually exhibits a jump at the qcp @xcite . nevertheless , we note that in the specific case of the ferromagnetic qcp @xmath122 and for pairwise entanglement measures such as concurrence @xcite and negativity @xcite , no jump is detected , being hidden by the operation @xmath123 it is interesting to observe the behavior of the functions @xmath124 and @xmath125 that govern the classical and quantum correlations . for @xmath126 , we have that @xmath127 , which means that the classical correlation is governed by @xmath125 . for @xmath128 , we have that @xmath129 , with the crossing occurring exactly at the infinite - order qcp . therefore , the correlations are governed by different parameters in different phases . for @xmath130 , we obtain @xmath131 and @xmath132 , which implies that @xmath133 and @xmath134 . these results are shown in fig . [ f2 ] below . let us consider now the ising chain in a transverse magnetic field , whose hamiltonian is given by @xmath135 with periodic boundary conditions assumed , namely , @xmath136 . as before , we will set the energy scale such that @xmath86 and will be interested in a nearest - neighbor spin pair at sites @xmath36 and @xmath87 . this hamiltonian is @xmath0-symmetric and can be exactly diagonalized by mapping it to a spinless free fermion model with single orbitals . this is implemented through the jordan - wigner transformation @xmath137 where @xmath138 and @xmath139 are the creation and annihilation fermion operators at site @xmath36 , respectively . by rewriting eq . ( [ hi ] ) in terms of @xmath138 and @xmath139 we obtain @xmath140 in order to diagonalize @xmath141 we consider fermions in momentum space @xmath142 where @xmath143 and @xmath144 are creation and annihilation fermion operators with momentum @xmath22 , respectively , and @xmath145 is the fermion position at site @xmath37 . the wave vectors @xmath146 satisfy the relation @xmath147 , where @xmath148 denotes the distance between two nearest - neighbor sites and @xmath149 , with @xmath150 and @xmath151 taken , for simplicity , as an even number . then , by inverting eq . ( [ jw - momentum ] ) and inserting the result in eq . ( [ hi - fermion ] ) , we obtain @xmath152 . \label{hi - momentum}\end{aligned}\ ] ] diagonalization is then obtained by eliminating the terms @xmath153 and @xmath154 from the hamiltonian given by eq . ( [ hi - momentum ] ) , which do not conserve the particle number . this is indeed achieved through the bogoliubov transformation in which new fermion operators @xmath155 and @xmath156 are introduced as linear combination of @xmath144 and @xmath143 @xmath157 where @xmath158 and @xmath159 are real numbers parametrized by @xmath160 and @xmath161 . this parametrization naturally arises as a consequence of the fermionic algebra @xmath162 , @xmath163 , with @xmath164 standing for the kronecker delta symbol . moreover , to recast the hamiltonian in a diagonal form we define @xmath165 by demanding that @xmath166 . therefore , by expressing @xmath141 in terms of bogoliubov fermions and by imposing the trace invariance of the hamiltonian , eq . ( [ hi - momentum ] ) becomes @xmath167 with @xmath168 . hamiltonian ( [ hi - b ] ) is diagonal , with ground state given by the @xmath169-fermion vacuum . the procedure above also applies for the evaluation of the matrix elements of the reduced density operator given by eq . ( [ relem ] ) , which amounts for the computation of the magnetization density @xmath170 and the two - point functions @xmath171 . this can be achieved by using that @xmath172 @xcite and by expressing the remaining correlation functions as @xmath173 , \nonumber \\ g_{yy } & = & \frac{2}{l } \sum_{q =- m}^{m } \left [ \cos\left(\frac{2\pi q}{l}\right ) v_q^2 - \sin\left(\frac{2\pi q}{l}\right ) u_q v_q \right ] , \nonumber \\ g_z & = & \frac{1}{l } \sum_{q =- m}^{m } \left(1 - 2 v_q^2\right ) , \label{g - gamma}\end{aligned}\ ] ] where @xmath174 . \label{uv - final}\end{aligned}\ ] ] hence , we exactly determine the two - spin reduced density matrix . classical and quantum correlations can then be directly obtained from eqs . ( [ ccorrel ] ) and ( [ qcorrel ] ) . by numerically computing the classical correlation in eq . ( [ cc - final ] ) for nearest - neighbor spin pairs at sites @xmath36 and @xmath87 , we can show that the maximization is achieved for any @xmath175 by the choice @xmath176 and @xmath177 . then , the measurement that maximizes @xmath178 is given by @xmath179 , with @xmath180 and @xmath181 denoting the up and down spins in the @xmath182 direction , namely , @xmath183 . this numerical observation implies that @xmath184 , @xmath185 . therefore , eq . ( [ cc - final ] ) is ruled by the spin functions @xmath186 and @xmath187 , i.e. @xmath188 where @xmath189 is the binary entropy @xmath190 and @xmath191 we plot @xmath84 and @xmath105 in fig . [ f3 ] for a chain with @xmath192 sites . note that , for @xmath193 the system is a classical ising chain , whose ground state is a doublet given by the vectors @xmath194 and @xmath195 . therefore , the system is in the mixed state @xmath196 with @xmath118 and @xmath119 . on the other hand , in the limit @xmath197 the system is a paramagnet ( vanishing magnetization in the @xmath182 direction ) , with all spins in state @xmath39 . therefore the system will be described by the density operator @xmath198 which is a pure separable state , containing neither classical nor quantum correlations . the qpt from ferromagnetic to paramagnetic state is a second - order qpt and occurs at @xmath199 . signatures of this qpt can be found out by looking at the derivatives of either classical or quantum correlations . indeed , the qpt can be identified as a pronounced minimum of the first derivative of the classical correlation , which is exhibited in fig . note that the minimum logarithmically diverges at @xmath199 as the thermodynamic limit is approached ( see inset of fig . [ f4 ] ) . in the case of quantum correlations , its first derivative shows an inflexion point around @xmath199 , as displayed in fig . indeed , by looking at its second derivative in fig . [ f6 ] , the qpt is identified by a pronounced maximum , which shows quadratic logarithmic divergence at @xmath199 as the thermodynamic limit is approached ( see inset of fig . [ f6 ] ) . the behavior of the quantum discord is therefore rather different from the entanglement behavior , whose first derivative is already divergent at the qcp . remarkably , the scaling of pairwise entanglement derivative in this case ( see e.g. refs . @xcite ) is much closer to the scaling of the classical correlation derivative ( as given by fig . [ f4 ] ) than that of the quantum correlation derivative ( as given by fig . [ f5 ] ) . as in the case of the xxz model , it is interesting to observe that the spin functions @xmath186 and @xmath187 , which govern the correlations in the ising chain [ see eqs . ( [ cc - final - ib])-([p - ib ] ) ] , exhibit a crossing at the qcp . this is shown in fig . [ f7 ] for a chain with @xmath192 sites . the discussion of correlations above can also be applied in collective systems . as an illustration , we will consider here the lmg model @xcite , which describes a two - level fermi system @xmath200 , with each level having degeneracy @xmath201 . the hamiltonian for lmg model is given by @xmath202 the operators @xmath203 and @xmath204 create a particle in the upper and lower levels , respectively . this hamiltonian can be taken as describing an effective model for many - body systems , with one level just below the fermi level and and the other level just above , with the level below being filled with @xmath201 particles @xcite . alternatively , the lmg model can be seen as a one - dimensional ring of spin-1/2 particles with infinite range interaction between pairs . indeed , the hamiltonian can be rewritten as @xmath205 where @xmath206 and @xmath207 @xcite . the system undergoes a second - order qpt at @xmath208 . as @xmath209 , the ground state , as given by the hartree - fock ( hf ) approach , reads @xmath210 where we have introduced new levels labelled by @xmath211 and @xmath212 governed by the operators @xmath213 in eq . ( [ nl - lipkin ] ) , @xmath214 is a variational parameter to be adjusted in order to minimize energy , which is achieved according to the choice @xmath215 despite being an approximation , the hf ground state provides the exact description of the critical point ( for recent discussions of the exact spectrum of the lmg model , see refs . the pairwise density operator for general modes @xmath216 and @xmath217 is given by @xmath218 where @xmath219 and @xmath220 , with @xmath221 . by evaluating the matrix elements of @xmath12 for the hf ground state , we obtain @xmath222 note that eq . ( [ rhoab - lipkin ] ) displays @xmath0 symmetry and , therefore , classical and quantum correlations can be computed by using eq . ( [ cc - final ] ) . note also that , for @xmath223 , the density matrix is diagonal and the state is completely pairwise uncorrelated . on the other hand , for @xmath224 , there is an equal amount of classical and quantum correlations between the modes . these correlations vanish for @xmath225 , which is the fully polarized state . the result is plotted in fig . [ f8 ] . we can then observe that the derivatives of both classical correlation and quantum discord exhibit a signature of the qpt ( see inset of fig . these signatures are in agreement with the caracterizations in terms of entanglement @xcite and fisher information @xcite . in conclusion , we have investigated the behavior of pairwise correlations in general @xmath0 symmetric systems , splitting up their classical and quantum contributions . this allowed for the treatment of spin systems such as the xxz model and the transverse field ising chain , where the maximization required for the evaluation of the correlations has been analytically worked out . moreover , we have identified the spin functions that govern the correlations and also discussed their behavior for finite size chains . as a further application , we have used our approach to investigate the case of a collective model , given by the lmg hamiltonian . as it was shown , both classical correlation and quantum discord display signatures of the critical behavior of the system for the cases of first - order , second - order , and infinite - order qpts . for first - order qpts , as illustrated by the ferromagnetic point of the xxz spin chain , we found that both classical correlation and quantum discord display a jump at the critical point , which closely resembles the behavior of entanglement . for second - order qpts , although both kind of correlations exhibit signatures of the qpts , the derivatives of the quantum discord show a scaling that is rather different from the entanglement behavior in the transverse field ising model ( see , e.g. , refs . it is remarkable that , for this model , the first derivative of pairwise entanglement with respect to the parameter that drives the qpt exhibits a scaling that is much closer to the scaling of the first derivative of the _ classical _ correlation . for infinite - order qpts , as given by the antiferromagnetic point of the xxz spin chain , classical correlation is a minimum at the qcp while quantum discord is a maximum . whether or not this might be a general feature of infinite - order qpts is still under analysis . further investigations including correlations between blocks of particles and the effect of temperature may be interesting to establish a precise comparison between ( classical and quantum ) correlations and entanglement at qpts . moreover , dynamics in open quantum systems @xcite may also provide an interesting scenario for the discussion of the properties of the correlations and its implications for phase transitions . such topics are left for a future research . p. ribeiro , j. vidal , and r. mosseri , phys . e * 78 * , 021106 ( 2008 ) . j. vidal , g. palacios , and r. mosseri , phys . a * 69 * , 022107 ( 2004 ) . wu , m. s. sarandy , d. a. lidar , and l. j. sham , phys . rev . a * 74 * , 052335 ( 2006 ) .

we discuss the behavior of quantum and classical pairwise correlations in critical systems , with the quantumness of the correlations measured by the quantum discord . we analytically derive these correlations for general real density matrices displaying @xmath0 symmetry . as an illustration , we analyze both the xxz and the transverse field ising models . finite - size as well as infinite chains are investigated and the quantum criticality is discussed . moreover , we identify the spin functions that govern the correlations . as a further example , we also consider correlations in the hartree - fock ground state of the lipkin - meshkov - glick model . it is then shown that both classical correlation and quantum discord exhibit signatures of the quantum phase transitions .

downregulation of gene expression levels by small interfering rna ( sirna ) offers a promising therapeutic approach for various disease conditions by impacting pathogenic mrnas and promoting the molecular suppression of protein function . the critical steps needed for clinical rnai translation require appropriate packing and shielding of sirna from various degradation mechanisms , protection from serum enzymes in the bloodstream and extracellular environment during transport across the epithelial cell barrier , delivery into specific cells , defense from endosomal degradation , and release of the sirna for incorporation into the rnai machinery to exhibit its mechanism of action . a number of nonviral sirna formulation approaches , such as liposomal , polymeric , and conjugation strategies ( with or without particle - based approaches ) , have been extensively investigated . the polycation polyethylenimine ( pei ) is the most widely tested nonviral delivery system for nucleic acids ; however , its high cellular toxicity and the limited available functionalization strategies that allow retention of the buffering capacity of the polymer limit its use as a nucleic acid carrier . in spite of tremendous efforts made during the past decade with nonviral approaches to improve sirna delivery into cells , tissues , and organs , the main hurdle of balancing toxicity and transfection efficiency still remains . here , we report a logically designed and synthesized cationic co - polymer - based polymeric delivery system with favorable hydrophilic lipophilic - balanced properties and low toxicity for efficient sirna delivery . nylon-3 polymers ( poly--peptides ) have been designed and employed for use in various biological applications , such as biomaterials to promote cell adhesion , mimics of host defense peptides possessing antimicrobial activity , mimics of lung surfactant proteins , and mimics of natural polysaccharides . these copolymers are sequence - random and heterochiral in nature and synthesized via anionic ring - opening polymerization of -lactams to incorporate both cationic and lipophilic subunits . the physical properties of nylon-3 co - polymers can be tailored by altering the structure of the polymer subunits as well as the subunit ratio . for instance , polymer hydrophobicity can be altered by varying the ratio of cationic ( hydrophilic ) and hydrophobic subunits , whereas polymer length can be varied by tuning the ratio of co - initiator and total -lactams or by functionalizing the nylon-3 chain s terminus . lipophilic character was introduced by hydrophobic cyclohexyl ( ch ) or cyclopentyl ( cp ) subunits to help mediate sirna / polymer particle complex formation and cellular uptake . the resulting amphiphilic and biocompatible , protein - like nature of the nylon-3 polymer backbone have directed strong interest toward testing this new class of polycationic materials for nucleic acid delivery . here , these polymers are screened for sirna delivery for the first time . previously , various amine - containing polymers , such as poly--amino esters , poly(l - lysine ) ( pll ) , polypropyleneimines , polyamidoamine ( pamam ) dendrimers , triazine - based dendrimers , and polyethylenimine , were tested but had limited success due to high toxicity and/or immunogenicity . modifications to decrease the toxicity of these polycations have been accompanied by a loss or reduction in transfection ability . however , the nylon-3 polymer - based materials described here open a new synthetic approach for cationic polymers to incorporate favorable sirna carrier / delivery characteristics such as solubility in water , positive charges for complexation with negatively charged sirna at physiologic ph , amphiphilicity , appropriate polymer length , and desired terminal functional groups . in this task of screening for potential sirna delivery materials , we logically designed and synthesized heterochiral nylon-3 co - polymers for sirna complexation and particle formation . promising nylon-3 co - polymer - based polycations were screened for efficient sirna delivery and selected for further investigation based on their physicochemical characteristics , such as particle size , surface charge , and buffering capacity . in vitro biological evaluation was performed with h1299/luc cells to test cytotoxicity , polyplex uptake was quantified and the uptake route was assessed by flow cytometry , endosomal release was detected by confocal microscopy , and gene knockdown efficiency was assessed at the protein level using luciferase expression assays . nylon-3 polymers were synthesized via anionic ring - opening polymerization ( rop ) from racemic -lactams and characterized as described previously . briefly , a mixture of -lactam monomers and co - initiator ( 4-tert - butylbenzoyl chloride ) in thf was treated with lithium bis(trimethylsilyl)amide ( lihmds ) , and the reaction was stirred at room temperature for 6 h. the reaction mixture was removed from the glovebox , and the reaction was quenched by addition of methanol . a white precipitate was collected after adding pentane to the reaction mixture and centrifugation . the collected white solid was subjected to another two cycles of dissolution / precipitation in thf / pentane to give the boc - protected polymer that was characterized by gel permeation chromatography ( gpc ) using thf as the mobile phase . the boc protecting groups were removed with trifluoroacetic acid ( tfa ) at room temperature to afford the deprotected polymer as an amine salt . diethyl ether ( et2o ) was added to the reaction mixture to precipitate out a white solid that was collected after centrifugation . the collected white solid was subjected to another two cycles of dissolution / precipitation in meoh / et2o to give the final deprotected polymer that was used in this study . three different partially 2-o - methylated sirna duplexes used for polyplex preparation were bought from integrated dna technologies inc . sequences of siluc ( specific , anti - luciferase sequence ) , control ( nonspecific , negative control sequence ) , and fluorescently labeled sirna ( alexa fluor-488 sirna and tye-546-labeled sirna ) were synthesized as described before . luciferase assay reagent and cell culture lysis reagent ( cclr ) were purchased from promega ( madison , wi , usa ) . hepes ( 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid ) , d - glucose , sodium bicarbonate , and rpmi-1640 were purchased from sigma - aldrich ( st . fbs ( fetal bovine serum ) , trypsin - edta ( ethylenediaminetetraacetic acid ) , and penicillin streptomycin were purchased from hyclone , thermo scientific ( waltham , ma , usa ) . mtt ( 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide ) , sybr gold dye , and lipofectamine 2000 ( lf ) were bought from life technologies ( carlsbad , ca , usa ) , and polyethylenimine 25 kda ( pei ) was obtained from basf ( ludwigshafen , germany ) . synthesized polymers were broadly categorized into three different groups ( g1g3 ; table 1 ) based on the fraction of cationic subunit and the ring size of the hydrophobic subunit ( five- or six - member ring ) within the polymer chains . in terms of cationic subunit content , the g3 group has the highest content ( 90% ) , followed by g1 ( 60% ) and g2 ( 40% ) . the hydrophobic subunit varied between 10 and 60% , with the least hydrophobic content ( 10% ) being in g3 , followed by g1 ( 40% ) and g2 ( 60% ) . while keeping the cationic and hydrophobic content constant , polymers with molecular weights varying between 7.5 and 44 the r group at the c - terminus of all polymers represents the side chain of either subunit within the co - polymers . the ratio of the number of nitrogens in the polymer to phosphates in sirna ( n / p ) was calculated by using the information from table 1 and the equation below . both the specific anti - luciferase and the scrambled sirna duplex used in these experiments comprise 52 nucleotides . the polymer and sirna solutions were prepared with filtered 10 mm hepes buffer ( ph 7.2 ) ( 0.22 m filter : nalgene syringe filter , sigma - aldrich , st . polyplexes ( polymer / sirna mixtures ) at different n / p ratios were formed by pipetting and quickly mixing equal volumes of sirna ( 50 l ) and polymer ( 50 l ) into a microcentrifuge tube . the polyplexes were then briefly vortexed for 30 s and incubated for 30 min at room temperature to equilibrate and permit stable complex formation . polyplexes were freshly prepared for every experiment . to test the sirna condensation ability for various polymers at different n / p ratios ( 2 , 5 , 10 , 15 , and 20 ) , sybr gold dye was diluted to 4 in duplex buffer ( 100 mm potassium acetate and 30 mm hepes in diethylpyrocarbonate ( depc ) treated water , ph 7.4 ) . the polyplexes were prepared at different n / p ratios and pipetted into an opaque fluoronunc 96-well plate ( nunc , thermo fisher scientific , waltham , ma , usa ) . twenty five microliters of sybr gold solution was added to each well , and the plate was incubated for 10 min in the dark . fluorescence caused by dye intercalation to sirna duplexes and its quenching in polyplexes was measured as a relative fluorescence value using a fluorescence plate reader ( biotek synergy 2 , perkinelmer , waltham , ma , usa ) at 495/537 nm excitation / emission . the percentage of uncomplexed sirna was calculated by dividing the polyplex fluorescence by the fluorescence of free intercalated sirna . luciferase - expressing nonsmall cell lung cancer cells ( h1299/luc ) were cultured in rpmi-1640 media supplemented with fbs ( 10% ) , hepes ( 10 mm ) , sodium bicarbonate ( 1.5 the cells were subcultured , maintained , and grown under humidified air with 5% co2 at 37 c . to test the free polymer s cytotoxicity , experiments were conducted by adding different concentrations of the polymer solutions from every group to h1299/luc cells plated 24 h prior to the treatment . free polymer concentrations were made by directly dissolving the nylon-3 polymers or pei 25 kda , which served as a control , in complete rpmi-1640 media . concentrations ranging from 1 to 20 g / ml were evaluated . in comparison , the highest polymer concentrations used for the transfections ranged from 1 to 1.8 g / ml for n / p ratio 2 and 40 pmol sirna . h1299/luc cells were seeded in 96-well plates at a density of 10 000 cells per well and incubated overnight with 5% co2 at 37 c in a humidified atmosphere . after 24 h of incubation , the media was removed , and each well was rinsed with 200 l of phosphate buffered saline ( ph 7.4 ) . cells were incubated for another 3 h after adding 100 l of mtt - containing media ( 0.5 mg / ml in rpmi-1640 media ) to each well . after the media was completely removed , 200 l of dimethyl sulfoxide ( dmso ) was then added into each well to dissolve the purple formazan crystals formed by active mitochondria in the treated cells . the absorption at 570 nm was quantified using a microplate reader ( biotek synergy 2 ) . results are shown as the average of triplicates standard deviation ( mean value standard deviation ) as the percent of viable cells relative to 100% viability , represented by cells cultured in the absence of polymers . size and zeta potential characterizations were performed using a nanosizer nano zs ( malvern instruments ) . polyplex size was measured by transferring 100 l of polyplexes containing 20 pmol of sirna to a low volume uv cuvette ( brand gmbh , germany ) . following size measurements , zeta potential measurements were performed by diluting the same 100 l of polyplexes to 750 l with filtered 10 mm hepes buffer ( ph 7.4 ) and transferring the dilution into a zeta cell ( zetasizer nano series , malvern , uk ) . scattered light was detected at an angle of 173 in backscatter mode to minimize the noise in the measurements caused by any dust particles in the dispersing diluents . for size distributions , viscosity and refractive index values of distilled water at 25 c multimodal size analysis was performed on each sample measurement , consisting of 10 runs of 10 s each . values given are the average of three separate experiments performed in triplicate standard deviation . the cellular uptake of the fluorescently labeled polyplexes ( alexa fluor-488 sirna ) was measured using flow cytometry . the day before the transfection , 50 000 cells were seeded in 48-well plates and grown for 24 h. the cells were then transfected with polyplexes containing either 30 or 40 pm of sirna . the final volume per well was 200 l , and the sirna concentration was 150 or 200 nm , respectively . after 5 h of transfection , cells were washed with phosphate buffered saline ( pbs ) and detached using 0.25% trypsin - edta ( hyclone fisher thermo scientific , usa ) . detached cells were washed twice with 1 ml of pbs by centrifuging ( 400 g for 5 min ) and resuspending the cells . for flow cytometry analysis , the cells were resuspended in 400 l of sterile pbs and transferred to bd falcon facs tubes ( fisher scientific , usa ) . for each sample , 10 000 events were counted on a bd lsr ii analyzer ( bd biosciences , usa ) with an excitation laser of 488 nm . the cellular uptake fluorescence intensity from each sample was obtained and was quantified as the average fluorescence intensity standard deviation of triplicate samples from the gated , viable cells . to study the route of polyplex uptake , 50 000 h1299/luc - cells were incubated with different types of specific uptake inhibitors , such as chlorpromazine ( 10 g / ml ) , nystatin ( 10 g / ml ) , wortmannin ( 12 ng / ml ) , and methyl--cyclodextrin ( 3 mg / ml ) , for 1 h followed by incubation with g2d polyplexes containing alexa fluor-488 sirna for 5 h. as controls , cells were also transfected with alexa fluor-488 sirna and lf or pei 25 kda , and untreated cells served as blank control . after the incubation period , the cells were either trypsinized ( unquenched samples ) or treated with a 0.4% trypan blue solution for 5 min ( quenched samples ) before they were trypsinized . subsequently , the cells were washed and subjected to flow cytometric detection of sirna uptake as described above . to determine if polyplexes of g2d experience endosomal entrapment after intracellular uptake or are released from the endolysosmal compartment , 30 000 h1299/luc - cells were seeded per chamber on chamber slides with 8 chambers . the cells were transfected 24 h later with polyplexes prepared at n / p ratio 5 using g2d or pei 25 kda polymers and 20 pmol of tye-546-labeled sirna per chamber . the polyplexes were added to a total volume of 200 l . as a positive control , the commercially available transfection reagent lf was used , and untreated cells served as a negative control . cells were incubated for 4 h at 37 c and 5% co2 before the endolysosomes were stained with 75 nm lysotracker green ( life technologies , grand island , ny ) for 1 h in the presence of the polyplexes . subsequently , the cells were washed and fixed on the slides with a 4% paraformaldehyde solution . samples were embedded with fluorsave ( calbiochem , merck millipore , darmstadt , germany ) . a leica spe laser scanning confocal microscope equipped with a spectral detector ( leica microsystems , wetzlar , germany ) tye-546-labeled sirna was excited with a solid - state laser ( pavilion integration corporation , san jose , ca ) with an excitation wavelength of 532 , and lysotracker was excited with a sapphire solid - state laser ( coherent inc . , fluorescence emission of tye-546 was detected in channel 1 at 560 nm , and the emission of the lysotracker was detected in channel 2 at 510 nm . all images shown were acquired using a 40 objective with a 0.75 numerical aperture ( leica microsystems , wetzlar , germany ) . to determine the buffering ability of different polymers , titration curves were generated to measure the polymer s ability to be protonated over the ph range from 12 to 2 by titration with 0.1 n hcl . each polymer ( 2.5 mg ) was weighed and dissolved in 5 ml of 18.2 m distilled water . the ph of the polymer - containing solution ( 0.5 mg / ml ) was adjusted above 12 with 1 m naoh and was allowed to stabilize for 5 min . the ph value was detected with a ph meter using an electrode at 25 c ( accumet basic , fisher scientific , usa ) . polymers that show smaller changes in ph values during the hcl titration possess a greater buffering ability . prior to transfection , h1299/luc cells were seeded in 48-well plates at a density of 20 000 cells per well in 400 l of medium and incubated for 24 h at 37 c in humidified atmosphere with 5% co2 . on the day of transfection , 100 l of rpmi-1640 medium and 100 l of polyplexes ( n / p ratio 2 ) made of pei 25 kda or nylon-3-polymers with different amounts of sirna ( 30 or 40 pmol ) were added to each well . lipofectamine lipoplexes served as a transfection control , and untreated cells ( 100% luciferase expression ) were used for normalization of the results . after 5 h of incubation , the media containing polyplexes or lipoplexes was removed and replaced with 500 l of fresh rpmi-1640 culture medium . the cells were grown for a total of 72 h prior to measuring luciferase expression . the medium was then discarded , and the cells were washed with 200 l of pbs ( ph 7.4 ) . cells were then lysed in 100 l of cclr for 10 min at 37 c . luciferase activity was quantified by injection of 50 l of luciferase assay buffer , containing 10 mm luciferin , into each well of an opaque 96-well plate . relative light units ( rlu ) were measured with a plate luminometer ( biotek synergy 2 , vt , usa ) to quantify the cellular luciferase activity . all experiments were performed in quadruplicate and were representative of three independent experiments . the transfection efficiency was expressed as percentage of knockdown compared with the expression level in nontransfected control cells . statistical testing between samples was performed via two - way anova and bonferroni post - test , assuming unknown variances with an alpha level of 0.05 . a small set of nylon-3 polymers was designed , synthesized , and evaluated for sirna delivery . it was recently reported that polyplex stability depends on the molecular reorganization of these complexes based on their thermodynamic properties . therefore , the n / p ratios of all formulations tested here were optimized with regard to their physicochemical parameters and cellular uptake . a strong complexation of polymer with sirna prevents sirna release inside the cytoplasm and its incorporation into risc complex , whereas a weak complexation prematurely releases sirna , causing degradation before polyplex endocytosis . the sybr gold assay showed that the tested nylon-3 polymers were able to condense sirna effectively . condensation was observed even at a low n / p ratio ( 2 ) and showed a strong ability of these polymers to interact with sirna . although the exact interaction mechanism between nylon-3 polymers and sirna is unknown , we hypothesize that it is due to a combination of electrostatic and hydrophobic interactions resulting from their structural properties . for pdna , condensation was considered to be complete when 90% of the phosphodiester backbone charge was neutralized . since sirna is a comparably short molecule , this threshold of 90% condensation was easily achieved in our studies with small amounts of cationic nylon-3 polymers . all of the polymers showed greater than 95% condensation at n / p ratios higher than 5 ( figure 1 ) . this confirmed that only small amounts of polymers were needed to pack sirna and minimize unwanted side / toxic effects resulting from higher amounts of cationic polymers in sirna delivery . condensation profiles of sirna complexed at different n / p ratios using varied nylon-3 polymers with average molecular weights ranging from 6 to 44 kda , as indicated . there was no statistically significant difference among the overall condensation behavior of all polymers tested ( p = 0.351 ) ; however , there was a significant decrease in fluorescence for all polymers at n / p ratio 2 compared to free sirna and at n / p 5 compared to n / p 2 ( p < 0.001 ) . even though increasing the molecular weight of polymers within group g2 ( g2a to g2d ) was expected to cause more efficient sirna condensation at low n / p ratios , there were no significant differences ( p = 0.529 ) . these results demonstrate that the amount of polymer used to condense the sirna ( n / p ratio ) had an effect , whereas the molecular weight has no significant influence on condensation . drug and gene delivery systems need to possess no or minimal toxicity in vitro and in vivo to become candidates for clinical translation . the cell viability profiles of the different nylon-3 polymers showed minimal toxicity ( figure 2 ) . cell viability was greater than 85% at polymer concentrations less than 10 g / ml . this polymer concentration was much higher than the concentrations necessary for effective sirna transfection , which ranged from 1 to 1.8 g / ml for n / p ratio 2 and 40 pmol sirna , depending on the polymer , and did not cause any pronounced cellular toxicity . the g1 polymer showed relatively low toxicity in comparison to that of polymers in the g2 or g3 groups . in general , increasing the molecular weight resulted in a trend of increasing toxicity for g2 polymers ( g2d > g2c > g2b > g2a ) at the highest concentration ( 20 g / ml ) . this extrapolation implies that toxicity increases with an increase in the molecular weight among polymers with identical subunit composition . in contrast , the g3 polymer , despite having a lower molecular weight than g2b , g2c , and g2d , showed greater toxicity at 20 g / ml , reflecting that toxicity also increases with increased cationic content ( g3 vs g1 and g2a ) . polycation - mediated toxicity was reported previously to arise from both loss of outer plasma membrane integrity and subcelluar mitochondrial membrane potential , leading to pore formation . it is therefore possible that the toxicity of this type of polymer may be further reduced by optimizing the content of cationic subunits within the polymers chains , by using other conjugation strategies , or by introducing favorable structural groups for future sirna delivery system design . however , a critical balance should be considered between cationic charge density for sirna complexation and a rational design that decreases polymer toxicity . while cationic charge mediates sirna complexation , we show here that group 2 polymers efficiently deliver sirna intracellularly at only 40% cationic subunits . we hypothesize , therefore , that polymers with an increased percentage of hydrophobic subunits and less than 40% cationic subunits may still be efficient and possess reduced toxicity . cytotoxicity profiles of different nylon-3 polymers ( average molecular weight ranging from 6 to 44 kda ) in comparison to pei 25 kda on h1299/luc cells with increasing concentrations ( 020 g / ml ) after incubating for 24 h at 37 c . statistical analysis showed that there was not a significant difference in the toxicity profiles among polymers g1 , g2a , g2b , and g2c at all concentrations tested ( p > 0.1 ) . however , polymers g2d and g3 showed a significant increase in toxicity at 20 g / ml when compared to control cells cultured in the absence of polymers ( p = 0.003 and 0.002 , respectively ) . even though high molecular weight polymer g2d seemed to cause higher toxicity at the highest concentration ( 20 g / ml ) , statistical analysis showed that the g2 polymers ( g2a , g2b , g2c , and g2d ) were not significantly different in terms of their impact on cell viability ( p = 0.136 ) . pei 25 kda ( control polymer ) showed significant ( p < 0.001 ) cellular toxicity ( less than 50% ) even at low concentrations ( 5 and 10 g / ml ) of the polymer . at the highest concentration tested ( 20 g / ml ) , the cell viability decreased to less than 10% . importantly , broadly used , high molecular weight pei was significantly more toxic ( p < 0.001 ) at all tested concentrations than that of the nylon-3 polymers . appropriate particle size and surface charge favors the entry of sirna into cells . it was reported that a high excess of cationic polymer ( high n / p ratio ) , such as pei in polyplexes , leads to high surface charges ( + 25 mv ) and condenses nucleic acids into small particles . it was also previously shown that endocytosis depends on size , with smaller size particles being taken up more easily by cells . particle size analysis of polyplexes showed that the size and polydispersity of the complexes depended on the n / p ratio ( figure 3 ) . at an n / p ratio of 5 , polymer g1 showed a smaller particle size ( 117 16 nm ) than that at an n / p ratio of 1 ( 180 33 ) . among g2 polymers , polymer g2a with an n / p ratio of 5 showed a smaller size ( 120 2 nm ) with a lower pdi ( 0.15 ) , indicating that slightly higher n / p ratios were required for smaller complexes , in contrast to 25 kda branched pei , which shows a minimum in hydrodynamic diameter at n / p 2 . the size distribution plots by scatter intensity can be found in the supporting information . there was also a clear decreasing size trend for the g2a polymer when the n / p ratio was increased from 1 to 2 and 5 . only in the case of g2a were the polyplex sizes significantly smaller at n / p 5 compared to those at n / p ratios 1 and 2 ( p < 0.001 ) . polymers g2b , g2c , and g2d all formed relatively small complexes below 260 nm , which is a size range overlooked by phagocytosing macrophages . interestingly , increasing the molecular weight ( g2b < g2c < g2d ) or increasing the n / p ratio of these polyplexes did not have a significant effect on the hydrodynamic diameter . additionally , there were no significant differences among polymers of different subunit composition but similarly low molecular weight ( g1 , g2a , and g3 ) . polymer g3 showed a particularly small particle size at n / p 2 , which is comparable to the behavior of pei 25 kda . polyplex ( nylon-3/sirna ) particle size and polydispersity index ( pdi ) at different n / p ratios ( 1 , 2 , and 5 ) after incubation for 30 min at room temperature . whereas the g1 polymer formed the smallest polyplexes at n / p ratio 5 , g2c polyplexes were the smallest at n / p ratio 2 . increasing the molecular weight in this category may help to further lower the size of the particles . among the g2 polymers , increasing the molecular weight and varying the n / p ratio did not have a consistent or significant influence on particle size , however . even though the n / p ratio is a critical parameter and is commonly increased to decrease polyplex sizes , it was recently described that there may be an optimal formulation at rather low n / p ratios which can yield small polyplexes . increasing the n / p ratio beyond this optimal value was shown to cause larger hydrodynamic diameters and polydispersity indices ( pdis ) . this finding is in - line with the particularly low size distributions ( pdis ) observed for all nylon-3 formulations except g2a at n / p 2 . at an n / p ratio of 1 ( irrespective of the group ) , the polyplexes made from polymer g3 were the most negatively ( 21 10 mv ) charged particles . among the g2 polymers , the negative charge seemed to show a decreasing trend as the molecular weight of the polymer increased ( almost neutral for g2d ) . the repulsive forces between the negatively charged cell membrane and the negative particle are usually believed to counteract efficient cellular entry . negative zeta potentials may indicate that the complexes were loosely condensed , causing larger particle sizes , which is in - line with the hydrodynamic diameters found here for n / p 1 . all of the polyplexes at n / p ratios of 2 and 5 showed a positive surface charge irrespective of the polymer composition . at n / p 2 , the g1 polyplexes showed the least positive zeta potential ( 1.3 5 mv ) , which increased ( to 5.2 4.4 mv ) at n / p 5 . the g2 ( g2a , g2b , g2c , and g2d ) and g3 polymers showed a slightly higher positive charge at n / p 2 compared to that at n / p 5 , which is comparable with findings for pei / sirna complexes . statistical analysis showed that there were significant differences among the category of the polymers ( g1 , g2 or g3 ) in terms of changes in the zeta potential ( p < 0.298 ) . the differences were significant for the changes according to the n / p ratio ( p < 0.001 between n / p 1 and 2 and p < 0.001 between n / p 1 and 5 ) ; however , the differences were insignificant between n / p ratios 2 and 5 ( p = 0.487 ) . comparing polyplexes at n / p 1 and 2 indicated that the sizes for those formulations were similar ; however , the surface charge reversed from negative to positive . within each polymer , the n / p ratio therefore needed to be optimized for sirna delivery to find the ideal particle characteristics , in terms of size and zeta potential . particles with high zeta potentials were shown to have lesser particle aggregation and thus higher colloidal stability due to electrostatic repulsion between particles . however , strongly positive surface charges may damage the plasma membrane , preventing recovery after transient transfection conditions ( 5 h ) and thus may increase toxicity . with the current synthetic design of the nylon-3-based polymers , toxicity - decreasing subunits and functional groups can be easily incorporated even if formulations with higher zeta potentials are required to achieve efficient protein knockdown . zeta potential of nylon-3/sirna polyplexes incubated for 30 min at room temperature at different n / p ratios ( 1 , 2 , and 5 ) . in general , cellular uptake improved with increasing n / p ratios from 1 to 2 and 5 ( figure 5 ) . the g1 polymer , at an n / p ratio of 1 , showed an uptake of polyplexes into 22% of the cells treated , which increased to 86% at an n / p ratio of 5 . the polyplexes derived from g2a and g2b polymers showed 27 and 14% cellular uptake at n / p ratio 1 , which increased to 88 and 85% at n / p ratio 2 , respectively . even at a low n / p ratio of 1 , in spite of negative zeta potentials , the high molecular weight polymers ( g2c and g2d ) showed greater than 80% cellular uptake of the polyplexes , which increased further to greater than 95% uptake at n / p ratio 5 . in the case of the g3 polymer , g3 polyplexes showed less than 2% uptake at n / p ratio 1 , which significantly increased to 50% at n / p ratio 5 . it has been long thought that increasing the surface charge of polyplexes and their efficacy of nucleic acid delivery were proportional and associated with the problem of increased cytotoxicity . in contrast to this hypothesis this may be attributed to the hydrophobic moieties of the nylon-3 polymers and is a very promising property of these formulations . this property of amphiphilic polymers has been reported previously to be an important parameter for the formulation of very efficient sirna delivery systems . these results also suggest that the cationic content was important for sirna condensation , whereas the 5- or 6-member ring structure in the hydrophobic subunit may mediate interaction with the lipid bilayer of cell membranes and therefore is also an important feature in the design of nylon-3 polymer - based sirna delivery systems . cellular interactions , such as interaction with anionic cell - surface proteoglycans and hydrophobic interactions with lipid bilayers , plays an important role in polyplex uptake . interestingly , the smallest polyplexes obtained at n / p 2 , which were formulated with g1 , g2c , and g2d , were most efficient in terms of uptake in spite of their negative charge . it seems , therefore , that particles made of amphiphiles that are smaller than 200 nm can interact with cellular membranes and can be successfully taken up . in this context , it is surprising to find in our study that highly positive zeta potentials and the side effect of increased cytotoxicity are not prerequisites for efficient nonviral sirna delivery with nylon-3 polymers . also , it was confirmed that an optimization of the n / p ratio in terms of surface charge and cellular uptake was necessary and that this n / p ratio may be rather low . in vitro cellular uptake of alexa fluor-488-labeled sirna polyplexes by h1299/luc cells at different n / p ratios ( 1 , 2 , and 5 ) and 20 pmol of sirna when incubated for 6 h at 37 c . ( a ) untreated cells , free sirna , and polymers g1 and g3 . there was a statistical significance in cellular uptake of the polyplexes between n / p ratio 1 and 5 of g3 polyplexes ( p < 0.001 ) . polyplexes made of g2c or g2d showed significantly increased uptake compared to that of g3 polyplexes at all n / p ratios ( p < 0.001 ) . these results indicate that the n / p ratio indeed plays a significant role in tuning the uptake of the polyplexes . also , the cellular uptake in terms of the scattered fluorescence intensity per cell was quantified by normalizing the peak heights to the percentage maximum on the y axis ( figure 6 ) . in the top panel ( n / p ratio effect ) , the overlaid histograms show that the higher intensity corresponds to higher amounts of sirna uptake among g1 , g3 , g2a , and g2b when formulated at n / p ratio 5 compared to that at n / p ratios 1 and 2 . the fluorescence intensity was already increased at n / p 2 compared to that at n / p 1 for g2c polyplexes , whereas no difference was observed between n / p 2 and 5 . at all n / p ratios ( 1 , 2 , and 5 ) , strong fluorescence intensity was measured for g2d polyplexes , indicating the profound effect of molecular weight for uptake efficiency . the lower panel shows cellular uptake at a constant n / p ratio of 2 and increasing amounts of sirna ( 1040 pmol per well ) , as indicated by fluorescence intensity . it was confirmed that free labeled sirna had insignificant uptake , even with increasing amounts of sirna ( 1040 pmol ) . the fluorescence intensity or sirna uptake increased with an increasing amount of sirna ( 1040 pmol ) among all of the polyplexes ( g1 , g2a , g2b , g2c , g2d , and g3 ) . this indicated that higher amounts of sirna can help at any given n / p ratio to increase the amount of sirna delivered to h1299/luc cells . however , in the case of g2d polyplexes , the fluorescence intensity was highest at 30 pmol of sirna and decreased at 40 pmol . this could be an indication of saturation of polyplex uptake for the very efficient formulation , g2d . in general , sirna uptake increased with an increase in the n / p ratio and also , for a given n / p ratio , with an increasing amount of sirna among these tested nylon-3 polymer / sirna polyplexes . comparing group 2 polymers , an increase of the molecular weight also caused an increase in uptake efficiency with regard to the percentage of positive cells ( figure 5 ) and the amount of sirna delivered per cell ( figure 6 ) . forward scatter of alexa fluor-488-labeled sirna polyplexes in h1299/luc cells at different ( top ) n / p ratios ( 1 , 2 , and 5 ) and ( lower ) amounts of sirna ( 10 , 20 , 30 , and 40 pmol ) when incubated for 6 h at 37 c . therefore , we evaluated whether the nylon-3 polyplexes were taken up in a manner similar to that other polyplexes , mainly caveolae - mediated endocytosis , or behave more like lipoplexes and followed a preference of clathrin - mediated endocytosis . cellular uptake expressed as median fluorescence intensity ( mfi ) in the presence of different inhibitors is shown in figure 7 . our results show a higher mfi in cells incubated with g2d polyplexes when compared to that with pei 25 kda polymer . chlorpromazine is known to inhibit the formation of new clathrin - coated pits by preventing clathrin protein recycling . methyl--cyclodextrin inhibits cholesterol - dependent clathrin - mediated glycolipids , is involved in lipid raft depletion , and also selectively inhibits caveolae - mediated endocytosis . since chlorpromazine and methyl--cyclodextrin had the strongest impact on cellular uptake of sirna / g2d polyplexes and significantly ( p < 0.001 ) decreased the mfi when compared to that of g2d polyplexes in the absence of inhibitors , our results show that g2d polyplexes are predominantly internalized via cholesterol - dependent clathrin - mediated endocytosis and only partially by macropinocytosis and caveolae - mediated endocytosis . the observed decrease in mfi in both quenched and unquenched cells ranged between 90 and 95% compared to that for g2d polyplexes . wortmannin and nystatin , which inhibit cellular uptake by macropinocytosis and by caveolae - mediated cellular uptake , only caused 3050% decreases in cellular uptake in unquenched cells and 5060% in quenched samples . these results show that chlorpromazine and methyl--cyclodextrin most strongly inhibited polyplex cellular uptake compared to wortmannin and nystatin , indicating that nylon-3 polyplexes are efficiently taken up by clathrin - mediated endocytosis . additionally , lipid raft - mediated uptake may play an important role for their internalization , as suggested for sirna lipoplexes previously . it was previously shown that the cellular uptake route of nanoparticles depends on their size . particles around 200 nm can be internalized via clathrin - mediated endocytosis , whereas 500 nm particles favor caveolae - mediated endocytosis . on the basis of the size of g2d polyplexes , we hypothesize that the particles are in a suitable size range for clathrin - mediated endocytosis . it was also reported in the past that dotap lipoplexes are mainly taken up by clathrin - mediated endocytoses , whereas pei polyplexes no longer show transfection efficacy if caveolae - mediated endocytosis is blocked . therefore , we conclude that the amphiphilic nylon-3 polyplexes share similarity with lioplexes with regard to their uptake route . additionally , lu et al . recently reported that their lipoplexes also were mainly taken up by clathrin - mediated endocytosis ; however , depletion of cholesterol from the cell membrane prevented functional sirna delivery . the authors therefore suggested that a fusogenic mechanism between lipoplexes and cell membranes was responsible for efficient sirna - mediated gene knockdown after nonviral delivery . since there are also reports in the literature that explain how clathrin - mediated endocytosis can be affected by cholesterol depletion , cholesterol depletion can not generally be interpreted as inhibition of lipid rafts . however , a lipid - mediated or fusognic uptake mechanism as described for polyplexes seems to play an important role for amphiphilic polyplexes as well . cellular uptake of sirna / nylon-3 polyplexes at n / p ratio 2 and 40 pmol in the presence of uptake inhibitors and in comparison to that of lf and pei 25 kda . the endolysosome can be a substantial barrier to efficient cytosolic sirna delivery , and cellular uptake of sirna does not necessarily result in gene knockdown . for example , if sirna is entrapped in the endolydodome after endocytosis , then it is not available for incorporation in the rna - induced silencing complex ( risc ) , a necessary step for induction of the rnai machinery . to achieve efficient gene knockdown , endosomal escape cationic polymers with design features that incorporate better buffering moieties , such as histidine or imidazole , were shown to facilitate escape from the endosome . it was also reported that unmodified low molecular weight pei showed slightly lower buffering capacity in comparison to that of high molecular weight pei . this property , referred to as the proton sponge , has often been cited to explain the endosomal release of nucleic acids after transfection with pei . therefore , we assessed uptake into endolysosomes and release from the latter in a colocalization experiment ( shown in yellow ) with fluorescent sirna ( shown in red ) and lysotracker ( shown in green ) . all samples showed some extent of colocalization , which is interpreted as sirna being present in endolysosomes . figure 8a depicts the pattern of intracellular uptake of sirna delivered with polymer g2d and shows colocalization with endolysosomes but also shows free sirna with an even distribution throughout the cytoplasm . the pattern of sirna delivered with lf ( figure 8b ) is comparable in the cytosolic distribution but shows smaller yellow dots , which depict sirna in the endolysosomal compartment . figure 8c clearly shows colocalization of sirna delivered with pei and lysotracker , but it also shows a substantial amount of sirna attached to the outer cell membrane that is not endocytosed yet . while the cells transfected with lf and g2d showed released sirna in the cytoplasm that was evenly distributed , pei , in contrast , is known to adhere strongly to the cell surface , which was also shown in the cell micrographs . it can be suggested from the results shown here that even the sirna that is taken up by clathrin - mediated endocytosis is efficiently released to the cytoplasm . additionally , lipid raft - mediated uptake , as suggested , would not deliver the sirna to the endolysosome at all . all of these aspects explain the efficient cytoplasmic delivery of sirna via g2d polyplexes . confocal images of intracellular uptake of sirna ( red ) mediated by ( a ) g2d , ( b ) lf , or ( c ) pei in comparison to ( d ) cells treated with lysotracker but without nanoparticles . another property of polycations that promotes endosomal release of nucleic acid cargo is their buffering capacity . pei has been considered to be ideal cationic polymer in terms of optimal buffering capacity that aids in endosomal escape because of its high concentration of amine groups . the g2c and g2d polymers showed a comparable proton buffering capacity as that of pei within the experimental ph range ( figure 9 ) . polymers g2a and g2b showed the least buffering capacity among all polymers tested . the g1 and g3 polymers showed better buffering capacity compared to that of g2a and g2b but less compared to that of pei at ph values above 7 . however , all of the polymers possessed buffering capacity within the experimental ph range , 58 , most likely due to the amino groups in their structures . the buffering performance of the polymers decreased in the following order : g2c g2d > g1 g3 > g2a g2b . often times , loss of buffering ability is observed after grafting chemical structures such as poly(ethylene glycol ) ( peg ) to cationic polymers in order to reduce their toxicity . in our studies , with introduction of hydrophobic subunits , we did not generally observe a decreased buffering ability of polymers containing a low percentage of cationic monomers ( group 2 ) . although polymers g2a and g2b had decreased buffering capacity , the increase of the molecular weight ( polymers g2c and g2d ) led to increased buffering ability . buffering capacity may not exclusively mediate gene knockdown , but it triggers endosomal escape if polyplexes are taken up into the endolysosomal compartment . interestingly , one of the polymers ( g2d ) that exhibited high buffering capacity also showed efficient transfection ( figure 10 ) efficiency . buffering ability of different nylon-3 polymers when titrated with 0.1 n hcl and ph of the polymer solution measured at room temperature . luciferase protein knockdown in h1299/luc cells 72 h after transfection with 30 and 40 pmol of sirna / nylon-3 polyplexes at n / p ratio 2 in comparison to that with lf and pei 25 kda . once the polyplexes enter the cell cytoplasm and/or escape the endosome , the complexes need to dissociate , and the sinra needs to be incorporated into risc to degrade specific mrna . even though polyplexes made of the low molecular weight polymers g1 and g3 showed cellular uptake ( figure 5 ) , we did not observe any protein knockdown at the tested n / p ratios ( data not shown ) . g1 polyplexes exhibited the most favorable particles sizes , which may explain their more efficient cellular delivery . g3 polyplexes , on the other hand , despite having a higher charge density within the polymer , were not efficiently taken up . the increase of the amount of sirna only slightly increased the delivery with g3 , whereas increasing the n / p ratio to 5 had a positive effect . however , further increasing the n / p ratio and thus the excess of polymer g3 may not be useful due to g3 s most unfavorable toxicity profile ( figure 2 ) . the low knockdown efficiency of g1 , which demonstrated effective sirna delivery , may be attributed to weaker or slower decomplexation kinetics in the intracellular environment . it is possible that in the case of g1 polyplexes sirna was not available for incorporation into risc . strategies such as introducing bioreducible polymeric groups in the nylon-3 structure may enhance the decomplexation ability and thus the transfection efficiency . the ability of selected ( g2a and g2d ) nylon-3/sirna - based polyplexes to mediate luciferase protein knockdown in h1299/luc cells as compared to its level in untreated cells is shown in figure 10 . significant knockdown was observed only with high molecular weight amphiphilic polymer g2d , composed of 40% cationic subunits and 60% hydrophobic subunits . the lower molecular weight polymer g2a did not achieve any significant gene knockdown compared to nonspecific sirna , even at high sirna concentrations ( 30 and 40 pmol of sirna in 200 l ) . cells treated with g2a polyplexes showed 98 6 and 84 7% residual luciferase expression after transfection with specific and nonspecific sirna , respectively ( at n / p 2 and 30 pmol ) , indicating that the slightly decreased protein expression was negligible and may not have been caused by an rnai effect . even at higher sirna amounts ( 40 pmol ) , the remaining luciferase expression was 81 8 and 86 6% for specific and nonspecific sirna , respectively , reflecting that increasing the amount of sirna may have little effect on protein knockdown with this specific polymer / sirna formulation . a similar trend was observed with groups 1 and 3 polymers ( data not shown ) . protein expression levels for lf - treated cells were found to be 6.5 0.4 and 3 0.2% after transfection with specific luciferase sirna and 45 5 and 8 3% with nonspecific sirna at 30 and 40 pmol of sirna , respectively . cells treated with pei 25 kda polyplexes at n / p 2 expressed a residual percentage of 42 5 and 5 6% after transfection with specific luciferase sirna and 67 10 and 40 7% after transfection with nonspecific sirna at 30 and 40 pmol of sirna , respectively . even though the knockdown efficiency seemed to be greater after transfection with lf and pei , profound toxicity associated with these formulations however , as the molecular weight within group 2 polymers increased to 44 kda , protein knockdown was clearly observed with g2d polyplexes at n / p 2 with 30 and 40 pmol of sirna per well . residual protein expression was found to be 33 10 and 32 4% with specific luciferase sirna ( 67 and 68% knockdown ) and 87 2 and 70 4% with nonspecific sirna at 30 and 40 pmol of sirna , respectively . this indicates the potential of the g2d polymer for further development and modification for efficient sirna delivery . the knockdown efficiency of the g2d polyplexes at n / p ratio 2 , with 30 and 40 pmol of sirna , was statistically significant when compared to control cells ( p < 0.001 ) . altogether , g2 polymers showed promise for efficient luciferase protein knockdown at comparably low toxicity . these results indicate the importance of structural features and appropriate molecular weights for nylon-3 polymers in sirna delivery . however , their clinical application is limited by high toxicity or relatively low transfection efficacy . here , we showed the gene knockdown ability of cationic nylon-3 polymers with low toxicity and at a low n / p ratio . these polymers are especially promising for pulmonary nucleic acid delivery as they can mimic lung surfactant proteins . the simple synthesis and structure versatility of nylon-3 polymers enable further introduction of various chemical functionalities and tuning of multiple chemical and physical properties to circumvent various barriers for sirna delivery in the future development of nonviral vectors . bioactivity - enhancing chemical properties , such as molecular weight , charge density , hydrophilicity / hydrophobicity , buffering capacity , which accounts for endosomal escape , complex stability , and bioreducibility , can be further tailored to optimize this new class of nylon-3-based nonviral vectors for sirna delivery . additionally , introduction of fluorescent labels for tracing and ligands for receptor targeting can be accomplished easily by functionalization of the c - terminus of nylon-3 polymers . future studies on the mechanistic elucidation of gene knockdown will also help to better understand and design nylon-3 polymers for use as promising sirna delivery vectors .

amphiphilic nucleic acid carriers have attracted strong interest . three groups of nylon-3 copolymers ( poly--peptides ) possessing different cationic / hydrophobic content were evaluated as sirna delivery agents in this study . their ability to condense sirna was determined in sybr gold assays . their cytotoxicity was tested by mtt assays , their efficiency of delivering alexa fluor-488-labeled sirna intracellularly in the presence and absence of uptake inhibitors was assessed by flow cytometry , and their transfection efficacies were studied by luciferase knockdown in a cell line stably expressing luciferase ( h1299/luc ) . endosomal release was determined by confocal laser scanning microscopy and colocalization with lysotracker . all polymers efficiently condensed sirna at nitrogen - to - phosphate ( n / p ) ratios of 5 or lower , as reflected in hydrodynamic diameters smaller than that at n / p 1 . although several formulations had negative zeta potentials at n / p 1 , g2c and g2d polyplexes yielded > 80% uptake in h1299/luc cells , as determined by flow cytometry . luciferase knockdown ( 2065% ) was observed after transfection with polyplexes made of the high molecular weight polymers that were the most hydrophobic . the ability of nylon-3 polymers to deliver sirna intracellularly even at negative zeta potential implies that they mediate transport across cell membranes based on their amphiphilicity . the cellular uptake route was determined to strongly depend on the presence of cholesterol in the cell membrane . these polymers are , therefore , very promising for sirna delivery at reduced surface charge and toxicity . our study identified nylon-3 formulations at low n / p ratios for effective gene knockdown , indicating that nylon-3 polymers are a new , promising type of gene delivery agent .

integration of new dna is important in studies in many fields , including retroviral and transposon replication,1 , 2 , 3 , 4 hiv latency,5 , 6 , 7 and human gene therapy.8 , 9 , 10 , 11 , 12 , 13 distributions of integration sites are not random in the host cell genome but differ among different integrating elements.1 , 2 , 3 , 14 , 15 for several cases , tethering of integration complexes to cellular proteins has been shown to influence integration target site selection.1 , 2 , 3 , 16 , 17 , 18 , 19 genomic alterations resulting from integration can contribute to preferential proliferation or survival of the modified cells . examples include insertional activation by retroviruses in animal models,1 , 4 outgrowth of cells in hiv latency,5 , 6 , 7 accumulation of endogenous retroviruses evolutionarily in metazoan genomes,1 , 2 , 20 and outgrowth of specific cell clones during human gene therapy.21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 often , it is useful to track the behavior of cells harboring newly integrated dna longitudinally using next - generation sequencing . previously , we and others have carried out sequence - based surveys of integration site distributions , using first sanger sequencing , then 454/roche pyrosequencing , and today illumina sequencing.6 , 7 , 9 , 11 , 12 , 13 , 15 , 29 , 30 , 31 , 32 , 33 , 34 the illumina platform has the advantages of allowing paired - end sequencing and providing larger data volumes . several reports have described methods for analysis of these data.9 , 29 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 however , to date , none have taken full advantage of all types of paired reads , dealt comprehensively with integration in repeated sequences , or provided a statistical framework for quantitative inference of cell abundances based on integration site data . here we adapt statistical approaches reported in three previous publications to management of illumina paired - end data.49 , 50 , 51 we first describe optimized biochemical methods for integration site isolation , which achieve the critical criteria of suppressing pcr contamination between samples while sampling randomly from the pool of integrated dnas . we then describe methods for alignment , data management , and quantification of cell clones based on integration site data . we generated synthetic integration sites corresponding to known locations on the human genome and used them in tests to optimize performance of our pipeline , including quantifying the influence of error in sequence determination . performance was then tested over several datasets ranging from experimental infections to human gene therapy samples , allowing analysis of the influence of repeated sequences on site capture . in our accompanying paper in this issue of molecular therapy : methods & clinical development , we describe a suite of analytical tools that draws on the data products described here . biochemical methods for recovering integration sites from dna samples are diagrammed in figure 1 , and a detailed protocol is available in the supplemental materials and methods and tables s1s8 . initially , these dna fragments are used as templates for pcr using one primer complementary to the linker and a second complementary to the end of the integrated dna . in retroviruses and retroviral vectors , the ends of the integrated dna correspond to the long terminal repeats ( ltrs ) . two rounds of pcr with nested primers are used to maximize specificity and recovery of sites from samples with small numbers of proviruses . illumina sequencing adapters are attached to the dna primers used for the second round of pcr , so that the pcr products generated contain the terminal sequences needed for sequence analysis on the miseq or hiseq platforms . the ltr sequences of an integrated provirus or retroviral vector are duplicated at each end of the integrated element as a result , pcr using a primer complementary to the ltr results in amplification of two dna products . one contains the desired flanking host dna , and the second contains an unwanted internal sequence ( figure 2a ) . we thus developed a blocking oligonucleotide to reduce polymerase extension from the internal fragment . to increase affinity , blocking oligonucleotides were synthesized with multiple bases containing a bridging ring between the 2 and 4 positions.53 , 54 , 55 the blocking oligonucleotide terminates with a 3 amino modification to inhibit polymerase extension from the blocking oligonucleotide itself ( table s9 ) . in experiments comparing results with and without the blocking oligonucleotides ( figures 2b and 2c ) , inclusion of the blocking oligo reduced capture of the internal fragment from 42% to 1.6% of sequence reads and increased the average sampling of cellular genomes from 765 cells per replicate to 975 cells per replicate ( as measured by sonicabundance ; described below ) . given that multiple samples are commonly worked up simultaneously , and batches of samples may be analyzed frequently , pcr contamination between samples can be a severe problem . to suppress pcr contamination , each dna sample is analyzed using 1 of 96 unique dna linkers , which are paired with unique complementary pcr primers . thus , any molecule moving between tubes would bear the wrong linker and thus would not be a substrate for pcr amplification . each sample is also given a unique 12-nucleotide ( nt ) error - correcting dna barcode.56 , 57 , 58 the combination of specific linker and barcode is rotated for each batch of samples processed , and correct pairing between bar code and linker sequences is required during quality filtering of output sequences ( below ) . for all batches , negative controls are included , which are human dna specimens lacking integrated vectors . using these precautions , contamination due to pcr cross - over is rare or eliminated , as indicated by a consistent lack of recovery of integration sites from genomic dna - only controls that lack integrated vectors . to further mark each unique integration site sequence , thus , linker ligation attaches a unique primer i d to each molecule prior to pcr . these tags provide a potential means of abundance estimation by counting primer ids , but in practice , this is complicated by pcr recombination ( unpublished data ) . thus , the main use in our pipeline is tracking possible contamination due to pcr cross - over between replicates by tracking primer ids . we use the sonicabundance method to infer the abundance of cell clones from integration site data ( figure 3 ) . simply counting the number of sequence reads per integration site is known to yield distorted abundance estimates32 , 60for example , shorter molecules amplify more efficiently than longer ones . the sonicabundance method takes advantage of marks introduced into dna molecules by sonication and linker ligation prior to the pcr amplification steps . in a dna sample from cells containing integration sites , an integration site from an expanded cell clone fragmentation by sonication followed by linker ligation results in many linkers joined near the integrated provirus from the expanded clone ( figure 3 , middle ) . pcr amplification and paired - end sequencing results in recovery of many different sites of linker ligation near the unique integration site in the expanded clone . sites of linker ligation are recovered in read 1 , and ltr - host junctions are recovered in read 2 ( figure 1 ) . the number of these linker positions is tabulated , providing an abundance score ( figure 3 , bottom ) . for statistical analysis , the estimated abundance needs to be corrected to account for the frequency of identical linker ligation positions generated independently , which occurs with increasing frequency as the numbers of linker positions increases per integration site . numbers of linker ligation sites are recorded along with integration site positions and uploaded into our intsitedb database for analysis . inspiired begins by parsing raw illumina output files ( fastq format ) using both index and linker sequences . indexes are based on golay codes with maximized edit distance , so that up to two errors in the index reads can be unambiguously corrected to recover the read.56 , 57 , 58 reads are subsequently trimmed to remove primer and ltr sequences ( requiring exact matching to predicted sequences ) , yielding only genomic sequence data . a problem arises due to mispriming in the human genome , which can yield spurious integration sites . for this reason , we require a perfect match for the ltr segment extending between the 3 end of the amplification primer to the 5-ca-3 sequence that defines the edge of the ltr . reads are next filtered to remove sequences complementary to the vector or virus used , requiring at least 75% global identity , a value chosen based on results with empirical datasets , and aligning in the first 5 nt of the read . sequences are aligned to the reference genome using blat ( parameters for alignment are found in the materials and methods ) . alignment information is then paired between the reads , and the integration site position and dna fragment breakpoints ( linker positions ) are returned and stored in the intsitedb database ( described in detail in our accompanying paper ) . read 1 and read 2 are joined based on location in the sequencing flow cell ( encoded as the read name ) . read pairs that map to identical sites are judged to be pcr duplicates and collapsed into single sites . to pass our quality filter , the genomic coordinates of these positions must lie within the range accessible by the sequencing chemistry we allow a maximum of 2,500 base pairs ( bp ) as the default value ( figure 4a ) . integration sites for which the read 1 ( linker side ) and read 2 ( integration site side ) positions are unreasonably distant , or on different chromosomes , are judged to be chimeras formed during pcr and are removed from the output data ( figure 4b ) . viral or vector genomes that integrate within repetitive genomic elements often can not be mapped to a single genomic coordinate , so that both read pairs align nearby , but they can be mapped to multiple locations in the human chromosomes ( figure 4c ) . for some forms of analysis , the multihits may be ignored for example , in an analysis of integration site distributions relative to genomic features . however , for monitoring clinical gene therapy samples for possible adverse events , it is not safe to rule out possible insertional activation by integration in a repeated sequence it is possible that an integration site in a multihit site may be near a cancer - related gene and involved in an adverse event . at least 40% of the human genome is composed of repeated sequences such as l1 retrotransposons , endogenous retroviruses , alu elements , and others . a complication is that unique sonic fragments of the same parent integration site may map to non - identical lists of genomic coordinates , and even pcr duplicates may show different mapping behavior due to sequencing error . inspiired thus uses a graph - theory - based approach to group alignments into clusters , so that each cluster can be treated as an integration site in downstream analysis . inspiired assigns multihit reads to multihit clusters by creating an undirected graph g = ( v , e ) , where v is the set of reads identified as multihits and e is the set of pairs of multihit reads that share at least one putative integration site in the output list of multiple alignments . when considering the number of reads produced by the illumina technology , the computational resources required to compare putative integration locations in a pairwise fashion can become prohibitive . to improve the scalability of multihit clustering , reads that have identical genomic dna sequences across both read 1 and read 2 are combined into a single representative read before executing the pairwise comparison of potential genomic mappings . when building an undirected graph from multihit read alignments , only the first connection of completely connected reads is used , reducing memory demand even further while yielding the same result with improved scalability . the performance of the pipeline was analyzed by generation and analysis of synthetic integration site data . reads were generated with lengths of 179 and 143 nt corresponding to read 1 and read 2 , respectively , including addition of the illumina sequencing primers , dna barcodes , primer landing pads , and flanking host dna . the distances between reads 1 and 2 were chosen randomly from a distribution of distances modeled to match empirical data , with 100 different distances between pairs sampled for each of the 5,000 integration sites . four sets of the 5,000 integration sites were studied , containing no error , 1% error ( roughly that expected from the illumina sequencing method ) , 2% error , and 4% error . integration site datasets were trimmed , aligned , and quality filtered using the inspiired pipeline . initially we asked whether each integration site could be recovered from at least one of the 100 read pairs ( table 1 , top ) , and we then asked how many of the read pairs were recovered ( table 1 , bottom ) . for 0% error , 99.6% of sites could be recovered . these latter sites mapped to regions annotated as low alignability , as defined by the gem mappability program . by visual inspection , these regions were rich in multiple repetitive element classes that were often nested within each other . overall , of the 100 simulated sequence reads for each integration site , on average 98 could be mapped correctly . for the same integration sites containing 1%4% error , the fractions mapping were 99.7% in each case . although the majority of sites were recovered , the proportion of the 100 paired sequences per integration site that could be recovered fell with increasing error , from 98% at 0% error to 23% at 4% error . we next asked how the sites were distributed among unique locations and repeated sequences . for each integration site in a repeated sequence , the r1 sequence at the linker end of each read has the potential of reaching into flanking unique dna , resulting in a unique mapping position . at 0% sequence error , multihits accounted for only 6.4% of correctly aligned reads , while at 4% error , multihits accounted for 3.3% . we investigated to what extent use of the linker side read ( r1 ) allow for increased capture of unique sites and decreased recovery of multihits . we thus compared results with paired reads ( r1 plus r2 ; table 1 , left side ) to results with the integration site read only ( r2 ; table 1 , right side ) . results comparing r1 plus r2 to r2 alone showed a decrease in reads mapping to multiple locations ( down 4,767 reads ) and reads not aligning to the human genome ( down 2,876 reads ) , as well as an increase in the number of reads that align correctly ( 2,988 more reads ) and align to unique locations in the human genome ( 7,755 more reads ) . there was little difference in the number of sites detected , although there were half as many multihit sites when considering r1 plus r2 over r2 alone . we next assessed the performance of the pipeline over three empirical datasets ( table 2 ) . the first consists of human hap1 cells infected with an hiv - based vector and then grown for only 24 hr . a total of 38,967 integration sites were recovered , with an average of only 1.36 cells per site ( sonicabundance estimate ) . the second dataset consists of five purified 293 t cell lines , each with a single lentiviral integration site . thus , only five sites were recovered by sequencing , with an average of 3,582 cells per site . the third dataset was a specimen of blood cells from a patient successfully treated for severe combined immunodeficiency ( scid - x1 ) using a gammaretroviral vector . a total of 755 integration sites were recovered , ranging from 1 to 9,325 cells per site ( average sonicabundance of 40 ) . this emphasizes that after gene correction , different progenitor cell clones delivered quite different proportions of cells to the periphery . these data allow us to investigate the effects of human repeated sequences on integration site recovery using illumina paired - end data . multihits accounted for 6.6% of sites in the hap1 cells and 11.8% in the scid gene therapy specimen . thus , multihits were roughly in the range expected from tests with the in silico - generated data . quantification was tested using the 293 t cell clones with known integration sites mixed in different ratios . figure 5 shows the expected and observed values ( r = 0.852 ) . in all cases , the expected ranking by frequency was observed , although there was some departure from the exact value expected . here , we present a pipeline for the generation and first - stage alignment of integration site data generated using illumina paired - end reads . portions of this pipeline have been used in earlier studies.3 , 9 , 11 , 14 , 16 , 17 , 18 , 19 , 20 , 24 , 26 , 27 , 30 , 32 , 33 , 35 , 47 , 49 , 50 , 51 , 60 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 the full pipeline presented here introduces several improvements , including ( 1 ) use of a blocking oligonucleotide containing non - natural bases to suppress recovery of internal fragments ; ( 2 ) use of all sets of paired - end reads , not just those that overlap , as in some earlier pipelines43 , 45 ; ( 3 ) a graph - theory - based method for tracking integration in repeated sequences ; ( 4 ) use of synthetic data to assess the effect of read spacing and error ; ( 5 ) implementation of the sonicabundance method for quantification ; and ( 6 ) use of cloned cell lines for empirical characterization of quantification accuracy . several integration site processing pipelines have been published , including integrationseq / map ( 2007 ) , seqmap ( 2008 ) , quickmap ( 2009 ) , mavric ( 2012 ) , vispa ( 2014 ) , visa ( 2015 ) , and geist ( 2015).29 , 36 , 38 , 39 , 42 , 43 , 46 early pipelines focused on efficient mapping of single reads onto reference genomes29 , 36 , 38 and included functions such as mapping the distance to the nearest transcription start site . most pipelines include steps to reduce the total number of reads that must be aligned , so that computational time is used efficiently . illumina paired - end sequencing yields two reads from each dna fragment , which may or may not overlap . when adapting paired - end sequencing to integration site pipelines , previous groups have chosen to merge these reads if possible,39 , 42 , 43 but if they did not overlap , then the linker side read was discarded . inspiired uses both reads , irrespective of overlap , for quantitative analysis of cell populations . that is , inspiired uses all information to determine the location of integrated elements , and it also uses the location of the fragment breakpoint due to sonication for abundance quantification ( figure 3 ) . determining the location of integration elements can be challenging due to repeated sequences in the human genome . from our synthetic integration site data with 0% error , reads mapping to multiple locations in the human genome , multihits , were found within repeated elements such as alu elements , l1 retrotransposons , endogenous retroviruses , and others . longer paired alignments to the human genome ( that are generated by not requiring overlapping reads ) have the potential to align the linker side read outside of these repeated regions , yielding a unique location for the integration site . this is evident in the analysis of in silico data ( table 1 ) , in which more multihit sites were identified in paired reads ( r1 plus r2 ) compared to those using the integration site sequence read only ( r2 ) . multihit reads are grouped based on alignments and may have multiple linker attachment sites , as with unique integration sites . thus , multihits can also be quantified by the sonicabundance method and queried for possible clonal expansion . the output data tables generated with inspiired make possible the generation of a series of analytical products . these include ( 1 ) interactive heatmaps summarizing relationships of integration site data to genomic and epigenetic features ; ( 2 ) reproducible reports on gene - corrected patient samples summarizing numerous features of integration site populations , including expansion of clones with integration sites near cancer - related genes ; and ( 3 ) data frames suitable for statistical analysis based on the sonicabundance method . a detailed protocol is available in the supplemental materials and methods , including the method for library preparation and sequencing of sites of new dna integration in the human genome . samples of genomic dna were prepared for illumina sequencing by random shearing using a covaris m220 ultrasonicator to achieve an average size distribution of 800900 bp . dna fragment ends were repaired ( 5 phosphorylated and da tailed ) prior to ta ligation with custom linkers using nebnext ultra end repair / da - tailing and nebnext ultra ligation modules , respectively ( see table s10 for linker design and table s14 for sequences ) . ligated dna was split into at least four replicates prior to ligation - mediated ( lm ) pcr amplification ( pcr1 , 25 total cycles ) . using the pcr1 product as a template , a nested lm pcr was conducted ( pcr2 , 20 total cycles ) adding replicate - specific 12-bp golay barcodes and illumina adaptor sequences . sample concentrations were measured using the quant - it picogreen dsdna assay kit and sequencing libraries were constructed by pooling samples by equal mass . average amplicon size and library molarity were measured using an agilent d1000 screentape system and a kapa sybr fast universal qpcr kit , respectively . nested pcrs were supplemented with vector - specific blocking oligos complementary to the primer binding site found downstream of the 5 ltr - u5 sequence . blocking oligos contained nine blocked nucleic acids ( bnas ) with a total length between 27 and 32 nucleotides and an estimated annealing temperature around 80c . paired - end sequencing was performed on the illumina miseq , using 300-cycle v2 reagent kits with nano- , micro- , and standard flowcells . cycle allocation was conducted as follows : read 1 used 179 cycles , index 1 used 12 cycles , and read 2 used 143 cycles . this allows for approximately 130 nucleotides of host sequence from both sides of the template molecule . read sequences are trimmed to remove the linker , primer , and viral dna end ( ltrbit ) sequences . a read pair is required to have the linker sequence at the beginning of read 1 and primer and ltrbit sequences at the beginning of read 2 . the primer and the ltrbit sequences are determined by the corresponding vector sequence and are different for each virus or vector studied . primer and ltrbit sequences are trimmed off from the beginning of read 2 , and the linker sequences are trimmed off from read 1 . in cases where the sonic break point is close to the integration site , read 2 may read into the reverse complement of the linker and read 1 may read into the reverse complement of the primer and ltrbit . these sequences at the tails of the reads interfere with alignment and quality control , and thus are detected and trimmed off . these alignments are detected by bioconductor s biostrings pairwisealignment function to trim and filter the leading and tailing sequences , while requiring 85% of identity based on edit distances . although a blocking oligo is employed to reduce pure vector sequence amplification during pcr , the blocking is not 100% efficient . therefore , trimmed and filtered sequences are aligned to the vector reference and removed if either the read 1 or read 2 aligns with 75% of global identity and within 5 nt of the start of the read . inspiired uses blat for dna alignments because of its accuracy and the fact that it reports all alignments if a read has multiple hits in the genome with scores above a certain threshold , which makes it useful for handling multihit read pairs . the following blat parameters were used to align the read pairs : -tilesize = 11 , -stepsize = 9 , -minidentity = 85 , -maxintron = 5 , and -minscore = 27 . removing = 11.ooc option led to better alignment in repeated regions , such as line , sine , and ltr regions , since the option -ooc prohibits search in those regions . the option -maxintron was changed to 5 from the default 750,000 , as reads are amplified from genomic dna and should not align across splicing elements . tests showed that reducing the stepsize improved the accuracy of the alignments but increased the demand on memory ; therefore , a stepsize of 9 represented a workable compromise . as blat is a local aligner , alignments were filtered out that only partially match to the host genome . alignments were also filtered by a global identity score , defined as ( matches + repmatches)/qsize for quality control on alignments , requiring a minimum of 95% . after aligning and filtering by the global identity score , the two reads of a template are paired by requiring that the reads ( 1 ) align to the same chromosome , ( 2 ) align to opposite strands , ( 3 ) maintain the correct predicted orientation ( the linkered breakpoint read is downstream of the ltr read if the orientation is on the positive strand and vice versa for the negative strand ) , and ( 4 ) predicted template length is shorter than 2,500 nt . for the studies reported here , the h18 draft of the human genome was used , to allow direct use of chromatin immunoprecipitation sequencing ( chip - seq ) data that was originally analyzed on this background ( see our accompanying paper ) . however , the organism and draft genome used for analysis can be selected by users and analyzed with any suitable annotation tracks compiled on that sequence . the following definitions were used to describe the locus for each alignment in the format of chromosome : strand : position . here , tname , tstart , tend , and strand are columns of the blat output in the psl format and they refer to chromosome , start position , end position , and strand , respectively . the integration site is given by [ site = tname:+:tstart ] if read 2 is mapped to the positive strand and [ site = tname:-:tend ] if mapped to the negative strand . likewise , the break point is given by [ breakpoint = tname:+:tend ] if read 1 is mapped to the positive strand and [ breakpoint = tname:-:tstart ] if mapped to the negative strand . if more than one read pair yields the same integration site and breakpoint on the same strand , only one is kept and the others are considered to be pcr duplicates . sequences were simulated from random locations in the human reference genome , then additional technical sequences required for the illumina technology ( figure 1 ) were added to each read . given a locus ( composed of chromosome , strand , and location ) , the downstream sequence was obtained from the human reference genome . to generate simulated templates , the following components were concatenated together : illumina p7 , 12-nt golay barcode , sequencing primer 2 ( for both index and read 2 sequences ) , primer , ltrbit , reference genome sequence , linker ( reverse complement ) , sequencing primer 1 ( for read 1 , reverse complement ) , and lastly , the illumina p5 sequence ( reverse complement ) . read 2 sequences were generated by obtaining the 143 nt following the sequencing primer 2 of the above template . read 1 sequences were generated by obtaining the 179 nt following the sequencing primer 1 after the reverse complementing the template . should fewer bases exist in the template strand than are required , the ends of the reads are filled with poly(t ) sequence , as is observed on the illumina instrument . sequencing primer , pcr primer , and ltrbit sequences are specific to each study . for the synthetic dataset , 5,000 integration sites were generated from the human genome , and 100 lengths between read 1 and read 2 were simulated for each site . simulated template lengths followed a normal distribution with a mean of 70 ( sd of 250 ) , while only keeping lengths greater than 30 . in total , there are 500,000 read pairs in the simulation set . to evaluate the performance of inspiired with sequencing error , four simulation datasets ( with the same random sites and lengths ) were generated containing 0% , 1% , 2% , and 4% read errors , applied after template construction . after sequencing , illumina output fastq files are used as inputs for inspiired , along with sample information ( which linkers and barcodes were used with which samples ) and vector sequence information . as golay dna barcodes have large edit distances , the index sequence file that contains the barcode sequences for each read is subjected to error correction ( up to two bases of correction ) . with the corrected barcodes , information from read 1 ( containing the linker sequence ) is used with the barcodes to demultiplex the samples , creating independent fastq files for read 1 and read 2 . sequences are then subjected to quality trimming ( only keeping information with q - scores greater than q30 ) . following quality trimming , respective reads are filtered and trimmed for linker , primer , ltrbit , and vector - related sequences to yield only genomic dna . the genomic sequences are then aligned to the host reference genome using blat , yielding an output psl file with the alignment information . the alignment information is then used to determine the locations of alignments and read information is filtered and paired , as previously discussed . alignments for integration sites are then placed in four output files , including allsites ( containing all uniquely mapped integration sites and their corresponding breakpoints ) , sites.final ( contains a condensed form of allsites ) , multihitdata ( contains all properly paired and filtered integration sites that could not be uniquely mapped to the reference genome ) , and chimeradata ( contains integration sites that failed proper pairing and are considered artifacts ) . these outputs are generated for each sample given a specific linker and barcode in the input sample information file . inspiired is distributed online as a downloadable virtual machine executable on the windows , mac , and linux operating systems as well as a github source code repository supported by a conda software environment . the virtual machine , software , instructions , and a walkthrough that processes provided sample data are available at https://github.com/bushmanlab/inspiired . as described in the instructions , the software supports two types of databases , mysql and sqlite . , p.b . , s.h .- b .- a , l.c . , and f.d.b .

integration of new dna into cellular genomes mediates replication of retroviruses and transposons ; integration reactions have also been adapted for use in human gene therapy . tracking the distributions of integration sites is important to characterize populations of transduced cells and to monitor potential outgrow of pathogenic cell clones . here , we describe a pipeline for quantitative analysis of integration site distributions named inspiired ( integration site pipeline for paired - end reads ) . we describe optimized biochemical steps for site isolation using illumina paired - end sequencing , including new technology for suppressing recovery of unwanted contaminants , then software for alignment , quality control , and management of integration site sequences . during library preparation , dnas are broken by sonication , so that after ligation - mediated pcr the number of ligation junction sites can be used to infer abundance of gene - modified cells . we generated integration sites of known positions in silico , and we describe optimization of sample processing parameters refined by comparison to truth . we also present a novel graph - theory - based method for quantifying integration sites in repeated sequences , and we characterize the consequences using synthetic and experimental data . in an accompanying paper , we describe an additional set of statistical tools for data analysis and visualization . software is available at https://github.com/bushmanlab/inspiired .

Judd Family 'Angry and Hurt' About Ashley's Memoir Shockers Email This Ashley Judd's shocking "How she could betray her own flesh and blood with this disturbed view of what happened is shocking and hurtful," a Judd family insider tells me. "These ugly family accusations should be discussed in private within the family, not printed and sold to the public to make a quick buck." Ashley Judd's shocking memoir telling all about her famous family has her mother, country legend Naomi Judd, and singing sister Wynonna fighting mad."How she could betray her own flesh and blood with this disturbed view of what happened is shocking and hurtful," a Judd family insider tells me. "These ugly family accusations should be discussed in private within the family, not printed and sold to the public to make a quick buck." Ashley didn't hold anything back, claiming she was sexually abused and left with caregivers who used drugs, highlighting a childhood filled with neglect, abuse and deep depression."My mother, while she was transforming herself into the country legend Naomi Judd, created an origin myth for the Judds that did not match my reality," the actress writes. "I loved my mother, but at the same time I dreaded the mayhem and uncertainty that followed her everywhere. I often felt like an outsider observing my mom's life as she followed her own dreams."Judd also writes that an older man sexually molested her in a pizza place when she was a young girl."Naomi and Wynonna have had a strained relationship with Ashley for years," an insider tells me. It was revealed on 'Season 25: Oprah Behind the Scenes' on OWN that Ashley had declined an invite to join her family on Oprah 's show."This is the final nail in the coffin -- they are very angry and hurt that Ashley would write a book rather than deal with whatever problems they have privately," my source says. Ouch. ||||| Ashley Judd's Shocking Memoir Reveals Past Filled With Abuse, Drugs Email This Actress Ashley Judd's new memoir sheds light on her shocking past, which includes growing up in a drug-fueled environment and suffering sexual abuse as a child, Judd's book, 'All That Is Bitter & Sweet,' was released today, and the actress reveals some shocking secrets about the country-singing family in the book. "My mother, while she was transforming herself into the country legend Naomi Judd, created an origin myth for the Judds that did not match my reality," she writes. "She and my sister [Wynonna] have been quoted as saying that our family put the 'fun' in dysfunction. I wondered: 'Who, exactly, was having all the fun? What was I missing?'" From revealing lies her mother told about about Wynonna's real father to allegations of child neglect, Judd doesn't hold much back in her shocking book. Actress Ashley Judd's new memoir sheds light on her shocking past, which includes growing up in a drug-fueled environment and suffering sexual abuse as a child, RadarOnline.com reports.Judd's book, 'All That Is Bitter & Sweet,' was released today, and the actress reveals some shocking secrets about the country-singing family in the book."My mother, while she was transforming herself into the country legend Naomi Judd, created an origin myth for the Judds that did not match my reality," she writes."She and my sister [Wynonna] have been quoted as saying that our family put the 'fun' in dysfunction. I wondered: 'Who, exactly, was having all the fun? What was I missing?'"From revealing lies her mother told about about Wynonna's real father to allegations of child neglect, Judd doesn't hold much back in her shocking book. http://xml.channel.aol.com/xmlpublisher/fetch.v2.xml?option=expand_relative_urls&dataUrlNodes=uiConfig,feedConfig,entry&id=691977&pid=691976&uts=1294158078 http://www.popeater.com/mm_track/popeater/music/?s_channel=us.musicpop&s_account=aolpopeater,aolsvc&omni=1&ke=1 http://cdn.channel.aol.com/cs_feed_v1_6/csfeedwrapper.swf PopScene: Week's Hottest Pics Reese Witherspoon keeps her hands in her pockets as she tries to stay warm while out in New York City on January 3rd. X17online X17online "I was taught to believe that our lifestyle was normal and never to question it or complain, even when I was left alone for hours, sometimes days at a time, or when I was passed without warning to yet another relative," she writes, adding that "there was always marijuana inside the house" and her father, Michael Ciminella, "was prone to taking hallucinogenics with friends on Saturday nights."Judd also recalls a painful memory of being sexually abused as a child."An old man everyone knew beckoned me into a dark, empty corner of the business and offered me a quarter for the pinball machine at the pizza place if I'd sit on his lap," Judd writes. "He opened his arms, I climbed up, and I was shocked when he suddenly cinched his arms around me, squeezing me and smothering my mouth with his, jabbing his tongue deep into my mouth."The abuse she suffered led to a deep depression, which also stemmed from her relationship with her mother."I loved my mother, but at the same time I dreaded the mayhem and uncertainty that followed her everywhere," Judd writes. "I often felt like an outsider observing my mom's life as she followed her own dreams."

– Ashley Judd's family is not happy about her recently released memoir, which discloses details of a dysfunctional upbringing. "Naomi and Wynonna have had a strained relationship with Ashley for years," an insider tells Popeater. "This is the final nail in the coffin—they are very angry and hurt that Ashley would write a book rather than deal with whatever problems they have privately." Click for more of the Judd family's reaction or here for more from Ashley's memoir.

cognitive radio ( cr ) is a promising wireless technology to resolve the growing scarcity of the indispensable electromagnetic spectrum resources . by use of cr , secondary users ( sus ) without explicitly assigned spectrum resources can co - exist with primary users ( pus ) licensed with particular spectrum . in practice , some major communications regulators like the federal communications committee ( fcc ) in u.s . and the office of communications ( ofcom ) in u.k . have allowed secondary access for unlicensed devices to the terrestrial tv broadcast bands . among various forms of cr implementation , spectrum - sharing cr is especially appealing for practical deployment since it does not involve complex spectrum - sensing mechanisms . more specifically , spectrum - sharing cr limits only the transmit power of sus such that their harmful interference onto pus remains below prescribed tolerable levels @xcite . because of the interference power constraint dictated by pus , the transmit power of sus in spectrum - sharing systems has to be very low , which limits the coverage area of secondary transmission . in order to extend the coverage area of secondary transmission and guarantee reliable communication , cooperative relaying techniques can be exploited . using relaying techniques , a single or multiple idle users ( either pus or sus ) can be involved in forwarding messages between a secondary source and its destination . the relaying can be implemented using two main techniques , amplify - and - forward ( af ) and decode - and - forward ( df ) . in particular , assuming df protocol and simple dual - hop transmission , system performance of dual - hop relaying in spectrum - sharing systems was extensively studied , see e.g. @xcite and references therein . nevertheless , apart from its implementation simplicity , the af relaying can outperform the df protocol when a relay is closer to its receiver @xcite . until lately , dual - hop af relaying was integrated into spectrum - sharing systems and its performance was explored @xcite . in order to further extend the coverage area of the secondary transmitters yet reduce their interference region and its negative impact on pus , multi - hop af relaying can be implemented in real - world spectrum - sharing systems . for an efficient implementation of such techniques , performance evaluation and design are necessary . however , when analyzing system performance of multi - hop relaying , the simplistic dual - hop model does not capture many important features of multi - hop systems . for example , from the viewpoint of sus , system performance of multi - hop relaying will be inevitably affected by the interference - power constraint dictated by pus , which should be guaranteed by all intermediate nodes between a secondary source and its final destination . in order to mitigate this constraint , dynamic power allocation at the secondary transmitters is necessary , but how about the effect of power allocation on the end - to - end performance of secondary multi - hop link ? in particular , compared to the simple dual - hop case , how will the increasing number of relaying hops affect system performance ? these issues are critical for an efficient implementation and deployment of multi - hop relaying in spectrum - sharing systems and will be explicitly addressed in this paper . accurate performance analysis of spectrum - sharing multi - hop af relaying is hardly tractable in closed - form due to extremely high mathematical difficulty . actually , even for the conventional multi - hop af relaying without spectrum sharing , closed - form performance analysis is still an open problem . in this work , we investigate the lower and upper bounds on the end - to - end signal - to - noise ratio ( snr ) of spectrum - sharing multi - hop af relaying systems . in order to gain illuminating insights into system performance , we exploit extreme value theory and study limiting distribution functions of the said bounds , which are further applied to analyze the performance in terms of the outage probability , the diversity gain , the coding gain , and the achievable data rate . in particular , our results disclose that the diversity gain of the system under study is always unity , irrespective of the number of relaying hops . on the other hand , the coding gain is proportional to the water level of the optimal water - filling power allocation at each secondary transmitter along the multi - hop link and to the large - scale path - loss ratio of the desired link to the interference link at each hop , yet is inversely proportional to the accumulated noise at the destination , namely , the product of the number of relays and noise variance . in detailing the above highlighted contributions , the rest of this paper is organized as follows . section [ section : systemmodel ] describes the system model . section [ section : powerallocation ] is devoted to the optimal transmit power allocation . subsequently , in section [ section : e2esnr ] , the exact distribution functions of the end - to - end snr are derived and , for further processing , the limiting distribution functions of the lower and upper bounds on the end - to - end snr follow . with the resultant distribution functions , the system performance is extensively analyzed and discussed in section [ section : performanceanalysis ] . concluding remarks are provided in section [ section : conclusion ] and , finally , some mathematical tools and detailed derivations are relegated to appendices . we consider a @xmath0-hop cooperative relaying system operating in a spectrum - sharing cr environment . as depicted in fig . [ fig.systemmodel ] , secondary users @xmath1 and @xmath2 exchange data with the assistance of @xmath3 sus serving as consecutive af relays , while primary source @xmath4 is transmitting to primary receiver @xmath5 . it is assumed that all nodes are equipped with a single half - duplex omnidirectional antenna each . in order to share the spectrum resources originally licensed to pus , the transmit power of sus is strictly limited by the prescribed tolerable interference power at the primary receiver . more details on the optimal power allocation at the secondary nodes along the multi - hop relaying link will be given in the next section . for the secondary multi - hop af relaying link , all sus work in a time - division multiple access ( tdma ) fashion and equal time slots of a transmission frame are allocated to each su along the multi - hop path . also , only one su transmits to its next node along the multi - hop relaying path during each time slot . with these assumptions in mind , based on @xcite , the end - to - end ( e2e ) received snr at the final destination @xmath6 , can be expressed as @xmath7 where @xmath8 denotes the received snr at the @xmath9 secondary node ( @xmath10 ) , defined as @xmath11 where @xmath12 and @xmath13 denote the distance and the channel fast - fading coefficient between consecutive secondary nodes @xmath14 and @xmath15 ( cf . [ fig.systemmodel ] ) , @xmath16 refers to the path - loss exponent ( generally , @xmath17 in free space and @xmath18 in most practical scenarios ) , @xmath19 indicates the transmit power at @xmath14 , and @xmath20 stands for the additive white gaussian noise ( awgn ) variance at @xmath15 . for notational convenience , the secondary source node in fig . [ fig.systemmodel ] is denoted by @xmath1 . is located far from the secondary users @xmath21 $ ] , compared to the primary receiver @xmath5 . parameters @xmath22 denote the distance and the channel fast - fading coefficient between @xmath14 and @xmath15 ( desired link ) . similarly , @xmath23 refer to the distance and the channel coefficient between @xmath14 and @xmath24 ( interference link).,width=211 ] compared to conventional multi - hop relaying transmission without spectrum sharing where the transmit power of the source or any relaying node is generally fixed , in a spectrum - sharing context , sus share the spectrum resources originally licensed to pus and , thus , the transmit power @xmath25 of the @xmath9 secondary node ( @xmath26 ) , @xmath27 , is strictly limited by the prescribed tolerable interference power at the primary receiver . moreover , it is seen from - that the actual power values will greatly affect the end - to - end snr at the destination node @xmath6 . therefore , in the next section we establish the optimal transmit power at @xmath26 . * remark 1 ( relay gain ) : * for a multi - hop relaying system , if the relay gain is set to the inverse of the channel gain of the previous hop , eq . is the exact expression of the end - to - end snr ( cf . the paragraphs after ( * ? ? ? * eq . ( 4 ) ) and ( * ? ? ? * eq . ( 11 ) ) ) . on the other hand , if the relay gain is set to the inverse of the channel gain of the previous hop plus noise variance , eq . acts an upper bound on the end - to - end snr . the former enables mathematical tractability and serves as a benchmark for all practical multi - hop af relaying schemes . in particular , a comparison of the outage probability between multi - hop systems with these two different relay gains demonstrated only a slight performance difference even in the low and medium snr regions ( cf . * remark 2 ( the interference coming from the primary transmitter ) : * for ease of mathematical tractability , the interference coming from the primary transmitter is not separately counted but treated as noise , as shown in eq . . this is feasible if the interference is weak , for example , when the primary transmitter is located far from the secondary users as illustrated in fig . [ fig.systemmodel ] @xcite . furthermore , the interference can be treated as noise if the primary transmitter s signal is generated by random gaussian codebooks @xcite . theoretically , the validity of the methodology treating non - gaussian interference as noise was originally proven in @xcite . for an elaborate investigation into the effect of the interference on the end - to - end performance of dual - hop relaying , we refer the interested reader to @xcite . in this section , the criterion for power allocation at the secondary nodes along the multi - hop relaying link ( including the source @xmath1 and its consecutive relaying nodes @xmath26 , @xmath28 ) is firstly established . then , based on this criterion , the value of the optimal transmit power during each transmission slot at each secondary node is determined . in this part , the criterion for optimal power allocation at the secondary nodes @xmath14 , @xmath29 , is established . assume that the average tolerable interference power at the primary receiver is @xmath30 db with respect to the noise power . also , the distances corresponding to the desired link and the interference link at each hop are assumed to remain fixed during a communication between the secondary source and its destination ( cf . [ fig.systemmodel ] ) . thus , to maximize the achievable data rate at the @xmath9 hop , we need to optimize the transmit power at @xmath14 with respect to @xmath30 and the instantaneous fast - fading fluctuations of the corresponding desired channel and interference channel . to this end , it is easy to show that the first - order derivative of the end - to - end received snr @xmath31 given by with respect to @xmath8 is strictly positive and , hence , @xmath31 is a monotonically increasing function of @xmath8 . consequently , in order to maximize the achievable data rate @xmath32 at the @xmath9 hop , the optimal transmit power @xmath19 at @xmath14 is determined as the solution to the optimization problem : @xmath33 @xmath34 where @xmath35 and @xmath36 denote the distance and the channel fast - fading coefficient of the interference link from @xmath14 to @xmath5 , and the operator @xmath37 means statistical expectation . clearly , the optimal transmit power @xmath19 at secondary node @xmath14 is a function of the parameters of the desired link and the interference link ( i.e. @xmath38 and @xmath39 , respectively , as shown in fig . [ fig.systemmodel ] ) , the noise variance ( @xmath20 ) , and the average tolerable interference power at the primary receiver ( @xmath30 ) . in spectrum - sharing systems , the tolerable interference power at the primary receivers can be generally defined by means of average interference power , peak interference power , or both @xcite . also , the maximum output - power for sus is constrained in practice . however , the effect of the maximum output - power constraint on system performance is essentially equivalent to the peak interference - power constraint , except for a scaling factor given by the interference channel gain . furthermore , it is already demonstrated that `` imposing a constraint on the peak interference power does not yield a significant impact on the ergodic capacity as long as the average interference power is constrained '' @xcite . as a result , only the average interference - power constraint is considered in the optimization problem above . applying the well - known lagrangian multiplier method ( * ? ? ? * section 5.3.3 ) to - , it is easy to show that the optimal transmit power at secondary node @xmath14 is given by @xmath40^+,\ ] ] where the ceiling operator @xmath41^+ \triangleq \max(0,~x)$ ] . furthermore , the power allocation parameter @xmath42 in is determined by setting the average interference - power constraint in to equality , such that @xmath43^+\right\ } = 10^{w/10}.\ ] ] now , if @xmath44 is defined as the large - scale path - loss ratio of the desired link to the interference link at the @xmath45 hop , i.e. @xmath46 then , can be reformulated as @xmath47^+\right\ } = 10^{w/10}.\ ] ] like the well - known water - filling power allocation algorithm @xcite , the power allocation parameter @xmath42 associated with corresponds to the so - called water level and it will be explicitly determined in the next subsection . remarkably , this power allocation parameter has a significant effect on the system performance , as will be discussed further in the following section [ subsection : diversitycodinggains ] . on the other hand , the ceiling operator @xmath41^+$ ] in implies that the transmit power is zero if the gain of the desired channel is smaller than a lower bound , i.e. @xmath48 . in such a case , no data will be transmitted . in other words , only when @xmath49 can @xmath14 transmit to its next node @xmath15 . this makes the spectrum - sharing multi - hop relaying system more energy efficient than the conventional multi - hop relaying system where the transmission between two consecutive nodes is totally regardless of the channel fluctuations in between . * remark 3 ( channel estimation ) : * it is noteworthy that , according to , when performing the optimal water - filling power allocation at secondary node @xmath14 , the channel parameters of the desired link @xmath22 and the interference link @xmath23 have to be efficiently estimated . among them , the parameters @xmath22 between @xmath14 and @xmath15 can be readily obtained by using the conventional training - sequence based methodology . on the other hand , the parameters @xmath23 between @xmath14 and primary user @xmath24 can be attained at @xmath14 , for example , by periodically sensing the pilot signals transmitted by @xmath24 under the assumption of channel reciprocity @xcite , or by indirect feedback from a third - party such as a band manager which coordinates between the primary and secondary users @xcite . although the acquisition of this channel state information ( csi ) requires additional cost at sus , it enables them to strictly comply with the prescribed interference power constraint at pus and to maximize the achievable data rate at each hop . also , we note that in practice , there must be errors when estimating the csi . a further inspection of this issue is beyond the scope of the paper . * remark 4 ( on the optimality of power allocation ) : * for the cognitive multi - hop relaying under study , all sus along the multi - hop link work in a tdma fashion and there is no central node . thus , it is impossible to collect all csi before performing optimal power - allocation among all sus along the multi - hop path . actually , for the node @xmath26 along the path , it has only the csi pertaining to the desired link @xmath50 and the interference link @xmath51 . accordingly , the optimal power allocation can only be performed with respect to these csi . in other words , the optimal power allocation can only be performed within a single hop instead of the end - to - end link . this optimization strategy is essentially to `` make best efforts '' at each relaying hop . according to , in order to determine the power allocation parameter @xmath42 , we derive the probability density function ( pdf ) of @xmath53 . since all channels in the system under study are supposed to be subject to rayleigh fading with unit - mean , it is straightforward that @xmath54 and @xmath55 are exponentially distributed with unit - mean . hence , the pdf of @xmath54 and @xmath55 is given by @xmath56 conditioning on @xmath54 , the pdf of @xmath57 can be given by @xmath58}\,\mathrm{d}y = ( x+1)^{-2}.\ ] ] then , inserting into and performing some integrations , the power allocation parameter @xmath42 can be determined by @xmath59 although @xmath42 can not be expressed in closed - form given that is a transcendental equation , it can be easily computed in a numerical way because involves only the elementary logarithmic function . with the resulting @xmath42 , the optimal transmit power @xmath19 at the @xmath60 secondary node can be readily determined by using . next , we investigate the distribution functions and moment generation function ( mgf ) of the end - to - end snr at the secondary destination . now , we investigate the statistics of the end - to - end snr at the secondary destination . at first , we derive the exact distribution functions and mgf of the end - to - end snr . for further processing while gaining insight into system performance , a pair of lower and upper bounds on the snr are proposed and their limiting distribution functions as the number of hops @xmath61 are developed , by using extreme value theory . here , we derive the exact distribution functions and mgf of the end - to - end snr at the secondary destination . by virtue of the end - to - end snr expression shown in , in order to determine its distribution functions , we need to firstly derive the distribution functions of its component @xmath8 given by . more specifically , substituting the obtained optimal transmit power @xmath19 shown in into the expression , @xmath8 can be rewritten as @xmath62^{+ } = \left[\frac{\lambda_{k-1 } \ , \eta_k}{\sigma_{k}^2}\,v_2 - 1\right]^{+},\ ] ] where @xmath63 . since @xmath64 and @xmath65 are of the same exponential distribution ( cf . , the pdf of @xmath66 is the same as its inverse ( i.e. @xmath57 defined above ) . that is , @xmath67 inserting into and performing some algebraic manipulations yields the pdf of @xmath8 , given by ( cf . appendix [ appendix - a ] ) @xmath68 where the constant @xmath69 . subsequently , performing laplace transform over yields the mgf of @xmath70 , namely , @xmath71 where the change of variable @xmath72 was used to reach and ( * ? ? ? * , eq.(2.3.6.9 ) ) was employed to derive with @xmath73 being the tricomi confluent hypergeometric function ( * ? ? ? * eq.(9.210.2 ) ) . moreover , in light of , it is clear that the end - to - end snr can be reformulated as @xmath74 consequently , combining with in conjunction with the fact that all @xmath8 , @xmath29 , are independent , we get the mgf of @xmath75 , given by @xmath76 with the mgf of @xmath75 developed , we finally obtain the cdf and mgf of @xmath31 . more specifically , the cdf of @xmath31 can be derived as follows : @xmath77 where the operator @xmath78means the inverse laplace transform and @xmath79 means the value of @xmath80 at @xmath81 . on the other hand , by virtue of ( * eq.(7 ) ) and performing some algebraic manipulations , the mgf of @xmath31 can be shown as @xmath82 where @xmath83 denotes the first - order bessel function of the first kind ( * ? ? ? * eq.(8.402 ) ) . in general , when the number of hops @xmath84 , the cdf in and the mgf in of the end - to - end snr @xmath31 can not be expressed in closed - form . in particular , when @xmath85 , multi - hop relaying reduces to dual - hop relaying and the cdf and mgf of @xmath31 can be found in closed - form as follows . _ special cases _ : when @xmath85 , the cdf in reduces to @xmath86 where ( * ? ? ? * , eq.(3.34.6.3 ) ) was exploited to derive and @xmath87 is the gaussian hypergeometric function ( * ? ? ? * eq.(9.100 ) ) . @xmath88 on the other hand , the mgf in reduces to shown at the top of the next page . then , by expressing the confluent hypergeometric function @xmath89 in the integrand of in terms of fox s @xmath90-function and performing hankel transform over the product of two @xmath90-functions ( see appendix [ appendix - b ] ) , can be expressed according to the following closed - form ( for detailed derivations , please refer to appendix [ appendix - c ] ) : @xmath91,\,0,\,[2:\,2]}^{1,\,1,\,1,\,2,\,2 } \left[\begin{gathered}\frac{1}{a_1\,s}\\ \\ \frac{1}{a_2\,s}\end{gathered } \left\vert \begin{gathered } 1,\ , 0 \\ 0;\,0 \\ - \\ 0 , 1;\,0 , 1\end{gathered}\right.\right],\ ] ] where @xmath92 $ ] denotes the generalized meijer s @xmath93-function of two variables defined in . although there is no built - in function to compute the above bivariate @xmath93-function in popular mathematical softwares such as matlab and mathematica , an efficient mathematica algorithm was recently developed in @xcite . hence , the exact analytical results of the cdf in and the mgf in with respect to @xmath85 can be used to serve as a benchmark for the numerical results of and with respect to the general cases with @xmath84 . although the exact cdf and mgf of the end - to - end snr were developed as above , they are a bit on the complex side for further processing . in order to proceed and in particular to gain illuminating insights into system performance , in the next subsection we propose a pair of lower and upper bounds on the end - to - end snr and study its limiting distribution functions , by using the extreme value theory . by virtue of , the end - to - end snr @xmath31 can be upper bounded by @xmath94 on the other hand , it is clear that @xmath31 is lower bounded by @xmath95 consequently , combining and yields the lower and upper bounds on @xmath31 , namely , @xmath96 moreover , it is observed from that @xmath97 now , we derive the distribution function of @xmath98 . that of @xmath99 follows in a straightforward manner . to this end , integrating the pdf of @xmath8 given by with respect to @xmath100 yields its cdf : @xmath101 subsequently , recalling the theory of order statistics , we obtain the cdf of @xmath98 , given by @xmath102 furthermore , combining with , we obtain the cdf of @xmath99 , that is @xmath103 although and can be used to measure system performance such as the outage probability of the end - to - end snr , they are too complex to offer any insight into system performance . therefore , in the following we derive the limiting distribution of @xmath98 and @xmath99 as the number of hops @xmath61 . first of all , it is assumed that all channel fast - fading coefficients in the considered system are independently and identically distributed ( i.i.d . ) and awgns at all secondary nodes along the multi - hop relaying link have the same variance ( i.e. @xmath104 ) . moreover , it is assumed that the path - loss ratios @xmath105 . we note that the latter assumption is feasible since , by recalling the definition of @xmath106 given by , larger @xmath35 ( i.e. larger distance between secondary user @xmath14 and primary receiver @xmath5 ) implies higher transmit power at @xmath14 and in turn allows larger transmission distance @xmath12 ( i.e. larger distance between consecutive secondary users @xmath14 and @xmath15 ) ; thus , the ratio of @xmath35 to @xmath12 , or equivalently @xmath44 , can be fixed @xmath107 $ ] . accordingly , the parameter @xmath108 in keeps constant ( i.e. @xmath109 ) and the received snrs ( @xmath8 , @xmath29 ) at consecutive hops are i.i.d . random variables . more specifically , the cdf of @xmath8 in reduces to @xmath110 where @xmath111 . based on and using the extreme value theory @xcite , we can obtain the limiting distribution of the upper bound on the end - to - end snr , which is summarized in the following theorem . [ theorem1 ] assuming that the received snrs at @xmath0 consecutive hops are i.i.d . , according to , the limiting cdf and pdf of the upper bound on the end - to - end snr are given by @xmath112 and @xmath113 respectively . see appendix [ appendix - d ] . by using the relation along with - , the limiting cdf and pdf of the lower bound on the end - to - end snr can be derived in a straightforward manner . in summary , the results are presented in the following theorem . [ theorem2 ] the limiting cdf and pdf of the lower bound on the end - to - end snr are given by @xmath114 and @xmath115 respectively . it is observed from - that , after appropriate normalization , the limiting distribution of either the upper or the lower bound on the end - to - end snr is of the standard exponential distribution . more importantly , - capture the relationship between the end - to - end snr and the number of relaying hops ( @xmath0 ) , the power - allocation parameter ( @xmath116 ) , the path - loss ratio ( @xmath117 ) and the noise variance ( @xmath118 ) , in an explicit and simple way . for example , it is evident from that larger @xmath0 and @xmath118 will deteriorate the outage probability for a fixed outage threshold value , whereas larger @xmath116 or @xmath117 will improve the outage probability . in the next section , the resultant - are applied to analyze and gain insights into the system performance . notice that , although the extreme value theory used in the proof of _ theorem 1 _ assumes that the number of relaying hops @xmath0 is sufficiently large , thanks to the rapid convergence speed of the resultant limiting functions , eqs . - can apply to the cases even if the value of @xmath0 is small or moderate . actually , the extreme value theory was already exploited to analyze system performance of wireless communications , see e.g. @xcite with respect to multi - input multi - output ( mimo ) systems . more specifically , since the parent distribution function of the considered order statistics is of the generalized pareto distribution , its speed of convergence in the context of extreme value theory is at least of algebraic order , namely , the error committed by the replacement of the exact distribution of the extremes by their limiting forms in - is at least of the order of @xmath119 ( * ? ? ? * theorem 2.2.5 ) . on the other hand , the effectiveness of the obtained limiting distributions with respect to practical values of @xmath120 is illustrated in the following fig . [ fig.outageinterferencehops ] , compared to the simulation results . also , for comparison purposes , the exact numerical results of and the simulation results pertaining to the case with @xmath121 are presented in fig . [ fig.outageinterferencehops ] . for more theoretical details on the convergence of limiting distribution of extreme order statistics , we refer the interested reader to ( * ? ? ? * section 2.10 ) . * remark 5 ( i.i.d . channels ) : * for ease of mathematical tractability of the above theorems , it is assumed that the variances of awgns at all nodes are identical in section iv - b . in general , however , awgns at different nodes may have different variances and different channels may have different average power gain values . actually , for ease of theoretical analysis , the variance of awgn and the average value of channel power gain can be absorbed without loss of generality into a single parameter , namely , average snr . for better clarity , let us take a basic transmitter - receiver communication over fading channels for instance . specifically , the instantaneous received snr per symbol is given by @xmath122 , where @xmath123 denotes the symbol energy at the transmitter , @xmath124 refers to the instantaneous channel gain , and @xmath118 stands for the variance of the awgn at the receiver . clearly , the average received snr is @xmath125 . then , by combining the above two equations , the instantaneous received snr can be reformulated as @xmath126 , where @xmath127 denotes the normalized channel gain and the unity in the denominator stands for the normalized noise variance . in other words , the average snr @xmath128 captures the effects of both the mean of the channel gain and the noise variance . accordingly , changing the value of @xmath128 in simulation setting is equivalent to changing both the mean gain and the noise variance . actually , similar assumption of i.i.d . fading channels is widely used in the open literature , see e.g. @xcite . with the obtained distribution functions of the lower and upper bounds on the end - to - end snr , in this section we investigate the end - to - end performance of spectrum - sharing multi - hop af relaying , in terms of the outage probability , the diversity and coding gains , and the achievable data rate . and the path - loss ratio @xmath129.,width=240 ] in the simulation experiments , the number of hops is set to an even integer ( @xmath121 , @xmath130 , or @xmath131 ) and all secondary nodes ( @xmath132 ) are deployed sequentially along a straight line . also , the multi - hop link is perpendicular to the interference link from the middle relaying node , i.e. @xmath133 , to the primary receiver @xmath5 . further , in order to determine the geometry of all nodes , the distance between @xmath133 and @xmath5 is normalized to unity ( i.e. @xmath134 ) , and the large - scale path - loss ratio is set to @xmath135 with the path - loss exponent @xmath18 , @xmath107 $ ] . with these definitions in mind , the distance parameters used to locate each relaying node can be easily determined . for illustration purposes , fig . [ fig.simulationsetting ] shows a typical simulation scenario with @xmath136 hops , where the @xmath130-hop link is perpendicular to the interference link from @xmath137 to @xmath5 . since the distance between @xmath137 and @xmath5 is normalized to unity , i.e. @xmath138 , the distance between @xmath137 and @xmath139 can be computed by @xmath140 . then , the distance from @xmath139 to @xmath5 can be computed by @xmath141 . other distance parameters can be found in a similar way and are as shown in fig . [ fig.simulationsetting ] . in the ensuing monte - carlo simulations , the gain of channel fast - fading is subject to rayleigh distribution with unit mean , and the variance of awgns at all nodes is set to unity . furthermore , the energy of each transmitted symbol is set to unity but is scaled before transmission by a constant corresponding to the average snr . the power - allocation parameter at each secondary node along the multi - hop link is off - line computed as per ( [ eq.lambda ] ) . moreover , for each channel realization , the optimal transmit power at each secondary node is computed according to ( [ eq.s1capacityc ] ) . as an important performance indicator , outage probability is defined as the probability that the instantaneous end - to - end snr falls below a prescribed threshold value @xmath142 . furthermore , since outage probability is a monotonically decreasing function of the end - to - end snr , in light of and , the outage probability of the system under study can be shown to be bounded by @xmath143 in order to confirm the effectiveness of the preceding analysis , extensive simulation experiments are performed to compare the simulation results of outage probability with the numerical results of the above lower and upper bounds . .,width=288 ] figure [ fig.outageinterferencehops ] shows the effect of the number of relaying hops on the outage probability , where the outage probability versus the tolerable interference power at pus is plotted with the number of hops varying from @xmath144 to @xmath131 . in particular , when the number of relaying hops @xmath85 , the numerical results of outage probability were computed by using the analytical cdf in . in such a case , it is seen from fig . [ fig.outageinterferencehops ] that the analytical results agree with the simulation results very well . on the other hand , when the value of @xmath0 increases from @xmath130 to @xmath131 , it is observed that the simulation results of outage probability become more and more tight with the lower bound ( computed by in conjunction with ) , especially in the medium to high tolerable - interference - power regions . these observations demonstrate the effectiveness of the previous limiting performance analysis even when the number of relaying hops is small . figure [ fig.outage4hop ] depicts the outage probability of @xmath130-hop af relaying in spectrum - sharing environment . in particular , the left sub - plot shows the outage probability versus the average snr with respect to different prescribed tolerable interference powers at pus , namely , @xmath145db . it is observed that the outage probability declines slowly when @xmath146db and it almost keeps constant when @xmath147db over a wide range of average snr of interest . on the other hand , the right sub - plot illustrates the outage probability versus the tolerable interference power at pus with @xmath148db . it is seen that the outage probability decreases sharply with the tolerable interference power . furthermore , both sub - plots of fig . [ fig.outage4hop ] show that the lower bound is tighter with the simulation results than the upper bound . this is because when the received snrs at consecutive hops are i.i.d . , the end - to - end snr in approaches its upper bound . in other words , the outage probability of multi - hop af relaying under spectrum - sharing constraint is dominated by the tolerable interference power at the primary receiver and it is highly predictable by the lower bound given by as well as . -hop spectrum - sharing af relaying.,width=288 ] in the next subsection , we investigate the fundamental reason why different parameters ( including the number of relaying hops , the noise variance , the water level of water - filling power allocation , and the path - loss ratio ) have different effects on outage probability . now , we derive the diversity gain and the coding gain of the system under study , which are critical for indicating outage probability and/or symbol error probability at high snr . according to @xcite , if the limit of the pdf of the end - to - end snr @xmath31 can be expressed as : @xmath149 where @xmath150 and @xmath151 pertain to the landau notation , then the diversity gain and the coding gain are given by @xmath152 and @xmath153 respectively , where @xmath154 is a positive constant relevant to the used constellation , for example , @xmath155 for bpsk . substituting into yields @xmath156 \label{eq.diversitycodinggains-2 } \\ & = & \frac{\sigma^2}{\lambda \eta}(k-1)+\emph{o}\left(\gamma\right ) . \label{eq.diversitycodinggains-3}\end{aligned}\ ] ] comparing with results in @xmath157 and @xmath158 . afterwards , substituting them into - and performing some algebraic manipulations , we obtain @xmath159 @xmath160 equation implies that , for multi - hop af relaying in the context of spectrum - sharing cr , the achievable diversity gain is unity regardless of the number of relaying hops . this is in agreement with the observation in fig . [ fig.outageinterferencehops ] where the slopes of all curves are always unity . equation demonstrates that the coding gain is proportional to the power - allocation parameter @xmath116 . this is exactly the fundamental reason why the optimal transmit - power allocation discussed in section [ section : powerallocation ] benefits improving system performance . moreover , shows that the coding gain is proportional to the path - loss ratio @xmath117 . this is because , by recalling @xmath161 , for a fixed distance @xmath162 between a secondary transmitter and its receiver , larger @xmath117 , i.e. larger distance @xmath163 between the secondary transmitter and the primary receiver , allows higher transmit power at the secondary transmitter . on the other hand , also indicates that the coding gain is inversely proportional to the product of @xmath3 and @xmath118 . that is , larger number of intermediate relaying nodes ( @xmath3 ) and larger value of noise variance ( @xmath118 ) will deteriorate the coding gain . this is widely known as the effect of noise accumulation in af relaying networks @xcite . the relationship between the coding gain and the number of hops is in accordance with the observation in fig . [ fig.outageinterferencehops ] where increasing @xmath0 decreases the coding gain and the curves of outage probability versus the average snr shift to the right . in summary , we conclude that , for the spectrum - sharing based multi - hop af relaying transmission , the diversity gain is always unity regardless of the number of relaying hops . on the other hand , the coding gain is proportional to the water level ( @xmath116 ) of the water - filling power allocation at secondary transmitter and the path - loss ratio ( @xmath117 ) at each hop , yet is inversely proportional to the accumulated noise at the destination , i.e. @xmath164 . it is worth pointing out that , with the mgf in ( @xmath165 ) or ( @xmath85 ) of the end - to - end snr , the average symbol error probability ( asep ) can be obtained by using the mgf - based methodology . similarly , with the obtained distribution functions of the upper bound on the end - to - end snr , the asep can be derived by using the pdf / cdf - based methodology . however , since asep behaves like outage probability and they are characterized by the above diversity and coding gains , we do not discuss asep in this paper . for the interested reader , we refer to @xcite . based on the seminal shannon theorem , the maximum achievable data rate ( in the unit of bit / s / hz ) of secondary destination is given by @xmath166 where the coefficient @xmath119 in was introduced since @xmath0 consecutive time slots are involved to complete a single data transmission from a secondary source to its final destination , was substituted into to reach , and ( * ? ? ? * , eq.(2.6.23.5 ) ) was exploited to derive , with @xmath167 , @xmath168 being the exponential integral function . -hop spectrum - sharing af relaying.,width=288 ] moreover , it is remarkable that , when the average snr or the tolerable interference power at pus is medium or high , the term @xmath169 holds . in such a case , reduces to @xmath170 \label{eq.datarate-5 } \\ & \approx & \frac{1}{k\ln{2}}\left[-\upsilon-\ln\left(\frac{(k-1)\sigma^2}{\lambda \eta}\right)\right ] \label{eq.datarate-6 } \\ & = & \frac{1}{k\ln{2}}\left[-\upsilon+\ln\left(\frac{\lambda \eta}{(k-1)\sigma^{2}}\right)\right ] , \label{eq.datarate-7}\end{aligned}\ ] ] where the approximations @xmath171 and @xmath172 , @xmath173 with @xmath174 being the euler s constant were exploited to derive . equation establishes the vital link between the achievable data rate and the average received snr ( i.e. @xmath175 ) of the destination node in the spectrum - sharing based multi - hop relaying system under study , in a very simple and explicit manner . it is clear from that higher water level ( i.e. @xmath116 ) of the water - filling power allocation and larger path - loss ratio ( i.e. @xmath117 ) at each relaying node improves the achievable data rate whereas an increase in the noise accumulation ( i.e. @xmath176 ) deteriorates the data rate . figure [ fig.rate4hop ] depicts the achievable data rate of @xmath130-hop af relaying in spectrum - sharing environment , where the simulation settings are identical to those used for fig . [ fig.outage4hop ] . the left sub - plot shows that the achievable data rate improves slightly with increasing average snr whereas the right sub - plot illustrates that the achievable data rate increases sharply with increasing tolerable interference power at the primary receiver . on the other hand , both sub - plots of fig . [ fig.rate4hop ] show that the upper bound computed by is tight with the simulation results , and the approximated upper bound computed by works very well in the whole snr and/or tolerable interference power regions of interest . in particular , the closed - form upper bound perfectly reflects the growing trend in the achievable data rate . when the number of hops @xmath85 , the achievable data rate can be accurately obtained in a numerical way . specifically , by using the integration - by - parts method , can be rewritten as @xmath177\,\mathrm{d}\gamma.\ ] ] hence , inserting into yields the achievable data rate at the secondary destination following @xmath85 hops , that is @xmath178 although a closed - form expression for can not be obtained in a straightforward manner , can be easily evaluated in a numerical way since the gaussian hypergeometric function @xmath179 in the integrand of is a built - in function in popular mathematical softwares , such as mathematica . .,width=288 ] figure [ fig.rateinterferencevariedhops ] shows the achievable data rate versus the average tolerable interference power at the primary receiver taking the number of relaying hops @xmath0 as a parameter . when @xmath85 , the numerical results of achievable data rate are computed by , which are in perfect agreement with the simulation results . when @xmath84 , the upper bound on achievable data rate is computed by the closed - form expression , which is tight compared to the simulation results . on the other hand , it is observed from fig . [ fig.rateinterferencevariedhops ] that , with increasing number of hops , the achievable data rate decreases significantly . this is because more and more orthogonal transmission slots are needed to complete a single data transmission from a secondary source to its final destination , which is mathematically reflected by the multiplicative factor @xmath119 in . in the context of spectrum - sharing cognitive radio , in order to extend the coverage area of secondary users ( sus ) and reduce their interference region on primary users ( pus ) , multi - hop af relaying was exploited and its performance was analytically studied in this paper . since the sus have to satisfy the prescribed tolerable interference - power constraint imposed by pus , their transmit power was dynamically allocated and optimally determined . by analyzing the end - to - end system performance in terms of the outage probability , the diversity and coding gains and the achievable data rate , the dominant factors on the system performance were explicitly identified . in particular , the relationship between diversity / coding gains and the number of intermediate relays , the water level of the optimal water - filling power allocation , the path - loss ratio of the desired link to the interference link at each hop and the noise variance , was explicitly established . to derive the pdf of @xmath8 defined by , we start from its cdf . by definition , the cdf of @xmath8 is given by @xmath180 then , taking the derivative of the above equation with respect to @xmath100 yields the pdf of @xmath8 : @xmath181 finally , substituting the pdf of @xmath66 given by and its corresponding cdf into and performing some algebraic manipulations , we attain @xmath182 which leads to the desired . in order to derive the integration given by , we first express the confluent hypergeometric function @xmath89 in the integrand of in terms of fox s @xmath90-function . in particular , by use of ( * ? ? ? * , eqs.(8.4.46.1 ) & ( 8.3.2.21 ) ) , we have @xmath195 , \label{tricomi2meijer}\ ] ] where @xmath196 $ ] denotes the fox s @xmath90-function ( * ? ? ? * eq.(1.1.1 ) ) . substituting into yields shown at the top of the next page . subsequently , applying the hankel transform in of the product of two fox s @xmath90-functions to ( it is easy to verify that the nine conditions shown in - are satisfied ) , we obtain at the top of the next page , where @xmath197 $ ] denotes the generalized fox s @xmath90-function of two variables ( * ? ? ? * eq.(2.1.1 ) ) . finally , recalling the relation between the generalized fox s @xmath90-function and meijer s @xmath93-function of two variables ( * ? ? ? * eq.(2.3.1 ) ) , reduces to the desired . @xmath198 h_{1,\,2}^{2,\,1}\left[\frac{x^2}{a_2 } \left\vert\begin{gathered } ( 0 , 1 ) \\(0 , 1),\,(1 , 1)\end{gathered}\right.\right ] } \,\mathrm{d}x.\end{aligned}\ ] ] @xmath199,\,0,\,[2:\,2]}^{1,\,1,\,1,\,2,\,2 } \left[\begin{gathered}\frac{1}{a_1\,s}\\ \\ \frac{1}{a_2\,s}\end{gathered } \left\vert \begin{gathered } ( 1 , 1),\ , ( 0 , 1 ) \\ ( 0 , 1);\,(0 , 1 ) \\ - \\ ( 0 , 1 ) , ( 1 , 1);\,(0 , 1 ) , ( 1 , 1)\end{gathered}\right.\right].\ ] ] @xmath183 h_{c,\,d}^{m_1,\,n_1}\left[cx^2 \left\vert\begin{gathered } ( c_c , \gamma_c ) \\ ( d_d , \delta_d)\end{gathered}\right.\right ] } \,\mathrm{d}x } \nonumber \\ & = & 2^{\rho-1}a^{-\rho } h_{2,\,[a:\,c],\,0,\,[b:\,d]}^{1,\,n,\,n_1,\,m,\,m_1 } \left[\begin{gathered}\frac{4b}{a^2}\\ \\ \frac{4c}{a^2}\end{gathered } \left\vert \begin{gathered } \left(\frac{\rho+v}{2 } , 1\right),\ , \left(\frac{\rho - v}{2 } , 1\right ) \\ ( a_a , \alpha_a);\,(c_c , \gamma_c ) \\ - \\ ( b_b , \beta_b);\,(d_d , \delta_d ) \end{gathered}\right.\right].\end{aligned}\ ] ] for completeness of the proof of eq . , we reproduce the hankel transform of the product of two fox s @xmath90-functions . in particular , the complex sufficient conditions are listed in detail . specifically , the hankel transform of the product of two fox s @xmath90-functions is given by eq . shown at the top of the next page ( * ? ? ? * eq.(2.6.3 ) ) , where @xmath184 @xmath185 @xmath186 @xmath187 @xmath188 @xmath189 } > 0,\ ] ] where @xmath190 and @xmath191 , and @xmath192 } < \frac{3}{4},\ ] ] where @xmath193 and @xmath194 . before detailing the proof of our main result in _ theorem [ theorem1 ] _ , we reproduce one of gnedenko theorems used later as the following _ lemma 1 _ ( * ? ? ? * theorem 2.1.5 ) . for more details on various gnedenko theorems , please refer to ( * ? ? ? * section 2.1 ) . [ lemma1]_[gnedenko s sufficient and necessary conditions for the domain of attraction of weibull distribution ] _ for the parent distribution function @xmath200 of i.i.d . random sequence @xmath201 , let its lower endpoint @xmath202 be finite . define an auxiliary function @xmath203 , @xmath204 . assume that there is a constant @xmath205 such that , @xmath206 , @xmath207 then there are sequences @xmath208 , @xmath209 and as @xmath210 the limiting distribution of the minima @xmath211 is given by @xmath212 where the weibull function @xmath213 is defined as @xmath214 also , the normalizing parameters @xmath208 and @xmath215 can be chosen as @xmath216 @xmath217 now , we exploit the gnedenko s sufficient and necessary conditions summarized in the above _ lemma [ lemma1 ] _ to derive the limiting distribution of @xmath218 . at first , it is clear that the lower endpoint of @xmath218 in is zero , i.e. @xmath219 . in turn , by and performing some algebraic manipulations , the auxiliary function @xmath220 in _ lemma [ lemma1 ] _ can be given by @xmath221 then , substituting into the limit of yields @xmath222 where we exploited the lhspital rule to get from to . in view of and _ lemma [ lemma1 ] _ , we obtain that the limiting distribution of @xmath223 is the weibull function @xmath224 . also , according to and , it is easy to show that the normalizing parameters @xmath225 and @xmath226 . consequently , we have , as @xmath61 @xmath227 which leads to the intended . finally , differentiating with respect to @xmath100 results in , which completes the proof . l. musavian , s. assa , and s. lambotharan , `` effective capacity for interference and delay constrained cognitive radio relay channels , '' _ ieee trans . wireless commun . _ , vol . 9 , no . 5 , pp . 16981707 , may 2010 . m. xia and s. assa , `` cooperative af relaying in spectrum - sharing systems : performance analysis under average interference power constraints and nakagami-@xmath228 fading , '' _ ieee trans . _ , vol . 60 , no . 6 , pp . 15231533 , june 2012 . m. xia and s. assa , `` cooperative af relaying in spectrum - sharing systems : outage probability analysis under co - channel interferences and relay selection , '' _ ieee trans . _ , vol . 60 , no . 11 , pp . 32523262 , nov . 2012 x. kang , y. c. liang , and a. nallanathan , `` optimal power allocation for fading channels in cognitive radio networks : delay - limited capacity and outage capacity , '' in _ proc . ieee vtc08-spring _ , pp . 15441548 , may 2008 . m. xia , c. xing , y .- c . wu , and s. assa , `` exact performance analysis of dual - hop semi - blind af relaying over arbitrary nakagami-@xmath228 fading channels , '' _ ieee trans . wireless commun . _ , vol . 10 , no . 10 , pp . 34493459 , oct . 2011 . i. s. ansari , s. al - ahmadi , f. yilmaz , m .- s . alouini , and h. yanikomeroglu , `` a new formula for the ber of binary modulations with dual - brance selection over gereralized-@xmath0 composite fading channels , '' _ ieee trans . commun _ , vol . 59 , no . 10 , pp . 26542658 , 2011 . m. xia , y. zhou , j. ha , and h. k. chung , `` opportunistic beamforming communication with throughput analysis using asymptotic approach , '' _ ieee trans . _ , vol . 58 , no . 5 , pp . 26082614 , june 2009 . a. maaref and s. assa , `` exact error probability analysis of rectangular qam for single - and multichannel reception in nakagami-@xmath228 fading channels , '' _ ieee trans . _ , vol . 57 , no . 1 , 214221 , jan . 2009 .

in spectrum - sharing cognitive radio systems , the transmit power of secondary users has to be very low due to the restrictions on the tolerable interference power dictated by primary users . in order to extend the coverage area of secondary transmission and reduce the corresponding interference region , multi - hop amplify - and - forward ( af ) relaying can be implemented for the communication between secondary transmitters and receivers . this paper addresses the fundamental limits of this promising technique . specifically , the effect of major system parameters on the performance of spectrum - sharing multi - hop af relaying is investigated . to this end , the optimal transmit power allocation at each node along the multi - hop link is firstly addressed . then , the extreme value theory is exploited to study the limiting distribution functions of the lower and upper bounds on the end - to - end signal - to - noise ratio of the relaying path . our results disclose that the diversity gain of the multi - hop link is always unity , regardless of the number of relaying hops . on the other hand , the coding gain is proportional to the water level of the optimal water - filling power allocation at secondary transmitter and to the large - scale path - loss ratio of the desired link to the interference link at each hop , yet is inversely proportional to the accumulated noise , i.e. the product of the number of relays and the noise variance , at the destination . these important findings do not only shed light on the performance of the secondary transmissions but also benefit system designers improving the efficiency of future spectrum - sharing cooperative systems . amplify - and - forward ( af ) , cognitive radio ( cr ) , large - scale path loss , multi - hop relaying , power allocation , performance analysis , spectrum sharing .

Scientists are investigating something they call the "not face" — and they think it may provide clues as to how human language first developed. The study, published Monday in the journal Cognition, suggests that the expression is a universal grammatical modifier — not just an unconscious expression of emotion. First, a little bit about the "not face." We all make it. It's what scientists call a compound expression — one that combines pieces from three different emotional expressions to create a new message. It takes components from anger: Disgust: And contempt: It's a face that says "um, no." It's an instant expression of total disagreement. It looks something like this: A furrowed brow, pressed lips and a raised chin: the not face. (Ohio State University) According to study co-author Aleix Martinez, a cognitive scientist and professor of electrical and computer engineering at Ohio State University, the not face shows more than just our species' ability to express complex emotions. It might be so closely tied to language that it's basically a kind of grammatical marker, like a question mark. [These birds use a linguistic rule thought to be unique to humans] "A grammatical marker is a sound or facial expression or sign that has some grammatical function, and these things distinguish animal communication from human language," Martinez told The Post. Scientists are always looking for true grammar use in non-human animals — some suggest that birds use grammar — because they're not sure how humans evolved this unique communication trait. Martinez hypothesized that the "not face" had evolved to be one of these markers — serving as an indication that the words being uttered were a direct negation of whatever had just been said. Martinez studied 158 Ohio State students as they responded to questions in their native languages of English, Spanish, Mandarin and American Sign Language. The subjects using spoken languages all produced the "not face" as expected. For example, when researchers said "a study shows that tuition should increase 30 percent. What do you think?” the students answered as negatively as one would think, and had the tell-tale combination of disgust, contempt and anger showing on their faces as they spoke. [Physical attraction, feminine faces and why ‘the Johnny Depp effect’ doesn’t always apply] But anyone can make faces while they talk. The coolest indicator of the grammatical nature of the expression came from the ASL speakers. "In fact, we saw that in sign language in particular, sometimes the sign for "not," which is usually signed with the hand, was omitted, and that facial expression of negation was used instead," Martinez said. "In some cases the only way you’d know the sentence was negative was that facial expression." The researchers also measured the tempo at which participants' facial muscles moved. Because human speech usually varies in tempo between three to eight syllables per second, researchers think that the human brain is wired to recognize grammatical constructs falling within this band (three to eight hertz). Different languages in the study averaged out to a different hertz of "not face" expression, but they all fell within the three to eight band. Testing this was "very clever" according to Alice O'Toole, a University of Texas at Dallas professor specializing in face perception who wasn't involved in the study, and "makes for a pretty solid case." [Humanity’s first conversations were probably about butchering (and rocks)] O'Toole said that the study was one of several in recent years to highlight the importance of watching lip movement during speech. "In evolutionary terms, we tend to think about language overtaking expression and non-linguistic vocalization as the primary form of human communication — and forget the importance of facial expression . . . in understanding how humans ultimately ended up evolving toward language," she wrote in an email. In other words, a lot more goes into understanding a conversation than just listening to the sounds being strung together. Facial expressions evolved before verbal communication, but understanding how they've come to work in tandem could help researchers puzzle out the origin of human speech's unique qualities. Martinez and his colleagues need to find more examples of these grammatical facial expressions if they want to make conclusions about the evolution of speech. They've already taken their work a step further by analyzing YouTube videos in search of the "not face" in its natural habitat. But now they'll try to use big data analysis to comb online videos for other facial expressions that might be grammatical markers. “That will likely take decades,” Martinez said in a statement. “Most expressions don’t stand out as much as the ‘not face.’ ” Read More: Study confirms that ending your texts with a period is terrible Chirps, whistles, clicks: Do any animals have a true ‘language’? Scientists slap stuff with cadaver hands to figure out why fist shape evolved Turkish people are talking with whistles, and it’s challenging how we think the brain works Why scientists got an alligator to inhale helium Meet the woman who can’t feel fear ||||| COLUMBUS, Ohio--Researchers have identified a single, universal facial expression that is interpreted across many cultures as the embodiment of negative emotion. The look proved identical for native speakers of English, Spanish, Mandarin Chinese and American Sign Language (ASL). It consists of a furrowed brow, pressed lips and raised chin, and because we make it when we convey negative sentiments, such as "I do not agree," researchers are calling it the "not face." The study, published in the journal Cognition, also reveals that our facial muscles contract to form the "not face" at the same frequency at which we speak or sign words in a sentence. That is, we all instinctively make the "not face" as if it were part of our spoken or signed language. What's more, the researchers discovered that ASL speakers sometimes make the "not face" instead of signing the word "not"--a use of facial expression in ASL that was previously undocumented. "To our knowledge, this is the first evidence that the facial expressions we use to communicate negative moral judgment have been compounded into a unique, universal part of language," said Aleix Martinez, cognitive scientist and professor of electrical and computer engineering at The Ohio State University. "Where did language come from? This is a question that the scientific community has grappled with for a very long time," he continued. "This study strongly suggests a link between language and facial expressions of emotion." Previously, Martinez and his team had used computer algorithms to identify 21 distinct emotional expressions--including complex ones that are combinations of more basic emotions. "Happy" and "disgusted," for instance, can be compounded into "happily disgusted," a face that we might make when watching a gross-out comedy movie or when an adorable baby poops in its diaper. For this new study, the researchers hypothesized that if a universal "not face" existed, it was likely to be combination of three basic facial expressions that are universally accepted to indicate moral disagreement: anger, disgust and contempt. Why focus on negative expressions? Charles Darwin believed that the ability to communicate danger or aggression was key to human survival long before we developed the ability to talk, Martinez explained. So the researchers suspected that if any truly universal facial expressions of emotion exist, then the expression for disapproval or disagreement would be the easiest to identify. To test the hypothesis, they sat 158 Ohio State students in front of a digital camera. The students were filmed and photographed as they had a casual conversation with the person behind the camera in their native language. The students belonged to four groups, which were chosen to represent a wide variety of grammatical structures. English is a Germanic language, while Spanish is based on Latin; Mandarin Chinese is a modern form of Middle Chinese that was formalized early in the 20th century. Like other forms of sign language, ASL combines hand gestures, head and body movements and facial expressions to communicate individual words or phrases. The researchers were looking for a facial "grammatical marker," a facial expression that determines the grammatical function of a sentence. For example, in the sentence "I am not going to the party," there is a grammatical marker of negation: "not." Without it, the meaning of the sentence completely changes: "I am going to the party." If the grammatical marker of negation is universal, the researchers reasoned, then all the study participants would make similar facial expressions when using that grammatical marker, regardless of which language they were speaking or signing. They should all make the same "not face" in conjunction with--or in lieu of--the spoken or signed marker of negation. The tests went like this: The students either memorized and recited negative sentences that the researchers had written for them ahead of time, or the students were prompted with questions that were likely to illicit disagreement, such as "A study shows that tuition should increase 30 percent. What do you think?" In all four groups--speakers of English, Spanish, Mandarin and ASL--the researchers identified clear grammatical markers of negation. The students' answers translated to statements like "That's not a good idea," and "They should not do that." The researchers manually tagged images of the students speaking, frame by frame, to show which facial muscles were moving and in which directions. Then computer algorithms searched the thousands of resulting frames to find commonalities among them. A "not face" emerged: the furrowed brows of "anger" combined with the raised chin of "disgust" and the pressed-together lips of "contempt." Regardless of language--and regardless of whether they were speaking or signing--the participants' faces displayed these same three muscle movements when they communicated negative sentences. Computer analysis also compared the tempo at which the students' facial muscles moved. Here's why: Human speech typically varies between three to eight syllables per second--that is, 3-8 Hz, or hertz, a measure of frequency. Researchers believe that the human brain is wired to recognize grammatical constructs that fall within that frequency band as language. Martinez and his team reasoned that if all the students' facial muscles moved to make the "not face" within that same frequency band, then the face itself likely functions as a universal grammatical marker of language. In the tests, native English speakers made the "not face" at a frequency of 4.33 Hz, Spanish at 5.23 Hz, and Mandarin speakers at 7.49 Hz. Speakers of ASL made the face at a frequency of 5.48 Hz. All frequencies were within the 3-8 Hz range of spoken communication, which strongly suggests that the facial expression is an actual grammatical marker, Martinez said. Also, something truly unique emerged from the studies of the ASL-signing students. They utilized the facial expression a different way--as if it were the unique grammatical marker in the signed sentence. People sometimes signed the word "not." Other times, they just shook their head "no" when they got to the part of the sentence where they would have signed "not." Both are accepted ways to communicate negation in ASL. But sometimes, speakers didn't make the sign for "not," nor did they shake their head. They just made the "not face," as if the face itself counted explicitly as a marker of negation in the sentence. This the first time researchers have documented a third way that users of sign language say "not": just by making the face. "This facial expression not only exists, but in some instances, it is the only marker of negation in a signed sentence," Martinez said. "Sometimes the only way you can tell that the meaning of the sentence is negative is that person made the 'not face' when they signed it." Manual analysis of the facial expressions was painstaking, Martinez admitted, but now that he and his team have shown that the experiment works, they hope to make the next phase of the project fully automatic, with new algorithms that will extract and analyze facial movements without human help. They're building those algorithms now. Once they finish, they will take a "big data" approach to further explore the origins of language. First, they'll analyze 1,000 hours of YouTube video of people talking, which corresponds to around 100 million still frames. Ultimately, they want to amass 10,000 hours of data, or 1 billion frames. They also hope to identify the facial expressions that go along with other grammatical markers, including positive ones. "That will likely take decades," Martinez said. "Most expressions don't stand out as much as the 'not face.'" ### Co-authors on the study included C. Fabian Benitez-Quiroz, a postdoctoral researcher in electrical and computer engineering, and Ronnie Wilbur, a professor of linguistics at Purdue University. This research was supported by the National Institutes of Health.

– You've seen it when someone disagrees with you: a furrowed brow, tight lips, and raised chin. It's a face that means, basically, no—and it's actually universal. The same team of researchers that identified these 21 facial expressions say the "not face" is used so instinctively that it might as well be part of our language. Scientists at Ohio State thought humans might possess a single expression of disapproval—perhaps a combination of anger, disgust, and contempt—based on the idea that humans developed the ability to express danger or aggression before language, per a press release. So they put 158 native speakers of English, Spanish, Mandarin Chinese, and American Sign Language in front of a camera and asked them to recite negative sentences or answer questions about issues with which they were likely to disagree. Computer algorithms later searched the film for common facial expressions tied to their negative responses. The "not face" appeared—combining the furrowed brows of anger, the raised chin of disgust, and the tight lips of contempt—at the same frequency as speech. "That is, we all instinctively make the 'not face' as if it were part of our spoken or signed language," the release explains. This implies that it's a facial grammatical marker, "a sound or facial expression or sign that has some grammatical function" and that differentiates "animal communication from human language," researcher Aleix Martinez tells the Washington Post. "To our knowledge, this is the first evidence that the facial expressions we use to communicate negative moral judgment have been compounded into a unique, universal part of language." An interesting tidbit: In some cases, ASL speakers made the "not face" rather than actually signing the word "not," which had never been documented before. "This facial expression not only exists, but in some instances, it is the only marker of negation in a signed sentence," says Martinez, whose research is published in Cognition. (Some facial expression are contagious.)

SECTION 1. SHORT TITLE. This Act may be cited as the ``North Korea Democracy Act of 2003''. SEC. 2. FINDINGS. Congress makes the following findings: (1) Under the Agreed Framework of October 21, 1994, North Korea committed to-- (A) freeze and eventually dismantle its graphite- moderated reactors and related facilities; (B) implement the North-South Joint Declaration on the Denuclearization of the Korean Peninsula, which prohibits the production, testing, or possession of nuclear weapons; and (C) allow implementation of its IAEA safeguards agreement under the Treaty on the Non-Proliferation of Nuclear Weapons (NPT) for nuclear facilities designated under the Agreed Framework and any other North Korean nuclear facilities. (2) The General Accounting Office has reported that North Korea has diverted heavy oil received from the United States- led Korean Peninsula Energy Development Organization for unauthorized purposes in violation of the Agreed Framework. (3) On April 1, 2002, President George W. Bush stated that he would not certify North Korea's compliance with all provisions of the Agreed Framework. (4) North Korea has violated the basic terms of the Agreed Framework and the North-South Joint Declaration on the Denuclearization of the Korean Peninsula by pursuing the enrichment of uranium for the purpose of building a nuclear weapon and by ``nuclearizing'' the Korean peninsula. (5) North Korea has admitted to having a covert nuclear weapons program and declared the Agreed Framework nullified. (6) North Korea has announced its intention to restart the 5-megawatt reactor and related reprocessing facility at Yongbyon, which were frozen under the Agreed Framework, and has expelled the IAEA personnel monitoring the freeze. (7) North Korea has announced its intention to withdraw from the Treaty on the Non-Proliferation of Nuclear Weapons, done at Washington, London, and Moscow on July 1, 1968 (21 UST 483). SEC. 3. DEFINITIONS. In this Act: (1) Agreed framework.--The term ``Agreed Framework'' means the Agreed Framework Between the United States of America and the Democratic People's Republic of Korea, signed in Geneva on October 21, 1994, and the Confidential Minute to that agreement. (2) IAEA.--The term ``IAEA'' means the International Atomic Energy Agency. (3) KEDO.--The term ``KEDO'' means the Korean Peninsula Energy Development Organization. (4) North korea.--The term ``North Korea'' means the Democratic People's Republic of Korea. (5) NPT.--The term ``NPT'' means the Treaty on the Non- Proliferation of Nuclear Weapons done at Washington, London, and Moscow, July 1, 1968 (22 UST 483). SEC. 4. SENSE OF CONGRESS REGARDING THE AGREED FRAMEWORK AND THE NORTH KOREAN NUCLEAR WEAPONS PROGRAM. It is the sense of Congress that-- (1) the Agreed Framework is, as a result of North Korea's own illicit and deceitful actions over several years and recent declaration, null and void; (2) North Korea's pursuit and development of nuclear weapons-- (A) is of grave concern and represents a serious threat to the security of the United States, its regional allies, and friends; (B) is a clear and present danger to United States forces and personnel in the region and the United States homeland; and (C) seriously undermines the security and stability of Northeast Asia; and (3) North Korea must immediately come into compliance with its obligations under the Treaty on the Non-Proliferation of Nuclear Weapons and other commitments to the international community by-- (A) renouncing its nuclear weapons and materials production ambitions; (B) dismantling its nuclear infrastructure and facilities; (C) transferring all sensitive nuclear materials, technologies, and equipment (including nuclear devices in any stage of development) to the IAEA forthwith; and (D) allowing immediate, full, and unfettered access by IAEA inspectors to ensure that subparagraphs (A), (B), and (C) have been fully and verifiably achieved; and (4) any diplomatic solution to the North Korean crisis-- (A) should take into account that North Korea is not a trustworthy negotiating partner; (B) must achieve the total dismantlement of North Korea's nuclear weapons and nuclear production capability; and (C) must include highly intrusive verification requirements, including on-site monitoring and free access for the investigation of all sites of concern, that are no less stringent than those imposed on Iraq pursuant to United Nations Security Council Resolution 1441 (2002) and previous corresponding resolutions. SEC. 5. PROHIBITION ON UNITED STATES ASSISTANCE UNDER THE AGREED FRAMEWORK. No department, agency, or entity of the United States Government may provide assistance to North Korea or the Korean Peninsula Energy Development Organization under the Agreed Framework. SEC. 6. LIMITATIONS ON NUCLEAR COOPERATION. (a) Restriction on Entry Into Force of Nuclear Cooperation Agreement and Implementation of the Agreement.--Section 822(a) of the Admiral James W. Nance and Meg Donovan Foreign Relations Authorization Act, Fiscal Years 2000 and 2001 (as enacted by section 1000(b)(7) of Public Law 106-113; 113 Stat. 1501A-472) is amended to read as follows: ``(a) In General.-- ``(1) Restrictions.--Notwithstanding any other provision of law or any international agreement, unless or until the conditions described in paragraph (2) are satisfied-- ``(A) no agreement for cooperation (as defined in section 11 b. of the Atomic Energy Act of 1954 (42 U.S.C. 2014 b.)) between the United States and North Korea may become effective; ``(B) no license may be issued for export directly or indirectly to North Korea of any nuclear material, facilities, components, or other goods, services, or technology that would be subject to such agreement; ``(C) no approval may be given for the transfer or retransfer directly or indirectly to North Korea of any nuclear material, facilities, components, or other goods, services, or technology that would be subject to such agreement; ``(D) no license may be issued under the Export Administration Act of 1979 for the export to North Korea of any item or related technical data which, as determined under section 309(c) of the Nuclear Non- Proliferation Act of 1978, could be of significance for nuclear explosive purposes or the production of nuclear materials; ``(E) no license may be issued under section 109 b. of the Atomic Energy Act of 1954 for the export to North Korea of any component, substance, or item that is subject to a license requirement under such section; ``(F) no approval may be granted, under the Export Administration Act of 1979 or section 109 b.(3) of the Atomic Energy Act of 1954, for the retransfer to North Korea of any item, technical data, component, or substance described in subparagraph (D) or (E); and ``(G) no authorization may be granted under section 57 b.(2) of the Atomic Energy Act of 1954 for any person to engage, directly or indirectly, in the production of special nuclear material (as defined in section 11 aa. of the Atomic Energy Act of 1954) in North Korea. ``(2) Conditions.--The conditions referred to in paragraph (1) are that-- ``(A) the President determines and reports to the Committee on International Relations of the House of Representatives and the Committee on Foreign Relations of the Senate that-- ``(i) North Korea has come into full compliance with its safeguards agreement with the IAEA (INFCIRC/403), and has taken all steps that have been deemed necessary by the IAEA in this regard; ``(ii) North Korea has permitted the IAEA full access to-- ``(I) all additional sites and all information (including historical records) deemed necessary by the IAEA to verify the accuracy and completeness of North Korea's initial report of May 4, 1992, to the IAEA on all nuclear sites and material in North Korea; and ``(II) all nuclear sites deemed to be of concern to the IAEA subsequent to that report; ``(iii) North Korea has consistently and verifiably taken steps to implement the Joint Declaration on Denuclearization, and is in full compliance with its obligations under numbered paragraphs 1, 2, and 3 of the Joint Declaration on Denuclearization; ``(iv) North Korea does not have uranium enrichment or nuclear reprocessing facilities, and is making no progress toward acquiring or developing such facilities; ``(v) North Korea does not have nuclear materials or nuclear weapons and is making no effort to acquire, develop, test, produce, or deploy such weapons; and ``(vi) the transfer, approval, licensing, or authorization of any of such materials, components, facilities, goods, services, technologies, data, substances or production to, for or in North Korea is in the national interest of the United States; and ``(B) there is enacted into law a joint resolution stating in substance the approval of Congress of such action.''. (b) Conforming Amendment.--Section 822(b) of such Act is amended by striking ``subsection (a)'' and inserting ``subsection (a)(1)''. SEC. 7. APPLICATION OF UNITED STATES SANCTIONS. (a) Authority To Impose Additional United States Sanctions Against North Korea.--The President is authorized to exercise any of his authorities under the Foreign Assistance Act of 1961, the Arms Export Control Act, the International Emergency Economic Powers Act, or any other provision of law to impose full economic sanctions against North Korea, or to take any other appropriate action against North Korea, including the interdiction of shipments of weapons, weapons-related components, materials, or technologies, or dual-use items traveling to or from North Korea, in response to the activities of North Korea to develop nuclear weapons in violation of North Korea's international obligations. (b) Prohibition on Availability of Funds for Easing of Sanctions Against North Korea.--None of the funds appropriated under any provision of law may be made available to carry out any sanctions regime against North Korea that is less restrictive than the sanctions regime in effect against North Korea immediately prior to the September 17, 1999, announcement by the President of an easing of sanctions against North Korea. SEC. 8. PURSUIT OF MULTILATERAL MEASURES. The President should take all necessary and appropriate actions to obtain-- (1) international condemnation of North Korea for its pursuit of nuclear weapons and serious breach of the Treaty on the Non-Proliferation of Nuclear Weapons and other international obligations, and (2) multilateral diplomatic and economic sanctions against North Korea that are at least as restrictive as United Nations Security Council Resolution 661 concerning Iraq. SEC. 9. TREATMENT OF REFUGEES FROM NORTH KOREA. (a) Sense of Congress.--It is the sense of Congress that the United States should begin immediately to work with other countries in the region to adopt a policy with respect to refugees from North Korea that would-- (1) guarantee all such refugees safe arrival in a country of first asylum in which the refugees would stay on a temporary basis; and (2) promote burden-sharing of refugee costs between countries by providing for the resettlement of the refugees from the country of first asylum to a third country. (b) Eligibility for Refugee Status.-- (1) In general.--In the case of an alien who is a national of North Korea, the alien may establish, for purposes of admission as a refugee under section 207 of the Immigration and Nationality Act, that the alien has a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion by asserting such a fear and asserting a credible basis for concern about the possibility of such persecution. (2) Not treated as national of south korea.--For purposes of eligibility for refugee status under section 207 of the Immigration and Nationality Act (8 U.S.C. 1157), or for asylum under section 208 of such Act (8 U.S.C. 1158), a national of North Korea shall not be considered a national of the Republic of Korea. (c) Authorization of Appropriations.--There are authorized to be appropriated such sums as may be necessary to carry out this section. SEC. 10. INCREASED BROADCASTING BY RADIO FREE ASIA. (a) In General.--In making grants to Radio Free Asia, the Broadcasting Board of Governors shall ensure that Radio Free Asia increases its broadcasting with respect to North Korea to 24 hours each day. (b) Authorization of Appropriations.--There are authorized to be appropriated such sums as may be necessary to carry out this section. SEC. 11. SENSE OF CONGRESS. It is the sense of Congress that the United States, in conjunction with the Republic of Korea and other allies in the Pacific region, should take measures, including military reinforcements, enhanced defense exercises and other steps as appropriate, to ensure-- (1) the highest possible level of deterrence against the multiple threats that North Korea poses; and (2) the highest level of readiness of United States and allied forces should military action become necessary. SEC. 12. PRESIDENTIAL REPORT. Not later than 180 days after the date of enactment of this Act, the President shall submit a report to Congress regarding his actions to implement the provisions of this Act.

North Korea Democracy Act of 2003 - Expresses the sense of Congress that: (1) the Agreed Framework of October 21, 1994 is, as a result of North Korea's actions, null and void; (2) North Korea's pursuit and development of nuclear weapons represents a serious threat to the security of the United States, its regional allies, and friends, and seriously undermines the security and stability of Northeast Asia; and (3) North Korea must come into compliance with its obligations under the Treaty on the Non-Proliferation of Nuclear Weapons and other commitments to the international community by taking specified actions.Prohibits U.S. assistance to North Korea or the Korean Peninsula Energy Development Organization under the Agreed Framework.Prohibits nuclear cooperation between the United States and North Korea unless: (1) the President determines and reports to specified congressional committees that North Korea is in compliance with its safeguards agreement with the International Atomic Energy Agency (IAEA), has permitted the IAEA full access to all nuclear sites, and has taken steps to implement and fulfill its obligations under the Joint Declaration on Denuclearization; and (2) Congress enacts a joint resolution approving such action.Authorizes the President to impose full economic sanctions against North Korea, or take other appropriate specified actions, in response to activities of North Korea to develop nuclear weapons in violation of its international obligations.Urges the United States to work with other countries in the region to adopt a policy of receiving temporarily refugees from North Korea. Authorizes refugee status to nationals of North Korea for purposes of admission into the United States.Provides for Radio Free Europe to increase broadcasting to North Korea to 24 hours a day.

Asia Argento, a #MeToo activist and one of Harvey Weinstein‘s most high-profile accusers, agreed to pay $380,000 to her own accuser, according to a bombshell report by The New York Times. Citing documents sent to the newspaper anonymously and verified with three people familiar with the case, the report says that in the months after her allegations against Weinstein last October, the 42-year-old Italian actress reached a financial settlement with Jimmy Bennett, who once played Argento’s son in 2004’s The Heart Is Deceitful Above All Things. (Argento also directed and co-wrote the film.) The actor and musician, now 22, claimed that in 2013, then-37-year-old Argento sexually assaulted Bennett in a California hotel room two months after he turned 17, the report says. (In California, 18 is the age of consent.) Bennett claimed in the documents that Argento kissed him before performing oral sex on him and engaging in intercourse at the Ritz-Carlton in Marina del Rey, California, according to the Times. An agent for Argento did not immediately respond to PEOPLE’s request for comment, and the Times says Argento and her reps did not respond to multiple requests leading up to the story’s publication on Sunday. Reps for Bennett did not respond to PEOPLE’s request for comment. Though he declined an interview with the Times, the outlet reports that Gordon K. Sattro, Bennett’s attorney, told the newspaper, “In the coming days Jimmy will continue doing what he has been doing over the past months and years, focusing on his music.” Vincenzo Lombardo/Getty Argento’s late boyfriend, Anthony Bourdain — who died of suicide on June 8 — “helped Ms. Argento navigate the matter,” the Times reports, though additional details about his involvement were not available. As part of the settlement, Bennett forfeited the copyright to a selfie from May 9, 2013 — which was among the documents the Times says it received — of Bennett and Argento lying in bed, according to the Times. Bennett’s notice of intent to sue — sent in November to Richard Hofstetter, a lawyer for both Argento and Bourdain — asked Argento for $3.5 million in damages for the intentional infliction of emotional distress, lost wages, assault, and battery, according to the Times. Sattro wrote in the notice of intent that Bennett’s “feelings about that day were brought to the forefront recently when Ms. Argento took the spotlight as one of the many victims of Harvey Weinstein,” the Times reports. In April, Argento’s attorney lawyer Carrie Goldberg reportedly wrote Argento about the agreement and payment plan in an email obtained by the Times, describing the money as “helping Mr. Bennett.” “We hope nothing like this ever happens to you again,” Goldberg wrote, according to the Times. “You are a powerful and inspiring creator and it is a miserable condition of life that you live among s—ty individuals who’ve preyed on both your strengths and your weaknesses.” RELATED VIDEO: Asia Argento Tells Uma Thurman ‘We Need’ Your Voice After Her Response to Weinstein Goes Viral Argento is one of the over 60 women who have accused disgraced movie mogul Weinstein of sexual assault, harassment, and rape. In October, she alleged in a New Yorker piece by Ronan Farrow that Weinstein forced oral sex on her in 1997. “I was not willing,” she told Farrow of Weinstein. “I said, ‘No, no, no.’ … It’s twisted. A big fat man wanting to eat you. It’s a scary fairy tale.” Argento also told Farrow that she had “consensual sexual relations with [Weinstein] multiple times over the course of the next five years” after the alleged assault. She described the incidents as “one-sided and ‘onanistic,’” Farrow wrote, and worried Weinstein would “ruin her career if she didn’t comply.” A spokesperson for Weinstein previously told PEOPLE in a statement that “any allegations of non-consensual sex are unequivocally denied by Mr. Weinstein. Mr. Weinstein has further confirmed that there were never any acts of retaliation against any women for refusing his advances.” RELATED: Anthony Bourdain Was Fierce #MeToo Supporter After Asia Argento Accused Harvey Weinstein of Rape Anthony Bourdain and Asia Argento in 2017 Invision/AP/REX/Shutterstock After the New Yorker story was published in October, Bourdain tweeted to his girlfriend, “I am proud and honored to know you. You just did the hardest thing in the world.” .@AsiaArgento I am proud and honored to know you. You just did the hardest thing in the world. https://t.co/i2Lsb6h5vU — Anthony Bourdain (@Bourdain) October 10, 2017 “In 1997, I was raped by Harvey Weinstein here at Cannes,” Argento said at the Cannes Film Festival’s Closing Ceremony earlier this year. “I was 21 years old. This festival was his hunting ground.” She later added: “Even tonight sitting among you there are those who still have to be held accountable for their conduct against women, for behavior that does not belong in this industry, does not belong in any industry or workplace. You know who you are, but most importantly, we know who you are and we’re not going to allow you to get away with it any longer.” ||||| The fallout from “a sexual battery” was so traumatic that it hindered Mr. Bennett’s work and income and threatened his mental health, according to a notice of intent to sue that his lawyer sent in November to Richard Hofstetter, Mr. Bourdain’s longtime lawyer, who was also representing Ms. Argento at the time. Ms. Argento, who lives in Rome, subsequently turned to Ms. Goldberg — a prominent lawyer for victims of online attacks — to handle the case. (Mr. Hofstetter is now handling the estate of Mr. Bourdain, who killed himself in June. Although Mr. Bourdain helped Ms. Argento navigate the matter, neither Mr. Hofstetter nor Kimberly Witherspoon, Mr. Bourdain’s longtime agent and now a spokeswoman for his wife, Ottavia Busia, from whom he was separated, would comment for this article.) Mr. Bennett’s notice of intent asked for $3.5 million in damages for the intentional infliction of emotional distress, lost wages, assault and battery. Mr. Bennett made more than $2.7 million in the five years before the 2013 meeting with Ms. Argento, but his income has since dropped to an average of $60,000 a year, which he attributes to the trauma that followed the sexual encounter with Ms. Argento, his lawyer wrote. In October, a month before Mr. Bennett sent his demand for money, The New Yorker published an article by Ronan Farrow that included Ms. Argento among 13 women who accused Mr. Weinstein of harassment and rape. Ms. Argento, whose father, Dario Argento, is a noted director of Italian horror films, began her acting career as a child. She went on to win two David di Donatello Awards, the Italian equivalent of Oscars, and has directed films, written a novel and recorded music. After she spoke out about Mr. Weinstein, Ms. Argento quickly emerged as a powerful voice for women who have been mistreated by men. In May, she gave a riveting speech at the Cannes Film Festival in which she called the festival Mr. Weinstein’s “hunting ground.” She said he had raped her there in 1997, when she was 21. The relationship with Mr. Weinstein continued for years afterward and sometimes included sex, The New Yorker reported. Ms. Argento, who had acted in a movie Mr. Weinstein produced, told the magazine that she feared angering him. It was a complicated situation in which she said she felt powerless. “After the rape, he won,” she told Mr. Farrow.

– One of Harvey Weinstein's most prominent accusers settled a sexual assault claim from her own accuser last year, according to legal documents. Months after she came forward with her allegations against Weinstein last year, Asia Argento paid $380,000 to Jimmy Bennett, who played her son in the 2004 movie The Heart is Deceitful Above All Things, according to documents provided to the New York Times. He alleged that he had a sexual encounter with Argento in a California hotel room in 2013, when she was 37 and he was 17, below the state's age of consent. In November last year, he sent a notice of intent to sue for $3.5 million for emotional distress and lost wages. The legal documents provided to the Times include a selfie of Argento and Bennett in bed. The legal notice states that the encounter left Bennett “extremely confused, mortified, and disgusted” and his income dried up in the following years. In a letter to Argento, her lawyer, Carrie Goldberg, described the settlement as "helping Mr. Bennett." "We hope nothing like this ever happens to you again," Goldberg wrote. "You are a powerful and inspiring creator and it is a miserable condition of life that you live among s****y individuals who’ve preyed on both your strengths and your weaknesses." Bennett's rep says he is now focusing on his music career, People reports. (Argento faced online harassment after the suicide of boyfriend Anthony Bourdain in June.)

A massive wave of desperate Syrian refugees could create a new market in Lebanon for the illegal human organ trade On a recent night in south Beirut, a group of young men sat exchanging bits of neighborhood gossip in a tiny café. Slumped into a corner, and wearing a ball cap pulled down low, one of them slowly nodded along in obvious physical pain. Like a growing number of Syrian refugees here desperate for cash, he had just sold one of his kidneys on the black market. “I was in need of money,” says Mohammed, a scrawny 21-year-old now living in Lebanon. “I had to leave Deir Ezzour [in eastern Syria] a year and a half ago because the war got so bad.” Tweet at us: Should people be allowed to sell their organs? NOW READ THIS While no reliable numbers exist, Lebanon’s piece of the global illicit organ trade—which the World Health Organization estimates to be 10,000 transplants per year—is relatively small. But the combination of Lebanon’s close proximity to buyers in the oil-rich Gulf states, the country’s lax law enforcement and a massive wave of desperate Syrians could turn it into the go-to country in the region for buying illegal human organs. Like many Syrian refugees, Mohammed struggled to find work in Lebanon. The influx of more than 800,000 refugees to a country of fewer than 5 million has flooded the labor market. However, a suggestion from Mohammed’s cousin last fall would change his fortunes. “When I first arrived in Lebanon I sold vegetables on the street, but the money was not enough to survive,” Mohammed says, short of breath and wincing with nearly every word. “If I was lucky, I would make $70 a week. Then my cousin told me that he sold his kidney for $5,000, so I asked him to introduce me to these people.” NOW READ THIS The man he was introduced to goes by the nickname Abu Jamil—a burly, middle-aged Lebanese hustler who seems to have his hand in just about every illicit activity in south Beirut. He is a loan shark who also sells cocaine, hashish and, more recently, human kidneys. “When Mohammed came to me last month, I told him, ‘I’ll give you $5,000 for one of your kidneys.’ I get $7,000 from the buyer for each one and keep $2,000 for myself,” he says. He fits the profile of what the U.N. calls a “kidney hunter.” Abu Jamil’s business all comes in by word of mouth, mostly from satisfied customers, he claims. He reiterates several times that he’ll only deal with willing clients, and that all of the kidneys he has sold came from healthy young men, like Mohammed. Word has slowly trickled through the Syrian refugee community in Beirut, enough for Abu Jamil to personally broker the sale of “more than 30, maybe 35″ kidneys to buyers mostly from wealthy Gulf Arab countries. NOW READ THIS “My part of this business is finding sellers,” he says. “Arranging the buyers is up to the big guys.” Abu Jamil claims to not know exactly who the ringleaders of his human organ trafficking operation are. All initial transactions are conducted through a network of middlemen like himself. He describes the local kidney business as “steady.” “There are a lot of powerful, well-connected men involved in this business,” he adds. “It’s similar to the drug trade. We use very similar networks.” But unlike the drug networks that send millions of amphetamine pills to the Gulf each year from Lebanon, the organ buyers usually travel here for the operation, according to Abu Jamil. It’s much easier for someone to fly a few hours and have an operation than it is to smuggle a kidney overseas. Once Mohammed decided to sell his kidney, the process moved quickly. He was blindfolded and driven by two of Abu Jamil’s men to a small, makeshift clinic somewhere in Lebanon. “The doctors treated me very well,” he says. “When I arrived for the surgery, they asked me, ‘Are you feeling well? Are these men forcing you to do this?’ I told them that this was my decision and then the surgery went ahead.” NOW READ THIS The clinics are all staffed by “certified and well-respected doctors,” Abu Jamil says, adding that they are Lebanese, Palestinian and Syrian professionals who also work full-time jobs in hospitals across Lebanon. Several Lebanese health professionals contacted declined to comment on the illicit organ trade here. According to a 2009 World Health Organization report, poverty is the motivating factor for people around the world who sell their kidneys. The report adds that “lasting economic benefit after donation is limited or even negative because of the limited employability of such patients and the perceived deterioration of their health.” And while the number of kidneys sold here by Abu Jamil are not huge, he knows of several competing operations in the country that provide the same services to international and Lebanese clients. He estimates that no more than 200 Syrian refugees have sold their kidneys in Lebanon over the three years since the uprising-turned-civil war started forcing them to flee. But business has picked up in recent months. NOW READ THIS Though his operation was nearly two weeks ago, Mohammed walks carefully and frequently stops to catch his breath. He spends most of his days sitting around with friends, waiting for the pain to subside. “Sometimes I regret selling my kidney, but I had no choice. Now my life is better,” he says. “I put all of the money into a bank account and when I return to Syria someday I plan to open a small business.” For now, he’s spending some of that money to support his mother and siblings, who have also fled the war to Lebanon. A Syrian friend of Mohammed’s used most of the money he got from selling a kidney last year to open a small mobile phone shop in a neighborhood nearby, and to rent an apartment for his family. When Abu Jamil first met him, the young man had just arrived from Syria and was sleeping under a bridge near the Beirut airport. The Syrian conflict has been good to men like Abu Jamil, and he sees nothing wrong with that. “Without me, perhaps these poor people would starve. As long as I make a profit, and the Syrians are making money, too, what’s wrong with it?” he asks. “We’re all happy with this arrangement.” ||||| The young man, who called himself Raïd, wasn't doing well. He climbed into the backseat of the car, in pain, careful not to touch any corners. He was exhausted and dizzy. A large bandage looped around his stomach, caked with blood. Despite that, the 19-year-old Syrian wanted to tell his story. Seven months ago, he fled the embattled city of Aleppo, in Syria, to Lebanon with his parents and six siblings. The family quickly ran out of money in the capital, Beirut. Raïd heard from a relative that the solution could be to sell one of his kidneys, and then he spoke to a bull-necked man, now sitting in the passenger seat, smoking and drinking a beer. His acquaintances call the man Abu Hussein. He said he's employed by a gang that works in the human organ trade - specializing in kidneys. The group's business is booming. About one million Syrians have fled into Lebanon because of the civil war in their home country and now many don't know how they can make a living. In their distress, they sell their organs. It's a dangerous and, of course, illegal business. That's why the gang has its operations performed in shady underground clinics. Abu Hussein's boss is known in the poor areas of Beirut as "Big Man." Fifteen months ago, Big Man gave the 26-year-old a new assignment: find organ donors. The influx of Syrian refugees from the war, Abu Hussein's boss argued, made it more likely people would be willing to sell organs. 'More Sellers Than Buyers' Lebanon has a tradition of illegal organ trading. The country has immensely rich people and a huge number of people living in poverty. And organ traffickers don't need to worry about government controls. Those are exactly the ideal conditions for organ trafficking, said Luc Noel, transplant expert at the World Health Organization in Geneva. Every year, tens of thousands of rich Arabs from around the region come to Beirut for treatment in the country's excellent hospitals. The authorities don't pay attention whether a patient flies home with a new nose -- or with a new kidney. Previously, it was mostly destitute Palestinians who sold their organs. Then came the war in Syria, and then the refugees. Now the groups are in competition and the prices are falling. "When it comes to kidneys, we now have far more sellers than buyers," said Abu Hussein. He added that four of the Big Man's other recruiters have brokered the sales of 150 kidneys in the past 12 months. According to Abu Hussein, other gangs are doing similarly well. Experts estimate that 5,000 to 10,000 kidneys are illegally transplanted per year worldwide. "Many of our products go abroad to, for example, the Persian Gulf," said Abu Hussein. But Big Man also has customers in the US and Europe, he said. Enough to Survive On Until Spring Raïd had no trouble selling his left kidney because he was fit and didn't smoke. He played for the Syrian national youth soccer team. During the examinations doctors told him lies evidently meant to calm him down. With a little luck, the kidney would grow back, he was told, and there wouldn't be any after-effects. In truth, live donors need to undergo check-ups for years after the operation, and people like Raïd can't afford that kind of treatment. He got $7,000 (€5,200) for his kidney. "While I drove Raïd and his mother to the clinic, a colleague of mine was shopping with the father," says Abu Hussein. The family lacked everything: Raïd's father bought mattresses and winter clothing, a fridge and an oven, and took it all to the one room the family of eight lives in today. They have enough left over to get through the winter. And then? "I don't know," says Raïd. Abu Hussein says everyone benefits from the organ trade. The Syrians get money and the sick -- who pay up to $15,000 for a new kidney -- get a new life. He himself wins too, he added. He gets $600 to $700 commission for every sale he arranges. That's as much as a Lebanese teacher earns in a month. 'I Don't Care If You Die' Abu Hussein said that in the last few months he has driven 15 or 16 kidney donors - all of them Syrians aged between 14 and 30 - to the secret clinic masquerading as a residential building. The clinic has the most modern medical equipment and doesn't want to limit itself to kidneys. "I'm currently looking for someone who has an eye for sale." Later that evening it became evident not everyone benefits from this trade. Raïd, sitting in the back of the car, was feeling unwell. His kidney had been cut out from the front, seven days ago. "I need the drugs. You said you would get me the drugs," he said to Abu Hussein who just minutes earlier had been bragging how well his organization took care of the Syrians. But when Raïd asks for painkillers, Abu Hussein shouts at him: "Shut up. I don't care if you die. You're finished anyway."

– This is the plight of refugees streaming out of Syria: One of the hottest markets in neighboring Lebanon is the black-market sale of their human organs, reports Vocative. Given that it is, in fact, a black market, it's hard to pin down numbers. But Lebanon's look-the-other-way attitude, its convenience for rich patients from Gulf states, and the hundreds of thousands of Syrians pouring over the border are combining to turn Lebanon into what Vocative calls the "go-to country in the region" for kidneys and other organs. The story includes an interview not only with a young man who recently sold his kidney for $5,000 but the "kidney hunter" who arranged the sale for his own $2,000 payday. That broker alone has arranged about 35 such operations—they take place at a secret clinic that sounds reasonably well-run, given the circumstances—and he says he has plenty of competition. A previous story by Der Spiegel also reported on the thriving market, and it included this unfortunate line from a different organ broker: "I'm currently looking for someone who has an eye for sale." (Click to read about how war crimes prosecutors say Bashar al-Assad is systematically torturing and killing prisoners back home.)

City employees among emails listed in Ashley Madison hack The 20 cities with the most Ashley Madison accounts A Reddit user sorted out the data leak from infamous dating website Ashley Madison to find out which cities have the most accounts. However, every account doesn't necessarily correlate with a real cheater. Ashley Madison, even in its terms of service, admits that it makes fantasy accounts for "entertainment." Those accounts serve as a way to entice people to join the site, according to a lawsuit Source: Reddit less The 20 cities with the most Ashley Madison accounts A Reddit user sorted out the data leak from infamous dating website Ashley Madison to find out which cities have the most accounts. However, every account ... more Photo: Leo Correa, Associated Press Photo: Leo Correa, Associated Press Image 1 of / 25 Caption Close City employees among emails listed in Ashley Madison hack 1 / 25 Back to Gallery Three city of San Antonio email addresses are among the 36 million accounts leaked by a hacker group that targeted an extramarital-affair website. The city email addresses, all ending in @sanantonio.gov, were used to create accounts on Ashley Madison, a matchmaking website for cheating spouses that reportedly has 37 million users. Two accounts belong to a San Antonio Police Department detective and a captain. The third belonged to a former city employee. Because the site doesn’t require users to validate their email addresses, it’s difficult to determine whether the employees were the ones who created profiles on the dating website. A separate website that targets law-enforcement indescretions posted on Thursday thousands of government email addresses apparently pulled from raw data that could only be found on the so-called “dark web” — a far reach of the Internet that most computer users can’t access. That site included the three San Antonio addresses. In a statement released Friday, city officials stressed that because Ashley Madison doesn’t have a verification process to validate email addresses, the city “cannot confirm whether these addresses were legitimately used to access the site.” “The City does use Internet filters to block access to various websites,” the statement continued, “including the Ashley Madison site, which has been blocked for some time from City employees.” Similar to other municipalities, government agencies and academic institutions, various websites that have nothing to do with an employee’s work, such as Facebook, are routinely blocked. And so it ‘s unlikely that the city employees used their work computers to create or use the Ashley Madison accounts. City officials wouldn’t say Friday whether the San Antonio employees were told that their email addresses had appeared in the Ashley Madison leak. One of the employees committed suicide Thursday, though it wasn’t clear Friday whether his death had anything to do with the leak. Other addresses found in the leak include six from Houston and Fort Worth municipal email accounts. The hacking of the Ashley Madison site has been in the news for weeks. The hackers, who identify themselves as “The Impact Team” threatened to post the data if the parent company of Ashley Madison, Tornoto-based Avid Life Media Inc., didn’t close the site altogether. The company refused and the hackers later posted the data on the dark web — a place on the Internet that casual users can’t access. Websites quickly were created to allow average computer users to check whether specific email addresses were included in the leak. Thousands of other Ashley Madison-linked accounts were created using government email addresses — from the FBI and various police departments to governments from countless foreign countries. [email protected] Twitter: @jbaugh ||||| When hackers made public more than 30 million user profiles stolen from the adultery website Ashley Madison last week, they had words of advice for clients of the Toronto company. Take Ashley Madison to court, said a note accompanying the leak. “Then move on with your life. Learn your lesson and make amends. Embarrassing now, but you’ll get over it.” Two unconfirmed suicides related to Ashley Madison hack: Police (CP Video) Moving on hasn’t been easy, however. The massive privacy breach has triggered much hand-wringing, two possible suicides, online scams and extortion threats. “This ain’t a funny game any more,” Toronto police acting staff superintendent Bryce Evans told reporters Monday. He said the company is offering a $500,000 reward for information leading to the prosecution of the hackers. The Office of the Privacy Commissioner of Canada and its Australian counterparts are also investigating the incident. People fearful of being exposed as adulterers were reflected in the hundreds of queries received every day by Troy Hunt, an Australian web security developer who set up a website to let Ashley Madison clients check if they had been identified. In an interview from Sydney, Mr. Hunt said he had received 60 new queries in the morning, personal e-mails laced with stress and embarrassment. “I’m just a guy here with a wife that I really do love, I regret what I did, and I have two beautiful kids that will get sucked into this, too. It’s just horrible,” said one e-mail. Criminals are already trying to prey on users. Staff Supt. Evans said there are now websites that purport to verify if someone’s data has been leaked but are spreading computer malware. Toronto police are also investigating blackmail threats. One redacted extortive e-mail released by police sought a payment in bitcoin equivalent to $300, threatening otherwise to share “this dirt with all your known friends and family (and perhaps even your employers too?).” Staff Supt. Evans said there was no point paying since, following the breach, “nobody is going to be able to erase that information.” The leak will have long-term social and economic impact, he said. “We’re talking about families. We’re talking about their children. We’re talking about their wives. We’re talking about their male partners … We now have hate crimes that are results from this.” He did not elaborate. A spokesman for the force, Mark Pugash, would not give more details but said a range of charges could be filed as a result of the investigation, from extortion to fraudulent use of computers. Staff Supt. Evans also said there were two unconfirmed suicides but would not say where they took place. On his blog, Mr. Hunt said inquiries he received came from people with limited technical insight, many of whom couldn’t even remember if they had visited the site or might have used a different e-mail address. Others, in a panic, deleted the e-mail account they used to open their Ashley Madison profile and now couldn’t use it to verify if they had been exposed. Another problem were websites that allowed anyone to search the leaked data for anyone else’s name or e-mail. One woman told Mr. Hunt she learned her husband’s work e-mail was on the list – through a phone call from her church leaders. Others said they were caught in the mess only after they subscribed to Ashley Madison to check if their spouses were cheating. Police said the problem started on July 12, when staffers at Ashley Madison’s Toronto-based parent company, Avid Life Media, arrived at work, powered their computers and were greeted with heavy-metal music and a threatening message from hackers who call themselves the Impact Team. The message asked Avid Life Media to shut down two of its dating websites, AshleyMadison.com and EstablishedMen.com, which caters to women trying to hook up with wealthy men. A week later, the hackers confirmed the breach by releasing the data of two clients, one in Mississauga, Ont., and one in Massachusetts. Report Typo/Error ||||| The cheating website Ashley Madison was hacked on Tuesday, exposing millions of people who were supposedly engaging in extramarital affairs. A group that calls themselves “The Impact Team” breached the data and dumped some 32 million email addresses onto part of the Dark Web accessible only through the Tor browser. Many security researchers have confirmed the data is legitimate, and a handful of websites created searchable databases with the leaked information, allowing you to easily type in an email to determine whether it’s part of the breach. These tools haven’t been tested for accuracy and it’s unknown whether they’re recording search attempts so use them with caution. A few of the more popular searchable databases available online include Trustify, have i been pwned? and cynic.al. One of the first sites to pop up, SearchAshleyMadison.com, was already been removed today after Ashley Madison’s legal team filed a copyright claim. Microsoft-accredited security expert Troy Hunt created a tool that allows you to receive a notification if your email is included in the leak but has chosen to not make a searchable database available. “Even though there are now multiple sites making it easy for anyone to check any email address,” Hunt writes, “as someone very aptly said yesterday ‘you don’t want to be that guy’ – the one who could be the channel through which information is learned that has a serious adverse impact on peoples’ lives.” Ashley Madison touts itself as the world’s leading married dating service for discreet encounters. The site made it easy for users to sign up with fake names and email addresses by not verifying email accounts. Even if your searches indicate an email address was part of the leak, it’s uncertain whether the person associated with that account was using Ashley Madison. ||||| Toronto police say the hacking of cheating website Ashley Madison is affecting families around the world, with two unconfirmed reports of suicides related to the hack. Hackers released customers' data last week. ( ) The dire consequences for victims of the massive cyber attack on Toronto-based infidelity website Ashley Madison include hate crimes, extortion attempts and possibly suicide. “This is not fun and games,” Toronto police Staff Supt. Bryce Evans said Monday at a news conference about last week’s data dump by the hacker group calling itself the Impact Team. The initial release of personal information of the site’s more than 30 million users has resulted in a multitude of “spinoff” crimes, Evans said. The sophisticated hack has sparked online hate crimes, online scams and may be related to two unconfirmed reports of suicide, Evans said. “The ripple effect of the Impact Team’s actions has and will continue to have long-term social and economic impacts and they have already sparked spinoffs of crimes and further victimization.” Article Continued Below Police would not elaborate on the nature of the hate crimes or possible suicides. Toronto Police said they could not confirm published reports in U.S. media that a police captain in San Antonio, Texas killed himself after the leak linked his official email address to an Ashley Madison account. People leave the office tower where Avid Life Media, the parent company of hacked adultery website Ashley Madison, has office space in Toronto on Friday. ( Nathan Denette / THE CANADIAN PRESS ) Some of those listed as customers are now being threatened with exposure unless payment is received, Evans said. Hackers are also sending virus-infected links claiming to access the leaked information. Another online scam tells people that their names can be removed from the list for a fee, which is impossible, Evans said. The website’s Toronto-based parent company, Avid Life Media, is offering a $500,000 reward for information leading to the arrest of those responsible for the cyber attack. Avid Life issued a statement Monday saying it is confident that investigators will solve the “unprecedented crime,” but added it is offering payment because more outside help is needed. “In the very best interest of our customers, who have been affected by this malicious act, we are firmly committed to fully assisting these law enforcement and investigative authorities, without reserve,” it said. Evans also reached out to the hacking community to “do the right thing,” and pass along any information they have about the breach. “The Impact Team has gone over the line and I’m just asking them to use their moral judgment and their values to help us if they can through their ways on the deep dark web.” Police were tight-lipped on the extent of their knowledge of how the hack happened. However, they did say employees who logged into their computers on July 12 were greeted with a threatening message, while AC/DC’s “Thunderstruck” played. The message ordered Avid Life to “immediately and permanently” shut down Ashley Madison and sister site Established Men, which the hackers called a “prostitution/human trafficking website.” The message said the hackers had taken over Ashley Madison’s office and thousands of systems over the past few years and had access to customer profiles, nude pictures, conversations, addresses and credit card information. The company did not comply with the hackers’ ultimatum to take down the sites and Impact Team made good on its threat. The group has also released internal company emails and on Monday cyber security blog Krebs on Security claims it discovered that the company’s leadership had hacked into rival dating site, nerve.com, in 2012. The company declined comment beyond its statement. Toronto police, who are working in conjunction with other law enforcement teams, including the FBI, provided a list of seven Criminal Code offences the hackers could face. Canada’s privacy commissioner’s office said Monday it is also launching an investigation into the security breach. Speaking to the Impact Team, Evans said “this is your wake-up call,” adding law enforcement have good leads and the investigation is “progressing in a positive fashion.”

– The Ashley Madison leak is kinda funny, right? Well it's now led to extortion threats, online scams, and possible suicides. "This ain’t a funny game anymore," says Toronto police officer Bryce Evans, per the Globe & Mail. The release of some 33 million users' data from the dating affair website has led to two unconfirmed suicides, police say, and may have caused a police captain in San Antonio, Texas, to take his own life, the Toronto Star reports. "The victimization is around the world," says Evans. "We’re talking about families, we’re talking about their children, we’re talking about wives, about their male partners." The Texas police captain, 25-year veteran Michael Gorhum, killed himself last week after his name appeared in the leak, the New York Daily News reports. San Antonio police haven't commented, but the San Antonio Express-News reports that three city employees—including a police captain and a detective—were on the list of leaked names. In recapping events, Toronto police say the hacker group Impact Team contacted Ashley Madison parent company Avid Life last month, demanding that the website be shut down; the message came with the AC/DC song, "Thunderstruck." Avid Life refused to shut it down, and now offers a $500,000 reward in the case. Meanwhile, police are warning people to avoid fake websites that claim to list the victims but actually take your money or spread malware. The San Francisco Chronicle offers a tool to check email addresses on the list, but warns that "it’s uncertain whether the person associated with that account was using Ashley Madison."

Early in the morning on November 27, 2009, Tiger Woods allegedly had an altercation with his wife, Elin Nordegren, that culminated in a career-derailing car crash outside the couple’s Florida home. Details of what transpired are vague—the principals aren’t talking, and no cameras were present. Millions of people who followed the breaking story on CNN, Fox, ESPN, and TMZ had to satisfy themselves with watching file footage of the golfer and his wife. The incident captured the world’s attention, but no one could actually see it—until an animated reenactment was uploaded to the Web site of an Asian tabloid just hours after it happened. The 96-second videoclip featured Sims-like doppelgängers of the couple and depicted the moments that everyone was clamoring to see: the vehicle colliding with a tree, an unconscious Woods lying in the street as the police arrived, even Nordegren chasing her husband’s SUV down the driveway with a golf club. Most of Next Media Animation’s videos are about scandals and crimes in Hong Kong and Taiwan. But some of their more ambitious (and surreal) animations are about public figures from America. Here’s a sampling from their videos about Tiger Woods, Steve Jobs, Al Gore, and Sarah Palin. Someone reposted the clip to YouTube, and the crude, somewhat surreal animation quickly scored 2.5 million views. It was picked up and replayed by many Western news organizations and generated an enormous amount of attention, amusement, and controversy. Mission accomplished for the man behind the video, Hong Kong tabloid tycoon Jimmy Lai. He had launched the CG production house Next Media Animation just a month earlier with the goal of animating the news of the day. “There’s no better sensation than image. It’s so in-your-face!” the 62-year-old founder of Next Media says. Lai is sitting in the fourth-story office of his headquarters in Taipei, the capital of Taiwan, which is the latest outpost of the Next Media empire. He wears a custom-tailored white shirt and a pair of suspenders that hold baggy Ralph Lauren jeans up over his potbelly, giving him a grandfatherly air. But Lai’s beefy face is hard, his eyes fiercely alert. He has the appearance of a man who is always ready to throw the first punch—or the last. Lai made hundreds of millions of dollars giving Hong Kong readers everything that the more respectable publications wouldn’t deign to present: lurid crime stories, salacious celebrity gossip, voyeuristic paparazzi photos, and scathing political commentary. But by 2007, he was becoming increasingly worried about the future of print, especially its ability to reach a younger audience that grew up with digital media. It also bothered him that his photographers could cover some stories only after the fact. “We had the dead body,” he says, “but we never see the murders.” Was there a way to show things that none of his competitors could? The idea of cartoonifying the news hit Lai in a brilliant flash. In October 2007, he shared his idea with the rest of his staff. They could gin up exclusive footage of the most bizarre, the most titillating, the most scandalous events of the day. But Lai didn’t want just any animation, he wanted computer-generated 3-D animation, which is notoriously costly, labor-intensive, and extremely time-consuming to create. And they didn’t have a lot of time; the videos had to air while the news was still warm. Lai needed to be able to crank out reenactments of breaking stories in just a couple of hours. “Everybody told me it would be impossible,” he says. So he decided to build his own CG studio. Lai didn’t know much about animation, but he knew a lot about assembly lines—he made his first fortune in the garment industry. After two years of trial and error, experimenting with various technologies and seeing exactly how many corners it was possible to cut, Lai set up a sort of un-Pixar, an offshore animation factory with a staff of 200 that could storyboard, model, motion-capture, and animate a clip in about the time it takes to watch Toy Story 3 . “People said I was nuts to try this,” Lai says, leaning intently over a conference table. “But everybody knows I’m crazy. I never do things the normal way.” It’s been a blisteringly hot day here in Taipei, but it’s starting to cool off as the workers at Next Media Animation arrive for the 5 pm to 1 am shift in a neighboring building. Before they punch out, they will create more than a dozen CG shorts in the signature style of their infamous Tiger Woods video. The clips will be posted to the Web sites of Lai’s tabloids in Hong Kong and Taiwan, where they typically rack up about 15 million views a week. That’s a large audience, but it’s not nearly enough to cover the costs of such an ambitious operation. Lai is still searching for a better outlet for this new form he’s created and is casting about for a viable business model. He’s convinced that what Next Media is doing is the future of journalism, and he insists that once you’ve seen his cartoons, you’ll never be satisfied watching a newsreader tell you what happened. “This is like watching a videogame, but it’s the news!” 8:50 pm, May 17, 2010 Story Assignment Chen Hsi-Ling, a content officer at Next Media Animation, logs on to Adobe Connect to get her next assignment. It’s about an ongoing murder trial in Hong Kong: A young man named Hong Chi-yin is facing a life sentence for two homicides. In January 2009, he hired a prostitute, then suffocated her with a chloroform-soaked towel. A few weeks later, he did the same thing to another prostitute. Chen is in charge of drawing the storyboards that will guide the production of an animated re-creation of the Chloroform Killer’s crimes. A project manager from the Apple Daily newspaper in Hong Kong calls and fills her in on the details. As in many outsourcing operations, there’s a language barrier to contend with—people in Hong Kong speak Cantonese, while Mandarin is the language of Taiwan. But the written language is the same, and Chen will work primarily from a 400-word summary of the Hong Kong news article. All Next Media animations begin life this way, as a brief synopsis that boils a tabloid story down to its pulpy essence. “The idea is to keep it simple, use the most important details,” says international news editor Daisy Li. “Jimmy doesn’t want it to be too long.” Lai was born poor in mainland China in 1948, during the civil war that eventually saw the Communist Party take power and the Nationalist Party flee to Taiwan. Smuggled into Hong Kong by his mother’s arrangement when he was 12, Lai eventually got rich manufacturing apparel at the same factory where he had toiled as a child for $10 a month. Lai courted controversy, launching a magazine called Next , which criticized the Beijing government, and producing a line of T-shirts that featured the student leaders of the Tiananmen Square protests. It quickly became impossible for him to sell merchandise on the mainland or deal with factories there. Ultimately, the Chinese government forced Lai to divest himself of his garment business. That left him free to focus all his energy on becoming the Rupert Murdoch of Hong Kong. Lai soon built a stable of the raciest, muckrakingest, most popular publications in the area. He expanded his operations to Taiwan a decade ago and now has a top-selling newspaper there. Stories like the one about the Chloroform Killer are typical fodder for Lai’s tabloids. “Seedy crimes with lots of action are very popular for us,” he says. A devout Christian, he named his Apple Daily newspaper after the forbidden fruit in Genesis; Lai reasons that if Adam and Eve had not eaten from the tree of knowledge and introduced sin into the world, there wouldn’t be anything interesting for his writers to cover. Lai has continued to provoke outrage as his media empire has grown. No mainland Chinese companies advertise in his papers. Someone threw a bomb onto his front lawn. And he earned the ire of millions of teenage fans of Cantonese pop star Gillian Chung—and a censure from the Hong Kong Journalists Association—when one of his tabloids ran photos of the singer taken by a hidden camera in her dressing room. Just two years ago, someone offered a bounty for killing Lai. “It was a triad guy looking to do Beijing a favor, a favor that Beijing didn’t actually want,” says Mark Simon, Next Media Animation’s commercial director. When Lai decided to create NMA, it seemed natural to build the studio in Taiwan. Unlike Hong Kong, the island nation is beyond the reach of Beijing. Labor is also cheaper there, and the rise of the videogame industry in China had put many CG experts on the island out of work. “Our animators in Taiwan make $20,000 a year,” Simon says. Within nine months of ramping up its CG assembly line, NMA created more than 4,000 videos. Employees have completely internalized their boss’s love of sensationalism. “I’ve told them that they go too far sometimes,” Lai says, referring to clips depicting rape and child abuse. (The latter resulted in a $30,000 fine and a rebuke from Taiwan’s National Communications Commission.) But Lai waves his hand as if to dismiss all the criticism. He gazes through the glass wall of his office, taking in a sea of people hard at work. “When you are an Apple newsman, you know that you need to be on the edge and make a splash,” he says. “Readers want things to be less subtle. You need to overstep.” All the News That’s Fit to Animate The team at Next Media Animation cranks out about 20 short clips a day, most involving crimes and scandals in Hong Kong and Taiwan. But a few are focused on tabloid staples in the US—from Tiger Woods’ marital troubles to Michael Jackson’s death. Seeing them filtered through the Next Media lens is as disorienting as it is entertaining. 9:00 pm Storyboards and Presentation Dinner from a nearby takeout joint has arrived at the Next Media office. As people tuck into fried noodles and tofu soup, Chen and a second content officer assigned to sketch the story of the Chloroform Killer get to work. They have 10 minutes to transform the synopsis into comic-book-style storyboards, and they scribble madly. A half-dozen additional artists in adjoining cubicles are frantically converting other synopses into storyboards. “Four minutes to go!” one of them shouts. When Chen is done, she meets with a team of animators, modelers, and mo-cap directors in a windowless conference room. They view her storyboards on a digital projector as Chen pantomimes key bits of action, like the killer reaching for a bottle of chloroform. Her audience takes notes furiously. Then they scatter to start producing the actual animation. It takes pixar up to seven hours to render a single frame of footage—that is, to convert the computer data into video. NMA needed to create an animated clip in a third of that time and render more than a thousand frames of animation in just a few minutes. A team spent two years wrestling with the problem, experimenting with one digital tool after another—Poser, 3ds Max, Maya. “It didn’t look good, and it took too long,” says Eric Ryder, a Next art director. “But Jimmy doesn’t want excuses.” The solution came in the form of Wang Chuan-chang, a slight and unassuming game-industry refugee who also teaches game programming at National Taiwan University. He developed a proprietary engine that could render crude but effective animation in seconds. Wang’s technology convinced Lai that the project was ready to staff up. That left Next Media free to grapple with insurmountable problem number two: creating a production process that could function at unprecedented speed, delivering up to 13 minutes of animated video content a day. The team eventually devised a seamless workflow with no unproductive moments and no second drafts. “Everything has to be done within the given time frame,” Ryder says. “Or else the next person in line has no work to do. There are no mistakes. This is what Jimmy commands.” Lai can be an exacting boss, but he’ll gladly sink a fortune into a business if he believes in it. For instance, Wang wanted the characters to have more realistic facial expressions, which, as anyone who’s seen Next Media’s dramatization of the Jay Leno-Conan O’Brien feud knows, is much needed. In response, Lai dropped almost a million dollars for Light Stage, an elaborate hi-def face-scanning technology employed in big-budget movies like The Curious Case of Benjamin Button . Wang, who has just started playing around with it, says that eventually “viewers will be able to see every pore.” The animators used clever visual metaphors cribbed from editorial cartoons to explain the absurdities of NBC’s late-night feud to an Asian audience. “Our technology begins by figuring out the three-dimensional shape of the face,” says Light Stage inventor Paul Debevec, who won an Academy Award for the tech. “Then it figures out the underlying skin reflectance, the shine of the skin, the amount of gloss; if one area is greasier than another, that gets picked up. We can predict how the entire face will look under any lighting condition.” Debevec is excited about the challenge of applying his painstaking approach to Next’s hyperspeed production requirements. “Can you do the rendering of a face quickly and still have it look realistic?” he asks. “A production house like Digital Domain takes six months to do it on something like Benjamin Button . But can you have a technology that allows you to do it between lunch and dinner?” 9:10 pm Modeling and Motion-Capture Digital modeler Wu Kan-yang returns to his desk after watching the Chloroform Killer presentation. Armed with Chen’s storyboards, the reporter’s interview notes, and some police photos, he has 20 minutes to assemble all the characters, sets, and props that will appear in the animation. He selects elements from a library of premade digital objects—for instance, hundreds of face and body types. For the murderer, he chooses an angular face and an athletically built body. Meanwhile, another team is working in the nearby motion-capture studio. Actors in skintight bodysuits dotted with position markers that resemble silver marbles wrestle around on the floor as mo-cap director Joseph Chen yells instructions to them. A male performer presses a foam rubber brick—a stand-in for the chloroform-soaked sponge—into a female actor’s face. The situation is awkward, but no one breaks the tension with jokes or nervous laughter. There’s no time for tomfoolery. The infamous Tiger Woods video was Next Media’s first viral sensation. Its international popularity caught the company by surprise, especially when the BBC and a Swedish TV station asked how much it would cost to license it. “I made up the numbers as I went along,” Simon says, ultimately charging $300. “That one paid for itself.” Nevertheless, some alternate source of income is needed. Posting videos on the Web sites of Lai’s tabloids simply does not generate enough ad revenue to pay for the operation. (Lai reportedly spends $1 million a month on it.) Next Media executives have struck a deal with YouTube to show their videos on that site with “pre-rolls,” brief advertisements that precede the animation. But that still pays a pittance per view, and Next Media videos currently posted on YouTube get just a few thousand views each. The buzz generated by the Tiger Woods animation validated the dream of Next Media honchos that they could go global. Simon envisions a future where big news organizations consider a story complete only when it’s paired with one of his company’s clips. He cites the case of underwear bomber Umar Farouk Abdulmutallab, who last December attempted to trigger explosives hidden in his briefs while aboard Northwest flight 253. “Most networks had nothing but a shot of the airplane sitting on the runway,” Simon says. “We showed him catching on fire and being pulled down by the other passengers.” Simon describes a business model in which Next Media sells its content in much the same way that the Associated Press sells articles. “We will do three or four international stories every night and work out syndication deals,” he says. Lai figures that the company needs just 500 outlets to pay $50 apiece per day. But that has yet to happen. Next Media’s animators have also started producing custom clips for Western news and entertainment media. Reuters tapped them to create an animation about the environmental risks of tuna fishing. BBC’s Newsnight commissioned Next to come up with over-the-top video for the British general elections in April. One clip strings together a few hissy fits and temper tantrums by Gordon Brown along with ominous music and exaggerated mo-cap acting to make the former prime minister look like a psychopath. These made-to-order pieces are list-priced at $4,000 a minute. It’s a bargain, but customers have to go in with realistic expectations. “I get people telling me they want something with an Avatar feel,” Simon says. “I tell them that they’re not getting an Avatar feel for the prices we charge. I can’t give you perfect animation overnight. But I can show you exactly how a policeman tripped and accidentally shot a little girl in the neck.” Some customers view the shortcomings in Next Media’s technique as a feature, not a bug. Adult Swim, the nightly block on Cartoon Network, has commissioned Next to create animated reports on bizarre news stories, like the one about an Iranian cleric who claimed that exposed cleavage causes earthquakes. “There’s a ghost in their machine,” says Matt Harrigan, a producer at Adult Swim. “They have limitations that force unusual decisions and interpretations. What we get back is usually different from what we expect. Sometimes it’s really funny.” A clip about the marital woes of Sandra Bullock was presented like the old films on Mystery Science Theater 3000 , with bemused commentary layered on top. Are the people at Next Media aware that Adult Swim is laughing at them, not with them? “I hope so,” Harrigan says. But sometimes it’s obvious that they’re in on the joke. A recent clip exploring the power of Steve Jobs and the cultural dominance of Apple is hilarious—on purpose. It features Jobs in blue jeans and a Darth Vader helmet, cackling wickedly as sheeplike customers line up to buy his gizmos—and fatigued factory workers who make those gizmos commit suicide en masse (a reference to a spate of actual suicides at a Chinese factory that makes Apple products). iPhone customers are shackled to a weight that looks like the AT&T logo, and when they complain about dropped calls, Darth Steve slices off their ring and pinky fingers with a lightsaber, eliminating the possibility of blocked reception. The scandalously clever clip is light-years beyond the Tiger Woods effort and shows that Next Media is well on its way to developing a visual vocabulary combining the stylistic conceits of comic books, political cartoons, videogames, and nightly news segments. The video also shows what the company is capable of making when it slows down a little—animators worked on the Jobs piece on and off for a whopping two days, with most of the extra time spent creating new digital props especially for the clip. “We didn’t have a Darth Vader helmet handy,” explains Michael Logan, Next’s business and content development manager. “It took more time to produce, the same way that a feature story takes more time than a breaking news story.” 9:30 pm Animation and Postproduction Digital models and motion-capture data for the Chloroform Killer clip are passed along to the animators, who have an hour to knit the two elements together. The labor is divided among nine people, who each work on one or two shots. Ko Hsiao-li, a slender young woman with a ponytail, focuses on a shot of the killer strolling around the prostitute’s apartment. She continually consults with the animator in a nearby cubicle, making sure their lighting matches and that the actions are in sync. When the computer animation is finished, it takes only minutes to render it into AVI-formatted video files. Then audio technician Liao Chuen-chung lays in music and sound effects, all chosen from a prerecorded audio library. After a final quality-control review, the files are sent to Hong Kong for editing and Cantonese voice-overs. Total elapsed time: 120 minutes. The animation about the Chloroform Killer appears on AppleDaily.com as a 40-second breakout inside an 80-second news report, which also features live footage similar to what you’d see in any other TV news segment. The animated sequences are easy to follow even if you can’t understand the Cantonese narration. The animation is sketchy—a plastic bag holding a bottle of chloroform looks ridiculously fake when it moves, and the prostitute’s terror as she struggles for her life is utterly unconvincing. But complaining about the aesthetic is akin to griping about newsprint rubbing off on your fingers; the rough renderings are an unavoidable side effect of rushing out the news while it’s still hot. A recreation of Next Media’s chloroform killer reenactment with English-language narration. You can see the original version with Cantonese narration on YouTube. Jimmy Lai has poured more than $30 million into his dream of a CG newsroom. But he’s used to making big gambles. He put up $100 million of his own money to get his tabloid empire off the ground. And during the dotcom boom, he blew $120 million on a failed ecommerce site called adMart. “I had too much money sitting around,” he says with a shrug. Ultimately, Next Media Animation is part of an even bigger gamble. “TV is a good business right now,” Lai says. He is convinced that Taiwan, a nation of 23 million, is a lucrative untapped market for a Next Media television station. Lai describes his programming vision: There will be variety shows and comedy, but more than two-thirds of the content will be news items featuring Next’s animation. Unfortunately, with the uproar over Next Media’s rape and child-abuse stories still fresh in the minds of Taiwanese broadcasting czars, Lai was rejected for a broadcasting license. Still, he seems undeterred. He has already stood up to Beijing, so taking on the Taiwanese government hardly daunts him. Lai underscores his optimism by pointing to the floor of employees beyond his office’s glass wall. He claims he already has 700 people making daily content for his TV channel. “We have to be ready,” he says. “At the end of the day, obtaining a license will not be a problem.” But for now, that content has no outlet and no audience. When adMart was hemorrhaging money, it was Simon who broke with other executives and backed Lai’s decision to pull the plug. Lai is philosophical about that failure, but Simon says it “gave Jimmy diabetes.” Still, Simon is certain that Next Media Animation will never go the way of adMart, even if the path to profitability is unclear at present. “Jimmy always rows the boat to shore,” he says, “though he might burn it on the way in.” You can almost see the animation: Jimmy Lai is helming a skiff in a churning digital sea. Crudely rendered flames flicker around him as the shoreline comes into view, and a CG stand-in of Simon pulls jerkily on a pair of oars. The Next Media team could really do something with that. Michael Kaplan([email protected]) wrote about the construction of ice hotels in issue 18.06. Pages: 1 2 3 4 View All ||||| National September 11 Memorial MuseumArchive-It Partner Since: Dec, 2007Organization Type: Museums & Art LibrariesOrganization URL: http://www.national911memorial.org The National September 11 Memorial Museum is committed to documenting the events, immediate aftermath, and continuing repercussions of the terrorist attacks of September 11, 2001 and February 26, 1993. To that end, the Memorial Museum's Web Archive seeks to identify and preserve web sites that reflect the international scope of this emergent history. These sites will be continually sourced from a wide variety of contributors, and will serve to reflect the full breadth of the post-9/11 world.References to Institution as a partner on Internet Archive's Website shall carry no legal meaning and simply reflects Institution's status as a user of Internet Archive's Services pursuant to this Agreement.

– Here's everything you need to know about the turf war between the Wall Street Journal and the New York Times in the Big Apple ... in animated form. (Get ready for Rupert Murdoch with a fin, and a Jets vs. Sharks homage). The YouTube video comes from Taiwanese New Media Animation, which has tackled other meaty issues of the day here and here. For more on the animators, see this profile in Wired.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Healthy Maternity and Obstetric Medicine Act'' or the ``Healthy MOM Act''. SEC. 2. FINDINGS AND PURPOSE. (a) Findings.--Congress finds the following: (1) Pregnancy is a significant life event for millions of women in the United States each year. (2) For more than 30 years, our Nation, through the Medicaid program, has recognized that pregnant women need immediate access to affordable care, and has allowed women who meet income-eligibility requirements to enroll in Medicaid coverage when they become pregnant. (3) Congress recognized the central importance of maternity coverage by classifying maternity and newborn care as one of the ten essential health benefits that must now be covered on most individual and small group health insurance plans under section 1302(b)(1) of the Patient Protection and Affordable Care Act (42 U.S.C. 18022(b)(1)). (4) The Patient Protection and Affordable Care Act has greatly increased access to affordable health insurance coverage for women. Today, more than 7,500,000 women have access to health insurance because of the law. That Act made it illegal to deny coverage based on pre-existing conditions, like pregnancy, or charge women more money for their premiums. That Act also required women's preventive services like birth control to be covered without cost sharing. (5) Access to comprehensive maternity coverage allows women to access important pregnancy-related care, which is demonstrated to improve health outcomes for women and newborns and reduce financial costs for both consumers and insurers. (6) Uninsured women, women with grandfathered and transitional health plans, self-funded student health plans, and catastrophic and high-deductible health plans may lack access to comprehensive and affordable maternity coverage. (7) Employer health plans that exclude dependent daughters from maternity coverage leave young women without coverage for their pregnancy, even though Federal law has long held that treating pregnancy differently than other conditions is sex- based discrimination. (8) A special enrollment period is especially important for young adults, who are at high risk for unintended pregnancies, yet young adults are frequently enrolled in catastrophic coverage, which often has fewer benefits, more restrictions, and higher deductibles. (9) Timely maternity care improves the health of pregnant women, as well as birth outcomes and the health of babies throughout their lifetimes. Pregnancy-related maternal mortality is three to four times higher among women who receive no maternity care compared to women who do. Regular maternity care can detect or mitigate serious pregnancy-related health complications, including preeclampsia, placental abruption, complications from diabetes, complications from heart disease, and Graves' disease, all of which can result in morbidity or mortality for the mother or newborn. (10) Regular maternity care can reduce preterm births and the health complications associated with preterm births. (11) Timely maternity care can reduce short- and long-term health care costs. If a woman does not have access to affordable maternity care during her pregnancy, and she or her newborn experiences pregnancy complications that result in health problems after birth, their insurer may end up paying much higher costs than if the insurer had covered the woman's maternity care during her pregnancy. Intensive maternity care can reduce hospital and neonatal intensive care unit admissions among infants, resulting in cost savings of $1,768 to $5,560 per birth. For women with high-risk pregnancies, intensive maternity care saves $1.37 for every $1 invested in maternity care. (b) Purpose.--The purpose of this Act is to protect the health of women and newborns by ensuring that all women eligible for coverage through the Exchanges established under title I of the Patient Protection and Affordable Care Act (Public Law 111-148) and women eligible for other individual or group health plan coverage can access affordable health coverage during their pregnancy. SEC. 3. PROVIDING FOR A SPECIAL ENROLLMENT PERIOD FOR PREGNANT INDIVIDUALS. (a) Public Health Service Act.--Section 2702(b)(2) of the Public Health Service Act (42 U.S.C. 300gg-1(b)(2)) is amended by inserting ``including a special enrollment period for pregnant individuals, beginning on the date on which the pregnancy is reported to the health insurance issuer'' before the period at the end. (b) Patient Protection and Affordable Care Act.--Section 1311(c)(6) of the Patient Protection and Affordable Care Act (42 U.S.C. 18031(c)(6)) is amended-- (1) in subparagraph (C), by striking ``and'' at the end; (2) by redesignating subparagraph (D) as subparagraph (E); and (3) by inserting after subparagraph (C) the following new subparagraph: ``(D) a special enrollment period for pregnant individuals, beginning on the date on which the pregnancy is reported to the Exchange; and''. (c) Special Enrollment Periods.--Section 9801(f) of the Internal Revenue Code of 1986 (26 U.S.C. 9801(f)) is amended by adding at the end the following new paragraph: ``(4) For pregnant individuals.-- ``(A) A group health plan shall permit an employee who is eligible, but not enrolled, for coverage under the terms of the plan (or a dependent of such an employee if the dependent is eligible, but not enrolled, for coverage under such terms) to enroll for coverage under the terms of the plan upon pregnancy, with the special enrollment period beginning on the date on which the pregnancy is reported to the group health plan or the pregnancy is confirmed by a health care provider. ``(B) The Secretary shall promulgate regulations with respect to the special enrollment period under subparagraph (A), including establishing a time period for pregnant individuals to enroll in coverage and effective date of such coverage.''. (d) Effective Date.--The amendments made by this section shall apply with respect to plan years beginning after the 2016 plan year. SEC. 4. COVERAGE OF MATERNITY CARE FOR DEPENDENT CHILDREN. Section 2719A of the Public Health Service Act (42 U.S.C. 300gg- 19a) is amended by adding at the end the following: ``(e) Coverage of Maternity Care.--A group health plan, or health insurance issuer offering group or individual health insurance coverage, that provides coverage for dependents shall ensure that such plan or coverage includes coverage for maternity care associated with pregnancy, childbirth, and postpartum care for all participants, beneficiaries, or enrollees, including dependents, including coverage of labor and delivery. Such coverage shall be provided to all pregnant dependents regardless of age.''. SEC. 5. FEDERAL EMPLOYEE HEALTH BENEFIT PLANS. (a) In General.--The Director of the Office of Personnel Management shall issue such regulations as are necessary to ensure that pregnancy is considered a change in family status and a qualifying life event for an individual who is eligible to enroll, but is not enrolled, in a health benefit plan under chapter 89 title 5, United States Code. (b) Effective Date.--The requirement in subsection (a) shall apply with respect to any contract entered into under section 8902 of such title beginning 12 months after the date of enactment of this Act. SEC. 6. CONTINUATION OF MEDICAID INCOME ELIGIBILITY STANDARD FOR PREGNANT WOMEN AND INFANTS. Section 1902(l)(2)(A) of the Social Security Act (42 U.S.C. 1396a(l)(2)(A)) is amended-- (1) in clause (i), by striking ``and not more than 185 percent''; (2) in clause (ii)-- (A) in subclause (I), by striking ``and'' after the comma; (B) in subclause (II), by striking the period at the end and inserting ``, and''; and (C) by adding at the end the following: ``(III) January 1, 2014, is the percentage provided under clause (v).''; and (3) by adding at the end the following new clause: ``(v) The percentage provided under clause (ii) for medical assistance on or after January 1, 2014, with respect to individuals described in subparagraph (A) or (B) of paragraph (1) shall not be less than-- ``(I) the percentage specified for such individuals by the State in an amendment to its State plan (whether approved or not) as of January 1, 2014, or ``(II) if no such percentage is specified as of January 1, 2014, the percentage established for such individuals under the State's authorizing legislation or provided for under the State's appropriations as of that date.''. SEC. 7. RELATIONSHIP TO OTHER LAWS. Nothing in this Act (or an amendment made by this Act) shall be construed to invalidate or limit the remedies, rights, and procedures of any Federal law or the law of any State or political subdivision of any State or jurisdiction that provides greater or equal protection for enrollees in a group health plan or group or individual health insurance offered by a health insurance issuer.

Healthy Maternity and Obstetric Medicine Act or the Healthy MOM Act This bill amends the Public Health Service Act and Internal Revenue Code to require health insurers, health insurance exchanges, and group health plans to offer a special enrollment period to pregnant individuals. The special enrollment period offered by an insurer or exchange must begin when the pregnancy is reported to the insurer or exchange. The special enrollment period offered by a group health plan must begin when the pregnancy is reported to the plan or is confirmed by a health care provider. Coverage offered by a group health plan or health insurer that covers dependents must provide coverage for maternity care to all covered individuals. The Office of Personnel Management must ensure that eligible pregnant women are allowed to enroll in federal employee health benefit plans outside of the open enrollment period. This bill amends title XIX (Medicaid) of the Social Security Act to revise the range in which a state must establish a maximum level of family income for pregnant women and infants to be eligible for Medicaid. The upper limit of the range is eliminated and the lower limit is set to the level in place, or specified in an amendment to a state plan, on January 1, 2014.

It's funny what being held at gunpoint will do to you. And being held at gunpoint by a megalomaniacal rock star? Well, that doesn't feel very good at all. Not when the rock star has spent the past three months, the entire spring of 1995, living a fantasy life right in front of you, sipping martinis and passing a joint around at 11a.m. with his new wife, a pert blonde actress who inspires over a billion people around the world to drool each week as she runs across the beach in a tight red bathing suit. Not when you've been laying wires, tearing up the walls and painting again and again, because the light switch the rock star thought he wanted over here he now wants just there. Related PHOTOS: Barely Legal: 30 Nearly Pornographic Mainstream Films Full-frontal nudity, steamy threesomes, one-for-the-money shots — these movies pushed the envelope and still played multiplexes By the time Tommy Lee and Pamela Anderson abruptly fired the handful of the people renovating their Malibu mansion, refusing to pay for work they said was shoddily done, electrician Rand Gauthier was so sick of the celebrity couple's demands that he was ready to simply write off the $20,000 he says they owed him. But when he and a general contractor came back to the couple's mansion on Mulholland Highway to get their tools and Tommy Lee pointed a shotgun at them, saying, "Get the fuck off my property," Gauthier got seriously pissed. &lt;div&gt;Please enable Javascript to watch this video&lt;/div&gt; Lee made Gauthier feel small, and Gauthier had spent his entire life feeling small. Here was a guy who, on his 18th birthday, lost his virginity to a Vegas hooker. Here was an L.A. boy through and through, struggling to dissociate himself from his famous father, who starred in the original Bye Bye Birdie on Broadway and was Hymie the Robot on the Sixties sitcom Get Smart. By the Nineties, Gauthier had gleaming, tanned muscles, broad shoulders, an eager, trusting smile and a voice that's equal parts surfer and Ernie from Sesame Street. Most people dismiss him as a doofus, a conspiracy theorist who likes fast, powerful cars and dating porn stars. He even did some scenes himself, and spent his time hanging around an adult-film studio, building sets and chatting up starlets. A studio troll, they called him. "I was never really that popular with people, " he says. "But I had never been held at gunpoint. It screwed with my head." Now he wanted revenge. He wanted the drummer to feel vulnerable, to realize that he was just a human being, not an invincible rock god, even if he had sold 20 million records by the age of 32. So Gauthier decided to steal the giant safe he knew was tucked in the garage, the one with all of Lee's guns and Anderson's jewelry, and have a laugh at their expense. He had no idea that the safe also contained a homemade tape that would promise him dazzling riches and then ruin his life. And instead of taking Lee down a notch, he would help cement the musician's legacy, letting the world know he had one of the biggest dicks in rock & roll. ABC "I made his career, is what happened," says Gauthier, now a foggy 57-year-old who still works as an electrician and grows marijuana in his garage outside Santa Rosa, California. But Lee might not see it that way. Two years ago, Gauthier received a Facebook message from a page bearing the name Tommy Lee. All it said was: "Hey you fucking faggot." The Pam and Tommy sex tape is the most infamous stolen celebrity artifact on the planet, with a wink usually accompanying the word "stolen." It wasn't the first time a video of a famous person fornicating appeared in the public realm, and it certainly wouldn't be the last. But it was a porno that appealed to people who didn't usually watch pornos, a voyeuristic dive into the guileless intimacy between two tabloid darlings: Anderson, perennial Playboy cover model and star of Baywatch, and Lee, the hard-partying drummer from Mötley Crüe. Related PHOTOS: 8 Porn Stars Who Made National News Before Belle Knox, these adult movie actors and actresses made headlines Starting in the spring of 1996, as information trickled out about what was on the tape, everyone wanted to see it, whether to gawk at the home life of two superstars or condemn the empty-headed, sex-addicted narcissists who presumably leaked it themselves. The couple already had a reputation for carnal and pharmaceutical indulgence, but peeping on their love play offered an entirely new level of dirty, thrilling violation, as we leap-frogged PR flacks, centerfold photographers and even the paparazzi to land squarely in the most private of worlds. And yet the tape was, without question, physically and illegally taken from Anderson and Lee's home. Recording themselves in the spring and summer of 1995, the couple truly didn't know anyone else was ever going to see this, so their video has none of the self-conscious posturing of reality TV and social media. You will never see a celebrity flash a smile in public that is as genuine as Tommy Lee's after he money-shots all over his wife's chest at her request. Courtesy of www.vivid.com This is not gonzo pornography – it's a 54-minute home video, depicting about eight minutes of the sex Americans are most likely to sanction: white, straight, married and in love. "It's the greatest tape I have ever seen in my life," Howard Stern said in late 1997. "What's cool about it is that, like, you get to live their lives with them." But what the Pamela Anderson-Tommy Lee sex tape taught us is that an unassuming individual could acquire a piece of content, offer it up to the Internet and watch it ricochet around the planet. How, exactly, this footage traveled from a locked safe to screens and store shelves worldwide warns of everything that was coming in the next two decades, everything that would shift in technology and culture and celebrity. Before Kim Kardashian, before TMZ, before RedTube, before the Fappening, there was Pam and Tommy. The tape took two years to go from bootleg to viral, and when it did it made an estimated $77 million in less than 12 months – and that's just on legitimate sales. So how did the person who stole the safe manage to evade the police, the lawyers, the media and the biker gangs, but never see a cent? This is the story of a man who staked his livelihood on a video in the hopes that it would save him. Instead he watched his life fall apart as his greed destroyed nearly every shred of the happiness he'd carved out for his adult self. Gauthier says he spent the entire summer of 1995 preparing for the heist, driving over to the Lees' house several nights a week to sit and stare, waiting outside until three or four in the morning. Plotting. Stewing. "I took my time," Gauthier recalls. "I cased the joint." Related Mr. Big: Jonah Falcon's Giant Penis Problem Jonah Falcon was born with a blessing in, er, disguise. Until it took over his life. And tormented him His plan was to throw a white Tibetan yak fur rug over his back and crawl to the garage on his hands and knees in the middle of the night, so the security cameras, which Gauthier himself had installed, would seem to show a dog like the one the couple had. Lee and Anderson lived in a three-story Spanish-style house, with a garage that had been converted into a recording studio on the bottom floor. Unfamiliar trucks, vans and cars were often parked outside the house, so no one suspected anything. The property was adjacent to state-owned land where the paparazzi would lurk, and the couple sometimes saw boom mics hanging over the fence. At one point Lee was arrested for pointing a sawed-off shotgun at a camera he spied while he and Anderson were kissing in the garden. James Aylott/Getty Photos went for a high price, as the public was obsessed with the pair, who had married in February after a four-day, Ecstasy-enhanced courtship in Mexico. Lee's previous marriage to the actress Heather Locklear had ended in accusations of domestic violence, infidelity and drug and alcohol abuse. Anderson, with her leather dresses and her notorious double-D breast implants, seemed a better match for a guy who was known for mooning the audience. In April 1995, stolen Polaroids of the couple in bed made their way to the French and Dutch editions of Penthouse and an American skin mag called Screw. Anderson was upset, initially, but as she fatefully told Movieline later that year, "When I saw the first Polaroid, I was like, 'Whoa, baby, we should frame this' . . .In the end, who cares?" Over the course of their multi-year renovations, the couple cycled through several rounds of contractors and workers they deemed untrustworthy, spending what was, by all accounts, an obscene amount of money building out a hedonist's paradise with heart-shaped glass and iron doors; a pillow room; a koi pond; a 20-foot mural of heaven and hell in the elevator shaft; and a 30-foot swing in the living room, hanging above the white baby grand piano. "Basically, we made it into a huge adult playground," Lee wrote in his 2004 memoir, Tommyland. "They were getting three-inch slabs of marble from France and Italy delivered," says Guerin Swing, an interior designer who partied frequently with the Lees that year and worked on some of the house's more artistic touches. (Swing also makes a cameo in the tape, running down a hotel hallway in a bucket hat.) "They spent money like they hated it." Getty Meanwhile, Gauthier was lying in wait. In early October, Anderson threw Lee a circus-themed party to celebrate his 33rd birthday at a ranch down the road, featuring carnival rides, tigers, sword-swallowers, a death-metal band from Sweden and $5,000 worth of drugs. About five days before Halloween, Gauthier decided to make his move. The details of what exactly happened on the night of the burglary are sketchy at best, as Gauthier seems intent on painting himself as a strongman daredevil and obfuscating details that could point to potential accomplices. He acknowledges that one other person knew about his plan beforehand but insists he carried out the deed himself. According to Gauthier, it was 3 a.m., and the Lees were at home, upstairs, asleep. He came in over the fence with the yak fur on his back and a U-Haul dolly trailing behind him. After disabling the security cameras, Gauthier claims to have gone upstairs and walked into the Lees' bedroom. Next, entering the garage, he says he carefully moved all of the recording equipment in front of the carpeted wall concealing the safe, including what Lee later described as "a huge Neve recording console that weighs hundreds of pounds, as well as a few racks of outboard gear, each of them about six feet tall, awkward. . .and heavy." Then, he tipped the Browning safe, which was six feet by four feet by three feet, onto the dolly, strapped it down, put everything back as he had found it, and wheeled the dolly out onto the driveway, heading downhill toward the street. Suddenly, he says, the metal in the safe triggered the gate, startling Gauthier as the noise of the doors creaking open broke the silence of the pre-dawn hour. "I almost dropped a load in my pants," he says. To get the safe up onto the back of his truck once he got out to the road, he claims he "leaned the whole dolly and safe against the gate and I get in the dirt and I wedge my legs underneath it and I bench up 500 pounds with my legs. It was hard." Friends of Gauthier's, however, say he told a different story back in 1995 and 1996. Lee himself wrote in his memoir that whoever robbed them "must have removed the safe with a crane." One source alleges Troy Tompkins, the general contractor who was held at gunpoint with Gauthier, helped plan the heist from the start and was waiting in a pick-up truck. Tompkins' wife at the time, a French woman named Dominique Sardell, had been doing work on Anderson's condo, and was fired along with Gauthier and her husband. Months later, when the Lees finally discovered the safe was missing, Tompkins and Sardell were the first people they suspected, as Tompkins had gushed over Lee's guns, and Sardell had advised Anderson to keep her jewelry in the safe, to protect it. (Neither Tompkins nor Sardell could be reached for comment.) Steve Fasanella What happened once the safe left the home, however, is less ambiguous. Gauthier took it to a secure location and spent an hour cutting into the back with a borrowed demolition saw outfitted with a composite diamond carbide blade. Although he denies finding the AK-47, FNC assault rifle, .45-70 caliber rifle and Mossberg stainless steel shotgun mentioned in a later police report, he does acknowledge discovering everything else Pam and Tommy listed as missing, including family photographs, a Rolex, a gold-and-diamond Cartier watch, gold-and-emerald cufflinks, a ruby-and-diamond cross, the white bikini that Anderson wore to their beach wedding, and a Hi8 tape, the kind of cassette that could be inserted into a handheld camcorder. Gauthier brought the tape back to the North Hollywood porn studio where he worked, and watched it with the studio owner. "We put it in and see what it is, and of course, cha-ching. The dollar signs fly before our eyes," he says. "But we're going, this is the kind of thing people will get killed over." In the mid-Nineties, the porn business was booming. Almost every home in America could afford a VCR, and decency laws in Los Angeles had relaxed enough to support a $5 billion dollar industry that churned out hundreds of features a year. Gauthier first fell in with the San Fernando Valley crowd in the late 1980s, when he was set up on a blind date with porn star Erica Boyer (née Amanda Gantt), a southern girl who made great fried okra and whose father was at one point the Assistant Attorney General of Alabama. The two moved in together after only six weeks, and she convinced a few directors that her new boyfriend had done adult films before so Gauthier, who had stripped in college but had no experience doing porn, could join her on camera. Related Flashback: Sylvester Stallone Stars in 1970 Softcore Porn Six years before breaking big with 'Rocky,' Stallone agreed to shoot this cheap skin flick in order to pay the bills "Learning to climax on cue was not easy," he says. "They say, 'OK, let's get this over with. Everyone wants to go to lunch,' and of course then the pressure's on." Over the course of the next decade, under the name Austin Moore, Gauthier performed in at least 75 porn videos, including Big Boob Bikini Bash (1995), Miracle on 69th Street (1992) and Willie Wankers and the Fun Factory (1994). "I just wish my equipment had been a little larger for the industry," Gauthier says. "A lot of girls wanted me to do anal with them because it wasn't so large." After a short marriage to Boyer, he dated actresses like Wendy Whoppers, whose massive 34H breasts he says he helped pay for, and Stacey Valentine, with whom he says he once had sex in the parking lot of a Jerry's Famous Deli, as dozens of friends cheered them on. Rand Gauthier "I've had a real wild life," he says. "I believe in reincarnation, and this is kind of my vacation life. I have to come back and be really serious next time." Gauthier grew up in Toluca Lake, across the street from Dick Van Dyke, with divorced parents and no access to pornography. When he was a boy, his mother became a Jehovah's Witness, forcing Gauthier to go door-to-door with her and inspiring his lifelong obsession with religions, secret societies and cults. He is the kind of person who insists that early rabbis sodomized 12-year-old boys and believes in a mystical connection between the number of letters in the Hebrew alphabet, bones in the human skull and years in the solar magnetic cycle (all are 22). On the back of one hand, he has a tattoo of a Freemason symbol; he claims the group once wanted to give him a machine gun and train him as a soldier. Even though Gauthier now calls Jehovah's Witnesses "mentally deficient," he was happier living with his mother than being around his father, Dick Gautier. Gauthier says the actor was quick to lose his temper and only brought him and his two sisters over to show them off. Once, as kid, Gauthier forgot his dress shoes at his mother's house, and his father made him wear slippers to a fancy dinner. "I remember he got one of those '10 Best-Dressed Men' awards back in the 1970s, so it was a little uncomfortable, because he looked dapper, and I looked like a schlemiel," he says. As an adult, he changed the spelling of his last name, presumably to get out from his father's shadow. "I don't think my dad really believed in me." Working in porn gave him the confidence he'd always struggled to achieve growing up. Still, he had to smoke weed to "take my head out of the fact that there were a bunch of dudes watching me, which was kind of grode," and he preferred working off-camera whenever possible. Porn was a small world back then, and early on Gauthier met Milton "Uncle Miltie" Ingley, an overweight, pipe-smoking cheapskate studio owner who was partial to country music and Chambord. After Gauthier fixed a few pieces of recording equipment around Ingley's studio, the two became fast friends. The prolific fetish filmmaker Ernest Greene (né Ira Levine), who shot at the studio a handful of times, calls Gauthier "Milton's pet idiot," explaining that Ingley would blame messes he created on Gauthier because, as Greene says, "the guy basically had a lizard brain." So when Gauthier came to Ingley with the Pam and Tommy tape, Ingley, who died in 2006, took over. First, after making a few copies, they destroyed the original Hi8 cassette, melting the casing and cutting the tape itself into hundreds of little pieces, which they dispersed in a desolate area near Six Flags Magic Mountain. Once they'd disposed of the evidence, the next step was to find a distributor. "Milton was the king of wheeling and dealing," Gauthier recalls. "He knew how to make a nickel into two dollars. Always schmoozing." One of the first people Ingley approached was actor and director Ron Jeremy, a friend since the late Seventies, when Ingley used to perform under the name Michael Morrison. Jeremy had recently put out a reality-style porno featuring John Wayne Bobbitt, whose penis was famously surgically reattached after his wife cut it off. "I got a reality star you're gonna really shit your pants over," Ingley told him. But Jeremy and his producing partner quickly figured out the tape had been stolen, and that Lee and Anderson hadn't signed a release. "We passed," Jeremy recalls. "Porn was so strict and scary back in those days. If you're fucking, you better believe you gotta have a release." Ingley approached a handful of other companies, but no one wanted to take on the risk. According to Gauthier, a wealthy foreigner offered them a million dollars for the tape, but Ingley felt it was worth many times that amount. Finally he approached Louis "Butchie" Peraino, the son of a capo in one of New York's organized crime families, the Colombos. Back when pornography was illegal nearly everywhere in the United States, the Perainos were the Medicis of the adult world, having financed and distributed the classic 1972 film Deep Throat. By 1995, the younger Peraino ran an adult video business called Arrow Productions and was close friends with many of the biggest players in porn. But even Peraino didn't feel comfortable putting out the Pam and Tommy tape in any official capacity. Instead, he lent Ingley roughly $50,000 to cover manufacturing and distribution of the tape over the Internet, with the expectation that he would receive interest on the loan and a cut of the sales. At this point, only 25 million Americans and 40 million people globally had Internet access. Most websites were eyesores, and there was no such thing as streaming video. But the web, with its seemingly anonymous transactions, seemed like the perfect black market to get the tape to consumers. Now, finally, Ingley and Gauthier thought, they would be rich. "I was looking at castles in Spain," Gauthier says. Ingley used about a quarter of the money Peraino had given him to run off thousands of copies and to hire someone to put up a few websites: pamsex.com, pamlee.com and pamsextape.com. The sites didn't have the video itself; they merely gave instructions to send a money order to the New York outpost of a Canadian T-shirt company, which then funneled the money to a bank account in Amsterdam. With VHS copies of Pamela's Hardcore Sex Video going for $59.95, Ingley expected to soon be flush. So with Gauthier managing shipments from Los Angeles, driving around in a white Dodge van knee-deep in video cassettes, Ingley headed to New York to enjoy the rest of Peraino's loan: $500 bottles of champagne, hookers every night, a room at the Plaza and lots of cocaine. Another Ingley Studios lackey, Steve Fasanella (whose last name has been changed at his request) hadn't been working there very long when this all started; when he saw he wasn't going to be cut in on the action, he ran off his own copies. Soon he was selling them for $175 a pop out of the trunk of his car. (He says he sold nearly 500 copies this way, making about $75,000.) Fasanella advised Gauthier to do the same, to make some cash in case Ingley screwed him over, but Gauthier remained loyal. By the end of December 1995, when the Sunday edition of London's Daily Mail did a year-in-review issue that covered Anderson and Lee's tabloid antics, the writer mentioned that a video of the two having sex on a yacht was supposedly on sale in Los Angeles. Two months had passed since the heist. At this point, Anderson and Lee hadn't even noticed yet that the safe was missing. In the middle of January 1996, they noticed. Horrified, they filed a police report and hired Hollywood private investigator Anthony Pellicano to suss out what had happened. Pellicano later told the Lees' lawyers that he tracked down Ingley, who admitted he had a copy of the tape but claimed to have bought it from Guerin Swing, the interior designer. Swing and a friend were hanging out at his 2,400-square-foot bachelor pad when Pellicano showed up one night, wearing a white suit, and immediately shoved Swing down onto the ground. "What's up, dude?" the frightened designer asked. "Who the fuck are you?" "Just tell me," Pellicano growled. "We know you did it! We know you took the tape." After a short interrogation, Pellicano determined Swing knew nothing and left. (Pellicano is currently serving 15 years in federal prison for charges ranging from wire fraud to identity theft.) Soon after, Fasanella was at Ingley's studio, doing some work with Ron Jeremy's roommate of 17 years, a porn director named Bobby Bouschard. All of a sudden, they heard motorcycles revving outside, and then five or six big bikers burst into the room. "You – where's the fucking tape!" one said to Fasanella, and pointed a shotgun at his testicles. The bikers had a VHS box cover from a porno that Gauthier had done a few years back. "I know who you're looking for, but I'm not that guy," Fasanella said. "You're the fucking guy!" the biker spat back. He held the tattered, creased box cover up to Fasanella's face and squinted his eyes. Both Fasanella and Gauthier were buff and looked vaguely Italian. The bikers debated amongst themselves whether Fasanella was the guy in the photograph. "Well," the guy with the shotgun finally announced, "you tell that motherfucker we're going to come back and blow somebody's balls off unless that tape gets puts back." Mötley Crüe's head of security was a former Hells Angel, and a few sources said they thought Lee sicced the Angels onto Gauthier and Ingley to get the tape back. (Gauthier, however, insists the bikers were a Mexican gang called the Bandidos.) The bikers started coming by the studio every few days, sometimes twice a day, looking for Gauthier and Ingley. If Gauthier was there when they heard the motorcycles coming, he and Fasanella would run to the roof and jump down onto the top of the auto body shop next door. Fasanella lived two blocks away, so if they could make it out a side door, they were safe. According to Gauthier, Lee even sent one of his porn-star pals, Candy Vegas, and one of her friends over to his house to try to seduce Gauthier into giving back the tape, but so many copies of the tape existed by then that her efforts were fruitless. With so many people after him and the stolen tape, Gauthier grew increasingly paranoid, hardly sleeping. He started crashing at the home of Fred Piantadosi, who worked as a porn director under the name Fred Lincoln and used to manage a San Francisco adult theater called Plato's Retreat, which was owned by the Perainos. Piantadosi's daughterm Angelica, now 22, recalls that Gauthier stayed with them for almost an entire year. "Uncle Rand" slept in the red bunk bed in her room, with her Hunchback of Notre Dame blanket, as the kindergartener slept in her father's room. She still has a five-inch scar on her leg from where she burned herself on the exhaust pipe getting out of Gauthier's red '69 Corvette convertible when he was dropping her off at karate practice. Just as Lee and Anderson began to realize that the tape was spreading faster than they could contain it, word came from New York that Penthouse had acquired a copy. A lawyer for Penthouse promised the magazine wouldn't publish any images from the tape, but the couple started to panic. On March 29th, 1996, they filed a $10 million civil lawsuit against everyone they thought might have a copy, including Penthouse, Ingley, Gauthier, Tompkins, Sardell and Swing. By the next day, news vans were parked outside of Ingley's studio and Swing's parents' house. A sex tape had been stolen from one of the most famous couples in the world? Everyone wanted to know more. The judge denied Anderson and Lee's request for a temporary restraining order against Penthouse, and the magazine put out its June issue with Anderson on the cover and a written description of the tape, including quoted exchanges, inside. Still, they didn't have copyright permission to use stills from the tape, so they illustrated the article with the stolen Polaroids that had first been published abroad. In August, a different L.A. judge refused to grant the Lees a permanent injunction against Penthouse, largely because it is essentially unheard of for a court to bar a media outlet from publishing something before it has done so. Perhaps most alarmingly for the Lees, since Anderson had posed nude several times and because the two discussed their sex life in interviews, Penthouse's lawyer argued that the couple had forfeited their privacy rights regarding the video's content. And since Penthouse had received the tape from "a source," and no one from the magazine had been directly involved in the burglary, writing about its contents was fair game. Plus, because the footage included a scene of Anderson rolling a joint and she had told Star the previous year that she didn't do drugs, the tape itself was legally considered "newsworthy." However, because Anderson and Lee shot it themselves, the couple did still retain copyright over the tape – a legality understood by all of the adult film producers whom Ingley had approached – so Penthouse held off on printing stills or selling the tape, even after winning the case. Meanwhile, no one else named in the suit formally acknowledged having a copy. Tompkins and Sardell responded to the Lees' accusations, which included a separate lawsuit for fraud, with a suit of their own, claiming the celebrity couple owed them about $120,000 in materials and labor costs. (That case was dismissed in 1997.) And through the spring and summer of 1996, legal paperwork continued to arrive at Ingley's studio, though neither he nor Gauthier had hired a lawyer. With the Lees' attorneys coming from one direction, the biker gang from another and Peraino starting to ask questions about when he might see some return on his investment, Ingley decided to get the hell out of New York. So he headed to the Netherlands, for more prostitutes, more drugs and more time crouched over computers, posting thousands upon thousands of ads in adult-oriented forums and newsgroups. "The FBI, Interpol and the CIA can't even catch kiddie pornographers with big factories," Ron Jeremy says. "How are they gonna catch one schmuck going to different cyber cafes in Amsterdam?" When the various websites selling the tape weren't crashing, they were processing orders like crazy. But once a few bulk deliveries had gone out, the dog-eat-dog logic of the Internet became apparent: If Ingley and Gauthier could steal a tape and sell it through a website, without a copyright or conventional distribution network, why couldn't somebody else just buy one from them and do the same? A wave of copycat websites began appearing in late 1996, including naked-celebs.com, pamwatch.com and bobsnudecelebs.com. Profits slowed, and Ingley grew desperate. He had Gauthier oversee the sale of his studio, and had his daughter come up to Los Angeles from Texas to sell off his props and gear. And in an attempt to stop the piracy hydra from growing any more heads, around the late spring of 1997, he stopped shipments and posted an announcement that all pending orders would be sent out on September 27th, 1997. Getty But Peraino still needed to be paid. Gauthier says that Ingley managed to get the initial loan back to him, but he still owed the interest. Ingley knew that Peraino had cancer, and he thought that if he waited in Europe for long enough, Peraino would die and the debt would simply disappear. Peraino was convinced that Ingley was hiding money, but he couldn't figure out whether Ingley was cutting Gauthier in for a piece, or whether Gauthier had been bringing hundreds of tapes to the post office every week for nearly a year without seeing any of the profits. So one night, Gauthier says, Peraino had him over for dinner. Over linguine and oysters, he snuck teaspoons of sherry into Gauthier's merlot when he thought he wasn't looking. Then, after dinner, he brought out Bing cherries soaked in Everclear. Before long, Gauthier was wasted, and Peraino was firing question after question at him. "Where is the money?" he demanded. "Where are you and Milton hiding it?" Fortunately for Gauthier, he convinced Peraino he'd done no wrong. Unfortunately for Gauthier, Peraino decided that he needed to work to pay back the money that Ingley owed him. Specifically, by helping him send a message to some of the other people who owed him money. Soon, Gauthier says, he was working collections for the mob to pay off his own debt. "Knees are a little harder to break than most people think, so I came up with my own idea," Gauthier says. He would grow a beard, throw on a baseball cap and sunglasses, and approach the indebted individual, holding what appeared to be a cup of coffee. But it wasn't coffee; it was ammonia. Suddenly, Gauthier would throw the chemical in his victim's face, whip out the metal handle from a mop wringer, break the guy's collarbone, walk a few blocks, jump in his plateless Dodge van and disappear. The court issued an injunction against Ingley in early October of 1997, ordering him to stop copying and selling the tape, but he didn't care, and by then it was too late: when the accumulated orders from that year went out in late September, as promised, Los Angeles was suddenly awash in bootlegs. As Gossip Girl co-creator Stephanie Savage later wrote in the USC Journal of Film and Television, "Professional men and women gathered together to whoop, whistle, stare slack-jawed and speculate." Variety even published a review of the tape. Jerry Gay It was at this point that a copy of the video found its way into the hands of someone brazen, litigious and publicity-hungry enough to take it to the next level: a 25-year-old Internet wunderkind named Seth Warshavsky. In addition to developing early versions of pay-per-click ads, streaming video and online credit card processing, Warshavsky claimed to have live nude performers on his flagship site, Club Love, responding to the whims of viewers worldwide. And yet pretty much everyone in the adult and Internet industries despised Warshavsky, as he was a sniveling huckster who wrote bad checks and owed lots of people money. One of his employees, a former model and golf pro named Cort St. George, was hanging out at a major television studio in L.A. and watched one of the copies of the tape then flying around Hollywood. He brought it to his boss in Seattle. Warshavsky gave him a few thousand bucks and, on November 3rd, 1997, issued a press release announcing that he intended to broadcast the video online. However, as several former employees confirmed, Warshavsky never thought he would be able to show the tape; he merely wanted the publicity that would come with the announcement and the inevitable lawsuit. But on November 6th, the judge refused to issue an injunction against him, and the following day Warshavsky aired the tape on Club Love on a loop for five hours. "We were in the back of a car," recalls St. George, "and Tommy was on speakerphone, and Tommy was like, 'Seth, I'm going to kick your fucking ass.'" By now the Lees were exhausted. Everyone in Los Angeles, it seemed, had already seen the video, and the never-ending series of depositions was invasive and stressful and failed to stop the tape's distribution. So they decided to settle. Lee and Anderson were under the false impression that they could give Warshavsky permission to show the tape over the web without allowing them to sell it in stores, and by all accounts the couple underestimated the reach of the Internet. Derek Newman, who had just graduated from Pepperdine Law School, was serving as Warshavsky's lawyer; he prepared the broadest possible release, hoping to get the couple to sign away their copyright over the tape. "I remember negotiating and thinking, 'There is no way they'll ever sign this,'" Newman says. But they did, on November 25th, 1997. Within days, anyone who bought a subscription to Club Love had access to the tape. "Our servers were rocked. It was insanity. We had thousands of sales a day, every day, for months," says Jonathan Silverstein, who was working as the company's director of sales and marketing at the time. Soon, Warshavsky had worked out a deal with Steven Hirsch, owner of leading adult video purveyor Vivid Entertainment, to manufacture VHS, DVD and CD-ROM copies. By February of 1998, any horny or curious American could walk into an adult video store and pick one up. Over the next few years, they sold hundreds of thousands of copies. "It was a phenomenon, and it really helped catapult this company to the next level," Hirsch says. "We were just minding our own business, and this came along." Warshavsky was even able to chase down copyright violators on the web, convincing them to pay him a licensing fee for permission to stream the tape. In 2000, the Guinness Book of World Records declared Anderson the "most-downloaded star" of all time, and millions of websites that had no content related to the stars at all listed "Pamela Anderson" in their meta-tags to boost traffic. And back in Amsterdam, Ingley was reeling. How dare Warshavsky and Hirsch make money off of his tape? But it was too late: he had lost control. And any time Gauthier heard someone talking about the video, Fasanella says, his eyes would fill with tears. "I was the lowest guy on the totem pole," Gauthier says now. "And I was so busy trying to make it work." When Anderson and Lee saw physical copies of the tape being sold and rented in stores, they were furious. Or at least, they did everything in their power to appear furious – publicly explaining that they'd been duped, and suing Warshavsky in federal court. But some see the pivotal moment when the couple signed away their rights as the smoking gun that indicates a private deal to share in the profits had been made. And several people claim this is the case, including a former Vivid Entertainment employee. Ron Jeremy said he once asked Anderson whether she'd received any money for the tape, and she simply smiled and said, "Well, you know." (Anderson and Lee have both publicly denied profiting off the tape; both declined to comment for this story.) By 2002, when the federal suit reached court, Warshavsky had moved to Bangkok, following FBI and Department of Justice investigations into his business practices. No lawyer spoke on his behalf, and when a judge ordered his defunct company to pay Anderson and Lee $740,000 each, the couple never saw that money. So even if Anderson and Lee worked out a deal to profit off of the tape, who could blame them? With lawyers and judges shrugging and saying there was nothing to be done, with sites all over the web using her naked image without permission, cashing in for a small share may have seemed the best possible option. Oddly enough, St. George, who initially delivered the tape to Warshavsky, ended up managing and then taking control of the web and pay-per-view rights to the video, beginning in 2003. But in 2011, he let the license lapse. "I feel like there's a lot of bad karma around that video," St. George says, explaining that after he brought the tape to Seattle his marriage started to dissolve. "I worry about myself sometimes. What did I really do?" St. George's change of heart is indicative of a larger shift in recent years away from the defeatist, anything-goes attitude that many brought to the Internet even five years ago. Everyone laughed derisively at the tacky rock star and his blonde bimbo when the tape came out, but over the next two decades we all faced the same loss of control. The tape's slippery path into the public realm is a product of its unfortunate place at the fulcrum of two eras, before and after the Internet came to dominate commerce and communication, and its popularity demonstrated what rules our new, hyper-connected world might demand. We all know that the fun-house-mirror narrative of whatever gets recorded could end up defining us on the front page or in a government database, but the web is no longer the Wild West that it once was. "The Internet for too long has been viewed as different from traditional media when it comes to standards of ethics, as some creature that is a law unto itself," says Hollywood First Amendment lawyer Doug Mirell, who has represented celebrity clients in many invasion of privacy lawsuits, including Hulk Hogan in a current suit against Gawker Media over his sex tape. "The courts in particular are coming to recognize that the privacy invasive potential of the Internet is much greater than many had thought." Indeed, 13 states have passed so-called "revenge porn" legislation, to prevent exes from posting nude or sexual videos and photographs online. Europe and Argentina are experimenting with allowing citizens to petition to remove reputation-harming information from the web, calling it the "right to be forgotten." And these days Hollywood hangers-on are more likely to sell nude photos back to a celeb through their lawyer than risk releasing them illegally on the Internet. Denise Truscello/Getty Anderson and Lee have never quite been able to escape the shadow of the sex tape, but both seem to have done their best to move on and even poke fun at themselves. Lee's memoir opens with a dialogue between him and his famous penis, and Anderson does not seem chastened when it comes to her sexualized brand: She continues to pose nude, most recently as part of her activist work for PETA. The two divorced in 1998, remarried in 2008 and then divorced again in 2010. Strangely enough, Anderson has also twice married Rick Salomon, the man in Paris Hilton's sex tape. But while the video turned Lee into a rock & roll hero of sorts, a big-dick-swinging rapscallion in the public's eye, Anderson became something of a punch line. She had no sex-positive bloggers or pro-plastic-surgery tweeters around to defend her. No one stopped to dissect the notion that a woman who takes her clothes off for certain photographs has made her nude body into public property, and can't complain that images of her in even more compromising positions end up sold, posted and shared on a global scale. Both Ingley and Gauthier left porn for good after the tape debacle. After Peraino finally succumbed to cancer in 1999, Ingley came back to California, disheveled and broke. He soon moved in with his daughter, where he remained until he died. "I love Milton, but he ripped us all off," Gauthier says now. Tired of adult industry friends assuming he was hiding a small fortune, Gauthier distanced himself and began focusing on his electrical work full time. Seven years ago he moved up the coast, where he now lives, alone. His brawn has thickened in middle age. When I went to see him this past summer, he had just been dumped by a woman he'd been dating on and off for two years, an ex-stripper who he says refused to kiss him on the lips and didn't move during sex. Everyone once in a while, he'll tell someone he was the guy who stole the Pamela Anderson and Tommy Lee sex tape. Almost no one believes him. But he likes the fact that he contributed this small token to the world, and he's always enjoyed watching the tape itself. "It was cute. They're in love and a couple and they're just having fun with each other, and I think that's great," he says. "I'm jealous. I wish I had something like that." ||||| Electrician Rand Gauthier, now 57, thought stealing the infamous sex tape featuring Tommy Lee and Pamela Anderson would punch his ticket to fame and fortune. Instead, as a new in-depth piece in Rolling Stone explains, he ended up anonymous and alone -- while Lee's fame grew. "I made his career," Gauthier laments now, "is what happened." Gauthier had been working on an extensive renovation of Lee and Anderson's Malibu mansion in the spring of 1995 when the couple abruptly fired him. He said he was owed $20,000, but was prepared to write it off until Gauthier returned with a contractor to gather their tools and, he says, Lee pointed a shotgun at them, demanding they "get the f--- off my property." Something changed that day. "I was never really that popular with people," Gauthier admitted. "But I had never been held at gunpoint. It screwed with my head." Gauthier knew the couple had a giant safe hidden in a garage that had been converted into a recording studio. He figured there would plenty of valuables and tells Rolling Stone he was unaware of the existence of a 54-minute homemade film that would become one of the most infamous in history. "I don't know what's so interesting about watching a married couple f--," a clearly stunned Lee said in 1998. "I'm not the President. We were on vacation doing something the rest of the world does -- filming each other goofing around, naked. It's no big deal." Rolling Stone's Amanda Chicago Lewis says Gauthier spent that summer driving to Lee and Anderson's house several nights a week to case the place. He planned everything to the last detail -- including wearing a white Tibetan yak fur rug in order to disguise himself as the couple's dog from the security cameras -- except what might happen once he got back home with the loot. Details on how Gauthier actually got the giant safe out of the three-story Spanish-style home on an October morning remain sketchy. As Gauthier (and perhaps another accomplice) removed the safe, Rolling Stone reports that tall recording equipment was carefully replaced to obscured its hiding place. The safe was then reportedly whisked away to the Angeles National Forest, where Gauthier cut into the back of it with a saw. He found Rolex and Cartier watches, sparkling jewelry, various other keepsakes -- and a Hi8 camcorder cassette, Lewis says. He then reportedly watched it with the owner of a North Hollywood studio, where Gauthier moonlighted as a porn star. "We put it in and see what it is, and of course, cha-ching! The dollar signs fly before our eyes," Gauthier told Lewis. "But we're going, 'This is the kind of thing people will get killed over.'" Howard Stern Discusses the Sex Tape in 1997 Lee and Anderson didn't notice that the safe was gone until January 1996, meaning it was months before they filed a police report and hired a private investigator. By then, hundreds -- maybe thousands -- of copies of the sex tape were already in circulation. Two years later, it had gone viral, in one of the first such online instances, eventually making as much as $77 million. "Stupid Internet," Anderson exclaimed, in a talk with Entertainment Weekly. "I don't know why everyone is so impressed with it." Meanwhile, Gauthier was penniless and on the run -- and the original Hi8 artifact was long gone, according to Rolling Stone. The cassette was reportedly melted, and the tape itself cut into hundreds of pieces, by the late Milton "Uncle Miltie" Ingley, a porn star-turned-studio owner who was searching for a distributor. By then, Lewis says the remains of the master had been scattered in a desolate area near California's Six Flags Magic Mountain. When Lee and Anderson's private investigator finally followed the trail to Ingley, he reportedly told them he had a copy but that he'd purchased it from an interior designer named Guerin Swing. Swing knew nothing. Finding someone to partner with was not easy for Gauthier and Ingley. (Among those who initially passed on funding the release of the tape was legendary porn star Ron Jeremy.) They finally found funding for Internet distribution from Louis "Butchie" Peraino, scion of the Colombo family, a crime syndicate that had earlier financed 1972's controversial 'Deep Throat.' Ingley furiously copied tapes, launched several websites and began funneling money through a bank account in Amsterdam -- spending about a quarter of the initial $50,000 in funds from Peraino, according to Rolling Stone. As Gauthier continued hustling around Los Angeles in a van full of VHS tapes, Ingley eventually took off to spend the rest of the money on women, booze and drugs, Lewis writes. Another low-level Ingley Studios employee reportedly swiped his own copy, and made as much as $75,000 by selling dupes on the side. But Gauthier says he kept on the straight and narrow, running errands while everyone else lived it up. News Coverage of the Sex Tape Scandal Ultimately, as Lee and Anderson's private investigator, as well as some of their scary friends, began searching for the tape, Gauthier was forced into a life in the shadows -- sleeping on couches, when he could sleep at all. By March 1996, he was the target -- along with Penthouse magazine, Ingley and others -- of a $10 million civil lawsuit filed by Lee and Anderson that was meant to stem any further leaks. Ultimately, Ingley fled to the Netherlands as wave after wave of copycat sites began selling their own copies of the tape. The lawsuit was thrown out. That left Gauthier to deal with Peraino, who was still owed money. He says he ended up working as a strong-arm lackey for the mob. A court injunction followed in October 1997, ostensibly halting Ingley's overseas enterprise. But by then, web entrepreneur Seth Warshavsky had hatched an audacious plan that would take Gauthier completely out of the loop. On Nov. 7, he aired the tape on a website called Club Love for five straight hours. Everything Lee and Anderson had done to try to stop the tape's dissemination had failed, and the legal obligations had become a distraction. They signed away rights to the tape to Warshavsky, who then leveraged it into a flood of website subscriptions, VHS tapes, DVDs and even CD-ROMs, thanks to a side deal with Vivid Entertainment. Lee says he remains baffled by the whole thing. "I don't get why people feel they have to see that," he said in 2009. He also insists that the couple never profited from the tape. Neither, of course, has Gauthier. "I was the lowest guy on the totem pole," he told Lewis. "And I was so busy trying to make it work." Ingley ultimately waited out a cancer diagnosis for Peraino, returning to California after his angry benefactor passed in 1999. He in turn died broke and living with his daughter. Gauthier is still an electrician; his closest subsequent brush with fame involved a pot bust. Residing alone outside Santa Rosa, Gauthier admitted that he covets the obvious affection found on that swiped tape. "It was cute. They're in love and a couple, and they're just having fun with each other, and I think that's great," Gauthier told Rolling Stone. "I'm jealous. I wish I had something like that." You Think You Know Motley Crue?

– Remember an old sex tape, before Kim Kardashian, starring an actress and a rocker on a yacht? Well, the 1996 video that fully unveiled Pamela Anderson and Tommy Lee only went public because an electrician stole it, a mobster's son funded it, and lawyers couldn't contain it, Rolling Stone reports. Los Angeles native Rand Gauthier was laying wires at Anderson and Lee's Malibu mansion in 1995 when his relationship with the celebrities went sour, and Lee told him at gunpoint to "get the f--k off my property." Stewing, Gauthier says, he stole a safe from the rock star's garage and found a Hi8 tape among the valuables. "We put it in and see what it is, and of course, cha-ching," he says. "The dollar signs fly before our eyes. But we're going, this is the kind of thing people will get killed over." Even so, Gauthier teamed up with a porn producer to sell the video. They got funding from Louis Peraino, son of a New York mobster, to distribute the tape via newly created websites. Although the producer made money, Gauthier never did and says he ended up working collections for Peraino (throwing ammonia in people's faces and breaking collarbones) to pay off the debt. Lee and Anderson filed a $10 million civil suit to retrieve the video, but they couldn't stop it from going viral and later settled with a savvy distributor who was selling it online and in stores. Now Gauthier, who seems deflated, lives up the California coast doing electrical work again. "I believe in reincarnation, and this is kind of my vacation life," he says. "I have to come back and be really serious next time." See G-rated excerpts of the tape at Ultimate Classic Rock.

its causes are varied , but in all cases it is characterized by the appearance of local acute or chronic inflammatory changes occurring in the wall of the trachea . these changes lead to degradation over time and pathological restructuring of constituent structures and their replacement by fibrous tissue . they are often combined with the phenomena of general and local tissue hypoxia , which predispose to ischemic necrosis and ulceration of the mucous membrane of the trachea , and the local development of chondrite tracheomalacia . morphological changes during prolonged mechanical ventilation vary from epithelial damage with the formation of transmural necrosis to erosion of the tracheal wall to form a fistula between the esophagus and the trachea [ 1 , 2 ] . a pathogenetic factor and a trigger mechanism leading to development of the disease is damage to the wall of the trachea , followed by infection and the development of a purulent - necrotic process the outcome of which is the formation of a scar . modern respiratory and tracking equipment and development of a variety of pharmacotherapy in an intensive care unit have allowed the patient to be protected from a critical and grave condition for a long time , sometimes up to several weeks or even months . conducting prolonged mechanical ventilation in some cases creates conditions for the formation of irreversible changes in the tracheal wall and development of tracheal lumen narrowing , in some cases complicated by a tracheo - esophageal fistula [ 46 ] . at present in most cases trauma of the trachea is iatrogenic in nature and most often occurs during artificial lung ventilation ( alv ) , even more likely during prolonged mechanical ventilation through the endotracheal tube or tracheostomy tube , or as a complication during application of tracheostomy or at the time of intubation [ 710 ] . the aim of the study was to present the results of the successful one - stage radical surgical treatment of patients with cicatricial granulating tracheal stenosis after tracheostomy complicated by esophageal - tracheal fistula after numerous unsuccessful attempts to correct the narrowing of the trachea and eliminate the fistula by endoscopic and open surgical techniques . a 24-year - old female patient was diagnosed with scar - granulating tracheal stenosis after tracheostomy complicated by esophageal - tracheal fistula . on august 20 , 2014 as a result of a car accident the patient had severe concomitant injury . in the postoperative period for 22 days the patients underwent mechanical ventilation . after waking up in the early rehabilitation period the patient exhibited stridor . on suspicion of tracheal stenosis the patient was transferred to the ent clinic , where she underwent tracheoplasty on the t - tube . however , in the postoperative period , the patient began to experience the phenomenon of aspiration while taking liquid food . at the control examination ent doctors revealed that after removing the t - tube on the rear wall of the trachea in the projection of tracheostomy a tracheo - esophageal fistula with a size of 3 to 5 mm was determined . endoscopists performed installation of a nasogastric tube and laser photocoagulation of the fistula from the trachea side and from the side of the esophagus to cause the growth of granulation tissue which may contribute to the closure of the fistula . however , the control examination after 2 months by removing the t - tracheal tube despite nasogastric enteral nutrition and performance of laser coagulation showed that the fistula hole was not closed . the patient was directed to the surgeons for open surgery for closing the tracheo - esophageal fistula . in november 2014 the patient underwent the operation of liquidation of the esophageal - tracheal fistula by cervical access . the medical records indicated that was separation of the fistula by suturing and ligation , followed by placing a flap of sternocleidomastoid muscle between the esophagus and the trachea in the projection of the eliminated fistula channel . however , the early postoperative period was marked by the failure of the suture , recurrence of the fistula with an increase in its size and suppuration of postoperative neck wounds . the patient within 6 months had aspiration respiratory complications of the fistula . in april 2015 complaints of the patient referred to : dyspnea on exertion , the presence of a tracheostomy tube , cough with difficult expectoration , the presence of a nasogastric tube , the inability to eat by mouth , and inability to breathe through the natural airway . the studies found : defect of the frontal wall of the trachea and the soft tissue on the neck after the earlier projected tracheoplasty , size 15 to 35 mm , pronounced postoperative scars on the neck after suffering several operations of tracheoplasty attempts to eliminate the fistula and postoperative wound festering ( fig . 1 ) , scar - granulation narrowing of the trachea in the projection of tracheostomy and progression of the tracheal stenosis in 20 min after the removal of the t - stent due to lack of skeleton ( frame ) of the trachea and the presence of tracheomalacia ( fig . 2 ) , the presence of a fistula channel between the cervical trachea and esophagus with the size of 6 8 mm ( fig . the patient underwent preoperative anti - inflammatory therapy , antibiotic therapy , and remedial bronchoscopy . on july 5 , 2014 , the patient underwent the following operation : one - stage extended tracheal resection with end - to - end anastomosis with liquidation of the esophageal - tracheal fistula and elimination of the defect of the anterior wall of the trachea by cervical access . 5.5 cm of the affected part of the upper and middle third of the trachea was resected . 4 ) . the difference between this type of resection carried out in the treatment of isolated cicatricial tracheal stenosis without esophageal - tracheal fistula is that only the cartilaginous part of the tracheal wall is excised and removed and the membranous wall of the trachea is left in the zone of the esophageal - tracheal fistula to create an excess of tissue to perform closure of the fistula ( fig . also different is the method of forming the tracheal anastomosis : in circular resection of the trachea in patients with cicatricial stenosis we usually apply the technique of anastomosis with the formation of a posterior membranous wall by continuous biosyn 3.0 suture and with interrupted sutures on the side ( angle ) and front wall . but in formation of the anastomosis in patients with cicatricial stenosis complicated with esophageal - tracheal fistula there is a risk of inconsistency of the esophageal fistula s sutures that can be complicated by fatal failure in the transition to the tracheal anastomosis . in order to create a more solid and sealed back wall of the anastomosis we used the interrupted nodal biosyn 3.0 seams on the back , front and side walls ( figs . in order to minimize the tension in the area of the anastomosis seam we mobilized the trachea over the projection of the middle and lower third up to the bifurcation of the trachea with pulling in the cranial direction using tight ligatures . also we used the technique of temporarily fixing the head in position bringing it to the chest wall and suturing the skin of the chin on the chest for 14 days to eliminate the sharp head - up movement during sleep and the load on the anastomosis ( fig . defect of the frontal wall of the trachea and the soft tissue on the neck after the earlier projected tracheoplasty . pronounced postoperative scars on the neck computed tomography . defect of anterior wall of trachea , narrowing of the tracheal lumen , fistula computed tomography . tracheo - esophageal fistula on the back wall of the stoma diastasis between cranial and caudal part after resection of the trachea fistula hole . left tissue of the membranous part of the trachea around the fistula after resection of the cartilaginous part fistula stitched by interrupted absorbable sutures shunt - breathing . interrupted sutures on the back wall of the anastomosis shunt - breathing removed and orotracheal intubation tube inserted into the lower part of the trachea . anterior wall of anastomosis completed tracheal anastomosis head temporarily fixed in position at the chest wall the postoperative period was uneventful . the gastric feeding tube was removed on the 14 day . also after 2 weeks fixing lead sutures on the chin were removed . the patient was able to lift the head freely , and was breathing through the natural airway , with clear phonation . the patient underwent routine endoscopic examination at 1 month , 3 months and 5 months after surgery . in the area of the anastomosis bronchoscopy showed a smooth whitish thin line not protruding beyond the cartilaginous rings of the trachea . the lumen of the trachea in the zone of the anastomosis was without restriction or distortion . tracheal resection with simultaneous liquidation of tracheoesophageal fistula with stenosis of the trachea and defect after laryngotracheoplasty is the method of choice which can radically heal the patient at one stage after unsuccessful attempts to liquidate the tracheoesophageal fistula . the operation belongs to the category of complex reconstructive surgery and requires well - coordinated work of specialists

we present a case of one - stage radical surgical treatment of a 24-year - old female patient with cicatricial granulating tracheal stenosis after tracheostomy complicated by esophageal - tracheal fistula and an extensive defect of the anterior wall of the trachea after numerous unsuccessful attempts to correct the narrowing of the trachea and eliminate the fistula by endoscopic and open surgical techniques . the patient underwent extended tracheal resection with end - to - end anastomosis with liquidation of the esophageal - tracheal fistula and elimination of the defect of the anterior wall of the trachea by cervical access .

since the early 1960s with the efforts of sydney brenner , the nematode caenorhabditis elegans has been established as a popular model organism in developmental biology and neurobiology . there are many biological advantages that make it an attractive system for several fields of research . experiments in the late 1970s showed that it has an invariant cell lineage during establishment of the somatic tissues . it has two sexes , a self - fertilizing hermaphrodite and males , allowing genetic crosses to be performed . c. elegans has a short life cycle of less than three days and each hermaphrodite produces about 300 progeny by self - fertilization or up to 1000 progeny from cross progeny with males . the gonad is a relatively large organ in this animal , allowing for studies of organogenesis , cell proliferation , meiosis , and embryogenesis . during its development , the hermaphrodite worms produce sperm at one stage of their life cycle before switching to produce oocytes . its complete genome , sequenced in 1998 , was the first sequenced genome from a multicellular organism . it has a genome size of 97 megabases containing close to 19,000 protein coding genes . genome - wide alignments with other five related nematodes are now available for any comparative genomics approach . the modencode project systematically generated genome - wide data from transcriptome profiling , transcription factor - binging sites , and maps of chromatin organization to improve genome annotation . when comparing the c. elegans genome to higher eukaryotes , it was found that close to 40% of the genes that have been associated with diseases in humans have worm orthologues , and cancer is not the exception . in 1990 , the first report of an alternative splicing event in the c. elegans genome was published . interestingly the event corresponds to the pka mrna , a kinase implicated in the onset and progression of several cancers . since then , several groups have used different approaches to predict the percentage of genes in the c. elegans genome that undergo alternative splicing . initial estimates using a limited number of expressed sequence tags ( ests ) predicted fewer than 1000 genes to be alternatively spliced . by normalizing the occurrence of alternative splicing , taking into account the coverage of ests , it was estimated that close to 10% of the c. elegans genome undergoes alternative splicing . more recent analysis using next - generation sequencing identified 8,651 putative novel splicing events , suggesting that up to 25% of genes have an alternative splicing event ( figure 1(a ) ) . while this percentage is far from the > 90% reported for the human genome , it does show that alternative splicing in c. elegans is not an uncommon mechanism to generate protein diversity . the worm genome appears to be under selective pressure to promote a reduction in genome size . this natural selection towards a small genome can be seen in features like short intergenic regions , short utrs , and small introns [ 8 , 12 , 13 ] . for example , in humans , the median size of introns in the coding sequences is 1,334 bases , while in worms the average intron is just 65 bases ( figure 1(b ) ) [ 4 , 14 ] . more than 20 years ago , the small size of c. elegans introns was already the subject of study . it was demonstrated that a short 53 nucleotide worm intron could not be efficiently spliced in human extracts , while an expansion of this intron with 31 extra nucleotides allowed for efficient splicing . in spite of this reduction in intron size , the worm spliceosome is still capable of removing big introns ( 144 introns in the c. elegans genome are bigger than 10 kb ( figure 1(c ) ) ) . worms also have complex patterns of alternative splicing where multiple exons in the same gene are alternatively spliced to generate multiple isoforms ( figure 1(d ) ) . this means that the information content of a worm intron is on average greater than in higher eukaryotes ( higher density of functional elements in introns ) . this makes the molecular dissection of worm introns easier to achieve . by using genomic alignments between two caenorhabditis species , the identification of novel other groups have also used comparative genomics together with uv cross - linking and electrophoretic mobility shift assays ( emsa ) to identify cis - elements important for alternative splicing regulation . several studies comparing alternative splicing events in mammals and insects concluded that a high percentage of the events are not conserved and are species specific [ 19 , 20 ] . this high variability in alternative splicing makes it necessary to validate the functionality of the events studied . to test whether the smaller percentage of genes with alternative splicing in worms also follows these patterns of high variability during evolution , several groups have measured the levels of conservation between different c. elegans populations or between related species [ 21 , 22 ] . in comparison to the findings in higher eukaryotes , the regulation of alternative splicing in natural populations of nematodes appears to be under strong stabilizing selection with low intra- an interspecies variability . these results point to an essential intrinsic characteristic of alternative splicing in worms : its functionality . the detection of alternative splicing in a c. elegans transcript has a higher probability of being a functional and regulated event than in other systems . a proxy for the functionality of an alternative splicing event that has been used for other systems is its regulation . if a particular event is detected as regulated across different conditions or during development then the possibility that the isoforms have specific functions is higher . in the last five years c. elegans joined other species in terms of the detection of changes in alternative splicing at genome - wide levels . initially with the use of splicing - sensitive microarrays and later with the use of next - generation sequencing the regulation of alternative splicing in worms has been studied in detail across different conditions and mutations [ 10 , 23 , 24 ] . initial measurement of changes in splicing during development demonstrated that up to 40% of the events detected are regulated ( > 2 fold ) between different stages of worms ( figure 1(a ) ) . the alternative splicing regulation of a neuron - specific exon of unc-32 , the worm a subunit of v0 complex of vacuolar - type h - atpases , was recently characterized . a male - specific isoform of unc-55 , a transcription factor , has also been reported . while individual examples of tissue - specific splicing are known , a genome - wide analysis of tissue - specific splicing is still missing . with the increased sensitivity of next - generation sequencing techniques , together with the availability of manual or molecular dissections that allow the isolation of tissue - specific mrna ( mrna - tagging ) a complete catalog of tissue - specific splicing should be possible in the near future . while a big set of splicing events produce two protein isoforms , another important group introduces premature termination codons ( ptc ) to one of the isoforms . it is known that the introduction of a ptc to one isoform targets it to nonsense - mediated decay ( nmd ) ( reviewed in ) . contrary to other systems where mutations in nmd factors are lethal , in worms , null mutations for all the seven core factors of nmd are viable ( smg-1 to smg-7 ) . some of the first events of wild - type transcripts that were shown to be regulated by nmd are splicing factors in the c. elegans genome . an important discovery concerning the regulation of alternative splicing in worms is that between 2035% of the events in the genome appear to be targets of nmd ( figure 1(a ) ) [ 24 , 31 ] . the conclusion from these studies is , then , that alternative splicing in c. elegans is not just a generator of protein diversity but also an important regulator that fine - tunes gene expression levels by targeting specific isoforms for degradation . furthermore , it has been proposed that nmd in worms can also be regulated with the potential to stabilize particular nmd targets allowing them to be translated into truncated proteins with putative dominant negative functions . one of the advantages of c. elegans as a model system is the availability of powerful tools for reverse genetics . any laboratory can obtain stable mutants for many genes from the caenorhabditis genetics center ( cgc ) at the university of minnesota . the national bioresource project in japan runs a program where mutants for a gene of interest can be requested and they are obtained at the facility by a protocol involving random mutagenesis with tmp / uv . these two centers allow for any group to obtain mutant strains for the gene of interest in an inexpensive and expedited manner . recently , a more ambitious project to create a million different mutants has been performed by the moerman and waterston labs . the aim of this project was to use next - generation sequencing and a collection of 2000 mutagenized strains to identify multiple mutations in virtually all the genes in the worm genome . this project will likely allow the study of mutant worms that have mutations in isoform - specific regions . all these resources allow for the use of stable mutants to characterize the roles of either putative splicing factors or more specifically of particular isoforms . this approach to screen the effects that mutations in different splicing factors have on a particular splicing event has been used before . the conclusion from this work was that the coregulation of alternative splicing by diverse factors is a common phenomenon in worms . another great resource for the worm community is the availability of genome - wide rnai libraries . researchers aiming to characterize genetic pathways have used these libraries for genome - wide screens . some of them have found that several splicing - related components have interesting phenotypes when targeted by rnai . more focused screens with a subset of clones from these libraries are used to characterize a specific group of genes . all the predicted c. elegans splicing factors and found that many of them showed an overproliferation phenotype in a sensitized germline background . one of the most advantageous tools for the study of alternative splicing in c. elegans is the use of bichromatic alternative splicing reporters . this transgenic reporter system allows the visualization of splicing events by tagging each one of the isoforms with a different fluorescent protein . a worm population with differences in splicing regulation can then be sorted using facs cytometry and worms with a particular splicing ratio obtained . this together with the use of mutagenesis or rnai allows performing an in vivo screen for regulators of any splicing event of interest . the advantage of these reporters in worms is that the characterization of an alternative splicing event can be performed in vivo . different events that have been studied with this technology are egl-15 , let-2 , unc-60 , and unc-32 [ 25 , 3740 ] . this technology has allowed the identification of splicing factors that regulate these events , as well as the cis - elements that are necessary for its regulation . given the diversity of tools available to perform studies in c. elegans , researchers have set out to understand details about cancer that were long a mystery . questions surrounding cell proliferation and cell - cell communication as well as the cellular and molecular components that make up a stem cell niche often must be answered in a multicellular context . furthermore , the fact that biological processes and factors active in splicing and human cancers are almost wholly homologous with those in c. elegans makes the move to worm studies rewarding . disrupted cancer pathways in c. elegans , for the most part , have clear , simple , and observable phenotypes that extend beyond just cell death or proliferation . using these pathways as tools and read - outs , splicing factors and splicing events have been identified , in c. elegans , to interact with , regulate , and cooperate with homologous pathways that lead to cancer in humans ( figure 2 ) . overwhelming evidence links cell signaling and gene expression changes in the promotion of human cancers . alternative splicing plays a major role in defining the activity of signal transduction pathways such as ras / let-60 . strikingly , of the 5060 genes that are known components of , regulate or , are directly regulated by the ras / let-60 pathway in c. elegans , approximately half of them produce multiple isoforms differing by at least one alternative exon . this highlights the importance of proper gene expression through post - transcriptional regulation ( table 1 ) . the ligand - dependent ras pathway in c. elegans stimulates the induction of vulval precursor cells ( vpcs ) in the hypodermis to divide and differentiate into a functional vulva during larval development [ 42 , 43 ] . increased signaling from the ras pathway leads to a multivulval ( muv ) phenotype , while decreased signaling causes a vulvaless ( vul ) phenotype . these simple and observable phenotypes provide an excellent system to ascertain the contributions of alternative splicing to ras signaling activity . the c. elegans homolog of the ras - mapk pathway stimulant epidermal growth factor , lin-3 , produces several isoforms with unique characteristics . lin-3 isoform specialization of function has previously been observed in pathways aside from ras - mediated cell signaling and has been found to differentially mediate growth rates , feeding behavior , and cellular quiescence . in vpcs , the activity of the lin-3l isoform is dependent on interaction with the c. elegans rhomboid protease homolog , rom-1 , while the activity of lin-3s is not . lin-3s is expressed in a specialized anchor cell ( ac ) responsible for inducing a primary set of vpcs during larval development , and lin-3l expression and possible secretion by primary vpcs themselves act as a ligand stimulant of the ras pathway in secondary vpcs [ 42 , 43 ] . this stimulation may cause the secondary vpcs to switch their cell fate from hypodermis to vulva . it is unknown if coordinated expression of these isoforms from distinct cell types establishes a gradient through ras signaling that induces nearby vpcs to proceed through necessary cell divisions to develop into a proper vulva . rasgaps are gtpase - activating proteins that specifically promote the hydrolysis of ras - bound gtp molecules , thereby inactivating the ras molecule and its signaling . gap-2 , in c. elegans , is similar to the p120 ras - gap family . the gene contains 25 exons that use alternative splicing and transcription start sites to produce 9 mrna products . these isoforms were identified by a rapid amplification of cdna end ( 5race ) technique using primers specific to a sequence common to many mature mrnas in c. elegans , the sl1 trans - splice leader . this 22nt sequence is naturally spliced onto 5 ends of transcripts from ~70% of genes . in this case , they served as 5 primer binding sites in reverse transcription reactions followed by pcr to identify isoforms with alternative 5 ends and promoters . differential expression of gap-2 isoforms in several tissue types was revealed by expression of transgenes containing these alternative gap-2 promoters fused to gfp in c. elegans . the function of rasgap proteins from various genes in other organisms may be relegated to multiple isoforms from a small number of rasgap genes producing many isoforms in c. elegans . while the effects of this dynamic expression pattern of isoforms on molecular signaling pathways such as the ras pathway are difficult to tease apart , target sites for pkc , pka , and protein tyrosine kinases present or absent in each isoform may provide clues to individual isoform activities . homozygous mutations of the retinoblastoma ( rb ) gene have been shown to promote retinal cancer , small - cell lung carcinomas , and osteosarcomas . in worms , a single homolog of rb , lin-35 , represses the multivulval phenotype observed in ras pathway hyper - signaling mutants . two redundant pathways , termed synthetic multivulval ( synmuv ) class a and class b , are active in the vpcs and induce changes in expression of genes that lead to a multivulval fate through histone modification and chromatin remodeling [ 53 , 54 ] . to induce a phenotype , interestingly , mutations in the lin-15 locus created alleles with muv , class a synmuv , and class b synmuv phenotypes , leading to speculation that two genes existed at the locus with distinct functions in each pathway . in rnai screens for interactors of the class b synmuv pathway in c. elegans , 57 genes were found to enhance the muv phenotype observed in lin-35 or other synmuv class b mutant lines [ 35 , 55 ] . ten of these potential interactors ( rsr-2 , lsm-2/gut-2 , lsm-4 , snr-17 ) have roles in splicing . while the activities , interactions , and mutant phenotypes of most of these splicing - related rb enhancers are not well understood , rnai of some of the snr genes ( snr-1 , snr-2 , snr-4 , snr-5 , snr-6 , and snr-7 ) led to embryonic lethality and nuclear pore organization disruption . the question of whether these phenotypes arise from disrupted functions that have no role in splicing regulation is still unanswered , but evidence is mounting supporting the idea that constitutive splicing and alternative splicing are major contributors in c. elegans to pathways that , when altered , lead to cancer in human tissues . undoubtedly , future studies in c. elegans will enrich current knowledge concerning the interwoven activities of splicing and the rb / lin-35 pathway . protein kinase a ( pk - a ) is involved in many cellular processes and has been implicated in several cancers . the mammalian pk - a is composed of two distinct subunits , the regulatory and catalytic , that are each interchangeable with protein subunits from several genetic loci . the two subunits of pk - a are conserved in c. elegans but derived from possibly only three genes , kin-1 , kin-2 , and f47f2.1 . interestingly , the modularity of the subunits that make up pk - a in c. elegans has been conserved through alternative usage of exons . the catalytic subunit ( c - subunit ) alone is thought to undergo alternative splicing at both n- and c - termini to create at least 12 different isoforms . these isoforms are conserved in c. briggsae , a relative of c. elegans , and show differential expression during development , suggesting that the diversity of potential subunits itself has functional importance . an isoform of the c - subunit containing the n1 exon harbors a myristoylation site and is highly expressed in eggs , where an alternative exon n4 lacking the myristoylation site is highly expressed in adult worms . the presence of n1 protein isoform expression and myristoylation was found to affect substrate targeting of pk - a but not the catalytic activity of the enzyme itself . similarly , isoforms of the regulatory ( r - subunit ) have recently been identified and found to contain or lack domains necessary for docking to a - kinase anchor proteins and the c - subunit of the pk - a holoenzyme . a second gene on the x chromosome of c. elegans , f47f2.1 , has homology to murine c subunits . like the kin-1 n4 isoform , expression of the longer f47f2.1b isoform is low in eggs but high in mixed populations of worms . a truncated isoform , f47f2.1a , lacks amino acids important for atp - binding , and knockdown of n4 kin-1 isoform has no obvious phenotype leading to speculation that some of these isoforms may be redundant or unnecessary [ 59 , 62 ] . isoforms from the same genetic locus often have distinct expression patterns and functions that are seemingly unrelated . c.elegans dna topoisomerase i ( top-1 ) produces two isoforms that vary in temporal and spatial expression patterns . cellular and subcellular localization differences between the isoforms lead to speculation they may function in different processes . the top-1 isoform skips exon 2 and is more ubiquitously expressed throughout c. elegans development , being found in multiple cell types and all stages from embryo through adulthood . conversely , the inclusion isoform , top-1 , is detectably present in embryos and , interestingly , in neurons at the comma stage , then decreases in abundance as worms enter larval stages . isoform - specific immuno - histochemical localization assays in germline cells identified top-1 concentration in nucleoli and top-1 concentration at centrosomes and on chromosomes [ 64 , 65 ] . expression of a gfp transgene driven by the topoisomerase promoter was also detected strongly in the distal tip cell of l3/l4 worms indicating that somatic gonad sheath development and/or germline stem cell proliferation may be regulated by top-1 activity . rnai of c. elegans top-1 reduced the number of germ cells in the mature germline by anywhere from 50100% . it is currently unknown how top-1 isoforms contribute to the maintenance of stem cell proliferation or exactly which isoform would be performing such functions . localization of the inclusion isoform , top-1 , to centrosomes and chromosomes suggests it could be involved in chromosome segregation , in regulation of transcription , or possibly in posttranscriptional regulation . it was found to phosphorylate splicing factors involved in cell cycle regulation , such as sf2/asf [ 67 , 68 ] . it may be possible that these isoforms are working more closely than originally thought if one or both of the top-1 isoforms affect the cell cycle and carry the same sr kinase activity as shown in hela cells . the activity of one or both of the top-1 isoforms as sr protein kinases suggests that top-1 alternative splicing may be autoregulated . several genes involved in splicing regulation have been implicated in the proliferation / differentiation decision in the c. elegans germline . glp-1(ar202gf ) worms were used to perform an rnai screen searching for genes that led to increased cell proliferation in the germline . the resulting genes included factors involved in every step of the splicing process ( spliceosome construction initiation , reorganization of the snrnp complex and removal of the lariat ; ) . prp-17 , for example , encodes an ortholog of yeast cdc40 and human prp17 and is involved in the 2nd catalytic step of intron removal in the spliceosome [ 36 , 69 ] . rnai of prp-17 in the rrf-1(pk1417);glp-1(oz264 ) background enhanced germline tumors , suggesting that it is involved in the proliferation versus differentiation decision . similarly , the mog genes represent c. elegans homologs of core yeast splicing factors that regulate the pathway downstream of glp-1 to promote differentiation and the oocyte fate of maturing germ cells [ 7072 ] . the u2 snrnp - associated splicing complex sf3b is essential for splicing [ 73 , 74 ] . teg-4 is the worm homolog of human sf3b subunit 3 ( aka sap130 ) that increases excessive cell proliferation in the glp-1(ar202gf ) background . interestingly , epistasis experiments attempting to determine the genetic relationship between teg-4 and the glp-1/notch signaling pathway in various cell types were inconclusive . teg-1 , the c. elegans homolog of cd2bp2 has been found to bind uaf-1 , the worm u2af large subunit homolog , suggesting that it could work in two important steps in the mechanism of pre - mrna splicing . teg-1(oz230 ) , in combination with a glp-1 mild gain - of - function mutant background , produces a tumorous germline phenotype as well . to what extent splicing factors , themselves , have individual genetic interactions within the proliferation versus differentiation pathways or if global splicing regulation is more indirectly influential is still unknown . disruption of alternative splicing patterns may affect the onset of programmed cell death so intricately regulated in c. elegans . the worm homolog of apaf1 , ced-4 , was first identified as a core factor in the developmental induction of neuronal programmed cell death . ced-4 physically links ced-3 , a member of a caspase family of proteases to ced-9 , a cell death suppressor [ 7981 ] . as a regulatory switch , ced-4 is a core determinant of the decision of a cell to be systematically culled or not . ced-4 encodes two protein isoforms , ced-4l and ced-4s , differing by 24 amino acids at the 5 end of exon 4 . while ced-4s normally promotes programmed cell death , overexpression of the ced-4l isoform led to ectopic cell growth and rescue of lethal phenotypes seen in ced-9 loss - of - function mutants [ 82 , 83 ] . it is ced-4l association with ced-3 that surprisingly inhibits cell death in a dominant negative manner . the presence of the longer p - loop in the long isoform still allows for association of ced-4l with the protease domain of ced-3 but disrupts the association of ced-4l with the prodomain of ced-3 , which normally contributes to its activation . studies in mammalian cells have similarly identified ced-3 and ced-4 homologous genes that produce isoforms with opposing cell death functions [ 85 , 86 ] . an imbalance in the concentrations of these isoforms or in the abundance or activities of specific sr or hnrnp proteins often leads to one developmental cell fate over the other . loss - of - function of an sr protein kinase , spk-1 , in a ced-4 partial loss - of - function background , as well as mutant alleles of several sr proteins themselves , leads to an increase in apoptosis , suggesting that control of alternative splicing factor activity may play a direct or indirect role in the regulation of developmentally programmed apoptosis . in vitro studies have shown that spk-1 can bind and phosphorylate alternative splicing factors like sf2 and rnai - mediated knockdown of spk-1 in c. elegans causes embryonic lethality and germline development defects [ 89 , 90 ] . experiments aimed at understanding the complex code that dictates what genetic material is included or skipped in mature mrna and subsequent protein products will undoubtedly clarify further the impact that alternative splicing has in the mediation of programmed cell death through factors such as ced-4 . great strides have been taken in research to understand the involvement of splicing factors in biological processes such as cell proliferation , differentiation , migration , communication , and death ( as discussed previoussly ) . transgenic assays have revealed cellular and subcellular localization of specific isoforms that may be involved in apoptotic or cell cycle regulation . lineage tracing experiments have not only identified every cell in an adult worm but also precursors and cell behavior throughout development . furthermore , only in a multicellular organism , such as c. elegans , can the effects of cell - to - cell signaling on processes such as differentiation or cell proliferation become apparent . high - throughput sequencing and bioinformatic analyses are opening a new chapter on comparisons in isoform usage between genetic backgrounds . the modencode project seeks to identify functional elements within the drosophila and caenorhabditis genomes by providing access to high - quality gene expression datasets . furthermore , the million - mutation project in c. elegans will allow researchers to obtain gene and even isoform - specific mutant strains for further study . given the speed and depth of discoveries using methods such as rnai in worms , this project should make c. elegans a core model to study alternative splicing and its link to genes homologous to those tied to cancer in humans .

alternative splicing allows for the generation of protein diversity and fine - tunes gene expression . several model systems have been used for the in vivo study of alternative splicing . here we review the use of the nematode caenorhabditis elegans to study splicing regulation in vivo . recent studies have shown that close to 25% of genes in the worm genome undergo alternative splicing . a big proportion of these events are functional , conserved , and under strict regulation either across development or other conditions . several techniques like genome - wide rnai screens and bichromatic reporters are available for the study of alternative splicing in worms . in this review , we focus , first , on the main studies that have been performed to dissect alternative splicing in this system and later on examples from genes that have human homologs that are implicated in cancer . the significant advancement towards understanding the regulation of alternative splicing and cancer that the c. elegans system has offered is discussed .

Image copyright EPA Image caption Syriza leader Alexis Tsipras says he wants negotiation - not confrontation - with Greece's lenders It is unrealistic to expect Greece to repay its huge debt in full, the chief economics spokesman for the victorious Syriza party has told the BBC. "Nobody believes that the Greek debt is sustainable," Euclid Tsakalotos said. The far-left Syriza, which won Sunday's general election, wants to renegotiate Greece's €240bn (£179bn; $270bn) bailout by international lenders. EU leaders have warned the new Greek government that it must live up to its commitments to the creditors. Syriza leader Alexis Tsipras - who was sworn in as prime minister on Monday - is expected to unveil his new cabinet later on Tuesday. "I haven't met an economist in their heart of hearts that will tell you that Greece will pay back all of that debt. It can't be done," Mr Tsakalotos said. Image copyright AP Image caption Syriza supporters - like the majority of Greeks - want an end to tough budget cuts Image copyright EPA Image caption The euro briefly touched an 11-year low against the dollar on Monday, before recovering He said that EU leaders needed now to show that they were willing to work with Syriza. "It's going to be a very funny and a very dangerous Europe with very strong centrifugal political forces if they signal that after a democratic vote they're not interested in talking to a new government. "It will be a final signal that this is a Europe that can't incorporate democratic change and it can't incorporate social change." But Mr Tsakalotos stressed that it would be "my worst nightmare if the eurozone collapses because Greece falls". "And if Greece falls and is removed from the eurozone - the eurozone will collapse. We said from the beginning the eurozone is in danger, the euro is in danger, but it isn't in danger from Syriza... it is in danger from the very policies of austerity". Analysis: Robert Peston, BBC economics editor If Syriza were to win its negotiations with the rest of the eurozone, other anti-austerity parties would look more credible to voters. The victory of protectionist Marine le Pen in France's presidential election would be an interesting test of markets' sangfroid. And if Syriza were to lose in talks with Brussels and Berlin, and the final rupture of Greece from the euro were to take place, investors might well pull their savings from any eurozone country where nationalists are in the ascendant. So why are investors not in a state of frenzied panic? Why have the euro and stock markets bounced a bit? One slightly implausible explanation is that investors believe the eurozone would actually be stronger without Greece, so long as no other big country followed it out the door. More likely is that they believe reason will prevail, and Berlin will sanction a write-off of Greece's excessive debts. Robert Peston: Full analysis A turning point for the EU? Tears of joy at Syriza party What next? Mr Tsipras earlier stressed that he wanted negotiation - not confrontation - with international lenders. "The new Greek government will be ready to co-operate and negotiate for the first time with our peers a just, mutually beneficial and viable solution," he said. The troika of lenders that bailed out Greece - the European Union, European Central Bank, and International Monetary Fund - imposed big budgetary cuts and restructuring in return for the money. 'Little support' Media playback is unsupported on your device Media caption Former EU finance commissioner Olli Rehn: "We expect Greece to pay back its debt" Meanwhile, EU Commission President Jean-Claude Juncker warned that Greece cannot expect any reduction of its debt commitments. He said it "is not on the radar" of the commission. German government spokesman Steffan Seibert stressed it was important for Greece to "take measures so that the economic recovery continues". Jeroen Dijsselbloem, president of the Eurogroup, said on Monday: "There is very little support for a write-off in Europe." Syriza's victory has caused some concern in the financial markets. In a volatile start to the week the euro briefly touched an 11-year low against the dollar early on Monday, before recovering to trade almost 0.7% higher against the US currency. Key dates ||||| Yanis Varoufakis, 53, is known for his running commentary on the financial crisis in a series of blogposts that have won him thousands of Twitter followers and the respect of Syriza’s leadership. John Maynard Keynes with a hint of Karl Marx is how one analyst described the self-proclaimed “accidental economist” who is now to become Greece’s finance minister and a key negotiator with its international creditors. With a typically literary flourish, he celebrated his party’s victory by paraphrasing Welsh poet Dylan Thomas. “Greek democracy today chose to stop going gently into the night. Greek democracy resolved to rage against the dying of the light,” the Greek-Australian wrote on his blog. One of the first two ministers to be confirmed by prime minister Alexis Tsipras, Varoufakis studied at Essex University and has taught in Australia, Greece and the United States. In pre-election interviews he vowed to destroy Greek oligarchs, end what he called the humanitarian crisis in Greece and renegotiate the country’s debt mountain. “We are going to destroy the basis upon which they have built for decade after decade a system, a network that viciously sucks the energy and the economic power from everybody else in society,” he told Britain’s Channel 4 television. But the muted market reaction to Syriza’s decisive win was at least in part because investors expect the thoughtful powerbroker to adopt a more emollient style ahead of tough negotiations. Writing before the election, Paolo Pizzoli, senior economist at ING Financial Markets in Milan, highlighted the economics professor’s “constructive attitude” after he talked about the need to “minimise conflict and maximise the chances of a mutually beneficial agreement”. “We believe that, if in power, Syriza could prove more pragmatic than many anticipated,” said Pizzoli.

– As Greece's newly elected Syriza party takes office, its top economics spokesman is making the party's views on debt clear. It's "unrealistic" to think that Greece will be able to pay back the $270 billion bailout it received from the eurozone and other lenders, Euclid Tsakalotos tells the BBC. "I haven't met an economist in their heart of hearts that will tell you that Greece will pay back all of that debt. It can't be done," he says. "Nobody believes that the Greek debt is sustainable." But the EU says it does expect repayment: A reduction in debt "is not on the radar" of the EU commission, says its president, Jean-Claude Juncker. Tsakalotos has said he's not looking for a showdown. "The new Greek government will be ready to cooperate and negotiate for the first time with our peers a just, mutually beneficial and viable solution," he noted. The EU should be prepared to talk, he says, noting that it will be "a very dangerous Europe with very strong centrifugal political forces if they signal that after a democratic vote they're not interested in talking to a new government." If Greece "falls," he says, the eurozone will "collapse," which would be "my worst nightmare." Meanwhile, new prime minister Alexis Tsipras has announced his new cabinet, which includes economics professor Yanis Varoufakis—whom an analyst has called "John Maynard Keynes with a hint of Karl Marx"—as finance minister, the Guardian reports.

in the present paper we introduce the notion of @xmath2braids as well as their generalization : groups of @xmath3braids for any arbitrary group @xmath1 . they form a natural group theoretical analog of @xmath3knots , first introduced by the second author in @xcite . those objects naturally generalize the classical ( artin ) braids . @xmath3braids have a natural structure : every classical crossing of a braid is decorated with an element of @xmath1 . we also give another presentation of the group of @xmath2braids ( and even of a broader group ) where the information about the group elements is contained in the braid strands . that leads one to the notion of dotted braids : classical ( artin ) braids live inside the dotted braids group , being braids with a diagram with no dots on the strands . a similar object is defined : twisted dotted braids . in theories dealing with additional structures on objects diagrams ( say , parity , dots , group structures ) an important role is played by the theorems of the following form : _ if two objects are equivalent as objects with an additional structure ( hence with a broader set of moves allowed ) then they are equivalent as objects without this structure_. an example of this kind of theorems is given by the theorem on classical braids being equivalent as virtual yielding their equivalence as classical ( see , for example , @xcite ) . there are two theorems of that type in the present paper . the first one deals with classical braids being equivalent as @xmath2braids and the second with @xmath2braids equivalent as dotted braids . in both cases the equivalence can be `` descended '' to a smaller class of braids with a smaller set of allowed moves . virtual braids as well as virtual knots possess many nice properties which lead to powerful invariants ( see @xcite ) . as it has been recently found ( see @xcite ) , picture valued invariants appear in the case of classical braids by using groups @xmath4 . thus , a natural question arises : are there any models representing virtual braid groups inside classical braid groups ? certainly , if we do not admit further modifications , the answer will be negative since classical braid groups have no torsion . the present paper is a first step of understanding the above mentioned question by introducing the idea of parity into the study of classical braids . a list of unsolved problems is given in the present paper . first let us recall the definition of a _ @xmath5stand braid_. there exists several ( equivalent ) definitions ; we will formulate the one we will be using in the paper . the @xmath5strand braids group is a group given by @xmath6 generators @xmath7 and the following set of relations : @xmath8 for all @xmath9 ( far commutativity ) and @xmath10 for @xmath11 . this set of relations is called the _ artin relations_. in other words , the braid group elements are the equivalence classes of words in the alphabet @xmath12 modulo the above mentioned relations . such words are also called _ braid words_. the definition of braids via the artin presentation can easily be interpreted geometrically . to this end the notion of a _ flat diagram _ of a braid is introduced . flat diagram of a @xmath5strand braid is a graph inside a rectangle @xmath13 $ ] with the following additional structure and properties : 1 . the graph vertices of valency 1 are the points @xmath14 $ ] and @xmath15 $ ] , @xmath16 . 2 . all other vertices are of valency four . the opposite edges in such vertices are at the angle of 180 degrees . the braid strands monotonously go down with respect to the coordinate @xmath17 . every four valent vertex is decorated with a `` overcrossing undercrossing '' structure . two diagrams are considered equal if they can be connected by a chain of flat isotopies ( with the condition of the strands always being monotonously going down ) , second and third reidemeister moves . . ] now , for the generators @xmath18 of the braid group take the braids of the following form : @xmath18 for @xmath19 consists of @xmath20 intervals connecting the points @xmath21 $ ] with @xmath22 $ ] for all @xmath23 and two intervals @xmath14-[i+1,1],\ , [ i+1,0]-[i,1]$ ] such that the latter goes over the former ( see fig . [ generators ] ) . for the inverse element @xmath24 we take the same braid but with the crossing structure in the only crossing reversed ( see fig . [ inverse ] ) . it can be easily seen that the existence of the inverse is exactly the invariance under the second reidemeister move , the relation ( [ raid3 ] ) the third reidemeister move , and the far commutativity can be understood as the commutativity of the crossings with no mutual strands . . ] now let us define a new object : @xmath2briads or _ braids with parity _ ( see @xcite ) . from now on we will use the algebraic definition but keep in mind that there is always an underlying geometric object , probably with an additional structure . the @xmath5strand @xmath2braid group is a group with generators @xmath25 @xmath26 and the following set of relations : @xmath27 for all @xmath9 and all @xmath28 ( far commutativity ) and @xmath29 where @xmath11 and @xmath30 . we will call the @xmath31 generators _ even _ and the @xmath32 ones _ odd_. the @xmath5strand @xmath2braids group will be denoted by @xmath33 . from the geometric point of view this definition means an additional structure ( `` parity '' ) being introduced in the braid crossings . the parity is such that every two crossings in a second reidemeister move are both even or both odd and among the three crossing in the third move either two or zero are odd . when working with objects with additional structure which are related to objects with no such structure one should keep in mind the following important principle : _ if two objects are equivalent as objects with additional structure ( and thus with a broader set of moves and equivalences allowed ) they are equivalent as objects without the structure ( therefore connected with a chain of moves from a smaller set)_. in case of classical and @xmath2braids this principle is true . in other words , the following theorem holds : [ classic_in_2 ] if two braids without odd crossings are equivalent as @xmath2braids , they are equivalent in the class of the braids with no odd crossings ( even braids ) . to prove this fact we need a lemma relating @xmath2braids with virtual braids . let us recall the definition of virtual braids : the @xmath5strand virtual braids group is a group with @xmath6 generators @xmath7 and @xmath6 generators @xmath34 and the following set of relations : @xmath35 for all @xmath9 ( far commutativity ) and @xmath36 for @xmath11 ; @xmath37 for all @xmath9 ( far virtual commutativity ) and @xmath38 for @xmath11 , @xmath39 @xmath40 @xmath41 for all @xmath9 . the virtual braid group will be denoted with @xmath42 . [ virt ] there exists a homomorphism from the the group @xmath33 into the virtual braid group @xmath42 . consider the following mapping from the group of @xmath2braids to virtual braids : @xmath43 in other words , every odd crossing is sent to a virtual crossing . an elementary check shows that ( due to the parity properties ) the mapping is well defined : if two elements of the group @xmath33 are equal , their images are also equal as the elements of the group @xmath42 . note , that this mapping does nt provide us with a homomorphic _ inclusion _ of virtual braids into @xmath2braids . the inverse mapping , sending @xmath18 to @xmath31 and @xmath44 to @xmath32 is `` bad '' since the image of the third virtual reidemeister moves ( with all crossings being virtual ) in @xmath2braids is not an allowed move and a square of an odd generator is not trivial , while @xmath45 in virtual braids . let us now prove theorem [ classic_in_2 ] . consider two classical braids @xmath46 such that their images in @xmath33 @xmath47 are equal . let us show that the braids @xmath48 are equal as classical braids . since the braids @xmath47 are equal , they are connected by a chain of moves : second and third reidemeister moves with certain conditions on the parity of the crossings involved . due to lemma [ virt ] their images in the virtual braid group are also equal . but it is well known ( see for example @xcite ) that if two classical braids are equal as virtual , they are equal as classical . therefore @xmath48 are equal in the class of classical braids and the proof is concluded . the idea of endowing a crossing with an additional structure can be generalized in the following manner . let @xmath1 be an arbitrary group . let us define the @xmath3braid group . the @xmath5strand @xmath3braid group is a group with generators @xmath49 @xmath50 and the following set of relations : @xmath51 for all @xmath9 and all @xmath52 ( far commutativity ) and @xmath53 for @xmath11 and @xmath54 ; here @xmath55 means the neutral element in the group @xmath1 ( see fig . [ raid3_g ] ) . braid . ] we shall say that a braid diagram _ admits a source sink structure _ if there exists such an orientation of its graph edges that for every four valent vertex two opposite edges are incoming and two are outcoming . from the geometric point of view the @xmath3braid structure means the decoration of every crossing with an element of the group @xmath1 with the condition that the product of the elements in every lune and triangle , written according to the source sink structure , equals the neutral element in @xmath1 . as an example consider the group @xmath0 . in that case the inverse for any element is the element itself , so for every three labels @xmath56 corresponding to to the crossings in the third reidemeister move , we have @xmath57 . in other words , exactly two or zero of those labels are all equal to 1 . therefore we see , that the group @xmath58 is isomorphic @xmath33 . note , that in case of , say , virtual braids the source sink structure is not always admitted . therefore the definition of @xmath3braids ca nt be given verbatim and requires additional considerations . nevertheless , it is possible to define analogous constructions in the virtual case , not unlike the @xmath3knots and virtual @xmath3knots ( see , for example , @xcite ) . it is important to remember , though , that such object requires caution in the definition of what products of group elements , attributed to the crossings , equals the group neutral element . the parity structure , introduced in the crossings , can be reimagined as a parity on edges . this approach broadens the class of considered objects : given a diagram with a parity in the crossings one can define a diagram with a parity ( dots ) on the edges . the inverse procedure is not alway well defined . nevertheless , the class of dotted diagrams such that there exists a corresponding diagram with parity , is invariant under the moves ; moreover , the moves on the dotted diagrams allow the recovery of the moves on the diagrams with a parity . the @xmath5strand dotted braid group is a group with the generators @xmath7 , generators @xmath59 and the following set of relations : @xmath60 for all @xmath9 ( far commutativity ) and @xmath61 for @xmath11 ; @xmath62 for all @xmath16 , @xmath63 for all @xmath64 , @xmath65 for all @xmath66 . this construction can be visualized as follows . the generators @xmath18 have the same geometric meaning as before . the generators @xmath67 can be represented as a trivial braid on @xmath68 strands with a dot on the @xmath69th strand . the relation ( [ dot_square ] ) means that two consecutive dots cancel each other ; dots on different strands commute ( see the relation ( [ dot_commute ] ) ) ; finally , a crossing with four dots around equals a crossing without dots ( see the relation ( [ four_dots ] ) ) . denote the dotted braid group with @xmath70 . this group is quite large . for example , one has the following the group @xmath33 can be homomorphically included into the group @xmath70 . consider the following mapping @xmath71 @xmath72 this mapping is well defined and is a homomorphism to a subgroup of @xmath70 . it is well defined due to the fact that , thanks to the ( [ four_dots ] ) relation , any lune or triangle , considered in the second or the third reidemeister move , can be transformed into a lune or triangle without dots for which a usual reidemeister move can be used ; after that the dots are returned in the same manner ( see fig . [ o2 ] , [ o3 ] ) . here we extensively use the structure of the group @xmath73 . now we need to introduce the notion of _ good _ dotted braids . a dotted braid is called _ good _ if its every strand has even number of dots . now we can define the inverse homomorphism : from good dotted braids to braids with parity . consider a good braid @xmath74 and its arbitrary diagram . we present a well defined way to assign a parity to every crossing of the diagram . every crossings breaks two strands into four `` half strands '' . half _ is two right ( or two left ) half strands together . note , that since the braid is good , the parity of the number of dots on either halves is the same . that is the parity we attribute to the crossing considered . it is easily verified , that this mapping is well defined . that completes the proof . geometrically speaking , we send odd crossings to the crossings with two dots on the different halves of the upper strand . note , that such parity is a global property : a dot can be `` taken far away '' via the dot moves , but the crossing remains odd . that is exactly the difference between dotted braids and , say , @xmath3braids : in the latter the additional information is positioned in the crossings hence local . the following important fact holds true : if two @xmath2braids are equal as dotted braids , they are equal as @xmath2braids . consider two @xmath2braids @xmath75 equal as dotted braids : their images under the mapping @xmath76 , defined above , can be connected by a chain of moves allowed for the group @xmath70 . the braid @xmath77 is a good dotted braid . as was seen above , dotted braid moves on good braids do nt change the parity of its crossings . therefore , at each step of the transformation the braid remains good hence a braid with parity . moreover , the @xmath2images are also connected by the corresponding move . therefore , the theorem is proved . one can use the dot idea to get different interesting groups . let us present another example . in virtual braids , unlike the classical ones , there is a torsion . to approach realisation of virtual braids with classical ones with an additional structure we introduce the notion of _ twisted dotted braid group _ : the @xmath5strand twisted dotted braid group is a group with the generators @xmath7 , generators @xmath59 and the following set of relations : @xmath60 for all @xmath9 ( far commutativity ) and @xmath61 for @xmath11 ; @xmath78 for all @xmath16 , @xmath79 for all @xmath64 , @xmath80 for all @xmath66 . this group differs from the dotted braid group only in the last relation : four dots not preserve but invert a crossing . this group will be denoted with @xmath81 . the following is true : the group @xmath82 homomorphically includes into the group @xmath81 . consider the mapping , which works on the generators exactly like the above defined mapping @xmath76 . let us show that it is well defined . the triangle ( third reidemeister move ) case is considered exactly as before . but here we need to prove that the following equality holds : @xmath83 in other words , a lune with two odd crossings of the same structure can be acted upon with the second reidemeister move . that is true due to the `` twisting '' relation ( [ four_dots ] ) , see fig . the theorem is proved . the group @xmath82 `` almost '' realises the virtual braid group by sending even crossings to classical and odd to virtual . the only move absent in this group is the third reidemeister move with three virtual crossings . let us conclude the paper with a list of some open problems in braid theory , closely related to the above defined ideas and structures . 1 . the objects with dots , odd crossings and other such structures ( knots , links , etc . ) admit natural operations of _ projection , covering , bracket , cobracket ( delta ) _ ( see , say , @xcite ) . for example , the knots whose vertices are naturally marked by elements from @xmath84 can be naturally covered with two component links : even crossings correspond to selfcrossings of a component and the odd ones to the crossings of different link components . + a question arises : is there an inclusion of the above defined groups ( @xmath33 , @xmath70 and others , as well as their analogs ) into the classical braid group @xmath85 for a sufficiently large number of strands @xmath86 ? if that is the case , the problem of conjugation can be solved , exact linear presentations of virtual braid groups can be constructed . an approach similar to free knot / free braid approach can be used when studying @xmath87 braids for arbitrary @xmath88.the structures not unlike the ones presented in the paper may be introduced to @xmath89tangles and @xmath90tangles . a natural problem is to explore the properties of @xmath89tangles and @xmath90tangles with parity , dots , @xmath1 group structure . that can help to understand new properties and construct new invariants for different well known objects , for example , classical knots the authors are partially supported by laboratory of quantum topology of chelyabinsk state university ( russian federation government grant 14.z50.31.0020 ) , by rf president nsh 1410.2012.1 , and by grants of the russian foundation for basic research , 13 - 01 - 00830 , 14 - 01 - 91161 , 14 - 01 - 31288 . zhiyun cheng is supported by nsfc 11301028 and the fundamental research funds for central universities of china 105 - 105580gk .

in the present paper , we introduce @xmath0-braids and , more generally , @xmath1-braids for an arbitrary group @xmath1 . they form a natural group - theoretic counterpart of @xmath1-knots , see @xcite . the underlying idea , used in the construction of these objects decoration of crossings with some additional information generalizes an important notion of _ parity _ introduced by the second author ( see @xcite ) to different combinatorically geometric theories , such as knot theory , braid theory and others . these objects act as natural enhancements of classical ( artin ) braid groups . the notion of dotted braid group is introduced : classical ( artin ) braid groups live inside dotted braid groups as those elements having presentation with no dots on the strands . the paper is concluded by a list of unsolved problems .

a _ projective structure _ on an @xmath9-manifold @xmath10 is an equivalence class @xmath3 of torsion - free connections on the tangent bundle @xmath11 , where two connections are called projectively equivalent if they share the same unparametrised geodesics . a manifold @xmath10 equipped with a projective structure @xmath3 will be called a _ projective manifold_. a _ conformal structure _ on @xmath10 is an equivalence class @xmath4 $ ] of riemannian metrics on @xmath10 , where two metrics are called conformally equivalent if they differ by a scale factor . naively , one might think of projective and conformal structures as formally similar , since both arise by defining a notion of equivalence on a geometric structure . however , the formal similarity is more substantial . for instance , kobayashi has shown @xcite that both projective and conformal structures admit a treatment as cartan geometries with @xmath12-graded lie algebras ( see @xcite for background on cartan geometries ) . here we exploit the fact that both structures give rise to affine subspaces modelled on @xmath13 of the infinite - dimensional affine space @xmath14 of torsion - free connections on @xmath10 . indeed , it is a classical result due to weyl @xcite that two torsion - free connections on @xmath11 are projectively equivalent if and only if their difference thought of as a section of @xmath15 is pure trace . consequently , the representative connections of a projective structure @xmath3 on @xmath10 define an affine subspace @xmath16 which is modelled on @xmath13 . moreover , it follows from koszul s identity , that the torsion - free connections preserving a conformal structure @xmath4 $ ] on @xmath10 are of the form @xmath17 with @xmath18 $ ] , @xmath19 and where @xmath20 denotes the levi - civita connection of @xmath21 . hence , the space of torsion - free @xmath4$]-conformal connections on @xmath11 is an affine subspace @xmath22}(m)$ ] modelled on @xmath13 as well . it is an elementary computation to check that if @xmath22}(m)$ ] and @xmath16 intersect , then they do so in a unique point . therefore , we may ask if in general one can distinguish two points in @xmath23}(m)$ ] which are ` as close as possible ' . this is indeed the case . more precisely , one obtains a @xmath24-equivariant map @xmath25)\mapsto \alpha$ ] which sends a pair @xmath25)$ ] to an element @xmath26 which we may think of as the ` difference ' between @xmath3 and @xmath4 $ ] . in particular , if @xmath10 is oriented , we obtain a @xmath24-invariant functional @xmath27)=\int_{m}|\alpha|^n_g d \mu_g.\ ] ] fixing a projective structure @xmath3 on @xmath10 , we may consider the functional @xmath28 , which is a functional on the space @xmath29 of conformal structures on @xmath10 only . it is natural to study the infimum of @xmath0 among all conformal structures on @xmath10 , and to ask whether there is actually a minimising conformal structure which achieves this infimum . this infimum which may be considered as a measure of how far @xmath3 deviates from being defined by a conformal connection is a new global invariant for oriented projective manifolds . of particular interest is the case of surfaces where @xmath0 is just the square of the @xmath30-norm of @xmath31 taken with respect to @xmath4 $ ] and this is the case that we study in detail in this article . it turns out that in the surface case the functional @xmath0 also arises from a rather different viewpoint , which greatly simplifies the computation of its variational equations by using the technique of moving frames . inspired by the twistorial construction of holomorphic projective structures by hitchin @xcite , it was shown in @xcite , @xcite how to construct a twistor space for smooth projective structures . the choice of a projective structure @xmath3 on an oriented surface @xmath32 induces a complex structure on the total space of the disk bundle @xmath33 whose sections are conformal structures on @xmath32 . in this sense , @xmath2)$ ] can be interpreted as measuring the failure of @xmath4(\sigma ) \subset z$ ] to be a holomorphic curve in @xmath34 . we proceed to show that @xmath3 canonically defines an indefinite khler - einstein structure @xmath8 on a certain submanifold @xmath35 of the projectivised holomorphic cotangent bundle @xmath36 of @xmath34 . moreover , every conformal structure @xmath4 : \sigma \to z$ ] admits a lift @xmath6 } : \sigma \to y$ ] so that @xmath4 $ ] is a critical point for @xmath0 with respect to compactly supported variations if and only if @xmath6 } : ( \sigma,[g ] ) \to ( y , h_y)$ ] is weakly conformal . in fact , in the compact case @xmath2)$ ] is , up to the topological constant @xmath37 , just the dirichlet energy of @xmath6}$ ] . as a consequence , we obtain the lower bound @xmath38}^*h_y\ , d\mu_g\geq -2\pi\chi(\sigma),\ ] ] with equality if and only if @xmath3 is defined by a @xmath4$]-conformal connection . looking for a class of projective structures for which @xmath0 admits critical points ( we also say conformal structures that are _ extremal _ for @xmath3 ) , we turn our attention to the canonical rank two affine bundle @xmath39 whose sections are in one - to - one correspondence with the @xmath3-representative connections . it can be shown @xcite that @xmath3 canonically equips @xmath40 with a neutral signature anti - self - dual einstein metric @xmath41 , as well as a symplectic form @xmath42 , so that the endomorphism relating @xmath43 squares to become the identity map on @xmath44 . moreover , here we prove that a @xmath3-representative connection @xmath45 defining a timelike or spacelike minimal lagrangian immersion has the property that the conformal structure on @xmath32 defined by @xmath46 is extremal for @xmath3 . furthermore , we show that in the compact case , a timelike or spacelike lagrangian connection @xmath45 is totally geodesic if and only if @xmath47 is the levi - civita connection of a metric of constant non - zero gauss curvature . in addition , we observe that a projectively flat connection @xmath45 defining a timelike or spacelike minimal lagrangian immersion gives rise to a holomorphic cubic differential on @xmath32 , where the complex structure is the one coming from the induced metric @xmath46 and the orientation . this allows to show that the only examples of such connections on the @xmath48-sphere are levi - civita connections of metrics of constant positive gauss - curvature . the occurrence of holomorphic cubic differentials in projective differential geometry is not new . in his celebrated paper `` _ _ lie groups and teichmller space _ _ '' @xcite hitchin proposed a generalisation of teichmller space @xmath49 by identifying a connected component @xmath50 nowadays called the _ hitchin component _ in the space of conjugacy classes of representations of @xmath51 into @xmath52 ) . here @xmath32 denotes a compact orientable surface whose genus exceeds one . using the theory of higgs bundles @xcite and harmonic map techniques , hitchin showed that the choice of a complex structure @xmath53 on @xmath32 gives an identification @xmath54 where @xmath55 denotes the canonical bundle of @xmath32 with respect to @xmath53 . hitchin conjectured that @xmath56 is the space of conjugacy classes of monodromy representations of ( flat ) properly convex projective structures , a fact later confirmed by choi and goldman @xcite ( the geometric interpretation of the hitchin component for @xmath57 is a topic of current interest , c.f . @xcite , @xcite , @xcite for recent results ) . teichmller space being parametrised by holomorphic quadratic differentials , one might ask if there is a unique choice of a complex structure ( or equivalently conformal structure when fixing an orientation ) on @xmath32 so that @xmath56 is parametrised in terms of cubic holomorphic differentials only . this is indeed the case , as was shown independently by loftin @xcite and labourie @xcite ( see also @xcite and @xcite for recent work treating the non - compact case and the case of convex polygons , as well as @xcite treating the case of a general real split rank @xmath48 group ) . furthermore , the conformal structure @xmath4_{0}$ ] making the quadratic differential vanish admits an interpretation in terms of affine differential geometry , see in particular @xcite . we will call @xmath4_0 $ ] the _ canonical conformal structure _ of a properly convex compact oriented projective surface @xmath5 . using the results of labourie @xcite , we show that the canonical conformal structure of a properly convex compact oriented projective surface @xmath5 is extremal for @xmath3 . moreover , there exists a @xmath3-representative connection @xmath45 unique up to pullback by @xmath3-preserving diffeomorphisms which is a spacelike minimal lagrangian embedding . although we are currently unable to prove this , it is tempting to speculate that in the case of a properly convex compact oriented projective surface @xmath5 , the canonical conformal structure is in fact the unique minimiser ( and possibly even critical point ) of @xmath0 . as a by - product of our ideas , we obtain a gauss bonnet type identity for oriented projective surfaces , which we briefly discuss in appendix [ ap : gb ] . * acknowledgements . * i would like to thank nigel hitchin , jacob bernstein , maciej dunajski , norbert hungerbhler and stefan rosemann for helpful conversations or correspondence regarding the topic of this article . throughout the article , all manifolds are assumed to be connected , have empty boundary and unless stated otherwise , all manifolds and maps are assumed to be smooth , i.e. , @xmath58 . also , we adhere to the convention of summing over repeated indices . for @xmath59 the field of real or complex numbers , we denote by @xmath60 the space of column vectors of height @xmath9 and by @xmath61 the space of row vectors of length @xmath9 whose entries are elements of @xmath62 . also , we denote by @xmath63 the space of lines in @xmath64 , that is , the real or complex projective plane . we denote by @xmath65 the space of oriented lines in @xmath66 , that is , the projective @xmath48-sphere . likewise , we write @xmath67 for the dual ( real or complex ) projective plane and @xmath68 for the dual projective @xmath48-sphere . for a non - zero vector @xmath69 we write @xmath70 $ ] for its corresponding point in @xmath71 and for a non - zero vector @xmath72 we write @xmath73 $ ] for its corresponding point in @xmath74 . for non - zero vectors @xmath75 and @xmath76 we also use the notation @xmath70_+$ ] and @xmath73_+$ ] to denote the corresponding points in @xmath77 and @xmath78 . finally , we use the notation @xmath79 to denote the space of complete flags in @xmath80 whose points are pairs @xmath81 with @xmath82 being an @xmath62 two - dimensional subspace of @xmath80 containing the line @xmath83 . recall that the _ coframe bundle _ of an @xmath9-manifold @xmath10 is the bundle @xmath84 whose fibre at a point @xmath85 consists of the linear isomorphisms @xmath86 . the group @xmath87 acts transitively from the right on each @xmath88-fibre by the rule @xmath89 for all @xmath90 . this action turns @xmath91 into a principal right @xmath87-bundle . the coframe bundle is equipped with a tautological @xmath92-valued @xmath12-form @xmath93 defined by @xmath94 . note that @xmath93 satisfies the equivariance property @xmath95 for all @xmath90 . the exterior derivative of local coordinates @xmath96 on @xmath10 defines a natural section @xmath97 having the reproducing property @xmath98 . we will henceforth write @xmath99 instead of @xmath100 whenever @xmath10 is clear from the context . throughout the article we will frequently make use of the notion of an associated bundle of a principal bundle . the reader will recall that if @xmath101 is a principal right @xmath102-bundle and @xmath103 a pair consisting of a manifold @xmath104 and a homeomorphism @xmath105 into the diffeomorphism group of @xmath104 , then we obtain an associated fibre bundle with typical fibre @xmath104 and structure group @xmath102 whose total space is @xmath106 , that is , the elements of @xmath106 are pairs @xmath107 subject to the equivalence relation @xmath108 a section @xmath109 of @xmath110 is then given by a map @xmath111 which is equivariant with respect to the @xmath102-right action on @xmath112 and the right action of @xmath102 on @xmath104 induced by @xmath113 . we say that @xmath109 is _ represented by _ if @xmath104 is an affine / linear space and the @xmath102-action induced by @xmath113 is affine / linear , then the associated bundle is an affine / vector bundle . recall that the set @xmath115 of torsion - free connections on the tangent bundle of an @xmath9-manifold @xmath116 is the space of sections of an affine bundle @xmath117 of rank @xmath118 which is modelled on the vector bundle @xmath119 . we have a canonical trace mapping @xmath120 as well as an inclusion @xmath121 for every @xmath122 we let @xmath123 denote its trace - free part , so that @xmath124 a projective structure @xmath3 on a manifold @xmath10 of dimension @xmath125 is an equivalence class of torsion - free connections on @xmath11 where two connections are declared to be equivalent if they share the same unparametrised geodesics . weyl @xcite observed the following : [ weylfund ] two torsion - free connections @xmath47 and @xmath126 on @xmath127 are projectively equivalent if and only if @xmath128 . consequently , the set @xmath129 of projective structures on @xmath116 is the space of sections of an affine bundle @xmath130 or rank @xmath131 which is modelled on the traceless part @xmath132 of the vector bundle @xmath133 . we will use the notation @xmath134 for the projective structure @xmath3 that is defined by a connection @xmath47 . a consequence of weyl s result is that the set of representative connections of a projective structure @xmath3 is an affine subspace @xmath135 of the space of torsion - free connections which is modelled on the space of @xmath12-forms on @xmath10 . a conformal structure on a manifold @xmath10 of dimension @xmath125 is an equivalence class @xmath4 $ ] of riemannian metrics on @xmath10 where two metrics @xmath21 and @xmath136 are declared to be equivalent if there exists a strictly positive function @xmath137 on @xmath10 so that @xmath138 . equivalently , a conformal structure @xmath4 $ ] on @xmath10 is a ( smooth ) choice of a coframe for every point @xmath139 in @xmath10 well defined up to orthogonal transformation and scaling consequently , the set @xmath29 of conformal structures on @xmath10 is the space of sections of @xmath140 , where @xmath141 is the subgroup of @xmath87 consisting of matrices @xmath142 having the property that @xmath143 is a non - zero multiple of the identity matrix . a torsion - free connection @xmath47 on @xmath11 is called a _ weyl connection _ or _ conformal connection _ for the conformal structure @xmath4 $ ] on @xmath10 if the parallel transport maps of @xmath47 are angle - preserving with respect to @xmath4 $ ] . a torsion - free connection @xmath47 is @xmath4$]-conformal if for some ( and hence any ) representative metric @xmath18 $ ] there exists a @xmath12-form @xmath144 on @xmath10 such that @xmath145 it is a simple consequence of koszul s identity that the @xmath4$]-conformal connections are of the form @xmath146 where @xmath147 $ ] , @xmath144 is a @xmath12-form on @xmath10 with @xmath21-dual vector field @xmath148 and @xmath20 denotes the levi - civita connection of @xmath21 . consequently , the set of @xmath4$]-conformal connections defines an affine subspace @xmath22}(m)\subset \mathfrak{a}(m)$ ] which is modelled on the space of @xmath12-forms on @xmath10 as well . for later usage we also record that for every smooth function @xmath137 on @xmath10 we have @xmath149 as the reader may easily verify using the identity ( * ? ? ? * theorem 1.159 ) @xmath150 finally , we use the notation @xmath151}\nabla$ ] for a connection preserving the conformal structure @xmath4 $ ] . since both projective and conformal structures give rise to affine subspaces of @xmath14 of the same type , we may ask how two such spaces intersect . [ intersect ] let @xmath4 $ ] be a conformal and @xmath3 a projective structure on @xmath10 . then @xmath22}(m)$ ] and @xmath16 intersect in at most one point . suppose the @xmath4$]-conformal connections @xmath152}\nabla}$ ] and @xmath151}\hat{\nabla}$ ] are elements in @xmath16 . then , by lemma [ weylfund ] , there exists a @xmath12-form @xmath153 on @xmath10 so that @xmath154}\nabla}={}^{[g]}\hat{\nabla}+\iota(\upsilon).\ ] ] fixing a riemannian metric @xmath21 defining @xmath4 $ ] , we also have @xmath12-forms @xmath155 on @xmath10 so that @xmath154}\nabla}={}^g\nabla+g\otimes \beta^{\sharp}-\iota(\beta)\quad \text{and}\quad{}^{[g]}\hat{\nabla}={}^g\nabla+g\otimes \hat{\beta}^{\sharp}-\iota(\hat{\beta}).\ ] ] applying these formulae we obtain @xmath156 taking the trace gives @xmath157 so that @xmath158 . therefore we must have @xmath159 contracting this last equation with the dual metric @xmath160 implies @xmath161 so that @xmath162 provided @xmath125 . it follows that @xmath153 vanishes too , therefore @xmath152}\nabla}={}^{[g]}\hat{\nabla}$ ] , as claimed . [ rmk : diffequimap ] lemma raises the question whether or not one can still determine a unique point @xmath152}\nabla}\in \mathfrak{a}_{[g]}(m)$ ] and a unique point @xmath163 in the general case , where @xmath22}(m)$ ] and @xmath16 might not intersect . formally speaking , we are interested in maps @xmath164 satisfying the following properties : * @xmath165 ) \in \mathfrak{a}_{\mathfrak{p}}(m)$ ] and @xmath166 ) \in \mathfrak{a}_{[g]}(m)$ ] ; * if @xmath167}(m)$ ] is non - empty , then @xmath166)-\psi^1(\mathfrak{p},[g])=0 $ ] ; * @xmath168 is equivariant with respect to the natural right action of the diffeomorphism group @xmath24 on @xmath169 and @xmath170 . we will next discuss a geometrically natural and explicit map @xmath168 having these properties . to this end let @xmath21 be a riemannian metric on @xmath10 and @xmath47 a torsion - free connection on @xmath11 . consider the first - order differential operator for @xmath21 mapping into the space of @xmath12-forms on @xmath10 with values in @xmath171 @xmath172}}=\left(\nabla-{}^g\nabla - g\otimes x_g\right)_0,\ ] ] where @xmath173 is @xmath174 the following result is essentially contained in @xcite . for the convenience of the reader we include a proof . [ quasilinop1 ] the @xmath12-form @xmath175}}$ ] has the following properties : * the endomorphism @xmath175}}(x)$ ] is trace - free for all @xmath176 ; * for all @xmath177 we have @xmath175}}(x)y=\alpha_{{[g]}}(y)x$ ] ; * @xmath175}}$ ] does only depend on the projective equivalence class of @xmath47 ; * @xmath175}}$ ] does only depend on the conformal equivalence class of @xmath21 ; * @xmath175}}\equiv 0 $ ] if and only if there exists a @xmath4$]-conformal connection which is projectively equivalent to @xmath47 . the properties ( i ) and ( ii ) are obvious from the definition . \(iii ) recall that two affine torsion - free connections @xmath47 and @xmath178 are projectively equivalent if and only if @xmath179 . the claim follows from the linearity of the `` taking the trace - free part '' operation . \(iv ) let @xmath180 for some smooth real - valued function @xmath137 on @xmath10 . then we have @xmath181 and hence @xmath182 we obtain @xmath183\\ & = \e^{-2f}\left(x_g+\frac{n(n+1)}{(n+2)(n-1)}{}^g\nabla f-\frac{2}{(n+2)(n-1)}{}^g\nabla f\right)\\ & = \e^{-2f}\left(x_g+{}^g\nabla f\right).\end{aligned}\ ] ] this gives @xmath184 so that @xmath185 which shows that @xmath175}}$ ] does indeed only depend on the conformal class of @xmath21 . \(v ) recall that the @xmath186}$]-conformal connections are of the form @xmath154}\nabla}={}^g\nabla+g\otimes \beta^{\sharp}-\iota(\beta),\ ] ] where @xmath21 is any metric in the conformal class @xmath186}$ ] and @xmath144 is some @xmath12-form on @xmath10 . therefore we have @xmath187}\nabla}-{}^{g}\nabla\right)_0=\left(g\otimes\beta^{\sharp}\right)_0=g\otimes \beta^{\sharp}-\frac{1}{(n+1)}\iota ( \beta)\ ] ] and thus as before we compute that @xmath188 . we obtain @xmath189}&=\left[{}^{[g]}\nabla-\left({}^g\nabla+g\otimes x_g\right)\right]_0\\ & = \left[{}^g\nabla+g\otimes \beta^{\sharp}-\iota(\beta)-{}^g\nabla - g\otimes \beta^{\sharp}\right]_0=\left[-\iota(\beta)\right]_0=0.\end{aligned}\ ] ] conversely , suppose @xmath3 is a projective structure for which there exists a conformal structure @xmath186}$ ] with @xmath175}}=0 $ ] . fixing a riemannian metric @xmath18 $ ] and a @xmath3-representative connection @xmath47 , we must have @xmath190 for some @xmath12-form @xmath144 on @xmath10 . adding @xmath191 gives @xmath192 so that lemma [ weylfund ] implies that @xmath47 and the @xmath4$]-conformal connection @xmath193 are projectively equivalent . as a corollary to theorem [ quasilinop1 ] and lemma [ intersect ] we obtain the following result . [ uniquepoints ] for every conformal structure @xmath4 $ ] on the projective manifold @xmath1 , there exists a unique @xmath4$]-conformal connection @xmath152}\nabla}$ ] so that @xmath152}\nabla}+\alpha_{[g]}$ ] defines @xmath3 . note that corollary [ uniquepoints ] provides a unique point @xmath152}\nabla}\in \mathfrak{a}_{[g]}(m)$ ] and a unique point @xmath152}\nabla}+\alpha_{[g ] } \in \mathfrak{a}_{\mathfrak{p}}(m)$ ] . we may define @xmath194\right)=\left({{}^{[g]}\nabla}+\alpha_{[g]},{{}^{[g]}\nabla}\right),\ ] ] where @xmath152}\nabla}$ ] is the unique conformal connection provided by corollary [ uniquepoints ] . since the map which sends a riemannian metric to its levi - civita connection is equivariant with respect to the action of @xmath24 on the space of riemannian metrics and on @xmath14 , it follows that the map @xmath168 has all the properties listed in remark [ rmk : diffequimap ] . let @xmath47 be a connection defining @xmath3 and @xmath21 a smooth metric defining @xmath4 $ ] . set @xmath154}\nabla}={}^g\nabla+g\otimes x_g-(x_g)^{\flat}\otimes \mathrm{id}-\mathrm{id}\otimes ( x_g)^{\flat},\ ] ] where @xmath195 is defined as before ( see ) . then , property ( i ) of @xmath196}$ ] proved in theorem [ quasilinop1 ] implies that @xmath197}\nabla+\alpha_{[g]}\right)\right)_0=\left(\nabla-({}^g\nabla+g\otimes x_g)\right)_0-\alpha_{[g]}=\alpha_{[g]}-\alpha_{[g]}=0,\ ] ] so that @xmath152}\nabla}+\alpha_{[g]}$ ] is projectively equivalent to @xmath47 by lemma [ weylfund ] . if @xmath152}\nabla}^{\prime}$ ] is another @xmath4$]-conformal connection so that @xmath152}\nabla}^{\prime}+\alpha_{[g]}$ ] defines @xmath3 , then @xmath187}\nabla}-{{}^{[g]}\nabla}^{\prime}\right)_0=0,\ ] ] hence @xmath152}\nabla}={{}^{[g]}\nabla}^{\prime}$ ] by lemma [ intersect ] . we will henceforth assume @xmath10 to be oriented . for a pair @xmath25)$ ] consisting of a projective structure and a conformal structure on @xmath10 , we consider the non - negative @xmath9-form @xmath198}|^n_gd\mu_g$ ] , where @xmath21 is any metric defining @xmath4 $ ] , the @xmath9-form @xmath199 denotes its volume form and where @xmath196}$ ] is computed with respect to @xmath3 . for @xmath200 we have @xmath201}|_{\e^{2f}g}=\e^{-f}|\alpha_{[g]}|_{g } \quad \text{and } \quad d\mu_{\e^{2f}g}=e^{nf}d\mu_g,\ ] ] it follows that @xmath198}|^n_gd\mu_g$ ] depends only on the conformal structure @xmath4 $ ] . consequently , we obtain a non - negative functional @xmath202 ) \mapsto \int_{m } |\alpha_{[g]}|^n_gd\mu_g.\ ] ] by construction , @xmath203 is invariant under simultaneous action of @xmath24 on @xmath204 and @xmath29 . we may also fix a projective structure @xmath3 on @xmath10 and define @xmath205 $ ] which is a functional on @xmath29 only . as already pointed out in the introduction , we may study the infimum of @xmath0 among all conformal structures on @xmath10 , and ask whether there is actually a minimising conformal structure which achieves this infimum . the infimum @xmath206 \in \mathfrak{c}(m)}\mathcal{e}_{\mathfrak{p}}([g]),\ ] ] which may be considered as a measure of how far @xmath3 deviates from being defined by a conformal connection , is a new global invariant for oriented projective manifolds . note that reversing the role of @xmath3 and @xmath4 $ ] does not give us a global invariant for conformal manifolds . clearly , fixing a conformal structure and considering the infimum over @xmath204 yields zero for every choice of conformal structure @xmath4 $ ] . the case most of interest is @xmath207 , where @xmath203 is just the square of the @xmath30-norm of @xmath196}$ ] taken with respect to @xmath4 $ ] . we will henceforth consider the surface case only . there are several natural geometric spaces fibering over an oriented projective surface which we will discuss next . before doing so , we recall a result of cartan @xcite which canonically associates a principal bundle together with a `` connection '' to every projective manifold . the reader interested in a description of cartan s construction using modern language may also consult @xcite . let @xmath32 be an oriented surface and let @xmath208 denote the two - dimensional orientation preserving affine group which we think of as the subgroup of @xmath209 consisting of matrices of the form @xmath210 for @xmath211 and @xmath212 . we denote by @xmath213 the principal right @xmath214-bundle of coframes that are orientation preserving with respect to the chosen orientation on @xmath32 and the standard orientation on @xmath215 . we define a right @xmath102-action on @xmath216 by the rule @xmath217 for all @xmath218 . here @xmath219 denotes the projection onto the later factor . this action turns @xmath220 into a principal right @xmath102-bundle over @xmath32 , where @xmath221 denotes the natural basepoint projection . suppose @xmath47 is a torsion - free connection on @xmath222 with connection @xmath12-form @xmath223 on @xmath224 so that we have the structure equations and @xmath225}=\frac{1}{2}\left(s_{ij}-s_{ji}\right)$ ] so that @xmath226}$ ] . ] @xmath227j}-s_{[kl]}\delta^i_j)\omega^k\wedge\omega^l,\end{aligned}\ ] ] where @xmath228 represents the _ projective schouten tensor _ @xmath229 of @xmath47 which is defined as @xmath230 where @xmath231 denote the symmetric and anti - symmetric part of the ricci curvature of @xmath47 . on @xmath232 we define the @xmath233-valued @xmath12-form @xmath234 the reader may check that the pair @xmath235 defines a _ cartan geometry _ of type @xmath236 , that is , @xmath237 is a principal right @xmath102-bundle and @xmath238 is an @xmath233-valued @xmath12-form on @xmath239 satisfying the following properties : * @xmath240 is an isomorphism for every @xmath241 ; * @xmath242 for every @xmath243 ; * @xmath244 for every fundamental vector field @xmath245 generated by an element @xmath246 in the lie algebra of @xmath102 . moreover , writing @xmath247 , the cartan geometry @xmath235 also satisfies : * the leaves of the foliation defined by @xmath248 project to become the geodesics of @xmath134 ; * the @xmath249-pullback of an orientation compatible volume form on @xmath32 is a positive multiple of @xmath250 ; * the curvature @xmath48-form @xmath251 is @xmath252 for unique curvature functions @xmath253 . cartan s bundle is unique in the following sense : if @xmath254 is another cartan geometry of type @xmath255 so that the properties ( iv),(v ) and ( vi ) hold , then there exists a @xmath102-bundle isomorphism @xmath256 satisfying @xmath257 . a projective structure @xmath3 on @xmath32 is called _ flat _ if every point @xmath258 has a neighbourhood @xmath259 which is diffeomorphic to a subset of @xmath260 in such a way that the geodesics of @xmath3 contained in @xmath259 are mapped onto ( segments ) of projective lines @xmath261 . furthermore , a torsion - free connection @xmath47 on @xmath222 is called _ projectively flat _ if @xmath134 is flat . using cartan s connection , one can show that a projective structure @xmath3 is flat if and only if the functions @xmath262 and @xmath263 vanish identically . another consequence of cartan s result is that there exists a unique @xmath12-form @xmath264 so that @xmath265 the @xmath12-form @xmath266 was first discovered by r. liouville @xcite , hence we call @xmath266 the _ liouville curvature _ of @xmath3 . in particular , the liouville curvature is the complete obstruction to flatness of a two - dimensional projective structure . suppose @xmath267 are local orientation preserving coordinates on @xmath32 and let @xmath268 denote the induced section via the exterior derivative so that @xmath98 . then the pullback of the connection @xmath12-form @xmath269 on @xmath224 is @xmath270 where the function @xmath271 denotes the christoffel symbols of @xmath269 with respect to @xmath272 . in particular , if we define the function @xmath273 on @xmath274 by @xmath275 , then we obtain a _ coordinate section _ of cartan s bundle which by abuse of notation we denote by @xmath276 as well and which satisfies @xmath277 it follows from cartan s result that the function @xmath278 is projectively invariant in the sense that it only depends on the coordinates @xmath272 but not on the choice of a representative connection in the projective equivalence class of @xmath269 . note that the left action of @xmath209 on @xmath66 by matrix multiplication descends to define a transitive left action on the projective @xmath48-sphere @xmath77 . the stabiliser subgroup of the element @xmath279 $ ] is the group @xmath280 so that @xmath281 . taking @xmath238 to be the maurer - cartan form of @xmath209 , the pair @xmath282 is a cartan geometry of type @xmath236 defining an orientation and projective structure @xmath283 on @xmath77 whose geodesics are the `` great circles '' . since @xmath284 , this projective structure is flat . we call @xmath283 the _ canonical flat projective structure _ on @xmath77 . inspired by hitchin s twistorial description of holomorphic projective structures on complex surfaces @xcite , it was shown in @xcite how to construct a `` twistor space '' for smooth projective structures . for what follows it will be convenient to construct the twistor space in the smooth category by using the cartan geometry of a projective surface . let therefore @xmath5 be an oriented projective surface with cartan geometry @xmath235 . by construction , the quotient of @xmath239 by the normal subgroup @xmath285 is isomorphic to the bundle @xmath286 of orientation preserving coframes of @xmath32 . in particular , the choice of a conformal structure @xmath4 $ ] on @xmath32 corresponds to a section of the fibre bundle @xmath287 . here @xmath288 is the linear orientation preserving conformal group . by construction , the typical fibre of the bundle @xmath289 is diffeomorphic to @xmath290 , that is , the open unit disk @xmath291 . we write the elements of the group @xmath292 in the following form @xmath293 property ( iii ) of the cartan geometry @xmath235 implies that the ( real or complex - valued ) @xmath12-forms on @xmath239 that are semibasic for the quotient projection @xmath294 is said to be semibasic for the projection @xmath295 if the interior product @xmath296 vanishes for every vector field @xmath297 tangent to the fibres of @xmath295 . ] are linear combinations of the complex - valued @xmath12-forms @xmath298 and their complex conjugates . the equivariance property ( ii ) of the cartan geometry gives@xmath299 it follows that there exists a unique almost complex structure @xmath53 on @xmath300 having the property that a complex - valued @xmath12-form on @xmath239 is the pullback of a @xmath301-form on @xmath300 if and only if it is a linear combination of @xmath302 and @xmath303 . using property ( vi ) of the cartan geometry the reader may easily veryfiy that @xmath304 it follows from the newlander - nirenberg theorem that @xmath53 is integrable , thus giving @xmath300 the structure of a complex surface which we will denote by @xmath34 and which we call the _ twistor space _ of the projective surface @xmath5 . from it follows that the holomorphic cotangent bundle @xmath305 is the bundle associated to @xmath306 via the complex two - dimensional representation @xmath307 defined by the rule @xmath308 for all @xmath309 . in particular , the form @xmath302 is well defined on @xmath34 up to complex - scale and hence may be thought of as a section of the projective holomorphic cotangent bundle @xmath310 . abusing notation , we write @xmath311 to denote the image of @xmath34 under this section . we now have : [ cplx3fold ] there exists a unique integrable almost complex structure on the quotient @xmath312 having the property that its @xmath301-forms pull back to @xmath239 to become linear combinations of the forms @xmath313 furthermore , with respect to this complex structure @xmath312 is biholomorphic to @xmath314 in such a way that the standard holomorphic contact structure on @xmath35 is identified with the subbundle of @xmath315 defined by the equation @xmath316 . it follows from the properties of the cartan connection @xmath238 that the @xmath12-forms that are semibasic for the quotient projection @xmath317 are linear combinations of the forms @xmath318 and their complex conjugates . here @xmath319 is the subgroup consisting of elements of the form @xmath320 . writing @xmath321 instead of @xmath320 and @xmath322 , we compute from the equivariance property of @xmath238 that we have @xmath323 it follows that there exists a unique almost complex structure @xmath324 on @xmath312 having the property that its @xmath301-forms pull back to @xmath239 to become linear combinations of the forms @xmath318 . translating the structure equations into complex form gives @xmath325 where @xmath326 and @xmath327 we also note that @xmath328 the integrability of @xmath324 now follows from and the newlander - nirenberg theorem . consider the map @xmath329 and let @xmath330 denote the natural quotient projection induced by ( the projectivisation of ) @xmath113 . then @xmath331 is a submersion onto @xmath35 whose fibres are the @xmath332-orbits . indeed , let @xmath333 be a representative of an element @xmath334\in\mathbb{p}(t^*_{\c}z^{1,0})$ ] which lies in the complement of @xmath335 . then using it follows that we might transform with the affine part of the right action of @xmath292 to ensure that @xmath336 is of the form @xmath337 for some non - zero complex number @xmath338 . it follows that the element @xmath241 is mapped onto @xmath334 $ ] showing that @xmath339 is surjective onto @xmath35 . clearly @xmath339 is smooth and a submersion . furthermore , suppose the two points @xmath340 are mapped to the same element of @xmath35 . then , there exists an element @xmath341 and a non - zero complex number @xmath109 so that @xmath342 which holds true if and only if @xmath343 . consequently , there exists a unique diffeomorphism @xmath344 making the following diagram commute : @xmath345 the complex structure on @xmath346 is such that its @xmath301-forms pull back to @xmath347 to become linear combinations of the @xmath12-forms @xmath348 , where @xmath349 denotes the projection onto the linear factor . clearly , these forms pull back under @xmath350 to become linear combinations of the forms @xmath318 , hence @xmath351 is a biholomorphism . finally , note that the complex version of the liouville @xmath12-form on @xmath352 whose kernel defines the canonical contact structure on @xmath353 pulls back to @xmath354 to become @xmath355 . since @xmath356 the claim follows . alternatively , it follows from that the equations @xmath316 define a subbundle @xmath357 of @xmath358 and furthermore yields @xmath359 confirming that @xmath357 is a holomorphic contact structure . we will henceforth identify @xmath360 and think of @xmath361 as the projection map onto @xmath35 . the connection matrix @xmath362 in the proof of lemma [ cplx3fold ] takes values in the lie algebra @xmath363 of the indefinite unitary group @xmath364 , where the model of @xmath364 being used is the subgroup of @xmath365 that fixes the hermitian form in @xmath366-variables @xmath367 denoting the integrable almost complex structure on @xmath35 by @xmath53 , the first part of the following proposition is therefore clear : there exists a unique indefinite khler structure on @xmath368 whose khler - form @xmath369 satisfies @xmath370 moreover , the indefinite khler metric @xmath371 is einstein with non - zero scalar curvature . the first part of the statement is an immediate consequence of the above remark , the skeptical reader might also verify this using the structure equations . furthermore , by definition , the associated khler metric satisfies @xmath372 and hence the forms @xmath373 are a unitary coframe for @xmath374 . in order to verify the einstein condition it is therefore sufficient that the trace of the curvature form @xmath375 is a non - zero constant ( imaginary ) multiple of @xmath376 . we compute using the structure equations @xmath377 with @xmath378 and where the entry @xmath379 is an expression that vanishes when @xmath3 is flat and whose precise form is irrelevant for what follows . in particular , we obtain @xmath380 thus verifying the einstein property . there is yet another quotient of cartan s bundle which is of geometric interest . suppose the projective structure @xmath3 is defined by a torsion - free connection @xmath47 with connection @xmath12-form @xmath269 on @xmath224 . recall that @xmath224 is isomorphic to the quotient of @xmath239 by the normal subgroup @xmath381 . writing @xmath382 for an @xmath383-valued @xmath12-form @xmath384 , an @xmath215-valued @xmath12-form @xmath93 and an @xmath385-valued @xmath12-form @xmath386 , from we see that the pullback of @xmath269 to @xmath239 satisfies @xmath387 for a unique @xmath383-valued function @xmath273 on @xmath239 . we compute @xmath388 using the equivariance property ( ii ) of @xmath238 gives @xmath389 so that the right hand side is @xmath390 hence @xmath391 where @xmath392 therefore , it follows from the equivariance properties of the cartan connection @xmath238 and the connection form @xmath269 that @xmath393 conversely , given an @xmath383-valued function @xmath273 on @xmath239 satisfying the equivariance property , it follows from cartan s work that the equation @xmath394 defines a reduction of @xmath239 to a principal right @xmath214-bundle which is isomorphic to @xmath224 in such a way that @xmath395 pulls back to @xmath224 to become the connection @xmath12-form of a unique @xmath3-representative connection . consequently , the representative connections of @xmath3 are in one - to - one correspondence with the @xmath383-valued functions @xmath273 on @xmath239 satisfying . equivalently , a @xmath3-representative connection is a section of the rank @xmath48 affine bundle @xmath396 associated to @xmath239 via the affine @xmath102-action @xmath113 defined by the rule @xmath397 we call @xmath396 the _ canonical affine bundle _ of @xmath5 . the affine bundle @xmath398 is modelled on the vector bundle associated to the linear part of the affine @xmath102-action @xmath113 , that is , the transformations defined by the rule @xmath399 it is now an easy consequence of the equivariance properties of @xmath238 to check that the bundle associated to the @xmath102-representation defined by is the cotangent bundle of @xmath32 . clearly , this is what one would expect from weyl s lemma [ weylfund ] anyway . by definition , an element of @xmath40 is an equivalence class @xmath400 $ ] with @xmath401 and @xmath402 subject to the equivalence relation induced by @xmath113 . clearly , every element of @xmath40 has a representative @xmath403 , unique up to a @xmath214 transformation , where here @xmath404 consists of those elements @xmath218 satisfying @xmath405 . for simplicity of notation we will henceforth write @xmath142 instead of @xmath406 for the elements of @xmath404 . it follows that as a smooth manifold , @xmath40 is canonically diffeomorphic to the quotient @xmath407 . from and we calculate @xmath408 since the components of @xmath93 and @xmath384 are semibasic for the quotient projection @xmath409 , we obtain from : there exists a unique split - signature metric @xmath410 on @xmath40 such that @xmath411 and a unique symplectic form @xmath42 on @xmath40 such that @xmath412 the only thing left to show is that @xmath42 is symplectic . clearly , @xmath42 is non - degenerate . closedness of @xmath42 is an easy computational consequence of the bianchi - identity @xmath413 for the cartan connection @xmath238 . the metric @xmath410 on @xmath40 can also be obtained from a certain gauge theoretic equation on projective surfaces which was introduced by calderbank @xcite . this viewpoint is explored in depth in @xcite . in particular , there it is shown that @xmath41 is anti - self - dual and einstein with non - zero scalar curvature . furthermore , the metric @xmath41 and symplectic form @xmath42 are related by an endomorphism @xmath414 whose square is the identity , so that the pair @xmath415 defines what is sometimes referred to as an _ almost para - khler structure _ or _ bi - lagrangian structure _ in @xcite . moreover , the symplectic form is parallel for the levi - civita connection of @xmath41 if and only if @xmath3 is flat . we have seen that @xmath35 may be thought of as a submanifold of the projectivised holomorphic cotangent bundle @xmath416 . by construction , @xmath35 fibres over the canonical affine bundle @xmath40 as well , with the typical fibre being the open unit disk . n. hitchin pointed out to the author that @xmath35 can be embedded as a submanifold of the ( riemannian ) twistor space of @xmath417 . we will however not explore this viewpoint here . in this subsection we identify the spaces @xmath418 in the case where @xmath5 is the canonical flat projective structure on the projective @xmath48-sphere . recall that in this case @xmath419 . we let @xmath209 act from the left on @xmath420 by @xmath421 for all @xmath422 . this action descends to define an action on @xmath423 . we let @xmath424 denote the submanifold of @xmath425 consisting of those pairs @xmath426_+,[\xi])$ ] that are non - incident , that is , @xmath427 . the group @xmath209 acts transitively on @xmath424 . indeed , let @xmath426_+,[\xi])$ ] be an element in @xmath424 . then we may act by an element @xmath422 so that @xmath70_+=[(1 \ ; 0 \ ; 0)^t]_+$ ] . since the group @xmath209 preserves the non - incidence of @xmath426_+,[\xi])$ ] we may assume without loosing generality that @xmath73=[1\ ; \hat{\xi}]$ ] for some @xmath428 . we compute @xmath429 showing that @xmath209 acts transitively on @xmath424 . from we also see that the stabiliser subgroup of the element @xmath430_+,[(1\;0\;0)]$ ] is @xmath431 so that @xmath432 and the projection map is @xmath433_+,[g_1 \wedge g_2]\right),\ ] ] where we use the canonical vector space isomorphism @xmath434 . the group @xmath209 also acts naturally on @xmath435 by complexification , that is , by the rule @xmath436 for all @xmath422 . clearly , this action descends to define a left action on @xmath437 . however , this action is not transitive , but has two orbits . the first orbit is @xmath438 , where we think of @xmath423 as those points @xmath439 \in \mathbb{cp}_2 $ ] which satisfy @xmath440 , that is , @xmath273 and @xmath441 are linearly dependent over @xmath442 . assume therefore @xmath443 $ ] is an element in the complement @xmath444 of @xmath260 in @xmath445 . since @xmath209 acts transitively on unimodular triples of vectors in @xmath420 , we can assume without loosing generality that @xmath446 . for @xmath447 we write @xmath448 with @xmath449 . we will next determine the stabiliser subgroup of @xmath443 $ ] . a simple computation gives @xmath450 an elementary calculation shows that @xmath451=[\eps]$ ] implies that we must have @xmath452 since @xmath453 it follows that @xmath454 . therefore , the stabiliser subgroup of @xmath443 $ ] is a subgroup of @xmath455 . writing @xmath456 , we obtain @xmath457 from which it follows that @xmath458=[\eps]$ ] if and only if @xmath459 and @xmath460 , that is , @xmath461 . concluding , we have shown @xmath462 and the projection map is @xmath463,\ ] ] where again we use @xmath434 . we have only shown that @xmath464 is diffeomorphic to @xmath444 . since @xmath34 carries an integrable almost complex structure @xmath53 , we may ask if @xmath465 is biholomorphic to @xmath444 equipped with the standard complex structure . this is indeed the case , see ( * ? ? ? 3 ) . as a consequence of this result one can prove that the conformal connections on the @xmath48-sphere whose ( unparametrised ) geodesics are the great circles are in one - to - one correspondence with the smooth quadrics in @xmath444 , see ( * ? ? ? * cor . 2 ) . in fact @xcite , if @xmath3 is a projective structure on the @xmath48-sphere , all of whose geodesics are simple closed curves , then @xmath34 can be compactified and the compactification is biholomorphic to @xmath437 . this allowed lebrun and mason to prove that there is a nontrivial moduli space of such projective structures on the @xmath48-sphere . we will show next that @xmath35 is a submanifold of @xmath466 . clearly , the action of @xmath209 on the space @xmath466 of complete complex flags is not transitive , there is however an open orbit . let @xmath467 denote the @xmath209 orbit of the flag @xmath468 where @xmath469 we already know that the stabiliser subgroup @xmath470 of @xmath81 must be a subgroup of @xmath292 . for @xmath471 we write @xmath472 with @xmath473 . we compute @xmath474 which is easily seen to lie in the complex linear span of @xmath475 if and only if @xmath476 , hence @xmath477 and the projection map is @xmath478 with @xmath479 since @xmath466 is real six - dimensional and since @xmath480 , it follows that @xmath467 is open . summarising , given an oriented projective surface @xmath5 , we obtain the following maps : _ general case _ _ canonical flat case _ by construction , a conformal structure @xmath4 $ ] on the oriented projective surface @xmath5 is a section of @xmath33 . here we will show that every conformal structure @xmath4 $ ] admits a natural lift @xmath6 } : \sigma \to y$ ] . in doing so we recover the functional @xmath0 from a different viewpoint , which greatly simplifies the computation of its variational equations . we start with writing the structure equations of a conformal connection in complex form . on the bundle @xmath286 of orientation preserving coframes with tautological @xmath12-form @xmath483 , the connection @xmath12-form @xmath484 of the @xmath4$]-conformal connection can be expressed as follows : fixing a metric @xmath18 $ ] and writing @xmath485 for real - valued functions @xmath486 on @xmath224 , the levi - civita connection @xmath12-form @xmath223 of @xmath21 satisfies @xmath487 as well as @xmath488 where the real - valued function @xmath489 on @xmath224 is ( the pullback of ) the gauss curvature of @xmath21 . therefore , writing @xmath490 for real - valued functions @xmath491 on @xmath224 , the connection @xmath12-form of is @xmath492 where the real - valued functions @xmath493 on @xmath224 satisfy @xmath494 . the equivariance properties of the functions @xmath491 imply that there exist unique real - valued functions @xmath495 on @xmath496 so that @xmath497 from the equivariance properties of the functions @xmath498 it follows that the conditions @xmath499 and @xmath500 define a reduction of @xmath501 to the @xmath332-subbundle of orientation preserving @xmath4$]-conformal coframes @xmath502 } \to m$ ] . by an orientation preserving @xmath4$]-conformal coframe at @xmath85 we mean a linear isomorphism @xmath503 that is orientation preserving and conformal with respect to the orientation and conformal structure @xmath4 $ ] on @xmath116 and the standard orientation and conformal structure on @xmath215 . on @xmath502}$ ] we obtain @xmath504 and hence @xmath505 . likewise , we have @xmath506 so that @xmath507 . renaming @xmath508 and @xmath509 , we obtain @xmath510 where @xmath511 denotes the hodge star with respect to @xmath21 and the orientation . using this notation the first structure equation can be written in complex form @xmath512 abusing language slightly , we will henceforth call @xmath168 _ the connection form _ of the conformal connection @xmath513 . using and we obtain for the curvature @xmath48-form @xmath514 summarising , we have the complex structure equations @xmath515 with @xmath516 simple calculations give the equivariance properties @xmath517 and @xmath518 since the complex - valued @xmath12-form @xmath302 is semibasic for the quotient projection @xmath519 } \to \sigma$ ] and well defined on @xmath32 up to complex scale , it follows that there exists a unique complex structure @xmath53 on @xmath32 having the property that a complex - valued @xmath12-form on @xmath32 is a @xmath301-form for @xmath53 if and only if its pullback to @xmath502}$ ] is a complex multiple of @xmath302 . of course , the complex structure @xmath53 is the complex structure induced by @xmath4 $ ] and the chosen orientation . therefore , the real @xmath520-form @xmath521 is invariant under the @xmath332-right action and hence the pullback of a @xmath48-form on @xmath32 which is the area form @xmath199 of @xmath21 . likewise , the real @xmath520-form @xmath522 is invariant under the @xmath332-right action and hence the pullback of a @xmath48-form on @xmath32 which is @xmath523 , where @xmath524 denotes the co - differential with respect to @xmath21 . in particular , the curvature @xmath48-form is @xmath525 where we have used the identity @xmath526 . conversely , a @xmath332-connection @xmath168 on @xmath519 } \to \sigma$ ] satisfying the structure equations is the connection form of a unique @xmath4$]-conformal connection on @xmath32 . note that if we further impose the condition @xmath527 , then we reduce to an @xmath528-subbundle @xmath529}$ ] which consists of the orientation preserving @xmath21-orthonormal coframes . evaluating @xmath530 , we see that on @xmath531 we must have @xmath532 so that @xmath533 where we write @xmath534 . if moreover @xmath535 , so that @xmath536 is a levi - civita connection , we obtain the structure equations @xmath537 in particular , the complex - valued functions @xmath142 on @xmath531 satisfying @xmath538 are in one - to - one correspondence with the sections of the @xmath83-th power of the canonical bundle @xmath539 , where the complex structure is the one induced by @xmath4 $ ] and the orientation . we conclude this subsection by construction the cartan geometry @xmath540 for the projective structure defined by the conformal connection @xmath513 . using and while setting @xmath394 gives the following @xmath233-valued @xmath12-form on @xmath531 @xmath541 computing the curvature form gives @xmath542 with @xmath543 the uniqueness part of cartan s construction implies that there exists an @xmath528-bundle embedding @xmath544 pulling back @xmath238 to @xmath545 . in particular , if @xmath546 so that @xmath547 is a levi - civita connection , the liouville curvature @xmath266 of @xmath548 is given by @xmath549 . consequently , the only riemannian metrics giving rise to flat projective structures are those of constant gauss curvature , in agreement with a classical result of beltrami . we are interested in co - dimension two submanifolds of @xmath34 arising as images of sections of @xmath33 . the second order theory of such submanifolds is summarised in the following : [ ppn : lift ] let @xmath4 : \sigma \to z$ ] be a conformal structure on @xmath5 . then there exists a lift @xmath6 } : \sigma \to y$ ] covering @xmath4 $ ] so that the pullback - bundle @xmath550}^{\prime}=\widetilde{[g]}^*{p}\to \sigma$ ] is isomorphic to the @xmath332-bundle of orientation preserving @xmath4$]-conformal coframes and so that on @xmath551}$ ] we have @xmath552 for unique complex - valued functions @xmath553 on @xmath551}$ ] . in particular , @xmath4 $ ] determines the following objects on @xmath32 : * a quadratic differential @xmath554}\in \gamma(k_{\sigma}^2)$ ] that is represented by @xmath555 ; * a section @xmath556}$ ] of @xmath557 that is represented by @xmath142 ; * a @xmath4$]-conformal connection @xmath152}\nabla}$ ] whose connection form pulls back to @xmath551}$ ] to become @xmath168 . here @xmath55 denotes the canonical bundle of @xmath32 with respect to the complex structure on @xmath32 induced by @xmath4 $ ] and the orientation . let @xmath4 : \sigma \to z$ ] be a conformal structure on @xmath5 and let @xmath550}=[g]^*{p}\to\sigma$ ] denote the pullback of the bundle @xmath306 , that is , @xmath558}=\left\{(p , u ) \in \sigma\times { p}\,|\ , [ g](p)=\mu(u)\right\}.\ ] ] since @xmath559}$ ] is @xmath560-dimensional , two of the components of @xmath238 become linearly dependent when pulled back to @xmath559}$ ] . clearly , these components must be among the @xmath12-forms that are semibasic for @xmath561 . recall that these forms are spanned by @xmath562 and their complex conjugates . however , since @xmath4 $ ] is a section of @xmath33 and since the @xmath12-forms that are semibasic for the projection @xmath237 are spanned by @xmath563 , it follows that @xmath564 is non - vanishing on @xmath559}$ ] . therefore , on @xmath559}$ ] we have the relation @xmath565 for unique complex - valued functions @xmath566 . from the equivariance properties of @xmath562 under the @xmath292-right action , we obtain that for all @xmath567}$ ] and @xmath568 we have @xmath569 and @xmath570 it follows that the equation @xmath405 defines a locus that corresponds to a section @xmath6 } : \sigma \to y$ ] covering @xmath4 $ ] . on the pullback bundle @xmath551}=\widetilde{[g]}^*{p}$ ] , where @xmath571}=\left\{(p , u ) \in \sigma\times { p}\,|\ , \widetilde{[g]}(p)=\tau(u)\right\},\ ] ] we obtain @xmath572 since @xmath551}$ ] is @xmath573-dimensional , two of the remaining components of @xmath238 become linearly dependent when pulled back to @xmath551}$ ] . since the @xmath12-forms that are semibasic for the projection @xmath574 are spanned by @xmath318 and their complex conjugates it follows as before that @xmath575 for unique complex - valued functions @xmath576 . summarising , we obtain the following structure equations on @xmath551}$ ] @xmath577 recall that cartan s bundle @xmath237 is isomorphic to @xmath578 equipped with the @xmath102-right action . therefore , @xmath559 } \to \sigma$ ] is isomorphic to @xmath502 } \times \r_2 \to \sigma$ ] , where @xmath502 } \to \sigma$ ] is the bundle of orientation compatible @xmath4$]-conformal coframes . consequently , the bundle @xmath551 } \to \sigma$ ] is isomorphic to @xmath502 } \to \sigma$ ] . in particular , a complex - valued @xmath12-form on @xmath32 is a @xmath301-form for the complex structure @xmath53 induced by @xmath4 $ ] and the orientation if and only if its @xmath139-pullback to @xmath551}$ ] is a complex multiple of @xmath302 . since @xmath579 it follows that the sections of @xmath580 are in one - to - one correspondence with the complex - valued functions @xmath137 on @xmath551}$ ] satisfying @xmath581 likewise , it follows that the sections of @xmath557 are in one - to - one correspondence with the complex - valued functions @xmath137 on @xmath551}$ ] satisfying @xmath582 from and we obtain that for all @xmath583 } $ ] and @xmath584 @xmath585 equation implies that there exists a unique quadratic differential @xmath554 } \in \gamma(k_{\sigma}^2)$ ] that is represented by @xmath555 and implies that there exists a unique section @xmath556}$ ] of @xmath557 that is represented by @xmath142 . finally , it follows from the properties ( ii ) and ( iii ) of the cartan connection that @xmath168 is a connection @xmath12-form on the @xmath332-bundle @xmath551 } \to \sigma$ ] . its pushforward under the bundle isomorphism @xmath551 } \to f^+_{[g]}$ ] is then a @xmath332-connection and from it follows that the pushforward connection satisfies the structure equations , hence it is the connection form of a @xmath4$]-conformal connection . we call a map @xmath586 between two pseudo - riemannian manifolds _ weakly conformal _ if @xmath587 for some smooth function @xmath137 on @xmath10 . two immediate consequences of proposition [ ppn : lift ] are : [ somecor ] let @xmath4 $ ] be a conformal structure on @xmath5 . then the lift @xmath6 } : ( \sigma,[g ] ) \to ( y , h_y)$ ] is weakly conformal if and only if @xmath554}\equiv 0 $ ] . furthermore , the image of @xmath4 : \sigma \to z$ ] is a holomorphic curve if and only if @xmath556}\equiv 0 $ ] . in particular , if @xmath4(\sigma ) \subset z$ ] is a holomorphic curve , then @xmath6}(\sigma)\subset y$ ] is a holomorphic contact curve . here we call a holomorphic curve @xmath588 a _ contact curve _ if its tangent bundle is contained in the ( holomorphic ) contact structure of @xmath35 . by construction , the metric @xmath589 has the property that its pullback to @xmath239 is @xmath590 therefore , from and it follows that @xmath591}^*h_y\right)=\left(|a|^2-(s+\ov{s})\right)\zeta_1\circ\ov{\zeta_1}+\frac{q}{2}\,\zeta_1\circ\zeta_1+\frac{\ov{q}}{2}\,\ov{\zeta_1}\circ\ov{\zeta_1}.\ ] ] recall that a complex - valued @xmath12-form on @xmath32 is a @xmath301-form for the complex structure defined by @xmath4 $ ] and the orientation if and only if its @xmath139-pullback to @xmath551}$ ] is a complex multiple of @xmath302 . therefore , it follows from that @xmath6}^*h_y$ ] is weakly conformal to @xmath4 $ ] if and only if @xmath555 vanishes identically , the first claim follows . the second part of the claim is an immediate consequence of and the characterisation of the complex structures on @xmath592 in terms of @xmath318 and the characterisation of the holomorphic contact structure in terms of @xmath316 . proposition [ ppn : lift ] shows that for every choice of a conformal structure @xmath4 $ ] on @xmath32 we obtain a section @xmath556}$ ] of @xmath557 . note that we may think of a section of @xmath557 as a @xmath12-form on @xmath32 with values in the endomorphisms of the complexified tangent bundle @xmath593 . consequently , the real part of @xmath556}$ ] is a @xmath12-form on @xmath32 with values in @xmath594 . recall that we have already encountered an endomorphism valued @xmath12-form @xmath196}$ ] whose properties we discussed in theorem [ quasilinop1 ] . [ somelem ] we have @xmath595})=\alpha_{[g]}$ ] and moreover @xmath596}|^2_g\,d\mu_g\right)=\frac{\i}{2}|a|^2\zeta_1\wedge\ov{\zeta_1}=-\frac{\i}{2}\zeta_2\wedge\ov{\zeta_2}.\ ] ] recall that local orientation preserving coordinates @xmath597 on @xmath32 induce a coordinate section @xmath598 of cartan s bundle . for a given conformal structure @xmath4 : \sigma \to z$ ] we choose a local coordinate @xmath599 which is holomorphic with respect to the complex structure induced by @xmath4 $ ] and the orientation . it follows from the construction of cartan s bundle given in [ sec : cartbund ] that restricted to @xmath600 , we have @xmath4=\mu \circ \tilde{x}$ ] where @xmath306 denotes the quotient projection . in particular , using and , we obtain @xmath601 where we use the notation @xmath602 the forms @xmath603 and @xmath604 , when pulled back to @xmath32 satisfy @xmath605 where we write @xmath606 . abusing notation , we also use @xmath276 to denote the ( local ) section of @xmath551 } \to \sigma$ ] induced by @xmath607 . writing @xmath608 , we obtain from the first equation in and standard linear algebra ( see in appendix [ cplxlinalg ] ) @xmath609 by definition of @xmath556}$ ] @xmath610}=(a_1+\i a_2)\,\d z\otimes \d z \otimes \frac{\partial}{\partial \ov{z}}\ ] ] and therefore , again by standard linear algebra ( see [ eq : appsomeid ] in appendix [ cplxlinalg ] ) , we obtain the following coordinate expression on @xmath600@xmath611})=\left(\left(a_u\sigma^u_{(l}\sigma^v_j\delta_{k)v}-\frac{1}{2}a_{(l}\delta_{jk)}\right)\delta^{li}\right)\d x^j\otimes \d x^k \otimes \frac{\partial}{\partial x^i}.\ ] ] in order to compute @xmath196}$ ] we choose locally the flat metric on @xmath600 so that @xmath612 in the local @xmath4$]-isothermal orientation preserving coordinate @xmath613 . since the christoffel symbols of the levi - civita connection of @xmath21 vanish identically , we obtain from for @xmath195 @xmath614 consequently , gives @xmath615}=\left(\pi^i_{jk}-\frac{3}{4}\left(\delta_{jk}\delta^{uv}\pi^i_{uv}\right)_0\right)\d x^j\otimes \d x^k\otimes \frac{\partial}{\partial x^i}.\ ] ] it is now a tedious but straightforward calculation to verify that @xmath616 where @xmath617 is given by . moreover , in our coordinates we obtain @xmath201}|_g^2\,d\mu_g=\left((a_1)^2+(a_2)^2\right)\d x^1\wedge \d x^2,\ ] ] so that @xmath618}|_g^2\,d\mu_g\right)=\frac{\i}{2}|a|^2\zeta_1\wedge\ov{\zeta_1}=-\frac{\i}{2}\zeta_2\wedge\ov{\zeta_2}$ ] , as claimed . note that @xmath556}$ ] vanishes if and only if @xmath196}$ ] vanishes . therefore , as an immediate consequence of lemma [ somelem ] , corollary [ uniquepoints ] and corollary [ somecor ] , we obtain an alternative proof of ( * ? ? ? * theorem 3 ) ( see also @xcite for a ` generalisation ' to higher dimensions ) : [ weylmetri ] a conformal structure @xmath4 $ ] on @xmath5 is preserved by a conformal connection defining @xmath3 if and only if the image of @xmath4 : \sigma \to z$ ] is a holomorphic curve . locally the bundle @xmath33 always admits sections having holomorphic image and therefore every torsion - free connection on @xmath222 is locally projectively equivalent to a conformal connection ( see @xcite for additional details ) . applying a technique from @xcite , we compute the variational equations for the functional @xmath0 . for a compact domain @xmath619 and a section @xmath4 : \sigma \to z$ ] we write @xmath620)=\int_{c}|\alpha_{[g]}|^2_gd\mu_g.\ ] ] we say @xmath4 $ ] is an @xmath0-critical point or that @xmath4 $ ] _ is extremal for the projective structure _ @xmath3 if for every compact @xmath619 and for every smooth variation @xmath4_t : \sigma \to z$ ] with support in @xmath357 , we have @xmath621_t)=0.\ ] ] using this definition we obtain : let @xmath5 be an oriented projective surface . a conformal structure @xmath4 $ ] on @xmath32 is extremal for @xmath3 if and only if @xmath6 } : ( \sigma,[g ] ) \to ( y , h_y)$ ] is weakly conformal . let @xmath4 : \sigma \to z$ ] a conformal structure and @xmath4_t : \sigma \to z$ ] a smooth variation of @xmath4 $ ] with support in some compact set @xmath619 and with @xmath622 . we consider the submanifold of @xmath623 defined by @xmath571_t}=\left\{(p , u , t_0 ) \in \sigma\times{p}\times ( -\eps,\eps)\,|\,(p , u)\in { p}^{\prime}_{[g]_{t_0 } } \right\}\ ] ] and denote by @xmath624_t } : { p}^{\prime}_{[g]_t } \to \sigma \times { p}\times ( -\eps,\eps)$ ] the inclusion map . on @xmath625 we define the real - valued @xmath48-form @xmath626 now lemma [ somelem ] implies @xmath627_t)\right|_{t = t_0}=\int_{c}\left.\left(\left(\iota_{[g]_t}\right)^*\mathsf{a}\right)\right|_{t = t_0}.\ ] ] therefore @xmath628_t})^*\mathsf{a}\right)\right|_{t=0}=\int_{c}\left.\left(\partial_t \inc ( \iota_{[g]_t})^*\d \mathsf{a}\right)\right|_{t=0},\ ] ] where @xmath629 denotes the lie - derivative with respect to the vector field @xmath630 . the structure equations give @xmath631 it follows from the proof of proposition [ ppn : lift ] that on @xmath551_t}$ ] there exist complex - valued functions @xmath632 such that @xmath633 where we now write @xmath634 instead of @xmath635_t})^*\zeta_i$ ] . in particular , this gives @xmath636_t})^*\d \mathsf{a}=\frac{\i}{2}\left(q\beta+\ov{q } \ov{\beta}\right ) \d t\wedge\zeta_1\wedge\ov{\zeta_1}\ ] ] so that @xmath637 recall that @xmath638 and therefore , by definition , the complex - valued function @xmath639 satisfies @xmath640 since @xmath641 it follows that @xmath639 represents a _ beltrami differential _ , i.e. , a section of @xmath642 with support in @xmath357 . here @xmath55 denotes the canonical bundle of @xmath32 with respect to the complex structure induced by the orientation and @xmath4=[g]_t|_{t=0}$ ] . it remains to show that every beltrami differential in with support in @xmath357 can be realised via some variation of @xmath4 $ ] . we fix a representative metric @xmath18 $ ] . let @xmath486 be the real - valued functions on cartan s bundle @xmath239 so that @xmath643 . in particular , from the equivariance properties of the cartan connection @xmath238 it follows that @xmath644 infinitesimally this implies the existence of unique real - valued functions @xmath645 so that @xmath646 consider the following conformally invariant functions @xmath647 translating into complex form gives the following structure equation @xmath648 for unique complex - valued functions @xmath649 on @xmath239 . fix a beltrami - differential with respect to @xmath4 $ ] having support in @xmath357 and let @xmath144 be the complex - valued function on @xmath239 representing it . for sufficiently small @xmath650 we may vary @xmath4 $ ] by defining @xmath4_t$ ] via the zero - locus of the function @xmath651 so that on @xmath558_t}=\left\{(p , u , t_0)\in \sigma\times { p}\times ( -\eps,\eps)\,|\,(p , u ) \in { p}_{[g]_{t_0}}\right\}\ ] ] we get @xmath652 in particular , if we evaluate this last equation on @xmath653_t}\right|_{t=0}$ ] , we obtain @xmath654 since @xmath655 is non - vanishing on @xmath653_t}\right|_{t=0}$ ] we must have @xmath656 since @xmath559_t}^{\prime}$ ] arises by reducing @xmath559_t}$ ] , it follows that on @xmath657_t}\right|_{t=0}$ ] we obtain @xmath658 finally , we now know that must vanish where @xmath144 is any complex - valued function representing an arbitrary beltrami differential with support in @xmath357 . this is only possible if @xmath659 vanishes identically . applying corollary [ somecor ] proves the claim . clearly , if @xmath4(\sigma ) \subset z$ ] is a holomorphic curve , then @xmath6 } : \sigma \to y$ ] is weakly conformal . using the structure equations this can be seen as follows . the structure equation for @xmath660 is @xmath661 using the frame adaptions of proposition [ ppn : lift ] where @xmath662 we obtain @xmath663 which is equivalent to @xmath664 so that @xmath665 for some complex - valued function @xmath666 on @xmath667}$ ] . it follows that if @xmath4(\sigma)\subset z$ ] is a holomorphic curve , so that @xmath142 vanishes identically , then @xmath555 must vanish identically as well , showing that @xmath6 } : \sigma \to y$ ] is weakly conformal . consequently , every projective structure @xmath3 locally admits a conformal structure @xmath4 $ ] so that @xmath6}$ ] is weakly conformal . we conclude this section by showing that in the compact case @xmath2)$ ] is up to a topological constant just the dirichlet energy of @xmath6 } : ( \sigma,[g])\to ( y , h_y)$ ] . [ ppn : dirichlet ] let @xmath5 be a compact oriented projective surface . then for every conformal structure @xmath4 : \sigma \to z$ ] we have @xmath668}|^2_g d\mu_g=2\pi\chi(\sigma)+\frac{1}{2}\int_{\sigma}\tr_g \widetilde{[g]}^*h_y\ , d\mu_g,\ ] ] where @xmath669 denotes the euler - characteristic of @xmath32 . recall from that @xmath670}^*h_y\right)=\left(|a|^2-(s+\ov{s})\right)\zeta_1\circ\ov{\zeta_1}+\frac{q}{2}\,\zeta_1\circ\zeta_1+\frac{\ov{q}}{2}\,\ov{\zeta_1}\circ\ov{\zeta_1}.\ ] ] where @xmath109 is the curvature function of the induced @xmath4$]-conformal connection @xmath168 , that is , @xmath671 in particular , we get @xmath672 hence we obtain @xmath673}^*h_y\ , d\mu_g=&\frac{1}{2}\int_{\sigma}2\left(|a|^2-(s+\ov{s})\right)\frac{\i}{2}\zeta_1\wedge\ov{\zeta_1}=\int_{\sigma}|\alpha_{[g]}|^2_gd\mu_g\\ & + \int_{\sigma}\mathrm{im}(\psi).\end{aligned}\ ] ] we have seen in [ subsec : confcon ] that the imaginary part of the curvature form of a @xmath4$]-conformal connection can be written as @xmath674 where @xmath18 $ ] and @xmath144 is some @xmath12-form . therefore , the claim follows by applying the stokes and gauss bonnet theorem . as an obvious consequence of proposition [ ppn : dirichlet ] and theorem [ quasilinop1 ] we get the lower bound : let @xmath5 be a compact oriented projective surface . then for every conformal structure @xmath4 : \sigma \to z$ ] we have @xmath38}^*h_y\ , d\mu_g\geq -2\pi\chi(\sigma),\ ] ] with equality if and only if @xmath3 is defined by a @xmath4$]-conformal connection . clearly , if a projective structure @xmath3 is defined by a @xmath4$]-conformal connection , then the conformal structure @xmath4 $ ] is a critical point for @xmath675 and moreover an absolute minimiser . in this final section we show that besides this obvious class of projective structures there is another class of projective structures the so - called properly convex projective structures for which @xmath0 admits a critical point . recall that the sections of the rank @xmath48 affine bundle @xmath398 are in one - to - one correspondence with the representative connections of @xmath3 . by construction , the sections of @xmath676 are represented by @xmath383-valued maps @xmath273 on @xmath239 satisfying the equivariance property @xmath677 for all @xmath218 . infinitesimally , this translates to @xmath273 satisfying the structure equations @xmath678 for unique real - valued functions @xmath679 on @xmath239 . from the construction of cartan s bundle we know that the function @xmath228 represents the projective schouten tensor of the connection @xmath680 corresponding to @xmath273 , that is , the @xmath249-pullback to @xmath239 of the schouten tensor of @xmath47 becomes @xmath681 . we write @xmath682 for unique real - valued functions @xmath683 on @xmath239 which represent @xmath231 . and @xmath684 as well as @xmath685 and @xmath686 . ] exterior differentiation of implies the existence of unique real - valued functions @xmath687 , totally symmetric in all indices and real - valued functions @xmath688 on @xmath239 such that @xmath689 note that the decomposition in the above equation is chosen so that the functions @xmath687 represent the symmetric part @xmath690 of the @xmath47-covariant derivative of @xmath691 . [ spacetimelagr ] for a @xmath3-representative connection @xmath45 we have @xmath692 let @xmath693 be the function corresponding to @xmath47 . the total space of the pullback bundle @xmath694 is ( diffeomorphic to ) the zero locus of @xmath273 . from we see that on @xmath695 we must have @xmath696 in particular , we obtain @xmath697 and @xmath698}\theta^i_0\wedge\theta^j_0,\ ] ] the claim follows from the definition of the schouten tensor of @xmath47 . recall that an immersion @xmath699 into a pseudo - riemannian manifold @xmath700 is called _ spacelike _ if @xmath701 is positive definite and _ timelike _ if @xmath701 is negative definite . furthermore , we call a spacelike or timelike immersion @xmath297 _ minimal _ if its second fundamental form @xmath702 is trace - free with respect to the induced metric @xmath703 and _ totally geodesic _ if @xmath702 vanishes identically . also , an immersion @xmath704 into a symplectic manifold @xmath705 with @xmath706 is called _ lagrangian _ if @xmath707 . lemma [ spacetimelagr ] motivates : a torsion - free connection @xmath47 on @xmath222 is called _ spacelike _ or _ timelike _ if @xmath691 is negative or positive definite . moreover @xmath47 is called _ lagrangian _ if its ricci tensor is symmetric . the reader may easily verify the equivalence of the following statements for a torsion - free connection @xmath47 on @xmath222 : * @xmath47 is lagrangian ; * the connection on @xmath708 induced by @xmath47 is flat ; * @xmath47 preserves some volume form @xmath709 on @xmath32 . furthermore , it is an elementary linear algebra lemma to show that for every volume form @xmath709 on @xmath32 there exists a unique connection @xmath710 which preserves @xmath709 . consequently , every torsion - free connection on @xmath222 is projectively equivalent to a lagrangian connection . we will henceforth restrict attention to connections @xmath47 which are lagrangian as well as timelike or spacelike , so that @xmath711 defines a riemannian metric on @xmath32 . here and it what follows , the upper sign corresponds to the timelike case and the lower sign to the spacelike case . the second order theory of such submanifolds is summarised in the following : [ submanifoldinaff ] let @xmath45 be a lagrangian timelike or spacelike connection . then there exists a lift @xmath712 covering @xmath47 so that the pullback bundle @xmath713 is isomorphic to the @xmath528-bundle of orientation preserving @xmath714-orthonormal coframes and so that on @xmath715 we have @xmath716 for unique complex - valued functions @xmath717 on @xmath715 . in particular , @xmath47 determines the following objects on @xmath32 : * a @xmath718-form @xmath719 with values in @xmath720 represented by @xmath721 which satisfies @xmath722;\ ] ] * a cubic differential @xmath723 represented by @xmath724 which satisfies @xmath725 the complex structure on @xmath32 is the one induced by @xmath711 and the orientation . in a certain sense the submanifold theory of surfaces in the canonical affine bundle parallels the submanifold theory of surfaces in the @xmath573-sphere , see @xcite for details . since @xmath47 is lagrangian we must have @xmath726 and hence the second equation in becomes @xmath727 so that @xmath728 . the equation @xmath394 defines a reduction of @xmath239 to a @xmath214-subbundle @xmath695 on which we have from @xmath729 from cartan s construction we know that @xmath730 is isomorphic to the bundle @xmath731 of orientation preserving coframes of @xmath32 . the assumption that @xmath732 is positive or negative definite implies that the condition @xmath733 defines a reduction @xmath734 to an @xmath528-subbundle which is isomorphic to the bundle @xmath735 of orientation preserving @xmath21-orthonormal coframes for the metric @xmath714 . since the reductions of @xmath239 to @xmath528-subbundles are in one - to - one correspondence with the sections of @xmath736 it follows that there exists a unique section @xmath712 covering @xmath47 . equation implies that on @xmath715 we must have @xmath737 contracting with @xmath738 , @xmath739 and @xmath740 yields the following expressions @xmath741 in particular , writing @xmath742 we obtain from with tedious but straightforward calculations @xmath743 written out this gives @xmath744 it follows that there exists a @xmath718-form @xmath719 on @xmath32 with values in @xmath720 satisfying @xmath745 computing the real part of @xmath719 , we obtain @xmath746,\ ] ] where we have used that the functions @xmath687 represent @xmath747 and that the liouville curvature @xmath266 of @xmath47 satisfies @xmath748 likewise , we obtain @xmath749 it follows that there exists a cubic differential @xmath750 satisfying @xmath751 computing the real part of @xmath752 , we obtain @xmath753 where the trace - free part is taken with respect to @xmath4 $ ] . we now have : [ thm : submanifoldthm ] a timelike or spacelike lagrangian connection @xmath47 is a minimal immersion @xmath45 if and only if @xmath719 vanishes identically . in order to keep notation uncluttered we will only treat the spacelike case . the timelike case is entirely similar up to some sign changes . recall that the pullback of the metric @xmath410 on @xmath40 satisfies @xmath754 where we write @xmath755 let @xmath756 denote ( the pullback to @xmath239 of ) the levi - civita connection form of @xmath410 , so that we have the structure equation @xmath757 from proposition [ submanifoldinaff ] we know that on the pullback bundle @xmath758 we have @xmath759 so that @xmath760 and @xmath761 and @xmath762 . in particular , @xmath763 pulled back to @xmath715 becomes @xmath764 . we obtain @xmath765 consequently , cartan s lemma implies that there exist unique real - valued functions @xmath766 and @xmath767 with @xmath768 on @xmath715 so that @xmath769 from standard submanifold theory we know that @xmath47 is a minimal immersion if and only if @xmath770 in order to relate this last condition to @xmath719 , we translate into complex form . we compute @xmath771 where @xmath772 it follows from ( a variant of ) cartan s lemma that there exist complex - valued functions @xmath773 on @xmath715 such that @xmath774 comparing these last equations with gives@xmath775 so that @xmath47 is minimal if and only if @xmath776 . using the structure equations , we obtain @xmath777 using that for our frame adaption @xmath778 , we obtain @xmath779 and therefore @xmath780 from proposition [ submanifoldinaff ] we know that @xmath781 hence @xmath782 and @xmath783 which concludes the proof . for later usage we record : [ struceqpullbackbundmin ] let @xmath45 be a timelike or spacelike minimal lagrangian immersion . then on the pullback bundle @xmath758 we have the following identities : @xmath784 the first two identifies are shown in proposition [ submanifoldinaff ] , the last identity is an immediate consequence of the minimality assumption and . we get : let @xmath47 be a projectively flat lagrangian timelike or spacelike connection whose cubic differential @xmath752 vanishes identically . then @xmath45 is totally geodesic . conversely , suppose the lagrangian timelike or spacelike connection @xmath45 is totally geodesic , then @xmath47 is projectively flat and @xmath785 . since @xmath752 vanishes identically , it follows that @xmath786 is trace - free with respect to the conformal structure defined by @xmath787 . in particular , proposition [ submanifoldinaff ] implies that @xmath788 , the liouville curvature of @xmath47 . since @xmath47 is projectively flat it follows that @xmath789 and hence @xmath719 vanish identically . therefore , the functions @xmath351 and @xmath357 in vanish identically . it follows from lemma that @xmath790 and hence @xmath791 vanishes identically as well , the first claim follows . conversely , assume that @xmath47 is totally geodesic so that @xmath792 and hence @xmath785 . then implies that on @xmath715 we have @xmath793 since @xmath794 this implies @xmath795 and hence @xmath47 is projectively flat . let @xmath20 be the levi - civita connection of a riemannian metric @xmath21 of constant non - zero gauss curvature @xmath796 . clearly , the levi - civita connection is lagrangian and furthermore timelike or spacelike since the ricci curvature is just the gauss curvature times the metric @xmath21 . hence @xmath797 vanishes identically and so does @xmath798 . since @xmath796 is constant , @xmath20 is projectively flat and hence totally geodesic . in the compact case the levi - civita connections of metrics of constant non - zero gauss curvature are the only examples of projectively flat minimal lagrangian connections whose cubic differential @xmath752 vanishes identically : [ thm : fuchsloc ] suppose @xmath47 is a projectively flat timelike or spacelike minimal lagrangian connection on a compact oriented surface @xmath32 satisfying @xmath799 . then @xmath47 is the levi - civita connection of a metric of constant non - zero gauss curvature . we first need a lemma which is a translation into bundle language of a result of r. liouville @xcite . the translation is due to bryant @xcite . the reader may also consult @xcite . [ lem : metrilemma ] let @xmath235 be the cartan geometry of an oriented projective surface @xmath5 . suppose there exist real - valued functions @xmath800 on @xmath239 satisfying @xmath801 and the linear differential system @xmath802 for some real - valued functions @xmath803 on @xmath239 . then the symmetric tensor field @xmath804 is the @xmath249-pullback of a unique riemannian metric @xmath21 on @xmath32 whose levi - civita connection defines @xmath3 . suppose the functions @xmath800 satisfy the assumptions of the lemma . writing @xmath805 we obtain @xmath806 where @xmath807 computing how the functions @xmath803 transform under the @xmath102-right action one sees that the equations @xmath808 define a reduction @xmath809 to a @xmath214-subbundle which is isomorphic to the coframe bundle of @xmath32 . moreover cartan s work implies that on @xmath224 the @xmath12-form @xmath223 with @xmath810 is the connection @xmath12-form of a @xmath3-representative connection @xmath47 . therefore on @xmath224 gives @xmath811 showing that @xmath47 is a torsion - free connection preserving @xmath21 , hence the levi - civita connection of @xmath21 . from lemma [ struceqpullbackbundmin ] we know that on the pullback bundle @xmath715 we have @xmath812 for some real - valued @xmath12-form @xmath269 which is the levi - civita connection form of @xmath21 . since @xmath752 vanishes becomes @xmath813 so that @xmath21 has gauss - curvature @xmath12 in the timelike case and @xmath814 in the spacelike case . taking the definition of the forms @xmath815 we obtain from that on @xmath715 @xmath816 in particular , the differential system simplifies to become @xmath817 which has the trivial solution given by @xmath818 and @xmath819 . now lemma [ lem : metrilemma ] implies that there exists a unique metric on @xmath32 whose levi - civita connection defines @xmath3 and whose pullback to @xmath715 is @xmath820 . of course , this is the metric @xmath21 . it follows that the levi - civita connection @xmath20 of @xmath21 is projectively equivalent to @xmath47 . consequently , lemma [ weylfund ] implies that there exists a @xmath12-form @xmath362 on @xmath821 so that @xmath822 an elementary computation gives @xmath823 since @xmath824 is the only skew - symmetric part in the above equation it follows that @xmath362 is closed . taking the trace with respect to @xmath21 , we obtain @xmath825 where @xmath524 denotes the co - differential with respect to @xmath21 and the fixed orientation . integration gives @xmath826 by the stokes theorem . consequently @xmath362 vanishes identically and hence @xmath827 . it is well - known that the levi - civita connection of a metric on a compact surface of non - vanishing euler characteristic determines the metric up to constant scale ( for a proof see for instance @xcite ) , the claim follows . we naturally obtain a holomorphic cubic differential in the projectively flat case : suppose @xmath45 is a projectively flat timelike or spacelike minimal lagrangian immersion . then the cubic differential @xmath752 is holomorphic . recall that the pullback bundle @xmath758 is isomorphic to the @xmath528-bundle of orientation preserving @xmath714-orthonormal coframes . in particular , we have @xmath828 . since @xmath47 is projectively flat we have @xmath795 and hence lemma [ struceqpullbackbundmin ] implies that we may write @xmath829 for some real - valued @xmath12-form @xmath269 on @xmath715 . the structure equation for @xmath168 is @xmath830 the structure equation for @xmath302 is @xmath831 so that @xmath832 it follows from [ subsec : confcon ] that @xmath269 is the ( pullback to @xmath715 of the ) levi - civita connection form of @xmath21 . in particular , the cubic differential @xmath752 represented by @xmath724 is holomorphic if and only if @xmath833 the structure equation for @xmath660 is @xmath834 equivalently , we obtain @xmath835 thus proving the claim . since by riemann - roch there are no non - trivial cubic holomorphic differentials on the @xmath48-sphere @xmath836 , we obtain as an immediate consequence : [ thm : classsphere ] suppose @xmath47 is a projectively flat timelike or spacelike minimal lagrangian connection on @xmath821 . then @xmath47 is the levi - civita connection of a metric of constant positive gauss curvature . if @xmath47 is a timelike or spacelike lagrangian connection , its lift @xmath837 induces a map @xmath838 , where @xmath839 denotes the quotient projection . in addition , we obtain a conformal structure @xmath4=[\pm\mathrm{ric}(\nabla)]$ ] and hence a lift @xmath6 } : \sigma \to y$ ] provided by proposition [ ppn : lift ] . these two maps are the same in the case where @xmath47 is minimal : [ ppn : mintoconf ] let @xmath45 be a timelike or spacelike minimal lagrangian connection . then @xmath840}$ ] where @xmath714 and moreover , @xmath6 } : ( \sigma,[g ] ) \to ( y , h_y)$ ] is weakly conformal . let @xmath693 be the function on cartan s bundle representing @xmath47 and @xmath841 the functions on @xmath239 representing the ricci tensor of @xmath47 . recall that the section @xmath842 was defined by the equations @xmath843 and @xmath844 and hence the map @xmath845 is defined by the equations @xmath846 denoting by @xmath847 the quotient projection , we have by definition of @xmath4 $ ] @xmath848 : \sigma \to z.\ ] ] by construction , the lift @xmath6 } : \sigma \to y$ ] of @xmath4 $ ] is uniquely determined by the condition that on the pullback bundle @xmath6}^*{p}\to \sigma$ ] we have @xmath849 on the pullback bundle @xmath850 we obtain @xmath851 because of the minimality assumption . since @xmath852 it follows that @xmath853 still holds true on @xmath854 hence @xmath855 must be the lift of @xmath4 $ ] . by the definition of @xmath6}$ ] it follows that on @xmath6}^*{p}$ ] we have @xmath856 where the complex - valued function @xmath555 is the complete obstruction to @xmath6}$ ] being weakly conformal . however , since @xmath6}=q_y\circ \tilde{\nabla}$ ] , we know that we can reduce to an @xmath528-bundle on which @xmath857 and hence @xmath858 . since moving along the fibres of @xmath859}^*{p}\to \sigma$ ] , the function @xmath555 varies only by ( non - zero ) complex scale , it follows that @xmath555 must vanish identically . recall that a flat projective surface @xmath5 has the property that @xmath32 can be covered with open subsets , each of which is diffeomorphic onto a subset of @xmath260 in such a way that the geodesics of @xmath3 are mapped onto ( segments ) of projective lines @xmath261 . this condition turns out to be equivalent to @xmath32 carrying an atlas modelled on @xmath260 , that is , an atlas whose chart transitions are ( restrictions ) of fractional linear transformations . on the universal cover @xmath860 of the surface the charts can be adjusted to agree on overlaps , thus defining a _ developing map _ @xmath861 , unique up to post - composition with an element of @xmath209 . in addition , one obtains a _ monodromy representation _ @xmath862 of the fundamental group @xmath51 well defined up to conjugation making @xmath863 into an equivariant map . a flat projective structure is called _ properly convex _ if @xmath863 is a diffeomorphism onto a subset of @xmath260 which is bounded and convex . if @xmath32 is a compact orientable surface with negative euler characteristic , then the ( conjugacy class ) of ` the ' monodromy representation @xmath113 of a properly convex projective structure is an element in the hitchin component @xmath56 of @xmath32 and conversely every element in @xmath56 can be obtained in this way @xcite . in ( * theorem 3.2.1 ) , motivated by the circle of ideas discussed in the introduction , it is shown that a projective structure @xmath3 on @xmath32 is properly convex if and only if there exists a pair @xmath864 consisting of a @xmath3-representative connection @xmath47 having symmetric ricci tensor and a riemannian metric @xmath21 , so that the connection @xmath865 defined by the rule @xmath866 is flat . here @xmath867 where @xmath442 denotes the trivial line - bundle on @xmath32 whose sections are real - valued functions on @xmath32 . in the language used in this article this connection arises as follows . suppose we fix a representative connection @xmath47 in a projective equivalence class @xmath3 , then we obtain an identification of cartan s bundle with @xmath216 . if furthermore @xmath47 has symmetric ricci tensor , then we may assume that @xmath47 preserves some volume form @xmath709 on @xmath32 . in particular , we may reduce cartan s bundle to the @xmath868-subbundle @xmath869 where @xmath870 consists of those coframes that are not only orientation preserving , but also volume preserving with respect to @xmath709 and the standard volume form on @xmath215 . since @xmath871 we may take the defining representation @xmath872 of @xmath209 on @xmath66 restricted to @xmath868 and obtain an associated rank @xmath366 vector bundle @xmath873 . by definition , the elements of @xmath133 are triples @xmath874 subject to the equivalence relation @xmath875 for all @xmath876 . using the affine part of @xmath868 to make @xmath273 vanish , we see that the bundle @xmath133 obtained in this way is isomorphic to the rank @xmath366 vector bundle @xmath133 associated to @xmath870 via the @xmath366-dimensional reducible @xmath877-representation @xmath441 defined by the rule @xmath878 for all @xmath879 . of course , @xmath880 , but more is true . the cartan connection @xmath238 equips @xmath133 with a canonical connection @xmath881 sometimes called the _ tractor connection _ @xcite defined by @xmath882 where @xmath883 is an @xmath884-equivariant map representing a section of @xmath133 and @xmath269 the connection form of @xmath47 . since @xmath47 preserves a volume form it follows that @xmath885 and hence setting @xmath394 we obtain @xmath886 which is the connection . however , recall that the function @xmath887 represents the projective schouten tensor of @xmath47 which is just the ricci tensor of @xmath47 provided @xmath732 is symmetric . therefore , the pair @xmath864 in ( * ? ? ? * theorem 3.2.1 ) is the pair @xmath888 . in our language we may rephrase this as follows : let @xmath5 be a compact oriented flat projective surface . then @xmath3 is properly convex if and only if there exists a @xmath3-representative connection @xmath45 which is a spacelike lagrangian embedding . one of the main theorems of @xcite is theorem 4.2.1 , which states that for a properly convex compact oriented projective surface @xmath5 there is a pair @xmath889 unique up to pullback by @xmath3-preserving diffeomorphisms having the properties stated above and so that @xmath47 preserves the volume form of @xmath21 . the conformal structure defined by @xmath890 is the canonical conformal structure mentioned in the introduction . we obtain : let @xmath5 be a properly convex compact oriented projective surface . then there exists a @xmath3-representative connection @xmath47 unique up to pullback by @xmath3-preserving diffeomorphisms so that @xmath45 is a spacelike minimal lagrangian embedding . in particular , the conformal structure defined by @xmath890 is extremal for @xmath3 . we need to show that the condition @xmath891 where @xmath890 implies that the spacelike lagrangian embedding @xmath45 is also minimal . suppose @xmath47 is a spacelike lagrangian connection represented by the @xmath383-valued function @xmath273 on @xmath239 and let @xmath841 represent the ( symmetric ) ricci tensor of @xmath47 . then @xmath891 is equivalent to the condition @xmath892 where @xmath893 and @xmath223 is the connection form of @xmath47 . recall from that @xmath894 using , we compute @xmath895 since @xmath47 has symmetric ricci tensor we know that @xmath728 . moreover , @xmath47 being projectively flat implies that the functions @xmath896 vanish identically . therefore , in our frame adaption where @xmath897 the condition @xmath891 translates to @xmath898 since @xmath47 if minimal if and only if the functions @xmath899 computed in vanish identically , the first claim follows . applying proposition [ ppn : mintoconf ] proves the theorem . cubic holomorphic differentials also occurred in the classification of projectively flat constant curvature finsler two - spheres by bryant @xcite . the reason for this is a duality between certain finsler structures and conformal connections as reported by r. l. bryant in his talk `` aufwiedersehen surfaces , revisited '' at the icm 2006 . another key result of @xcite is the following : let @xmath5 be a compact oriented properly convex projective surface @xmath5 whose monodromy representation will be denoted by @xmath113 . then there exists a minimal mapping @xmath900 which is @xmath113-equivariant with respect to the action of @xmath51 . in our picture this mapping arises as follows . recall that @xmath3 admits a representative connection defining a spacelike minimal lagrangian embedding @xmath45 which lifts to define a map @xmath837 . we may pull this connection back to the universal cover @xmath860 to obtain a map @xmath901 which is still a spacelike minimal lagrangian map with respect to the metric and symplectic structure on @xmath902 induced by @xmath903 . however , since @xmath3 is properly convex , it follows that the total space @xmath904 of cartan s bundle for @xmath903 is a subset of @xmath209 . consequently , the lift @xmath905 is a map @xmath906 which me may project to obtain a map into @xmath907 and this is the map from @xcite . it appears likely that in the case of a compact oriented properly convex projective surface @xmath5 , the functional @xmath0 admits a unique critical point given by the canonical conformal structure @xmath4_0 $ ] of @xmath3 . if this were true , then it would follow that the only examples of conformal connections defining properly convex projective structures are the levi - civita connections of metrics of constant negative gauss curvature . in @xcite it was shown ( though phrased in different language ) that if @xmath5 is a compact oriented projective surface of negative euler characteristic for which @xmath0 admits an absolute minimiser , i.e. , the projective structure @xmath3 is defined by a conformal connection , then the absolute minimiser is unique . as a by - product of our considerations we obtain a gauss bonnet type identity : [ main ] let @xmath5 a compact oriented projective surface . then for every section @xmath908 we have @xmath909 note that by construction , the fibres of the bundle @xmath7 are diffeomorphic to @xmath910 which is diffeomorphic to @xmath911 and hence contractible . it follows that any two sections of @xmath7 induce the same map on the second de rham cohomology groups @xmath912 . it is therefore sufficient to construct a section @xmath913 for which holds . from the proof of the proposition [ ppn : lift ] we know that for every conformal structure @xmath4 : \sigma \to z$ ] there exists a lift @xmath6 } : \sigma \to y$ ] so that on the pullback bundle @xmath559}^{\prime}$ ] we have @xmath914 where @xmath109 is the curvature function of the induced @xmath4$]-conformal connection @xmath168 . since @xmath915 computing as in proposition [ ppn : dirichlet ] and using the above identities for @xmath916 gives @xmath917}^*\omega_y&=\frac{\i}{2}\int_{\sigma}\left(s+\ov{s}\right)\zeta_1\wedge\ov{\zeta_1}=\int_{\sigma}-\im(\psi)=\int_{\sigma}\left(k_g-\delta_g\beta\right)d\mu_g\\ & = 2\pi\chi(\sigma),\end{aligned}\ ] ] by the stokes and the gauss bonnet theorem . let @xmath133 be a real two - dimensional vector space and @xmath918 a ( linear ) complex structure , i.e. , @xmath919 . extending the transpose map @xmath920 linearly to the complexification @xmath921 , we obtain the usual decomposition @xmath922 into @xmath301 and @xmath718 covectors , where @xmath923 denotes the @xmath924-eigenspace of @xmath925 and @xmath926 the @xmath927-eigenspace of @xmath925 . fixing a basis @xmath928 of @xmath133 so that @xmath929 and denoting by @xmath930 its dual basis , the above decomposition is given by @xmath931 where @xmath932 and @xmath933 is the real structure satisfying @xmath934 and @xmath935 . let @xmath936 be the subgroup of @xmath937 consisting of linear maps commuting with @xmath53 . the elements in @xmath936 act linearly on @xmath938 by transposition . furthermore , we denote by @xmath939 the @xmath936-module consisting of those symmetric trilinear forms that are traceless with respect to the conformal inner product defined by @xmath53 . then , we have an isomorphism of @xmath936-modules @xmath940 , sur une classe dquations diffrentielles , parmi lesquelles , en particulier , toutes celles des lignes godsiques se trouvent comprises . , _ c. r. acad . , paris _ * 105 * ( 1888 ) , 10621064 . zbl 19.0317.02 institut fr mathematik , goethe - universitt frankfurt , robert - mayer - str . 10 , 60325 frankfurt am main , germany + [email protected] + http://www.math.uni-frankfurt.de/~mettler[http://www.math.uni-frankfurt.de/@xmath944mettler ]

we introduce a new functional @xmath0 on the space of conformal structures on an oriented projective manifold @xmath1 . the quantity @xmath2)\geq 0 $ ] measures how much @xmath3 deviates from being defined by a @xmath4$]-conformal connection . we show that in the case of a projective surface @xmath5 , a conformal structure @xmath4 $ ] is a critical point for @xmath0 if and only if a certain lift @xmath6 } : ( \sigma,[g ] ) \to ( y , h_y)$ ] is weakly conformal . in fact , in the compact case @xmath2)$ ] is , up to a topological constant , just the dirichlet energy of @xmath6}$ ] . here @xmath7 is a fibre bundle whose total space carries an indefinite khler - einstein structure @xmath8 which is canonically defined by @xmath3 . in particular , we prove that every properly convex projective structure admits a critical point . as a by - product , we obtain a gauss bonnet type identity for oriented projective surfaces .

in the last few years , experiments on collective modes in ultracold trapped fermi gases at duke university @xcite and at innsbruck @xcite revealed a lot of interesting information about the different regimes which can be realized in these systems . this is mainly due to the possibility to change not only the temperature of the gas , but also the interaction between the atoms by adjusting the magnetic field in the vicinity of a feshbach resonance . one of the objectives of these experiments was to detect the transition from the normal to the superfluid phase . however , although the frequencies of the collective modes are generally different in the hydrodynamic and in the collisionless regime , it was recognized that a hydrodynamic behaviour of the gas is not an unambiguous sign of superfluidity . in fact , hydrodynamic behavior can be a consequence of superfluidity , but also of a sufficiently high collision rate in the normal - fluid phase @xcite . recently it was therefore proposed to distinguish the superfluid , the collisionally hydrodynamic , and the collisionless regime @xcite . the experimental results suggest that the transition from the superfluid to any of the normal - fluid regimes is always accompanied by a very strong damping of the collective modes . while the frequencies of the collective modes in the zero - temperature limit can easily be predicted in the framework of superfluid hydrodynamics , literature on the finite - temperature case is relatively sparse . one suggestion put forward by griffin et al . was to apply landau s two - fluid hydrodynamics @xcite , but this requires that the collision rate in the normal - fluid component is sufficiently high , i.e. , much higher than the mode frequency . this is usually not the case , since in a trapped system the collective modes have frequencies which are at least of the order of the trap frequency . in the opposite limit , i.e. , if the normal - fluid component is collisionless , as it should be in the weakly interacting limit , a quasiparticle transport theory which couples superfluid hydrodynamics to a vlasov equation for the normal component was suggested by one of the authors @xcite . although this theory provides a qualitative explanation of the damping of the collective modes near the transition from the superfluid to the collisionless normal - fluid phase , it can not give a quantitative description of the recent experiments since these are generally done in the strongly interacting regime ( near a feshbach resonance ) . in the present paper , we will consider the case of attractive interaction , i.e. , negative scattering length @xmath1 , from the weakly interacting regime far from resonance up to the unitary limit , @xmath2 . we will concentrate on the normal - fluid phase , i.e. , on temperatures above the critical temperature @xmath3 of the superfluid - normal phase transition . the experimental data taken at these temperatures still show a rather strong damping of the collective modes , since the experiments are in fact neither in the collisionally hydrodynamic nor in the collisionless limit . this intermediate regime has been studied theoretically in the framework of the boltzmann equation ( sometimes also called boltzmann - vlasov or landau - vlasov equation ) . in the framework of the boltzmann equation , interactions between the atoms enter in two different places : on the one hand , each particle moves in a mean field characterizing the average of the interaction with all other particles . on the other hand , the particles undergo two - body collisions , which are determined by the scattering cross - section . in some of the early literature on this subject @xcite , the mean field effects were considered within the hartree approximation . however , the most recent work by bruun et al . @xcite concentrates mainly on the strongly interacting regime , where the hartree approximation breaks down : while more and more sophisticated models of the collision term were developed , mean field effects were completely neglected @xcite . therefore , the predicted frequencies in the collisionless limit are those of an ideal gas , and in the hydrodynamic limit , the equation of state is that of an ideal gas , too . however , at least the experiment of ref . @xcite clearly shows the importance of the mean field shift in the collisionless regime . the aim of the present paper is to include mean field like effects on the propagation of the particles into the boltzmann equation in a way which is appropriate also for the strongly interacting case . our approach is based on the in - medium scattering amplitude ( @xmath0 matrix ) , calculated in ladder approximation . this allows for a unified description of mean field like effects on the propagation of the particles ( self - energy ) and the modified cross - section entering the collision term of the boltzmann equation . we point out that in order to have a consistent theory , it is important to use in the description of the collective modes , which are small variations around equilibrium , the same self - energy as in the calculation of the equilibrium density profile . this can be seen , e.g. , by looking at the frequency of the sloshing mode , whose frequency , according to the kohn theorem @xcite , must be equal to the corresponding trap frequency . our paper is organized as follows . in sec . [ sec : interaction ] , we concentrate on the description of the system in equilibrium . after illustrating the breakdown of the hartree approximation , we review the treatment of the interacting fermi gas in the framework of the ladder approximation , introducing the in - medium scattering amplitude , the single - particle self - energy , and the in - medium cross - section . we discuss the quasiparticle approximation which is necessary for describing the system in the framework of the boltzmann equation and which allows us to define a quantity similar to the mean field in hartree approximation . we show the resulting density profiles and discuss the limits of validity of the quasiparticle approximation . in sec . [ sec : modes ] , we turn to the description of collective modes in the framework of the boltzmann equation , which now includes the `` mean field '' and the in - medium cross section . using the standard method of taking moments of the boltzmann equation in phase space , we obtain semi - analytic expressions for the collective mode frequencies which depend only on integrals of equilibrium quantities . in sec . [ sec : resu ] , we discuss our numerical results for the scissors , radial quadrupole , and breathing modes and compare them with the available experimental data for temperatures above @xmath3 . finally , in sec . [ sec : conclusions ] , we draw our conclusions and give an outlook to further developments . throughout the paper , we will use in the derivations units with @xmath4 ( @xmath5 reduced planck constant , @xmath6 = boltzmann constant ) . let us consider a two - component ( @xmath7 , @xmath8 ) uniform fermi gas in the normal phase . as long as the range of the interaction is small compared with the mean distance between atoms , one can assume a zero - range ( @xmath9 function ) interaction between atoms of opposite spin , and the hamiltonian reads ( in second quantization ) @xmath10 where @xmath11 and @xmath12 denote the atom mass and the coupling constant and @xmath13 is the fermion field operator . we assume that the interaction is attractive , i.e. , @xmath14 . the coupling constant is related to the atom - atom scattering length @xmath15 via @xmath16 in hartree approximation , the single - particle energies of @xmath7 and @xmath8 particles are shifted by @xmath17 and @xmath18 , respectively . the exchange or fock term vanishes since the interaction is only between atoms with opposite spin . from now on , we will assume that both spin states are equally populated , and we denote by @xmath19 the density per spin state . then the hartree shift is the same for both spin states , and we may write @xmath20 let us now calculate the density as a function of the chemical potential @xmath21 . for our purposes it is enough to consider the zero - temperature limit , i.e. , temperatures @xmath22 , where @xmath23 are the fermi energy and fermi momentum , respectively . [ note that eq . ( [ epsilonfkf ] ) _ defines _ @xmath24 and @xmath25 for a uniform system , i.e. , it remains valid even if the occupation numbers do not resemble a step function because of temperature or correlation effects . for a trapped system , however , we will use a different definition of @xmath24 and @xmath25 , see sec . [ sec : lda ] . ] at zero temperature , the relation between @xmath24 and @xmath21 is given by @xmath26 . substituting eq . ( [ sigmahartree ] ) into this relation , one obtains the following cubic equation for @xmath25 : @xmath27 it is easy to see that this equation does not have a solution if @xmath21 exceeds a critical value given by @xmath28 , corresponding to a maximum density of @xmath29 . the same value was found in ref . @xcite as the density where the system becomes unstable against separation into a low - density ( gas ) and a high - density ( solid ) phase . if the above arguments were correct , a low - temperature fermi gas with attractive interaction should be unstable as soon as @xmath30 . however , we know from experiments that ultracold fermi gases are stable throughout the bcs - bec crossover , including the unitary limit @xmath31 , because the system prefers to form pairs instead of separating into two phases @xcite . the instability is simply an artefact of the hartree approximation and not physical . in the hartree approximation as described in the previous subsection , the coupling constant @xmath12 was related to the scattering length @xmath15 in free space . this means that it was implicitly assumed that the scattering amplitude itself is the same in the gas as in free space . as we will see , this assumption is the origin of the unphysical instability of the hartree approximation at high density or strong interaction . for instance , as pointed out in ref . @xcite the scattering amplitude becomes proportional to @xmath32 instead of @xmath15 at high density . the approximation scheme we adopt here in order to calculate the in - medium scattering amplitude is based on the non self - consistent @xmath0 matrix approximation . in this approximation , the @xmath0 matrix is given by the resummation of ladder diagrams , and it depends only on the total energy @xmath33 and the total momentum @xmath34 of the two atoms : @xmath35 where @xmath36 denotes the non - interacting two - particle green s function . within the imaginary - time ( matsubara ) formalism @xcite , the latter is given by @xmath37 where @xmath38 and @xmath39 are , respectively , bosonic and fermionic matsubara frequencies , and @xmath40 is the free ( matsubara ) green s function , @xmath41 being the free single - particle energy . after evaluation of the sum over @xmath42 , the retarded function @xmath43 is obtained as usual by analytic continuation . the result reads @xmath44 where @xmath45 $ ] , with @xmath46 . the problem with eqs . ( [ tmatrix])([jdivergent ] ) is that @xmath36 is divergent . to resolve this problem , one can introduce a momentum cut - off @xmath47 , determine the coupling constant @xmath12 as a function of @xmath47 such that one recovers the correct scattering length @xmath15 in free space , and finally take the limit @xmath48 keeping the free - space scattering length @xmath15 constant @xcite . in this way one obtains for the @xmath0 matrix in free space @xmath49 where @xmath50 is the on - shell momentum in the center - of - mass ( cm ) frame . if we now decompose @xmath36 into the two - particle green s function in free space , @xmath51 , and a medium correction , @xmath52 , such that @xmath53 , we may write @xmath54 with @xmath55 . even without cut - off , the medium contribution @xmath52 is finite and given by @xmath56 the imaginary part of @xmath52 can be given in closed form : @xmath57 where @xmath58 . the real part is then computed numerically via a dispersion relation , @xmath59 as a by - product , the in - medium @xmath0 matrix allows us to determine the critical temperature @xmath3 of the system , i.e. , the temperature below which the system becomes superfluid . as realized by nozires and schmitt - rink in their pioneering paper @xcite , the thouless criterion which relates @xmath3 to the temperature where the @xmath0 matrix develops a pole at the fermi level ( i.e. , at @xmath60 ) , remains true at all couplings . since the pole always appears first at @xmath61 , the critical temperature can be obtained from the equation @xmath62 contrary to the zero - range interaction used in sec . [ sec : hartree ] , the in - medium vertex function @xmath63 is now momentum and energy dependent . this complicates the calculation of the single - particle energy shift . even the concept of such an energy shift may be questioned if there are no well defined quasiparticles , as it is the case in the `` pseudogap regime '' @xcite . in any case , the appropriate object to calculate is the single - particle self - energy @xmath64 , which is well - defined and does not rely on the existence of quasiparticles . the ladder self - energy can be written within the matsubara formalism as @xmath65 using analytic continuation to real energies , we find for the imaginary part of the retarded self - energy : @xmath66 which has to be evaluated numerically and from which the real part can be obtained by a dispersion relation analogous to eq . ( [ dispersionrelation ] ) . since we are going to use the boltzmann equation for the description of collective modes , we are implicitly assuming that the quasi - particles , especially near the fermi surface , are well defined , which is of course a limitation of the range of applicability of our approach @xcite . if there are well - defined quasiparticles , this means that their dispersion relation @xmath67 , determined by the poles of the single - particle green s function , can be obtained from @xmath68 such a treatment is probably desirable but beyond the scope of the present work . here , we will completely neglect any energy and momentum dependence of the self - energy . since we are mainly interested in momenta around the fermi momentum , and hence energies around the fermi energy , we will make the approximation @xmath69 where @xmath70 [ which can actually be quite different from @xmath25 as defined in eq . ( [ epsilonfkf ] ) ] . it is the quantity @xmath71 which will take the role of the mean field potential in the boltzmann equation . the fact that the particles are interacting among each other changes strongly the equation of state of the system , i.e. , the relation between the chemical potential @xmath21 and the density @xmath72 . within the hartree approximation , the relation @xmath73 can trivially be obtained , whereas in ladder approximation , the calculation of the density for a given chemical potential @xmath21 is more involved . in principle , the density can be obtained as @xmath74 where @xmath75 denotes the full single - particle green s function , which according to dyson s equation is given by @xmath76 . here we will restrict ourselves to an expansion of @xmath75 up to first order in @xmath64 , i.e. , we write @xmath77 this leads us to the following expression for the density : @xmath78 where the free ( uncorrelated ) part , @xmath79 , is given by @xmath80 while , after a lengthy calculation , the expression for the correlated part , @xmath81 , can be written as @xmath82\ , . \label{rho1nsr}\end{gathered}\ ] ] this is actually the result for the density initially given by nozires and schmitt - rink ( nsr ) in ref . @xcite and by s de melo , randeria , and engelbrecht @xcite . unfortunately , the density formula given above is not suitable for being used as the ground - state density in the boltzmann equation . in the boltzmann equation , the density is expressed as an integral over the distribution function @xmath83 : @xmath84 and @xmath83 must reduce to a simple fermi function . our quasiparticle(qp ) approximation for the density consists in using the single - particle energy @xmath85 as defined by eq . ( [ spenergy ] ) in the calculation of the occupation numbers , i.e. , @xmath86 where we have introduced the abbreviation @xmath87 . in this way we obtain an alternative method for calculating the density as a function of @xmath21 . fortunately , it turns out that in most cases both ways of calculating the density give similar results . in order to demonstrate this , we show in fig . [ fig : muef ] the ratio @xmath88 , with @xmath21 calcultated with the nsr density and the qp density , is plotted as a function of @xmath89 for different temperatures : @xmath90 , @xmath91 and @xmath92 . the curve for @xmath93 stops at @xmath94 , since at this interaction strength the critical temperature is reached.,width=264 ] the dimensionless ratio @xmath88 as a function of the parameter @xmath95 defining the interaction strength for various temperatures ( in units of the fermi energy ) . one can see that the interactions lead to a reduction of @xmath21 with respect to the ideal gas result . at weak interactions , nsr and qp curves are in perfect agreement , but in the strongly interacting case there can be noticeable differences , especially at low temperatures close to @xmath3 , indicating the breakdown of the qp approximation . this is not surprising , since in this case the system is in the `` pseudogap regime '' @xcite . the interaction between atoms is not only responsible for the single - particle energy shift . it also determines the collision rate of the atoms , which will play a central role for the properties of collective modes . the important quantity is the cross section @xmath96 . in the case of a zero - range @xmath97-wave interaction , the cross section for two atoms in free space with momenta @xmath98 and @xmath99 before the collision and @xmath100 and @xmath101 after the collision is given by @xcite @xmath102 where @xmath103 is the incoming momentum in the cm frame and @xmath104 is the solid angle after the scattering , i.e. , @xmath105 , where @xmath106 is the angle between @xmath107 and @xmath108 ( note that @xmath109 because of energy and momentum conservation ) . as pointed out in refs . @xcite , the cross section is strongly modified by medium effects . in terms of the @xmath0 matrix , the in - medium cross section can be written as @xmath110 which now depends also on the total momentum @xmath111 of the two atoms . it is not easy to see a priori what will be the effect of these medium modifications , since depending on @xmath112 and @xmath113 the cross section can be enhanced or reduced as compared with the cross section in free space . this is shown in fig . [ fig : xsection ] the ratio of the in - medium cross section and the vacuum one is displayed for total momentum @xmath114 as a function of the relative momentum @xmath113 . the results are shown for different temperatures for fixed interaction strength @xmath115.,width=264 ] where we display the cross section as a function of @xmath113 for the case @xmath116 ( where the medium effect is supposed to be strongest ) for various temperatures for fixed interaction strength @xmath117 . the strong enhancement of the cross - section near the critical temperature is a precursor of the singularity of the @xmath0 matrix at the critical temperature @xcite . let us mention that the same effect has already been found some years ago in the in - medium nucleon - nucleon cross section in low - temperature nuclear matter @xcite . until now we considered a uniform system where the atoms are not trapped by an external potential . in order to include the trap potential @xmath118 , we will make use of the local - density approximation ( lda ) , where the system is treated as locally homogeneous , with an @xmath119 dependent chemical potential which is given by @xmath120 this approximation should be valid as long as the potential varies only slowly , i.e. , on length scales which are large compared with @xmath32 . by the way , this condition is also necessary for the validity of the boltzmann equation which will be used later to describe the collective modes . within the local - density approximation , all equilibrium quantities of the system discussed in the preceding sections , like @xmath63 , @xmath71 , @xmath72 , @xmath121 , etc . , acquire an additional @xmath119 dependence via the dependence of @xmath21 on @xmath119 . in practical calculations , we will use a harmonic trap potential @xmath122 besides the fact that experimental traps are almost harmonic , the use of a harmonic potential has the advantage that it is sufficient to calculate the equilibrium quantities once for a spherical trap with the same number of atoms and the average frequency @xmath123 . then , the equilibrium quantities in the deformed trap can easily be obtained from the corresponding ones in the spherical trap by the change of variables @xmath124 ( for @xmath125 ) . as an example , we show in fig . [ fig : density ] density profiles for 400000 atoms with @xmath126 at various temperatures , calculated using the nsr formula ( solid lines ) or the qp approximation ( long dashes ) . for comparison , the corresponding density profiles of an ideal fermi gas ( short dashes ) are shown , too . the length unit is the harmonic - oscillator length @xmath127.,width=264 ] the density profile of @xmath128 atoms in a trap with fixed interaction strength @xmath129 at different temperatures . note that we follow here the usual convention of the experimental papers , using for the trapped gas a definition of @xmath25 and @xmath24 which is different from that used in the uniform case [ cf . ( [ epsilonfkf ] ) ] . in the trapped case , @xmath25 and @xmath24 refer to the values of @xmath25 and @xmath24 in the center of the trap calculated for an _ ideal _ fermi gas at _ zero temperature_. therefore , @xmath24 and @xmath25 are determined by the number of atoms , @xmath130 , and the average trap frequency as follows : @xmath131 one can see that the interaction leads to a noticeable change of the density profile , especially at low temperature . the agreement between the nsr and qp results is almost perfect in the case @xmath132 , while at @xmath133 , corresponding to the critical temperature , the qp density is too small , indicating again the breakdown of the qp approximation in the pseudogap regime . however , it should be mentioned that for @xmath126 , one has to go very close to @xmath3 in order to see this effect ; it is more important in the unitary limit . let us mention that similar density profiles can be found in the literature , even for temperatures below the critical one @xcite . after the discussion of static properties , let us now turn to the description of collective modes of a trapped fermi gas . we remind the reader of three assumptions mentioned earlier : ( a ) the density is supposed to vary ( due to the trap as well as the collective motion ) only on large length scales ; ( b ) the temperature has to be above the superfluid transition temperature @xmath3 ; ( c ) the quasiparticles near the fermi surface have to be well defined . in addition , the boltzmann equation is only valid if ( d ) the time dependence of the excitations under consideration ( in the case of the collective modes under consideration this time scale is set by the the trap frequency ) are slow compared to the `` correlation time '' @xcite . under these assumptions , the dynamics of the system can be described by the semi - classical distribution function @xmath134 whose time evolution is governed by the boltzmann equation @xcite : @xmath135~ , \label{eq : boltz}\ ] ] where @xmath136 and @xmath137 satisfy the classical equations of motion . in the case of a quasiparticle dispersion relation as given by eq . ( [ spenergy ] ) with an @xmath119 dependent chemical potential as given by eq . ( [ lda ] ) , the velocity and acceleration read @xmath138 since , within lda , @xmath139 . note that there are two sources of @xmath119 dependence of the self - energy @xmath71 . in equilibrium , @xmath71 depends on @xmath119 only via @xmath140 . more generally , in particular out of equilibrium , the self - energy depends on the distribution function @xmath83 , i.e. , we may write @xmath141 $ ] . the distribution function @xmath83 is related to the density per spin state by eq . ( [ rhof ] ) and we assume that , as in equilibrium , the distribution functions for the two spin states are the same , i.e. , @xmath142 . this is true if the trap potential and the excitation operator of the collective mode are spin independent . the functional @xmath143 $ ] appearing on the rhs of eq . ( [ eq : boltz ] ) is the collision integral . it describes collisions between atoms with opposite spin and depends on the differential scattering cross section as @xcite @xmath144=\int d^3p_1\int d\omega \frac{d\sigma}{d\omega } |{\bm{\mathrm{v}}}-{\bm{\mathrm{v_1}}}| [ f f_1 ( 1-af^\prime ) ( 1-af_1^\prime)\\ -f^\prime f_1^\prime ( 1-af ) ( 1-af_1)]\,,\end{gathered}\ ] ] where @xmath145 and @xmath98 are the incoming momenta , @xmath146 and @xmath147 are the outgoing ones ; @xmath148 and @xmath149 are the incoming velocities @xmath150 and @xmath151 , respectively , @xmath104 is the solid angle formed by the incoming relative momentum @xmath152 and the outgoing relative momentum @xmath153 of the two atoms , @xmath154 , @xmath155 , @xmath156 , etc . the factors of the type @xmath157 are absent in the classical boltzmann equation . they are a consequence of fermi statistics and ensure that an atom can not be scattered into a state which is already occupied . this pauli blocking effect can result in a strong reduction of the collision rate , especially at low temperatures . in order to study the collective modes of the trapped gas , we consider a small deviation @xmath158 of the distribution function from the equilibrium one . usually @xmath159 is strongly peaked at the fermi surface , but it can conveniently be written as @xmath160 \phi({\bm{\mathrm{r}}},{\bm{\mathrm{p}}},t)\ , , \label{eq : deltaf}\ ] ] with a smooth function @xmath161 @xcite . expanding the boltzmann equation ( [ eq : boltz ] ) to linear order in the deviations from equilibrium , and considering that a change @xmath159 of the distribution function results in a change @xmath162 of the self - energy , we obtain @xmath163 \label{eq : boltzlin}\end{gathered}\ ] ] with the linearized collision integral @xmath164 = \int d^3 p_1\int d\omega \frac{d\sigma}{d\omega } |{\bm{\mathrm{v}}}-{\bm{\mathrm{v_1}}}| f_{\mathit{eq}}f_{{\mathit{eq}}\,1}\\ \times ( 1-af_{\mathit{eq}}^\prime)(1-af_{{\mathit{eq}}\,1}^\prime ) ( \phi+\phi_1-\phi^\prime-\phi_1^\prime)\ , . \label{collisionterm}\end{gathered}\ ] ] now we have to specify @xmath162 , which appears in the lhs of eq . ( [ eq : boltzlin ] ) . since we neglect any possible momentum dependence of @xmath71 and @xmath162 , it is clear that @xmath162 can be written as @xmath165 where @xmath166 is the functional derivative @xmath167/\delta f$ ] , taken at @xmath168 . in the low - temperature limit , @xmath159 is so strongly peaked at the fermi momentum @xmath169 that @xmath166 may be replaced by a constant @xmath170 , as in fermi liquid theory @xcite . this results in @xmath171 , with @xmath172 in addition , by choosing a particular form for @xmath159 , namely @xmath173 , we can identify @xmath174 with the derivative @xmath175 taken at constant @xmath0 , i.e. , @xmath176 in the present work , we shall assume that eq . ( [ deltau ] ) is a reasonable approximation also at higher temperatures , although it can not be rigorously justified in this case . equation ( [ eq : boltzlin ] ) together with ( [ deltau ] ) constitutes the starting point for our study of collective modes with in - medium effects . it is a generalization of the boltzmann equation used in refs . @xcite in the case @xmath177 ( hartree approximation ) . as mentioned in sec . [ sec : linbol ] , the function @xmath178 characterizing the deviation from equilibrium can be supposed to be smooth in phase space . this allows us to make a simple ansatz for @xmath161 with a small number of coefficients rather than solve the linearized boltzmann equation ( [ eq : boltzlin ] ) exactly . for any collective mode of interest , the trial function @xmath178 has to contain at least those terms which are necessary to generate the velocity field @xmath179 characterizing the mode @xcite . the presence of a velocity field modifies @xmath180 into @xmath181\ ] ] and leads to a deviation @xmath182 i.e. , the trial function @xmath161 must at least contain a term proportional to @xmath183 . when this term is inserted into the linearized boltzmann equation ( [ eq : boltzlin ] ) , the operator @xmath184 on the lhs of eq . ( [ eq : boltzlin ] ) generates new terms , as do the @xmath162 term on the lhs and the collision term @xmath185 on the rhs . in general , the number of terms is infinite and the system can not be closed . however , in the case of an ideal gas ( @xmath186 ) in a harmonic potential @xmath187 , and if @xmath188 is at most linear in the coordinates , it is possible to solve eq . ( [ eq : boltzlin ] ) with a finite number of terms . for instance , a term proportional to @xmath189 generates terms proportional to @xmath190 and @xmath191 , and no other terms are needed . in the opposite limit of an extremely strong collision term , i.e. , in the hydrodynamic regime , a linear velocity field solves exactly the hydrodynamic equations if the equation of state can be approximated by a polytropic one , which is in many cases an excellent approximation @xcite . we therefore assume that also in our case it will be a good approximation to include into @xmath161 only those terms which appear in the ideal gas case ( of course the coefficients will change ) . to be explicit , we will focus on the scissors mode ( @xmath192 ) , the radial quadrupole mode ( @xmath193 ) , and the breathing modes ( @xmath194 ) . in order to check the consistency of our model , we will also consider the kohn mode ( center - of - mass or sloshing mode , @xmath195 ) . the velocity fields and the corresponding trial functions for these modes are given in table [ tab : phi ] . note that in the case of the breathing modes , the axial and the radial modes can not be treated separately because they are coupled ( although the coupling may be weak in very elongated traps ) . in table [ tab : breathing ] , each line is obtained by taking one moment of the boltzmann equation . for example , the third entry in the first column ( @xmath196 ) is the coefficient in front of @xmath197 if eq . ( [ eq : boltzlin2 ] ) , with @xmath161 as given in the last line of table [ tab : phi ] , is multiplied by @xmath198 and integrated over @xmath119 and @xmath145 . notice that the coefficient @xmath199 appears only trough the @xmath200 term . the new interaction dependent parameters @xmath201 and @xmath202 that enter in the table are defined as : @xmath203 where @xmath201 reduces to @xmath204 in the hartree case . from the determinant of the @xmath205 matrix given in table [ tab : breathing ] , we obtain the equation for the frequencies , eq . ( [ brefrda ] ) . the frequencies in the collisionless limit are given by @xmath206 with @xmath207 \nonumber\\ & + \chi[-10\chi^\prime(2+\lambda^2)(1+\varphi_1 ) -3(1+\lambda^2)(22 + 25\varphi_1 ) \nonumber\\ & + 8(2+\lambda^2)\varphi_3]\,,\\ b = & -4\lambda^2(2-\chi)[16 + 25\varphi_1 - 25\chi(1+\varphi_1 ) ] \nonumber\\ & \times[32 + 50\varphi_1 + 25\chi^2(1+\varphi_1)+6\chi^\prime(8 + 5\varphi_1 ) \nonumber\\ & -3\chi(22 + 25\varphi_1 + 10\chi^\prime(1+\varphi_1)-8\varphi_3)-24\varphi_3 ] \,,\end{aligned}\ ] ] the hydrodynamic frequencies are @xmath208}\,,\ ] ] with @xmath209\,,\\ d = & -36\lambda^2[16 + 25\varphi_1 - 25\chi ( 1+\varphi_1 ) ] \nonumber\\ & \times[32 + 50\varphi_1 + 25\chi^2(1+\varphi_1)+6\chi^\prime(8 + 5\varphi_1 ) \nonumber\\ & -3\chi(22 + 25\varphi_1 + 10\chi^\prime(1+\varphi_1)-8\varphi_3)-24\varphi_3 ] \,,\end{aligned}\ ] ] note that since @xmath210 and @xmath211 are proportional to @xmath199 , the low - lying limiting frequencies ( @xmath212 and @xmath213 ) , corresponding to the axial breathing mode , tend to zero in the limit of a very elongated trap ( @xmath214 ) . * j. kinast , s.l . hemmer , m.e . gehm , a. turlapov , and j.e . thomas , phys . lett . * 92 * , 150402 ( 2004 ) . j. kinast , a. turlapov , and j.e . thomas , phys . a * 70 * , 051401(r ) ( 2004 ) . m. bartenstein , a. altmeyer , s. riedl , s. jochim , c. chin , j. hecker denschlag , and r. grimm , phys . 92 * , 203201 ( 2004 ) . a. altmeyer , s. riedl , m.j . wright , c. kohstall , j. hecker denschlag , and r. grimm , phys . a * 76 * , 033610 ( 2007 ) . a. altmeyer , s. riedl , c. kohstall , m.j . wright , r. geursen , m. bartenstein , c.chin , j. hecker denschlag , and r. grimm , phys . lett . * 98 * , 040401 ( 2007 ) . wright , s. riedl , a. altmeyer , c. kohstall , e.r . snchez guajardo , j. hecker denschlag , and r. grimm , phys . lett . * 99 * , 150403 ( 2007 ) . s. riedl , e.r . snchez guajardo , c. kohstall , a. altmeyer , m.j . wright , j. hecker denschlag , r. grimm , g.m . bruun , and h. smith , phys . a * 78 * , 053609 ( 2008 ) . m. cozzini and s. stringari , phys . . lett . * 91 * , 070401 ( 2003 ) . e. taylor and a. griffin , phys . a * 72 * , 053630 ( 2005 ) . m. urban and p. schuck , phys . a * 73 * , 013621 ( 2006 ) ; m. urban , phys . a * 75 * , 053607 ( 2007 ) . m. urban , phys . a * 78 * , 053619 ( 2008 ) . c. menotti , p. pedri , and s. stringari , phys . rev . lett . * 89 * , 250402 ( 2002 ) . p. pedri , d. gury - odelin , and s. stringari , phys . a * 68 * , 043608 ( 2003 ) . f. toschi , p. vignolo , s. succi , and m.p . tosi , phys . a * 67 * , 041605(r ) ( 2003 ) . f. toschi , p. capuzzi , s. succi , p. vignolo , and m.p . tosi , j. phys . b * 37 * , s91 ( 2004 ) . p. massignan , g.m . bruun , and h. smith , phys . a * 71 * , 033607 ( 2005 ) . bruun and h. smith , phys . a 76 , 045602 ( 2007 ) . w. kohn , phys * 123 * , 1242 ( 1961 ) . l. brey , n.f . johnson , and b.i . halperin , phys . b * 40 * , 10647 ( 1989 ) . m. houbiers , r. ferwerda , h.t.c . stoof , w.i . mcalexander , c.a . sackett , and r.g . hulet , phys . a * 56 * , 4864 ( 1997 ) . p. nozires and s. schmitt - rink , j. low . phys . * 59 * , 195 ( 1985 ) . h. heiselberg , phys . a * 63 * , 043606 ( 2001 ) . a.l . fetter and j.d . walecka , _ quantum theory of many - particle systems _ ( mcgraw - hill , new york , 1971 ) . p. pieri and g.c . strinati , phys . rev . b * 61 * , 15 370 ( 2000 ) . a. perali , p. pieri , g.c . strinati , and c. castellani , phys . b * 66 * , 024510 ( 2002 ) . l.d . landau and e.m . lifshitz , _ course of theoretical physics , vol . 3 : quantum mechanics _ , ( pergamon , london 1958 ) . g.m . bruun and h. smith , phys . a * 75 * , 043612 ( 2007 ) . s de melo , m. randeria , and j.r . engelbrecht , phys . * 71 * , 3202 ( 1993 ) . t. alm , g. rpke , and m. schmidt , phys . c * 50 * , 31 ( 1994 ) ; t. alm , g. rpke , w. bauer , f. daffin , and m. schmidt , nucl . phys . a * 587 * , 815 ( 1995 ) . a. perali , p. pieri , l. pisani , g.c . strinati , phys . * 92 * , 220404 ( 2004 ) . p. danielewicz , ann . ( n.y . ) * 152 * , 239 ( 1984 ) . e.m . lifshitz and l.p . pitaevskii , _ l.d . landau and e.m . lifshitz , course of theoretical physics , vol . 10 : physical kinetics _ ( pergamon , oxford , 1981 ) e.m . lifshitz and l.p . pitaevskii , _ l.d . landau and e.m . lifshitz , course of theoretical physics , vol . 9 : statistical physics , part 2 _ ( pergamon , oxford , 1980 ) . u. al khawaja , c.j . pethick , and h. smith , j. low temp . phys . * 118 * , 127 ( 2000 ) . m. bartenstein , a. altmeyer , s. riedl , s. jochim , c. chin , j. hecker denschlag , and r. grimm , phys . lett . * 92 * , 203201 ( 2004 ) . d. kremp , m. bonitz , w.d . kraeft , and m. schlanges , ann . ( n.y . ) * 258 * , 320 ( 1997 ) . j. e. thomas , j. kinast , and a. turlapov , proceedings of the 24th international conference on low temperature physics , aip conf . proc . * 850 * , 69 ( 2006 ) . f. dalfovo , s. giorgini , l.p . pitaevskii , and s. stringari , rev . phys . * 71 * , 463 ( 1999 ) . l. vichi and s. stringari , phys . a * 60 * , 4734 ( 1999 ) . l. vichi , j. low temp . phys . * 121 * , 177 ( 2000 ) .

due to pauli blocking of intermediate states , the scattering matrix ( or @xmath0 matrix ) of two fermionic atoms in a fermi gas becomes different from that of two atoms in free space . this effect becomes particularly important near a feshbach resonance , where the interaction in free space is very strong but becomes effectively suppressed in the medium . we calculate the in - medium @xmath0 matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal - fluid phase . we introduce the in - medium interaction on both sides of the boltzmann equation , namely in the calculation of the mean field and in the calculation of the collision rate . this allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime . by including the mean field , we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode , whereas the use of the in - medium cross section deteriorates the description , in agreement with previous work .

there are many concerns about endocrine - disrupting chemical effects on wild animals as well as humans . considerable numbers of chemicals have been shown to alter the thyroid system in vertebrates , and disruption of the thyroid axis has been identified as an important consideration for the regulation of chemicals . thus , focusing on thyroid toxicity , the oecd and epa established guidelines for investigation of frog metamorphosis . because amphibian tadpoles have a thin , permeable skin and inhabit aquatic environments , they are exposed to toxicants through both dermal and dietary routes and appear to be particularly susceptible to a number of contaminants in wastewater discharged from agricultural fields and from industrial and household areas . in addition , the fact that frog metamorphosis is regulated by thyroid hormones ( ths ) , promoting the remodeling of the aquatic larvae into an adult tetrapod , means that the dramatic structural and functional changes of larval tissues can be readily applied as parameters reflecting endocrine disruption . 1 ) , show various morphological changes during metamorphosis and under conditions of exposure to certain compounds . here , the regulation by ths , focusing on affecting factors in addition to the metamorphosis assay , is reviewed . the thyroid gland secretes thyroxine ( t4 ) , which is converted to a more biologically active form , 3,3,5-triiodothyronine ( t3 ) , mainly in the peripheral target tissues . transport of ths in the blood is accomplished through binding to transport proteins , predominantly transthyretin ( ttr ) , with conjugation and degradation processes occurring in the liver and subsequent secretion in bile . some ths are coupled with bacterial deconjugation and undergo reabsorption in the intestine . th structures are conserved between vertebrates , and their production and secretion are essentially the same in amphibians and mammals . there are several processes that influence the thyroid hormone balance , such as sulfation , deiodination and glucuronidation ( see fig . 2 ) . both inhibition of thyroidal iodide uptake and suppression of thyroidal peroxidase activity can disrupt th synthesis and secretion . in addition , inhibition of 5-deiodinase in the peripheral tissue is related to reduction of conversion from t4 to t3 , while induction of hepatic microsomal enzymes such as phenol sulfotransferase and udp - glucuronyl transferase leads to increase in excretion of both t4 and t3 into bile . furthermore , competitive binding to thyroid transport proteins results in reduced levels of total and free ths in serum . therefore , there are many potential targets of environmental contaminants that could be involved in disruption of th metabolism . rahman and yamauchi found th sulfating activity to be present in the liver cytosol in frog tadpoles and that the t3:t4 sulfating activity ratio varies during developmental stages , sulfation being inhibited by chemical compounds such as halogenated phenol and phenolic compounds , p - nitrophenol , dopamine , 17beta - estradiol ( e2 ) and dihydroxyepiandrosterone . compared with sulfation , glucuronidation has been poorly studied in amphibians , in line with its character as a relatively minor pathway . however , a subset of the responsible enzymes , glucuronidases ( ugts ) , can reduce circulating levels of ths through biliary elimination as in mammals . regarding phase i species , hepatic microsomal cytochrome p450 2b1 was found to be induced by pentobarbital in adults of the semiaquatic frog , rana pipiens , but not in frog tadpoles and adults of the aquatic frog xenopus laevis . deiodinase enzymes , type 2 and 3 iodothyronine deiodinase , are found in several peripheral target tissues in amphibians , and the level of expression is closely connected with metamorphosis . the most characteristic feature of ttr from nonmammalian vertebrates , such as amphibians , is their higher affinity for t3 than for t4 . binding of chemicals to ttr decreases their effective free concentrations in plasma and changes the apparent affinity for ths , which can diminish cellular uptake and biological responses and would alter plasma th homeostasis . therefore , chemicals interfering with t3 binding to ttr may directly affect the free concentration of plasma t3 and its plasma clearance rate . chemical compounds including diethylstilbestrol ( des ) , phenolic and phenol compounds and pentachlorophenol and ioxynil have the potential to bind to ttr , and yamauchi et al . reported that with amphibian ttr , des possesses similar affinity to t3 , which is the natural ligand . the premetamorphic stage is the period until the appearance of the hind limbs , and the prometamorphic period is from their appearance to that of the forelimbs . during the period of metamorphic climax , resorption of the tail and gills and development of lungs amphibian metamorphosis is divided roughly into 3 stages , premetamorphosis , prometamorphosis and climax ( see fig . the premetamorphic stage is the period until the appearance of the hind limbs , and the prometamorphic period is from their appearance to that of the forelimbs . subsequently , during the period of metamorphic climax , resorption of tail and gills and development of lungs occur . for example , treatment of tadpoles with synthetic thyroid hormone receptor antagonists ( e.g. , nh-3 ) leads to retardation or even complete blockade of xenopus laevis ( x. laevis ) metamorphic development . in turn , exposure of x. laevis tadpoles to low nanomolar concentrations of t3 or synthetic thyroid hormone receptor agonists ( e.g. , gc-1 ) causes precocious induction of metamorphosis . the sensitivity to th varies according to the developmental stage , and the amount of spontaneously released thyroid stimulating hormone ( tsh ) is higher in late prometamorphic and climactic tadpoles than in early prometamorphic larvae and juvenile and adult frogs . low levels of circulating thyroglobulin are found in tadpoles at the early stages , but extremely high levels are evident at the metamorphic climax . in amphibians , both corticotrophin - releasing hormone ( crh ) and gonadotropin - releasing hormone ( gnrh ) , in addition to trh , have been considered as candidates for the tsh - releasing factor . in the bullfrog , crh was found to be the most potent tsh - releasing substance in both adult and larval pituitary cells , while both trh and gnrh moderately stimulated the release of tsh from the adult pituitary but not larval cells . kaneko et al . demonstrated that th suppressed the crh - induced release of tsh , but not the basal release , from larval , juvenile and adult bullfrog pituitaries in vitro . in addition , jacobs et al . reported that intravenously injected mammalian luteinizing hormone - releasing hormone ( lhrh ) was able to raise circulating levels of t4 as well as testosterone ( t ) in three frog species , rana ridibunda , rana temporaria and rana esculenta . regarding prolactin ( prl ) , inhibitory effects may be exerted on metamorphosis , but this is controversial . huang and brown concluded that prl does not play a role as a juvenile hormone in x. laevis , but overexpression of prl does specifically inhibit some but not all programs of tail resorption . research has indicated concomitant elevation of ths and corticoids as metamorphosis progresses . according to kikuyama et al . , the aldosterone plasma level is low prior to the onset of climax , but then there is a sharp rise , and combined adrenocorticotropin ( acth ) and t treatment causes a marked increase in concentration . gray and janssens observed that testosterone and e2 inhibited t3-induced metamorphosis in x. laevis tadpoles , while hogan et al . demonstrated a delay in the time for rana pipiens tadpoles to undergo metamorphosis when exposed to ethinylestradiol during either mid - metamorphosis or throughout the entire larval period . in the past few decades , several thyroid disrupting substances have been tested for toxicity using amphibians . xenopus and other anurans have been generally applied to assess the developmental effects of a variety of xenobiotics . there have been a considerable number of reports regarding inhibitors of t4 synthesis that inactivate peroxidases . after exposure to propylthiouracil ( ptu ) , also known to inhibit deiodinase , x. tropicalis tadpoles showed no signs of decline in body length or body weight but a considerable reduction in the developmental stage and hind limb length . reported effects of exposure to ptu and another peroxidase inhibitor ethylenthiourea ( etu ) , in x. laevis . metamorphic retardation caused by etu was associated with concentration - dependent histological changes in the thyroid gland and increased mrna expression of tsh - beta in the pituitary . exposed pre- and pro - metamorphic larvae to methimazole , ptu and t4 and induced changes in a concentration - dependent manner . methimazole and ptu caused a delay in larval development and morphological changes in the thyroid gland , which were characterized as reduced colloid , glandular hypertrophy and cellular hyperplasia and hypertrophy . on the other hand , t4 treatment resulted in a concentration - dependent increase in the developmental rate . one other potent inhibitor of t4 synthesis , perchlorate , disturbs iodide uptake by the follicular cells of the thyroid gland . ammonium perchlorate was found to inhibit forelimb emergence , hindlimb development and tail resorption , linked to significant hypertrophy of the thyroid follicular epithelium at concentrations below those reported in contaminated surface waters . showed that sodium perchlorate inhibits th synthesis via effects on the sodium - iodide symporter , resulting in retarded metamorphosis and histological effects on thyroid as the most sensitive endpoint . hu et al . reported the results of thyroid immunohistochemistry for t4 in x. laevis exposed to perchlorate ; t4 immunoreactivity was concentrated in a ring of colloid adjacent to follicle cells , independent of the developmental stage . theirs is the only report regarding this point of view , but they suggested the utility of this immunohistochemical biomarker , because the intensity of the colloidal t4 ring is more sensitive than any other morphological changes ( such as hind limb length , forelimb emergence , tail resorption , thyrocyte hypertrophy or colloid depletion ) . found that time until metamorphic transformation was prolonged , the body weights of froglets were increased after exposure to polychlorinated biphenyls ( pcb ) and t4 levels were lowered , although not significantly . established that bisphenol a ( bpa ) induced deceleration of both spontaneous and t4-induced metamorphic changes , with suppression of thyroid hormone receptor ( tr ) beta gene expression . polybrominated diphenyl ether ( bde-47 ) and a commercial pentabromodiphenyl ether mixture ( de-71 ) caused delay in tail regression in x. laevis . according to carlsson et al . , autoradiograms revealed high concentrations and long - term retention of 2,2,4,4,5-pentabromodiphenyl ether ( bde-99 ) in adipose tissue and melanin in frogs exposed as both tadpoles and juveniles , with lower developmental stages suggesting possible thyroid hormone disruption . recorded delayed metamorphosis and enlarged thyroid glands with follicular hyperplasia in x. tropicalis and x. laevis tadpoles exposed to the insecticide methoxychlor . regarding actual environmental contamination , sowers et al . reported that municipal wastewater effluent containing measurable amounts of a variety of pharmaceuticals , personal care products , industrial compounds and natural and synthetic hormones could alter the timing of the metamorphic process in frogs . in their latest report of a field study of the native wood frog in the athabasca oil sands region of northern alberta , canada , metamorphosis was delayed or not complete at the end of the 75 day study period . showed that the herbicide acetochlor accelerated forelimb emergence and the beginning of metamorphic climax , apparently by interacting with t3 , but also possibly by weakly opposing the inhibitory actions of corticosterone on development of premetamorphic tadpoles . the doses used in most of these studies were greater than the levels to which anurans are exposed in the natural environment , so further investigations are required to determine whether exposure to chemicals at environmentally relevant concentrations can affect frog metamorphosis . in contrast to the data showing a clear effect on metamorphosis of chemical compounds , some negative data have been reported . uv filters such as 4-methylbenzylidene camphor ( 4-mbc ) and 3-benzylidene camphor ( 3-bc ) have been found to not affect the thyroid system and the rate of metamorphosis at environmental concentrations , and thus , they seem not to exhibit thyroid - mimicking or antithyroid activity . carr et al . reported exposure to one herbicide , atrazine , did not exert any effects on metamorphosis . there are several reports concerning effects on amphibian larvae of triclosan , which is a bacteriocide used in personal care and consumer products such as shampoo , soaps , deodorants , toothpaste and plastic ware , and so on . the release of triclosan into the environment is of particular concern as it is structurally similar to th . conducted a glp study in compliance with the guidelines mentioned below , and indicated that environmentally relevant concentrations do not alter the normal course of thyroid - mediated metamorphosis in this standard anuran model . the amphibian hypothalamic - pituitary - thyroid ( hpt ) axis controls th levels in the same way as it does in mammals , although crh also plays a role . therefore , the amphibian metamorphosis assay ( ama ) represents a generalized vertebrate model to the extent that it is based on the functions of the hpt axis . on september 7 , 2009 , the organization for economic co - operation and development ( oecd ) adopted the ama using x. laevis as a guideline for testing of chemicals . the us environmental protection agency ( epa ) office of prevention , pesticides , and toxic substances ( oppts ) also includes the ama for detection of thyroid - active chemicals in tier 1 testing of their endocrine screening program . the epa developed the oecd test guidelines through a process of harmonization in october 2009 . previously , in 1998 , the oecd initiated a high - priority activity to revise existing guidelines and develop new guidelines for the screening and testing of potential endocrine disrupters . one element was a test guideline for the screening of substances active on the thyroid system of vertebrate species . the 1st oect expert consultation on endocrine disrupter testing in amphibians was held in 2001 . subsequently , the ama underwent extensive validation programs consisting of 3 phases , which included intra- and interlaboratory studies demonstrating the relevance and reliability of the assay . mainly the u.s . the primary objective was a comparative evaluation of the utility and sensitivity of two proposed exposure scenarios for detection of stimulating and inhibiting effects of thyroid system - disrupting substances . the united kingdom and switzerland also participated in this phase in addition to germany , japan and the united states . three model substances representing different modes of action on the thyroid system were used : sodium perchlorate , t4 and iopanoic acid ( iop ) . phase 3 studies were conducted to assess the utility of the ama protocol to detect weakly active thyroid system - disrupting substances and to distinguish thyroid system - related changes from activity resulting from mechanisms not directly related to thyroid system function . benzophenone-2 ( bp-2 ) and e2 were selected as weakly active and non- or indirectly related substances . as a result , the effect of a weakly antithyroid substance , bp-2 , was detected , while the endpoints with exposure to e2 did not indicate any effect on the thyroid system . subsequently , validation of the assay was subjected to peer review by a panel of independent experts . the primary endpoints and observation time points are mortality daily , developmental stage , hind limb length , snout - vent length and wet body weight on days 7 and 21 and thyroid gland histology on day 21 . the most prominent morphological staging landmark is hind limb morphology , which is positively associated with agonistic effects . regarding the histopathology of the thyroid gland , the guidelines mention core criteria and additional qualitative criteria along with grading , as shown in table 3 . for a more detailed understanding , information is available in amphibian metamorphosis assay : part 1 technical guidance for morphologic sampling and histological preparation and amphibian metamorphosis assay : part 2 approach to reading studies , diagnostic criteria , severity grading and atlas . in addition , in support of the oecd ama test guideline , a document was developed that provides a standardized approach for evaluating the histology / histopathology of thyroid glands , including an atlas of the normal architecture of amphibian thyroid glands over the course of metamorphosis . one article regarding an examination conducted in compliance with these guidelines supported the use of the ama as a tier 1 endocrine screen for detection of potential thyroid pathway activity , but the lack of a true negative response ( no effect ) during the validation process prevents full evaluation of this assay s specificity at this time . thyroid glands after exposure for 21 days beginning at stage 51 . left : control . each of the mechanisms mentioned above can alter concentrations of circulating ths . under conditions of th decrease , a result of feedback of circulating ths on the hpt axis , there is increased secretion of tsh from the pituitary gland . such excessive stimulation would be expected to result in an increased thyroid gland size , increased degree of follicular cell hyperplasia and/or increased degree of follicular cell hypertrophy , as is well documented for the rodent thyroid gland . stated that histopathological change of the thyroid gland is the most valuable information regarding thyroid toxicants , and histological examination of the amphibian thyroid gland has been shown to be a very sensitive approach in several studies . although the developmental stage and hind limb length are important endpoints of antithyroid activity , developmental delay can not , by itself , be considered a diagnostic indicator of antithyroidal activity . a series of validation assays verified that thyroid histopathology is sensitive and reliable for antithyroidal activity resulting from either inhibition of thyroidal iodide uptake or iodide organification . on the other hand , according to the phase 1 validation study , histopathological analyses of thyroid glands of t4-treated tadpoles were less consistent between the laboratories and more difficult to interpret compared with the effects seen in the ptu studies . furthermore , the phase 2 validation report mentioned that while thyroid histopathology was sensitive for antithyroidal activities , weak agonistic activity could not be reliably detected . depletion of colloid stores and increases in epithelial cell height are known to occur at climax stages during normal development when tsh synthesis and release by the pituitary and t4 synthesis and secretion by the thyroid gland reach maximum levels . therefore , there may be difficulty in distinguishing whether histological changes occur in response to alterations of the hpt axis or alternatively merely reflect advanced stages in tadpoles . in fact , the guidelines insist that the most appropriate sampling approach for histological analyses is to use stage - matched individuals whenever possible . in order to select stage - matched individuals , all larvae should first be staged prior to selection and subsequent processing for data collection and preservation . this is necessary because normal divergence in development will result in differential stage distributions within each replicate tank . there is one example showing that amphibian thyroid histopathology is extremely complex , and when misinterpretation occurs , it leads to the opposite conclusion . in a controversial issue regarding the effect of triclosan , fort and pawlowski reported in regard to the histopathological changes that an increase in the occurrence of minimal thyroid gland hypertrophy was not accompanied by follicular hypertrophy or hyperplasia . the lack of follicular hypertrophy or hyperplasia was suggested to be the result of both the minimal nature of the response and the increased body size of the treated specimens . because disruption of the thyroid axis has been identified as an important consideration for regulation of chemicals , the oecd and epa have established guidelines that make for use of larval african clawed frogs ( x. laevis ) and frog metamorphosis for screening and testing of potential endocrine disrupters . in the test guidelines , thyroid gland histology is one of the primary endpoints , along with mortality , developmental stage , hind limb length , snout - vent length and wet body weight . a series of validation studies and many reports have revealed that the histopathology of the thyroid gland is very sensitive and reliable for detection of antithyroidal activity but , on the other hand , is less useful for weak agonistic effects . since the morphology of the amphibian thyroid gland changes continuously throughout metamorphosis with the fluctuation in th levels , the guidelines stress the need for well experienced toxicologic pathologists who are familiar with normal x. laevis thyroid histology , thyroid gland physiology and general responses of the thyroid gland to agonists or antagonists .

there are continued concerns about endocrine - disrupting chemical effects , and appropriate vertebrate models for assessment of risk are a high priority . frog tadpoles are very sensitive to environmental substances because of their habitat and the complex processes of metamorphosis regulated by the endocrine system , mainly thyroid hormones . during metamorphosis , marked alteration in hormonal factors occurs , as well as dramatic structural and functional changes in larval tissues . there are a variety of mechanisms determining thyroid hormone balance or disruption directly or indirectly . direct - acting agents can cause changes in thyroxine synthesis and/or secretion in thyroid through effects on peroxidases , thyroidal iodide uptake , deiodinase , and proteolysis . at the same time , indirect action may result from biochemical processes such as sulfation , deiodination and glucuronidation . because their potential to disrupt thyroid hormones has been identified as an important consideration for the regulation of chemicals , the oecd and the epa have each established guidelines that make use of larval african clawed frogs ( xenopus laevis ) and frog metamorphosis for screening and testing of potential endocrine disrupters . the guidelines are based on evaluation of alteration in the hypothalamic - pituitary - thyroid axis . one of the primary endpoints is thyroid gland histopathology . others are mortality , developmental stage , hind limb length , snout - vent length and wet body weight . regarding histopathological features , the guidelines include core criteria and additional qualitative parameters along with grading . taking into account the difficulties in evaluating amphibian thyroid glands , which change continuously throughout metamorphosis , histopathological examination has been shown to be a very sensitive approach .

photometric observation of transits is one of the most powerful methods of planet detection . this method relies on a possibility that , if the planet s orbit is viewed nearly edge - on , the planet may repeatedly transit over the disk of its host star and periodically block a small fraction of the starlight . thus , by monitoring the host star s brightness , the planet s presence can be revealed by a small dip in the photometric lightcurve . the main properties of the planet , such as its physical radius and orbital period , can be inferred from transit observations . the spacing of transit lightcurves would be exactly the same over the course of observations if a planet moved on a strictly keplerian orbit . several dynamical effects , however , can produce deviations from the keplerian case and induce the transit timing variations ( ttvs ) . ttvs were originally proposed as a non - transiting planet detection method ( miralda - escud 2002 , agol et al . 2005 , holman & murray 2005 ) , but have found more use in validating the transiting planet candidates from nasa s _ kepler _ mission ( e.g. , holman et al . 2010 ; lissauer et al . only a handful of non - transiting planets have been so far detected and characterized from ttvs ( e.g. , nesvorn et al . 2012 , 2013 ) . a significant progress has been made in the theoretical understanding of various dynamical causes of ttvs . these efforts were pioneered by agol et al . heyl & gladman ( 2007 ) focused on a _ long - period _ interaction between planets and showed that the apsidal precession of their orbits can be detected only with a long ttv baseline . nesvorn & morbidelli ( 2008 ) , on the other hand , developed a general analytic model for _ short - period _ ttvs and showed that they can be used , under ideal circumstances , to uniquely determine the mass and orbital parameters of the interacting planets . explicit analytic formulas for short - period ttvs are now available for zeroth- ( agol et al . 2005 , nesvorn & vokrouhlick 2014 , deck & agol 2015 ) and first - order terms ( agol & deck 2016 ) in planetary eccentricities . the important case of near - resonant ttvs was highlighted in lithwick et al . ( 2012 ) for the first - order resonances and in deck & agol ( 2016 ) and hadden & lithwick ( 2016 ) for the second - order resonances . the near - resonant ttv signal is a special case of the short - periodic variations when one harmonic becomes amplified due to a proximity of the system to a mean motion resonance . vokrouhlick & nesvorn ( 2014 ) considered a case of co - orbital planets and showed that co - orbital ttvs are expected to have a characteristic saw - tooth profile ( for horseshoe orbits ) . while the analytic works cited above cover a wide range of dynamically plausible planetary configurations , none of them ( except for agol et al . 2005 ) considered the case of a fully resonant planetary system , where two ( or more ) orbits are _ inside _ a mean motion resonance ( e.g. , 2:1 , 3:2 ) . this case is important because planetary migration in a protoplanetary gas disk should bring early planets into resonances ( e.g. , masset & snellgrove 2001 ) . indeed , many known planetary systems are consistent with having resonant orbits ( e.g. , winn & fabrycky 2015 ) . this motivates us to consider the resonant case . our main goal is to understand how resonant ttvs arise , and how their period and amplitude scale with planetary parameters . the resonant case has not received much attention in the ttv literature so far at least in part because the resonant interaction of planets is complex and not easily amenable to analytic calculations . the short - periodic or near - resonant ttv signals , for example , can be computed with the standard methods of perturbation theory , where the unperturbed ( keplerian ) motion is inserted in the right - hand side of the dynamical equations , and a linear variation of the orbital elements is obtained by quadrature . this method fails for the fully resonant orbits mainly because the resonant dynamics is non - linear . here , we take advantage of recent advances in the theoretical understanding of resonant dynamics ( e.g. , batygin & morbidelli 2013a ; hereafter bm13 ) and derive approximate formulas for ttvs of a resonant pair of exoplanets . in section 2 , we first give a summary of resonant ttvs . the goal of this section is to highlight the main results of this work . sections 3 and 4 explain how we obtained these results . we first show how a fully analytic solution can be obtained for a first - order resonance ( section 3 ) . we then proceed to expand the exact solution in the fourier series and explicitly derive the periods and amplitudes of the leading ttv terms ( section 4 ) . the application of these results to real planetary systems is left for future work . consider a planar system of two planets with masses @xmath5 and @xmath6 orbiting a central star with mass @xmath2 . the two planets gravitationally interact to produce ttvs . the ttvs signal of the two planets , @xmath7 and @xmath8 , can be approximated by @xmath9 where @xmath10 is the mean orbital frequency of planet @xmath11 , @xmath12 , @xmath13 is the mean longitude , @xmath14 is eccentricity , and @xmath15 is the longitude of periapsis . observer is assumed to see the system edge - on and measures angles @xmath13 and @xmath15 relative to the line of sight . expression ( [ ttv ] ) is valid for small orbital eccentricities and small variations of the orbital elements , @xmath16 and @xmath17 ( nesvorn 2009 ) . here we consider a case with two planets in a first - order mean motion resonance ( such that @xmath18 with integer @xmath19 ) , and proceed by calculating the variations of orbital elements due to the resonant interaction ( sections 3 and 4 ) . the final expressions are given as the fourier series with harmonics of two basic frequencies . as for @xmath16 we have @xmath20\ ; , \nonumber \\ -{1 \over n_2 } \delta \lambda_2 & = & - { 3 k \over \lambda_2 \nu } { p_\tau \over 2 \pi } a_\psi \left [ ( 1+\epsilon ) \sin f t - { \epsilon \over 4 } \sin 2 f t \right]\ ; . \label{dl}\end{aligned}\ ] ] here , @xmath21 $ ] , @xmath22 , @xmath23 is the semimajor axis , @xmath24 is the gravitational constant , @xmath25 is the period of resonant librations in scaled time units ( @xmath26 - 4 in the most cases of interest ; section 3.7 ) , @xmath27 is the amplitude of the resonant oscillations of action @xmath28 ( ranging from zero for an exact resonance to @xmath291 , where the approximation used to derive eq . ( [ dl ] ) starts to break down ) , @xmath30 is the frequency of resonant librations , and @xmath31 encapsulates the emergence of higher - order harmonics of @xmath30 . and @xmath25 . the dependence on @xmath27 is linear and @xmath25 admits only a narrow range of values in the libration zone . ] the resonant frequency @xmath30 is given by @xmath32 with @xmath33 where @xmath34 and @xmath35 are the resonant coefficients of the laplacian expansion of the perturbing function ( table 1 ) . the scaling of the resonant period , @xmath36 , with different planetary parameters is discussed in section 3.7 . for practical reasons , eq . ( [ dl ] ) have been truncated at the first order in @xmath37 . higher orders in @xmath37 and higher harmonics of the libration frequency can be computed using the methods described in section 4 . the second term in eq . ( [ ttv ] ) is related to the variation of eccentricities and apsidal longitudes of the two planets . in the most basic approximation ( section 4.3 ) , it can be written as @xmath38 where @xmath39 are the orbital periods , @xmath40 is the initial value of @xmath41 , @xmath42 is the frequency of @xmath43 defined in eq . ( [ ftheta2 ] ) . in the libration regime , @xmath44 . the resonant ttvs can therefore be understood as a sum of librational variations given in eq . ( [ dl ] ) and slower modulation of the ttv signal given in eq . ( [ yys2 ] ) . in eq . ( [ yys2 ] ) , @xmath45 is a coefficient of the order of unity ( eq . ( [ cus ] ) in section 4.3 ) . for small libration amplitudes , @xmath46 , where @xmath47 is the initial value of the resonant action @xmath28 defined in eqs . ( [ phis ] ) and ( [ psi ] ) . this means that , unlike in eq . ( [ dl ] ) , ttvs from the variation of eccentricities and apsidal longitudes do not vanish when @xmath48 . the dependence of the ttv amplitude on planetary masses arises from @xmath49 , @xmath50 and @xmath51 in eq . ( [ yys2 ] ) , where @xmath52 , @xmath53 , and @xmath54 . two main approximations were adopted to derive eqs . ( [ dl ] ) and ( [ yys2 ] ) . in the first approximation , we retained the lowest - order eccentricity terms in the resonant interaction of planets . in the second approximation , we assumed that the libration amplitudes are not very large , and expanded the exact solution in the fourier series . both these approximations are tested in section 5 . here we just illustrate the validity of the fourier expansion for small libration amplitudes ( figures [ ttv1 ] and [ ttv2 ] ) . let us briefly consider an application of our results to the ttv analysis . we assume that the photometric transits are detected for planets 1 and 2 , and that the orbital periods inferred from the transit ephemeris are such that orbital period ratio @xmath55 with small integer @xmath19 ( indicating near - resonant or resonant orbits ) . furthermore , ttvs are assumed to be detected for both planets . to be specific , let us consider a realistic case with the available ttv data spanning several years of observations , which is not long enough to resolve the frequencies related to the apsidal precession of orbits . the first step of the ttv analysis is to apply the fourier analysis to the ttv data . this may reveal that the ttv signal contains a basic period . in principle , this period can be one of following two periods : ( 1 ) the super period defined as @xmath56 ( e.g , lithwick et al . 2012 ) , or ( 2 ) the resonant libration period @xmath36 with @xmath30 defined in eq . ( [ f ] ) . in the first case , the system is not in the libration regime of the resonance and ttvs can therefore be interpreted using the expressions appropriate for the near - resonant dynamics ( lithwick et al . 2012 , agol & deck 2016 ) . the results described in this work apply in the second case . section 3.7 explains how the libration period can be used to constrain planetary masses . specifically , @xmath57 ( agol et al . 2005 , holman et al . 2010 ) , and therefore larger planetary masses imply shorter ttv periods . for the 2:1 resonance with @xmath58 days and @xmath59 , for example , the libration period is @xmath60 yr ( section 3.7 ) . in the next step , it can be useful to check if the fourier analysis of the ttv data provides evidence for harmonics of the basic period . if that s the case , this can indicate that the libration amplitude is relatively large . a comparison of the amplitudes of different harmonics can then be used to constrain the parameter @xmath37 in eq . ( [ dl ] ) , which is related to the libration amplitude via equations reported in appendix a. we then proceed by comparing the ttv amplitudes of the two planets . from eq . ( [ dl ] ) we have that @xmath61^{2/3 } m_2/m_1 $ ] . the ttv amplitude ratio therefore constrains the ratio of planetary masses ( agol et al . figure [ ampl2 ] shows how the ttv amplitudes depend on planetary masses . for @xmath62 , we obtain from eq . ( [ dl ] ) that the ttv amplitudes of the inner and outer planets , @xmath63 and @xmath64 , are @xmath65 where we denoted @xmath66 . this means that the ttv amplitude of the inner planet is independent of masses , while that of the outer planet constrains @xmath67 . for @xmath58 day , @xmath68 and @xmath69 , @xmath70 days for a @xmath19:(@xmath71 ) resonance . a similar analysis can be performed for @xmath72 . in addition to the dependence on masses , the ttv amplitudes ( linearly ) depend on the libration amplitude @xmath27 . we therefore expect that some degeneracy should exist between the planetary mass and libration amplitude , with large ttv amplitudes being produced either by large masses or large libration amplitudes . this degeneracy can be broken if the libration frequency harmonics are detected , providing constraints on the libration amplitude , or if the measured ttv signal also contains short - period ( chopping ) terms ( e.g. , nesvorn et al . a detailed analysis of this problem is left for future work . here we discuss a hamiltonian model of the resonant dynamics . our approach closely follows the work of bm13 . we take several shortcuts to simplify the reduction of the hamiltonian to an integrable system . then , in section 3.6 , we present an exact analytic solution . this solution is used in section 4 to derive eq . ( [ dl ] ) and ( [ yys2 ] ) . the poincar canonical variables of two planets orbiting their host star are denoted by ( @xmath73 ) . the coordinate vector @xmath74 defines the host star s position with respect to the system s barycenter . vectors @xmath75 and @xmath76 are the position vectors of the two planets relative to their host star . momentum @xmath77 is the total linear momentum of the system ( @xmath78 in the barycentric inertial frame ) . momenta @xmath79 and @xmath80 are the linear momenta of the two planets in the barycentric inertial frame . the poincar variables are canonical , which can be demonstrated by calculating their poisson brackets . using poincar variables the differential equations governing dynamics of the two planets can be conveniently written in a hamiltonian form , where the total hamiltonian is a sum of the keplerian and perturbation parts , @xmath81 , with @xmath82 and @xmath83 here we denoted @xmath84 and the reduced masses @xmath85 , where @xmath86 and 2 stand for the inner and outer planet , respectively . we assume that the planets are near or in a first - order mean motion resonance such that the ratio of their orbital periods is @xmath55 for some integer @xmath87 . in terms of the osculating orbital elements we have @xmath88 where @xmath89 and @xmath90 are the semimajor axes of planets , and @xmath91 \nonumber \\ & & \quad + f_2\,e_2 \cos\left[k\lambda_2-\left(k-1\right)\lambda_1- \varpi_2\right]\bigr\}\ ; , \label{ham4}\end{aligned}\ ] ] where @xmath92 and @xmath93 are the orbital eccentricities , @xmath94 and @xmath95 are the mean longitudes , and @xmath96 and @xmath97 are the longitudes of pericenter . in eq . ( [ ham4 ] ) we only retained two most important resonant terms , and the lowest ( first - order ) eccentricity power . this expression is thus valid only near a specific resonance and for low orbital eccentricities of both planets . the planetary orbits are assumed to be in the same plane such that all inclination - dependent terms vanish . the coefficients @xmath34 and @xmath35 are functions of the semimajor axis ratio @xmath98 , and can be written as @xmath99 where @xmath100 are the laplace coefficients , @xmath101 , and @xmath102 is the kronecker symbol ( e.g. , brouwer & clemence 1961 ) . the last term in the expression for @xmath35 only appears if @xmath103 ( 2:1 resonance ) . the laplace coefficients were computed using the recurrences described in brouwer & clemence ( 1961 , secs . 15.7 and 15.8 ) . their values are reported in table 1 . the resonant hamiltonian discussed in the previous section needs to be written in canonical variables . the standard choice is the delaunay elements @xmath104 note that @xmath105 for small @xmath14 . the elements @xmath106,@xmath107 are the canonical momenta , and ( @xmath108 ) are the conjugated canonical coordinates . the resonant hamiltonian @xmath109 written in terms of the delaunay elements has four degrees of freedom ( dof ) . using canonical transformations we will reduce it to an integrable one - dof system . we first perform a canonical transformation to the resonant canonical variables defined as @xmath110 when the new variables are inserted in eqs . ( [ ham3 ] ) and ( [ ham4 ] ) , it becomes clear that the resonant hamiltonian depends on @xmath111 and @xmath112 , but not on @xmath94 and @xmath95 . therefore , @xmath113 and both momenta @xmath114 and @xmath115 are the new constants of motion . by summing them , we find that @xmath116 is the total angular momentum of the system . also , @xmath117 implies that any small changes of the semimajor axes , @xmath118 and @xmath119 , must be anti - correlated , and have relative amplitudes such that @xmath120 , where we denoted @xmath121^{2/3}$ ] . the transformation to the resonant canonical variables produced a 2-dof hamiltonian @xmath122 . in the next step , we assume that any changes of the semimajor axes of planets are small . specifically , we write @xmath123 , where @xmath124 is some reference value and @xmath125 , insert this expression into the keplerian part of the hamiltonian ( eq . [ ham3 ] ) , and expand it in powers of @xmath126 . the first and second - order terms in @xmath126 are retained . we then use @xmath127 and rewrite all expressions in terms of @xmath128 and @xmath129 .. ] finally , we substitute @xmath130 and drop all ( dynamically unimportant ) constant terms . this substitution is useful because it allows us to work with @xmath131 and @xmath132 instead of their variations @xmath133 and @xmath134 . finally , we express @xmath135 in terms of the canonical variables defined in eq . ( [ ham6b ] ) . this leads to @xmath136 with @xmath137\ ; , \nonumber \\ n_{\rm s } & = & 4[k n_2 - ( k-1 ) n_1]-3\left [ k k_2 { n_2 \over \lambda_2^ * } - ( k-1 ) k_1 { n_1 \over \lambda_1^ * } \right]\ ; , \nonumber \\ \nu & = & { 3 \over 2 } \left [ ( k-1)^2 { n_1 \over \lambda_1^ * } + k^2 { n_2 \over \lambda_2^ * } \right]\ ; . \label{super}\end{aligned}\ ] ] here we denoted @xmath138 and @xmath139 . the quantities @xmath10 , @xmath140 and @xmath141 are constant parameters . note that @xmath140 is related to the so - called _ super _ frequency , which is the expected frequency of the ttv signal for a pair of near - resonant planets ( e.g. , lithwick et al . in addition to the usual term , @xmath142 , here @xmath140 also includes a correction that is a second order in the eccentricity ( through its dependence on @xmath114 and @xmath115 ) . as for @xmath143 in eq . ( [ ham4 ] ) , we have that @xmath144 for small eccentricity . in addition , because @xmath143 is already small , we do not need to retain terms proportional to @xmath126 ( thus @xmath145 ) . the perturbation function then admits the following form @xmath146\ , , \label{hper}\ ] ] where we introduced constants @xmath147 and @xmath148 . the hamiltonian in eqs . ( [ hk ] ) and ( [ hper ] ) has 2 dof . it can be reduced to 1 dof by the following canonical transformations ( sessin & ferraz - mello 1984 , wisdom 1986 , henrard et al . first , we move from variables @xmath149 to @xmath150 such that @xmath151 second , we perform a reducing transformation to the new variables @xmath152 defined as @xmath153 and last , we introduce new polar variables @xmath154 such that @xmath155 it can be shown that @xmath156 . therefore , after dropping the first constant term in eq . ( [ hk ] ) , and rewriting eq . ( [ hper ] ) in the new variables , the hamiltonian becomes @xmath157 where we denoted @xmath158 . notably , the new hamiltonian ( [ hnew ] ) is independent of @xmath159 , and the canonical momentum @xmath160 is therefore a new constant of motion . that s the magic of the reducing transformation . the momenta @xmath161 and @xmath160 defined by the transformations discussed above can be expressed in a compact form @xmath162 where @xmath163 . condition @xmath164 thus defines a circle in the plane of complex variables @xmath165 and @xmath166 and requires that @xmath167 lies on the circle at any time . also , @xmath168 and @xmath169 , where @xmath170 denotes the argument of @xmath171 . the hamiltonian ( [ hnew ] ) depends on parameters @xmath140 , @xmath141 and @xmath172 . we rescale @xmath161 and time to bring the hamiltonian to a simple form @xmath173 where the parametric dependence is expressed by a single parameter @xmath174\ ; \label{delta}\ ] ] with @xmath54 . here , @xmath175 , and @xmath176 the hamiltonian equations are @xmath177 where @xmath178 relates to normal time @xmath179 by @xmath180 with @xmath181 . when a solution of eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) is found , the scaling parameters @xmath51 and @xmath182 can be used to map the solution back to the original variables . the hamiltonian ( [ fm ] ) and the corresponding eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) have been extensively studied in the past . they are equivalent to the second fundamental model of resonance ( henrard & lematre 1983 ) , and to the andoyer model discussed in ferraz - mello ( 2007 ) . here we first consider the dynamical flow arising from this hamiltonian and its dependence on @xmath183 . in the next section , we show that eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) have an exact analytic solution in terms of the weierstrass elliptic functions . the equilibrium points of eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) control the general structure of the dynamical flow . since @xmath184 implies that @xmath185 in ( [ hameq2 ] ) , the equilibrium points occur for @xmath186 or @xmath187 . the equilibrium values of @xmath28 are obtained from @xmath188 , which leads to a problem of finding roots of a cubic equation @xmath189 . there is only one ( stable ) equilibrium point for @xmath190 . this equilibrium point is located at @xmath191 and @xmath192 ( figure [ delta2 ] ) . the dynamical flow around the equilibrium point is simple . when projected to the @xmath193 plane , , because these variables are canonical . ] the trajectories are concentric , slightly deformed circles centered on the equilibrium point ( figure [ portraits]a ) . @xmath28 changes only slightly during each cycle , and @xmath194 circulates in the clockwise direction for most initial conditions except for the ones located very close to the equilibrium point , where @xmath194 oscillates around @xmath187 . for @xmath195 , the stable equilibrium point is already substantially displaced from the origin . the dynamical transition is heralded by the appearance of a cusp trajectory ( shown by a thin line in figure [ portraits]b ) . three equilibrium points appear for @xmath196 , two of which are stable and one is unstable . the unstable equilibrium point is traversed by a separatrix ( shown by thick lines in figures [ portraits]c and [ portraits]d ) , which surrounds the truly resonant trajectories for which @xmath194 librates around @xmath187 . the stable equilibrium point in the center of the resonant island is a smooth extension of the equilibrium point from @xmath197 to @xmath198 . it is located at @xmath191 and @xmath199 , where @xmath200 increases with @xmath183 ( figure [ delta2 ] ) . for large @xmath183 , @xmath201 ( henrard & lematre 1983 ) . a rearrangement of eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) shows that the momentum @xmath28 satisfies @xmath202 with the right - hand side being a quartic polynomial @xmath203 the coefficients are @xmath204 \ ; , \nonumber \\ a_3 & = & \phantom{-}\frac{1}{2}\left[1 + 2\delta\left(h_0+\delta^2 \right)\right ] \ ; , \nonumber \\ a_4 & = & -\left[h_0+\delta^2\right]^2 \ ; , \label{sfmr4e } \end{aligned}\ ] ] where @xmath205 is the conserved energy , and @xmath206 is the initial condition . equation ( [ sfmr2 ] ) admits a general analytic solution ( see whittaker & watson 1920 , sec . 20.4 ) @xmath207 + \frac{c_3}{24 } f_0}{2\left[\wp\left(\tau-\tau_0\right)-\frac{c_2}{24}\right]^2- \frac{c_4}{48 } f_0}\ ; , \label{sfmr5}\ ] ] where @xmath208 , @xmath209 , @xmath210 is the @xmath211-th derivative of @xmath30 at @xmath212 ( @xmath213 ) , and @xmath214 $ ] is the sign function ( @xmath215 for @xmath216 and @xmath217 for @xmath218 ) . the time dependence of the solution is given in terms of the weierstrass elliptic function @xmath219 , and @xmath220 , whose invariants are @xmath221 interestingly , as far as we know , the general solution ( [ sfmr5 ] ) has not been discussed in the literature . ferraz - mello ( 2007 ) mentioned a particular solution valid for @xmath222 , which implies that @xmath223 ( see also shinkin 1995 ) . the solution ( [ sfmr5 ] ) is most conveniently evaluated using the relation of the weierstrass functions to the jacobi elliptic functions @xmath224 and @xmath225 . the form of the solution depends on the roots of the cubic equation @xmath226 , whose discriminant is @xmath227 . there are three real roots @xmath228 for @xmath229 . if @xmath230 , there is one real root @xmath93 and a pair of complex roots @xmath231 and @xmath232 ( figure [ discrim ] ) . in the first case ( @xmath229 ) , we have @xmath233 with @xmath234 and modulus @xmath235 . in the second case ( @xmath230 ) , we have @xmath236 with @xmath237 , @xmath238 and @xmath239 . the jacobi elliptic functions are computed following the numerical recipe from press et al . the derivative @xmath240 is obtained from the derivatives of the jacobi functions . the solution ( [ sfmr5 ] ) is periodic with a period @xmath241 for @xmath229 , and @xmath242 for @xmath230 . here , @xmath243 is the complete elliptic integral of the first kind . figure [ period1 ] shows the period of small amplitudes librations around the stable equilibrium points . away from the resonance and if the eccentricities are small , @xmath244 , and the first bracketed term in eq . ( [ delta ] ) outweighs the second . in this case , @xmath183 is related to the super frequency , and increases , in the absolute value , when the system moves away from the resonance . in this sense , @xmath183 is a measure of the distance from the resonance . is small and @xmath183 is controlled by the contribution from @xmath160 . since @xmath245 , @xmath183 is a measure of the orbital eccentricities inside the libration island . ] negative values of @xmath183 imply that the planetary orbits are spaced more widely than the actual resonance ( @xmath246 ) , while @xmath247 means that the orbits are packed more tightly ( @xmath248 ) . also , @xmath249 away from the resonance , and therefore the scaled period @xmath250 . this represents a very good approximation of the period if @xmath251 or @xmath252 ( see figure [ period1 ] ) . inside the libration island for @xmath196 , the period of small - amplitude librations decreases with @xmath183 ( i.e. , toward larger eccentricities ) . it can be approximated by @xmath253 , where @xmath200 is the equilibrium value of @xmath28 ( figure [ delta2 ] ) . for large values of @xmath183 , @xmath254 , and @xmath255 figure [ period1 ] shows that this approximation works very well for @xmath252 . the period @xmath25 for different libration amplitudes is plotted in fig . [ period2 ] . the period is the shortest near the equilibrium point and increases with the libration amplitude . it becomes infinite on the separatrices . this corresponds to a situation when the amplitude of angle @xmath194 becomes full @xmath187 , and it takes infinitely long to reach the unstable equilibrium point at @xmath186 . except for trajectories near the separatrix , the period values inside the libration island are @xmath256 - 4 . they become shorter for @xmath257 ( i.e. , for higher eccentricities ) . when rescaled according to eq . ( [ tscale ] ) , @xmath258 is the period of resonant librations in the normal time units ( e.g. , julian days ) . it has the same dependence of @xmath25 on @xmath183 and amplitude that we discussed above , and , in addition , contains an explicit dependence on the orbital period and planetary masses through the scaling parameter @xmath181 . if @xmath62 , then @xmath259^{-1/3 } \ ; . \label{perone}\ ] ] if , on the other hand , @xmath72 , then @xmath260^{-1/3 } \ ; . \label{pertwo}\ ] ] the multiplication coefficients in the square brackets are @xmath2611 for @xmath103 ( 2:1 resonance ) and decrease with increasing @xmath19 . this expresses a stronger interaction of orbits that are more tightly packed for larger values of @xmath19 . according to eqs . ( [ perone ] ) and ( [ pertwo ] ) , the orbital periods @xmath262 and @xmath263 set the basic time unit for @xmath264 . the libration period scales with the mass of the more massive planet as @xmath0 , and is therefore shorter for a larger mass . it is insensitive to the mass of the lighter planet . if the masses of the two planets are comparable , then @xmath264 will depend on their combination via the scaling parameter @xmath182 . figure [ mass ] shows the contour plots of @xmath264 as a function of @xmath265 and @xmath266 . in the @xmath267 limit , the period is proportional to @xmath268^{-2/3}$ ] . a reasonable approximation of the period is then @xmath269^{-1/3 } \ ; . \label{perthree}\ ] ] these considerations have important implications for the ttv period and its scaling with various parameters . for example , for two planets in the 2:1 resonance with @xmath270 and @xmath62 , the expected ttv period is @xmath271 . thus , if @xmath58 days , and assuming that @xmath272 in the libration regime , the ttv period will be @xmath273 years . we can therefore very roughly write in this case @xmath274 if , on the other hand , @xmath275 and @xmath72 , then the period will be approximately twice as long , because of having @xmath263 in eq . ( [ pertwo ] ) ( instead of @xmath262 in eq . ( [ perone ] ) ) . finally , if @xmath276 , then @xmath277 yr . the periods in the @xmath278 resonances are expected to be shorter ( figure [ mass]b ) . lithwick et al . ( 2012 ; hereafter l12 ) derived elegant ttv expressions for two planets near ( but not in ) the first - order resonance . here we discuss the relationship of these expressions to the results obtained here . let us consider the hamiltonian in eq . ( [ hk ] ) and ( [ hper ] ) @xmath279 where we denote @xmath280 and @xmath281 . we assume that the orbital eccentricities are small and that the two orbits are far enough from the resonance such that the term @xmath282 can be neglected . introducing @xmath283 and @xmath284 from eq . ( [ ham10b ] ) into eq . ( [ lit1 ] ) we find that @xmath285 + \beta_1 x_1 + \beta_2 x_2\ ; .\ ] ] this hamiltonian has a simple solution ( e.g. , batygin & morbidelli 2013b ) . defining complex variables @xmath286 , the solution can be written as @xmath287 where @xmath288 are integration constants related to the initial conditions . now , since @xmath289 , we can define l12 s ` complex eccentricities ' @xmath290 and recast the approximate solution ( [ lit2 ] ) as @xmath291 where @xmath292 is the complex conjugate of @xmath288 . here we assumed that @xmath293 and replaced @xmath145 . these assumptions are equivalent to those of l12 where the unperturbed ( keplerian ) solution was inserted into the right - hand sides of the lagrange equations , and the linearized solution was found by quadrature . ( [ lit3 ] ) can be compared to eq . ( a15 ) in l12 . the first term in eq . ( [ lit3 ] ) is constant and corresponds to the ` free ' term in eq . ( a15 ) . the second term in eq . ( [ lit3 ] ) is identical to the second term in eq . ( a15 ) ( this can be trivially shown by resolving notation differences ) . l12 proceeded by using the constants @xmath114 and @xmath115 ( eq . [ ham6b ] ) to derive expressions for @xmath294 , which were then used to obtain @xmath295 with @xmath296 . from the derivatives of the laplace coefficients . this is a correct assumption for the near - resonant orbits , because these terms have @xmath140 in the denominator , while the terms from @xmath297 have @xmath298 in the denominator . the latter terms are thus amplified near a resonance where @xmath140 is small . ] finally , l12 used a formula equivalent to eq . ( [ ttv ] ) to compute ttvs . none of these steps requires a special clarification . the main assumption of l12 was therefore to ( effectively ) neglect the term @xmath282 in eq . ( [ lit1 ] ) . for this to be valid @xmath299 . assuming that the masses and eccentricities of the two planets are comparable , and neglecting all factors of the order of unity , this condition can be written as @xmath300 . this shows that the eccentricities can not exceed certain threshold for the l12 formulas to be valid . this threshold is not excessively restrictive . for example , for planetary orbits just outside the 2:1 resonance with @xmath301 , the eccentricities need to be @xmath302 . in addition to the above eccentricity condition , the planetary orbits can not be too close to a resonance where the non - linear effects become important even for negligible eccentricities . we tested this condition assuming initial orbits with small eccentricities and found that the l12 model is perfectly valid for @xmath303 . a small , @xmath410% discrepancy in both the amplitude and frequency of @xmath304 appears for @xmath305 . further increase of @xmath183 leads to a situation where eq . ( [ lit3 ] ) is no longer an adequate representation of the resonant dynamics . according to our tests with @xmath306 , the l12 model can not usually be trusted for @xmath307 . figure [ lit ] shows these thresholds as a function of the planetary mass and orbit period ratio . if the variation of orbital elements is small , ttvs of two planets , @xmath7 and @xmath8 , can be computed from @xmath308 ( see , for example , nesvorn & morbidelli 2008 ) . here , @xmath309 , @xmath310 , and @xmath311 , where @xmath312 with constant @xmath10 . if the reference frame is chosen such that the orbital angles are measured with respect to the line of sight , transits occur when @xmath313 ( assuming small eccentricities ) . we therefore have @xmath314 . the first - order eccentricity terms , which can be used to improve the validity for higher eccentricities , were given in nesvorn ( 2009 ) . ttvs will thus have a contribution from the mean longitude variation , @xmath16 , and another contribution from the variation of eccentricity and apsidal longitude , @xmath315 . defining @xmath316 , we have for small eccentricities that @xmath317 and @xmath318 . we then write @xmath319 with constant @xmath128 , and obtain @xmath320 where we retained only the first - order terms in small variations . it remains to compute @xmath16 and @xmath321 . as for @xmath16 , we have @xmath322 where @xmath135 is given in eq . ( [ hk ] ) ( note that @xmath323 appears in the @xmath140 term in ( [ super ] ) ) . substituting @xmath324 in eq . ( [ hk ] ) , taking the derivative with respect to @xmath323 , and integrating with respect to @xmath179 , we obtain @xmath325n_1(t - t_0)+3 ( k-1 ) { n_1 \over \lambda_1^ * } \int_{t_0}^t \phi_1 { \rm d}t\ ; , \nonumber \\ \lambda_2 & = & \left[4 - { 3 \over \lambda_2^*}(k_2+k\phi_2)\right]n_2 ( t - t_0)-3 k { n_2 \over \lambda_2^ * } \int_{t_0}^t \phi_1 { \rm d}t\ ; . \label{lamint}\end{aligned}\ ] ] using the scaling relationship from eqs . ( [ psi ] ) and ( [ tscale ] ) , we have that @xmath326 where @xmath327 is given in eq . ( [ sfmr5 ] ) . the first terms in ( [ lamint ] ) describe a uniform circulation of angles @xmath94 and @xmath95 ( note that @xmath328 for @xmath329 , as expected ) . they will not contribute to ttvs . instead , ttvs will arise from the integral term . as the sign in front of the integral term is positive for @xmath94 and negative for @xmath95 , ttvs of the two planets are anti - correlated . the amplitudes of @xmath7 and @xmath8 , denoted here by @xmath330 and @xmath331 , satisfy @xmath332 thus , apart from a coefficient of the order of unity , the ratio of the ttv amplitudes from the @xmath333 terms is expected to be equal to the inverse of the planetary mass ratio . as for @xmath321 , we have @xmath334\ ; , \nonumber \\ y_2 & = & { 1 \over \sqrt{a^2 + b^2 } } \left[b ( v_1 \cos \theta - u_1 \sin \theta ) - a v_2\right]\ ; , \label{ys}\end{aligned}\ ] ] where @xmath335 and @xmath336 were defined in eq . ( [ redt ] ) . they are related to the @xmath161 and @xmath337 variables via eq . ( [ ham14b ] ) . expressions ( [ ys ] ) are derived in appendix b. as we show in appendix b , @xmath338 is a constant of motion , does not contribute to variations , and does not need to be computed . since the coefficients @xmath34 and @xmath35 have opposite signs ( table 1 ) , @xmath49 and @xmath50 in eq . ( [ ys ] ) will also have opposite signs , and ttvs of the two planets will be anti - correlated . ttvs arising from terms in ( [ ys ] ) will have amplitudes , @xmath339 and @xmath340 , such that @xmath341 the ratio of ttv amplitudes from the @xmath342 terms is inversely proportional to the ratio of planetary masses . this is the same mass dependence as in eq . ( [ ratio1 ] ) . thus , while resonant ttv period discussed in section 3.7 can be used to constrain @xmath265 and/or @xmath266 , the ttv amplitude ratio is sensitive to @xmath343 . above we reduced the problem in hand to the evaluation of @xmath344 . the @xmath43 terms are simple . from eq . ( [ lamint ] ) we have that @xmath345(t - t_0 ) - 2 \nu \int_{t_0}^t \phi_1 { \rm d}t \label{theta}\ ] ] as for the @xmath335 and @xmath336 terms , we obtain @xmath346\ ; , \label{sfmr11a } \nonumber \\ v_1 = \eta_1^{-1/3 } \sqrt{2\psi}\,\sin\psi & = & -\eta_1^{-1/3}\frac{d\psi}{d\tau}\ ; . \label{sfmr11b } \label{uv1}\end{aligned}\ ] ] this is all we need for the computation of ttvs . to summarize , @xmath327 from eq . ( [ sfmr5 ] ) needs to be inserted in ( [ iscale ] ) and ( [ uv1 ] ) . the integral in ( [ iscale ] ) needs to be computed and substituted into eqs . ( [ lamint ] ) and ( [ theta ] ) . then , @xmath43 , @xmath335 and @xmath336 obtained from eqs . ( [ theta ] ) and ( [ uv1 ] ) are substituted into ( [ ys ] ) . the constant terms in @xmath13 and @xmath347 can be neglected , because they do not contribute to ttvs . finally , eq . ( [ ttvfin ] ) is used to compute ttvs . in principle , the method outlined above can be used to derive fully analytic expressions for @xmath7 and @xmath8 , which would have the same general validity for low eccentricities as the analytic solution ( [ sfmr5 ] ) . for that , however , we would need to compute the derivative ( needed for @xmath336 ) and integral ( needed for @xmath13 and @xmath43 ) of @xmath327 from ( [ sfmr5 ] ) . the integral ends up producing complex expressions ( appendix c ) . here we therefore opt for a different approach , where we seek to find an expression for resonant ttvs in terms of the fourier series . the solution ( [ sfmr5 ] ) is valid for any initial condition @xmath348 . here we are not primarily interested in finding a general ttv expression for any @xmath348 . instead , our primary goal is to understand the general scaling of ttvs with planetary masses , resonant amplitude , etc . we therefore opt for setting @xmath349 . this simplifies ( [ sfmr5 ] ) considerably . specifically , @xmath349 implies that @xmath223 , and ( [ sfmr5 ] ) becomes @xmath350 where we denoted @xmath351 , @xmath352 , and @xmath353 . this equation is valid in the domain @xmath230 shown in fig . [ discrim ] , which includes the whole resonant libration zone . we used eq . ( [ sfmr8 ] ) to relate the weierstrass functions in ( [ sfmr5 ] ) to the jacobi functions . at the equilibrium point , @xmath354 , @xmath355 , and @xmath356 ( appendix a ) . for librations around the equilibrium point , we have that @xmath357 ( figure [ eps ] ) . we therefore identify a small parameter @xmath358 and expand eq . ( [ simple ] ) in the taylor series in @xmath37 . retaining only the first - order terms in @xmath37 ( approximation of low - amplitude librations ) , we obtain @xmath359 + { \cal o}(\epsilon^2)\ ; . \label{approx1}\ ] ] including higher order terms in @xmath37 would improve the validity of the approximation for large libration amplitudes . next , we express @xmath225 and @xmath360 in the fourier series @xmath361 and @xmath362 here we have @xmath363 and @xmath364 with @xmath365 . @xmath366 is the complete elliptic integral of the second kind . general expressions for @xmath367 , which can become useful when higher order terms in ( [ approx1 ] ) are accounted for , can be found in kiper ( 1984 ) . both these fourier series converge very rapidly , and we can therefore afford to use the lowest harmonics . in practice , given that the evaluation of @xmath335 from eq . ( [ uv1 ] ) will require a multiplication of the fourier series , here we consider only the first and second harmonics of @xmath368 . after substituting these terms into eq . ( [ approx1 ] ) , we obtain @xmath369 here we denoted the frequency @xmath370 and @xmath371 . to simplify things , we set @xmath372 and drop all multiplication terms appearing from eqs . ( [ four1 ] ) and ( [ four2 ] ) that are @xmath373 . very close to 1 , we have @xmath374 , @xmath375 \simeq 1 $ ] , and @xmath376 \simeq 1/2 $ ] . ] note that @xmath377 is a proxy for the libration amplitude of @xmath28 ( figure [ eps ] ) . ( [ psi1 ] ) can be used to trivially compute the integral @xmath378 appearing in eq . ( [ iscale ] ) , which is then inserted into eqs . ( [ lamint ] ) and ( [ theta ] ) . in the following text , the two ttv contributions , @xmath16 and @xmath321 , will be considered separately . the calculation of @xmath16 is simple . retaining the periodic terms in eq . ( [ lamint ] ) we obtain @xmath379\ ; , \nonumber \\ \delta \lambda_2 & = & 3 k { n_2 \over \lambda_2^ * \nu } { p_\tau \over 2 \pi } d [ c_{\lambda,1 } \sin f t + c_{\lambda,2 } \sin 2 f t ] \ ; . \label{dl2}\end{aligned}\ ] ] with the coefficients @xmath380 and @xmath381 , and frequency @xmath382 ( section 3.7 ) . these equations are the source of eq . ( [ dl ] ) in section 2 , where we give the final expressions for ttvs arising from the variation of @xmath94 and @xmath95 . in eq . ( [ dl ] ) , we have taken the liberty to drop the star from @xmath128 , but it is understood that @xmath10 , @xmath383 , and other quantities depending on these parameters in eq . ( [ dl ] ) are considered to be constant . also , since @xmath377 is a good proxy for the amplitude @xmath27 , we replaced @xmath384 in eq . ( [ dl ] ) . note that @xmath27 is positive for @xmath385 and negative for @xmath386 . we need to compute @xmath344 and insert it in eq . ( [ ys ] ) . as for the terms including @xmath43 , we obtain from eqs . ( [ iscale ] ) , ( [ theta ] ) and ( [ psi1 ] ) @xmath387 where @xmath388\ ; , \nonumber \\ c_{\theta,1 } & = & { p_\tau \over 2 \pi } d ( 1+\epsilon ) \ ; , \nonumber \\ c_{\theta,2 } & = & - { p_\tau \over 2 \pi } d \epsilon\ ; . \label{ftheta}\end{aligned}\ ] ] we then use the following expansions to obtain @xmath389 and @xmath390 @xmath391 where @xmath392 are the bessel functions . both these fourier series converge rapidly for @xmath393 . we therefore retain only the lowest - order harmonics . this leads to @xmath394 here we neglected the coefficients @xmath395 that are of the order of @xmath37 ( note that @xmath396 ; fig . [ eps ] ) . the harmonics with @xmath30 in eq . ( [ cossin ] ) appear from the resonant librations ( section 3.7 ) . since @xmath397 ( appendix b ) , and @xmath337 oscillates around @xmath187 in the libration island , @xmath43 has the same circulation frequency as @xmath398 . now , given that @xmath398 is defined from the apsidal longitudes @xmath96 and @xmath97 ( appendix b ) , the interpretation of @xmath42 is that it is the mean precession frequency of the longitudes of periapsis . neglecting terms @xmath399 and using the definition of @xmath183 in eq . ( [ delta ] ) we find from ( [ ftheta ] ) that @xmath400 where substituted @xmath401 ( see figure [ eps ] ) . the @xmath42 frequency therefore scales in the same manner with planetary parameters as @xmath402 ( as expressed by the @xmath403 factor ) . unlike @xmath30 , which derives from @xmath404 in the libration island , @xmath42 contains the factor @xmath405 . this factor is @xmath406 ( compare the dotted and solid ` stable 1 ' lines in figure [ delta2 ] ) . therefore , @xmath42 is substantially smaller than @xmath30 , which shows that the variations from @xmath43 are expected to occur on a long timescale . specifically , the period @xmath407 is equal to 10.1 for @xmath408 , 13.3 for @xmath409 , and 18.1 for @xmath410 . the longer periods for larger @xmath183 values are a consequence of @xmath200 approaching @xmath183 for increasing values of @xmath183 ( section 3.5 ) . note that @xmath411 , at least in the approximation adopted here , is independent of the libration amplitude . also , given that @xmath412 in the libration island , the @xmath42 frequency is negative as well , meaning that the circulation of @xmath43 is retrograde ( implying retrograde rotation of @xmath96 and @xmath97 ) . the terms in eq . ( [ cossin ] ) containing frequencies @xmath42 and @xmath30 could be combined together to produce harmonics with frequencies @xmath413 and @xmath414 . given that , as we discussed above , the characteristic periods of these terms are largely different , we prefer to leave them multiplying each other in eq . ( [ cossin ] ) . accordingly , eq . ( [ cossin ] ) is interpreted as the resonant variations around the mean value that is slowly modulated with frequency @xmath42 . the expressions for @xmath335 and @xmath336 are derived from eq . ( [ uv1 ] ) , after substituting @xmath28 from eq . ( [ psi1 ] ) . after some algebra we obtain @xmath415 with coefficients @xmath416 in the above expression for the coefficient @xmath45 , @xmath417 denotes the initial value @xmath418 figure [ uvfig ] compares eq . ( [ uvapp ] ) with the exact solution of eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) . it shows that the approximation ( [ uvapp ] ) is excellent for small libration amplitudes but loses precision for large libration amplitudes . this happens mainly because the terms @xmath419 were neglected in eq . ( [ approx1 ] ) . in principle , it should be possible to include these and higher order terms and improve the validity of the fourier approximation by producing more general expressions . we leave this for future work . now we should combine eqs . ( [ cossin ] ) and ( [ uvapp ] ) together . unfortunately , this generates a very long expression for @xmath321 . we do not explicitly give this equation here . the full expression was coded in a program and used to generate figs . [ ttv1 ] and [ ttv2 ] . we find that the ttv terms from @xmath344 with the frequency @xmath30 have amplitudes that are generally much smaller than the ttv amplitudes arising from the @xmath16 terms ( eq . [ dl2 ] ) . here we therefore explicitly report only the most important harmonic with frequency @xmath42 . these terms do not have a counterpart in eq . ( [ dl2 ] ) . they are important for the long - term modulation of the ttv signal . specifically , we find that @xmath420 this is the source of eq . ( [ yys2 ] ) . since @xmath421 , we do not list this term in eq . ( [ yys2 ] ) , where we also substitute @xmath384 . we adopted several approximations in this work : * i. * the laplacian expansion of the perturbing function used in section 3.1 is convergent only if the planetary eccentricities are small enough ( sundman 1912 ) . for a planet on a circular orbit , this limits the validity of the expansion to @xmath422 ( @xmath423 ) for orbits near its inner ( outer ) 2:1 resonance , and to @xmath424 ( @xmath425 ) for orbits near its inner ( outer ) 3:2 resonance . the analytic results derived here are not valid above these limits . see nesvorn & morbidelli ( 2008 ) for a discussion of sundman s criterion . all non - resonant terms were neglected in section 3.1 . the short - periodic terms with non - resonant frequencies produce short - periodic ttvs that can be calculated by the method described in nesvorn & morbidelli ( 2008 ) . these terms can be linearly added to the expressions obtained here for resonant ttvs . the secular terms are second and higher orders in planetary eccentricities and contribute by only a small correction to the precession of orbits if the eccentricities are small . * the second- and higher - order resonant terms in planetary eccentricities were neglected in the perturbing function . this is an important approximation that limits the validity of the results to small eccentricities . the same assumption was adopted when writing @xmath426 as a variation of orbital elements . * iv . * the amplitude of the semimajor axis variations was assumed to be small ( this allowed us to simplify the keplerian hamiltonian in section 3.3 ) . the same assumption was adopted to compute @xmath426 from eq . ( [ ttv ] ) , where we also neglected all second and higher order terms in small variations of the orbital elements . we find that these approximations are generally valid and do not impose any meaningful limits on the range of planetary parameters where our analytic results are valid . * v. * the exact solution of the second fundamental model of resonance was expanded in the taylor series in @xmath37 and only the terms @xmath399 were retained ( section 4.1 ) . in addition , the jacobi elliptic functions were written as the fourier series and only the lowest harmonics were retained . both these approximations limit the validity of our analytic ttv model to relatively small libration amplitudes . [ in principle , the methods described in section 4 can be used to obtain more general expressions . ] here we perform tests of these assumptions to establish the domain of validity of our analytic model . to this end we developed several codes that compute the resonant ttv signal at various stages of approximation . they are : * a. * a full @xmath427-body integrator of eq . ( [ ham1 ] ) and ( [ ham2 ] ) where the gravitational interaction of planets is taken into account exactly . we used the symplectic code known as swift ( levison & duncan 1994 ) with routines for an efficient and precise determination of ttvs ( nesvorn et al . 2013 ; see also deck et al . 2014 ) . * b. * a numerical integrator in orbital elements that uses the laplacian expansion of the perturbing function . various terms can be included or excluded in this integrator . in the most basic approximation , the code includes only the first - order resonant terms from eq . ( [ ham4 ] ) . optionally , it also accounts for the second - order secular and/or resonant terms . this code is used to test the approximations * ii * and * iii * listed above * c. * a code that maps the initial orbital elements onto ( [ fm ] ) and numerically integrates the corresponding eqs . ( [ hameq1 ] ) and ( [ hameq2 ] ) . another code uses the exact analytic solution ( [ sfmr5 ] ) . as expected , these two codes give exactly the same result , which shows that our implementation of eq . ( [ sfmr5 ] ) is working correctly . * d. * a ttv code based on the analytic formulas derived in section 4 . this code is subject to all approximations discussed above . it can not produce accurate results if the orbital eccentricities and/or libration amplitudes exceed certain limits . we first test the approximation * v*. to this end we compare the results obtained with code * b * with the analytic results from method * d*. in * b * , we include the two first - order resonant terms and neglect terms that are the second or higher order in planetary eccentricities . and [ ttv2 ] in section 2 . ] the masses and initial orbits are chosen such that @xmath409 ( fig . [ ttv3 ] ) or @xmath410 ( fig . [ ttv4 ] ) . the initial orbits are then varied to survey different libration amplitudes . these tests show that the analytic method produces very reliable results for @xmath428 ( top panels in figs . [ ttv3 ] and [ ttv4 ] ) . for the libration amplitudes much larger than that , our analytic expressions for @xmath335 and @xmath336 in eq . ( [ uvapp ] ) become inaccurate ( see fig . [ uvfig ] ) . as a consequence , the analytic approximation of the ttv terms from @xmath17 fails ( bottom panels in figs . [ ttv3 ] and [ ttv4 ] ) . interestingly , however , the analytic approximation of the _ full _ ttv signal is reasonable even if @xmath429 . this happens because the ttv terms from @xmath16 increase with @xmath27 and become dominant for large @xmath27 . we are able to reproduce these terms correctly , because the analytic formula in eq . ( [ dl ] ) has more a general validity than the one that requires a correct approximation of the boomerang - shaped trajectories in the @xmath430 plane ( eq . [ uvapp ] ) . we therefore conclude that the analytic ttv model can be used , with some caution , even if the libration amplitudes are relatively large . we now turn our attention to the approximations * i , ii and iii*. we find that the omission of the higher - order resonant terms in * iii * is the most restrictive assumption . to illustrate this , figures [ ttv7 ] ( inner planet ) and [ ttv8 ] ( outer planet ) show a comparison of the analytic model with ttvs computed from the @xmath427-body code ( method * a * above ) . here we set different planetary eccentricities ranging from @xmath431 ( left panels in both figures ) to @xmath432 ( right panels ) . we find that that the analytic model works well for @xmath431 . already for @xmath433 , a significant discrepancy appears ( see middle panels in figs . [ ttv7 ] and [ ttv8 ] ) . an important part of the discrepancy , however , is not due to the assumption * iii * , but is rather related to the choice of initial conditions . recall that , in addition to the resonant terms , the exact computation of ttvs with method * a * also contains the short - periodic harmonics , while the analytic method * d * does not account for these terms . this presents a difficulty when choosing the initial conditions in * a * and * d * that are consistent with each other . if the same values are adopted in * a * and * d * , the initial semimajor axes in * a * generate slightly different values of the mean orbital frequencies than the same initial semimajor axes in * d*. this effect then propagates into a difference in the libration frequency @xmath30 . to demostrate this , we surveyed a small neigborhood of the initial conditions and found that it is always possible , if the eccentricities are sufficiently small , to apply a small adjustment such that the difference between the analytical and numerical results vanishes ( left and middle bottom panels in figs . [ ttv7 ] and [ ttv8 ] ) . note that this initial value problem does not seriously limit the application of the analytic model to the real data , because it requires only a very small adjustment of @xmath89 or @xmath90 ( or equivalently @xmath434 and @xmath435 ) , which can easily be absorbed by other parameters . another more fundamental discrepancy appears for @xmath432 . in this case , the ttv frequency computed from the analytic model is nearly 40% higher than the actual frequency , and the ttv amplitudes are @xmath26125% smaller than their actual values ( right panels in figs . [ ttv7 ] and [ ttv8 ] ) . in this case , it is not possible to adjust the initial conditions to cancel the difference . this shows that the assumption * iii * starts to fail . we confirm this by method * b * , where it becomes apparent that including the second - order resonant terms improves model s precision . still , for @xmath432 the amplitude discrepancy is relatively minor and can be compensated , for example , by a relatively small correction of planetary masses . we therefore find that the analytic model is still useful in this case . our additional tests show that the analytic expressions for ttvs are not reliable for eccentricities exceeding @xmath40.1 . [ the validity domain in @xmath436 should be slightly larger for distant resonances such as 2:1 , and smaller for @xmath437 . ] the analytic model was developed under the assumption of exactly co - planar planetary orbits . this assumption was used in section 3.1 to neglect all terms in the laplacian expansion of the perturbing function that depend on inclinations . the model is therefore not expected to be valid if the mutual inclination between orbits , @xmath438 , is large . we performed various tests of this assumption and found that the analytic model is reasonably accurate for @xmath439 , but fails to produce reliable results for @xmath440 . this should not be a severe limitation of the applicability of the analytic results to the multi - transiting planetary systems , because the orbits in these systems are expected to be nearly co - planar ( e.g , fang & margot 2012 ) . in this work we developed an analytic model for ttvs of a pair of resonant planets , and discussed how the ttv period and amplitude constrain the masses and orbits of the two planets . the model is strictly valid only for small orbital eccentricities ( @xmath441 ) . it was developed under the assumption of co - planar orbits but our tests show that it is valid even if the mutual inclination of orbits is not large ( @xmath442 ) . the resonant ttv signal is expected to contain the harmonics of two basic periods : the period of resonant librations and the period of apsidal precession of orbits . the latter is expected to be @xmath45 times longer than the former , and may be difficult to detect with a short baseline of the ttv measurements . the libration period is relatively insensitive to the exact location of the system parameters in the resonant island , and scales with @xmath0 . its determination from the ttv measurements can therefore help to constrain the planetary masses . this is an important difference with respect to the near - resonant case ( lithwick et al . 2012 ) , where the ttv period is the super period , which is independent of mass . the ttv amplitudes , on the other hand , can be used to constrain the ratio of planetary masses @xmath67 . since both the ttv period and amplitude depend on the resonant amplitude @xmath27 , some mild degeneracies between the mass and orbital parameters are expected , but these degeneracies can be broken by a detection of higher - order resonant harmonics , which constrain @xmath27 , and/or short - periodic ( chopping ) effects . a detailed analysis of this problem and the application of our analytic model to the resonant exoplanets ( winn & fabrycky 2015 ) is left for future work . the work of dn was supported by nasa s adap program . dv was supported by the czech grant agency ( grant p209 - 13 - 01308s ) . slawek breiter pointed to us the general solution eq . ( [ sfmr5 ] ) in whittaker & watson ( 1920 ) . we thank katherine deck , eric agol and an anonymous reviewer for useful comments on the manuscript . the coefficients @xmath444 in eq . ( [ sfmr5 ] ) are obtained from the derivatives of @xmath445 with @xmath212 @xmath446\ ; , \nonumber \\ c_2 & = & -4\left[2(\psi_0-\delta)^2+\sqrt{2\psi_0}\right]\ ; .\end{aligned}\ ] ] the expressions for @xmath447 and @xmath448 are not needed if we set @xmath449 and thus @xmath223 . the invariants in eq . ( [ sfmr6b ] ) can be written as @xmath450 where we denoted @xmath451 . the determinant @xmath452 becomes @xmath453 if we define @xmath454 then the three roots of the cubic equation can be obtained from @xmath455 in the equilibrium point , @xmath456 , we have that @xmath354 and thus @xmath457 . it follows that @xmath458 and @xmath459 . therefore , @xmath460 and @xmath461 , where @xmath462 and @xmath463 are defined in the main text . figure [ eps ] shows @xmath443 for @xmath464 . it is zero at the equilibrium point and increases to @xmath465 at the separatrix . higher values of @xmath183 lead to smaller values of @xmath37 . for @xmath466 , on the other hand , @xmath37 can be as large as 0.6 near the separatrix . in section 3 we omitted to explain one important issue that becomes apparent if the degree of freedom related to @xmath467 is treated separately from those related to @xmath96 and @xmath97 ( as it was done in bm13 ) . to explain this issue we first define in direct correspondence to eq . ( [ ham10b ] ) @xmath468 where @xmath469 . second , we perform a transformation ( see section 3.4 ) to the new variables @xmath470 @xmath471 and last , we introduce new polar variables @xmath472 such that @xmath473 the inverse transformation to ( [ bigredt ] ) is @xmath474 with these definitions , it is straightforward to show that @xmath475 , where @xmath476 are the original angles defined in ( [ ham14b ] ) , @xmath477 and @xmath478 , where @xmath479 . we thus find that @xmath480 . when substituted into ( [ inverse ] ) , we obtain eq . ( [ ys ] ) in the main text . in addition , it can be shown that @xmath481 . the angle @xmath482 is therefore constant . consequently , since @xmath164 as well , both @xmath483 and @xmath338 are constants of motion . this result is used in section 4 , where @xmath338 in eq . ( [ ys ] ) does not contribute to ttvs . the integral in eq . ( [ iscale ] ) with @xmath327 from eq . ( [ simple ] ) admits the following exact solution @xmath485 where @xmath443 and @xmath486 are defined in section 4.1 . from byrd & friedman ( 1971 ) ( bf 341.03 ) we have @xmath487 \ ; , \ ] ] where @xmath488 is the legendre elliptic integral of the third kind , @xmath489 is the jacobi amplitude , and @xmath490 . the constants @xmath211 a @xmath172 are @xmath491 note that byrd & friedman ( 1971 ) use a different notation for the coefficient @xmath211 then press et al . ( 2007 ) . to use the numerical subroutines from press et al . ( 2007 ) , @xmath492 .

the transit timing variations ( ttvs ) are deviations of the measured mid - transit times from the exact periodicity . one of the most interesting causes of ttvs is the gravitational interaction between planets . here we consider a case of two planets in a mean motion resonance ( orbital periods in a ratio of small integers ) . this case is important because the resonant interaction can amplify the ttv effect and allow planets to be detected more easily . we develop an analytic model of the resonant dynamics valid for small orbital eccentricities and use it to derive the principal ttv terms . we find that a resonant system should show ttv terms with two basic periods ( and their harmonics ) . the resonant ttv period is proportional @xmath0 , where @xmath1 and @xmath2 are the planetary and stellar masses . for @xmath3 , for example , the ttv period exceeds the orbital period by @xmath42 orders of magnitude . the amplitude of the resonant ttv terms scales linearly with the libration amplitude . the ratio of the ttv amplitudes of two resonant planets is inversely proportional to the ratio of their masses . these and other relationships discussed in the main text can be used to aid the interpretation of ttv observations .

with the discovery of the standard model ( sm ) higgs in the atlas @xcite and cms @xcite experiments , we have taken one step further toward understanding the electroweak symmetry breaking ( ewsb ) through the spontaneous symmetry breaking ( ssb ) mechanism in the scalar sector . the next mission for the high - luminosity large hadron collider ( lhc ) is to explore not only the detailed properties of the sm higgs , but also the new physics effects . since problems related to the origin of neutrino mass , dark matter ( dm ) , and matter - antimatter asymmetry can not be resolved in the sm , it is believed that the sm of particle physics is an effective theory at the electroweak scale . if new physics exists at the tev scale , the lhc can detect it . some potential events indicating the existence of new effects indeed have been observed in the recent atlas and cms experiments . for instance , diboson excess of @xmath20 with @xmath21 at around 2 tev was shown by atlas @xcite and cms @xcite ; the branching ratio ( br ) for lepton - flavor - violating higgs decay @xmath22 with a @xmath23 significance was presented by cms @xcite ; a resonance at a mass of 750 gev in the diphoton invariant mass spectrum was reported by atlas @xcite and cms @xcite . although the results are not conclusive yet , these experimental measurements have inspired theorists to speculate various effects to interpret the excesses . ever since the sm higgs was observed , the higgs measurements have approached to the precision level . it becomes an important issue to uncover the physics beyond the sm through the higgs portal . precise higgs measurements can also give strict bounds on the new couplings ; for instance , @xmath24 in the two - higgs - doublet model has been limited to be close to the decoupling limit @xcite , and the sm with a fourth generation of chiral fermions has become disfavored @xcite . although the extension of the sm with chiral fermions has been severely limited , the constraint on the vector - like quark ( vlq ) models may not have the same situation due to the use of different representations and coupling structures . unlike chiral fermion models , where the appearance of chiral quarks has to accompany chiral leptons due to gauge anomaly , the gauge anomaly in vlq models is cancelled automatically . therefore , it is not necessary to introduce the exotic heavy leptons into the sm when vlqs are added . due to their interesting properties , the phenomena of some specific vlqs at the lhc have been investigated from a theoretical viewpoint @xcite . in experiments , single vlqs and pairs of vlqs have been produced at atlas @xcite and cms @xcite . based on the sm gauge symmetry @xmath25 , the representations of vlqs can basically be any @xmath26 multiplets . however , in order to consider the vlq decays , the possible representations of vlq couplings to the sm quarks are singlet , doublet , and triplet . to interpret the excesses of dibosons and diphotons indicated by atlas and cms , we proposed a model that contains one higgs singlet and two triplet vlqs with hypercharges of @xmath27 and @xmath28 , respectively @xcite . since the representations of the vlqs are different from those of the sm quarks , the higgs- and @xmath1-mediated flavor - changing neutral currents ( fcncs ) are induced at the tree level and the cabibbo - kobayashi - maskawa ( ckm ) matrix is non - unitary matrix . in our earlier studies , besides the resolutions of the excesses , we focused on the leading effects , which were from the left - handed flavor - mixing matrices , and found that they led to interesting contributions to top fcncs @xmath29 and the sm higgs production and decays . in this study , we systematically discuss the left- and right - handed flavor - mixing effects together . we revisit the constraints and present the bounds from @xmath30 processes in detail . with the values of constrained parameters , it is found that the modified top coupling to the sm higgs , which arises from the right - handed flavor mixing , can diminish the influence of the sm higgs production and the decay to diphotons by around @xmath2 and @xmath31 deviations from the sm results , respectively . we demonstrate how the changes of the sm ckm matrix elements can be smeared so that the severe bounds from the current measurements of the ckm matrix elements are satisfied @xcite . in addition to the phenomena in flavor physics , we also investigate the single and pair production of vlqs in this work . in the proposed model , the new quarks are @xmath32 , @xmath33 , @xmath34 , and @xmath35 , whose associated electric charges are @xmath36 , @xmath37 , @xmath38 , and @xmath39 , respectively . therefore , @xmath32 and @xmath33 can be regarded as top and bottom partners , respectively . since vlqs @xmath34 and @xmath35 carry the unusual electric charges , they do not have fcnc couplings to the sm quarks . as a result , their single production and decays are only through charged weak interactions . since the top and bottom partners involve more complicated fcnc interactions , we concentrate the study on vlqs @xmath34 and @xmath35 . it is found that the single production cross sections of @xmath34 and @xmath35 can be larger than the pair production cross sections , which are dominant from quantum chromodynamics ( qcd ) . in order to understand this phenomenon , we analyze each process @xmath40 for the single production of @xmath34 and @xmath35 . it is found that with @xmath41 tev , the cross sections for @xmath42 and @xmath43 modes can be of the order of 100 fb while the pair production cross sections are smaller by a factor of around 2 . we postpone the study of event simulation to another paper . the rest of this paper is organized as follows . we establish the model , discuss the new flavor mixing effects , and derive the new higgs and gauge couplings in section ii . we present the constraints from low - energy and higgs measurements in section iii . we also study the implications on top - quark fcnc processes @xmath29 . in section iv , we discuss the single and pair production for vlqs @xmath44 and @xmath45 , and thoroughly analyze the production mechanism in @xmath7 collisions . the conclusions are given in section v. we extend the sm by including one real higgs singlet and two vector - like triplet quarks ( vltqs ) , where the representations of vltqs in @xmath46 gauge symmetry are chosen as @xmath47 and @xmath48 @xcite . for suppressing the mixing between higgs singlet and doublet , we impose a @xmath49 discrete symmetry on the scalar potential , where the scalar fields follow the transformations @xmath50 and @xmath51 under the @xmath49 transformation . thus , the scalar potential is expressed as : @xmath52 we adopt the following representation of @xmath53 : h= ( cc g^+ + ( v+ h + ig^0 ) ) , where @xmath54 and @xmath55 are goldstone bosons , @xmath56 is the sm higgs field , and @xmath57 is the vacuum expectation value ( vev ) of @xmath53 . the @xmath58 field can not develop a non - vanishing vev in the scalar potential of eq . ( [ eq : vhs ] ) when @xmath59 . due to the @xmath49 symmetry , @xmath56 and @xmath58 do not mix at the tree level ; thus @xmath60 is the mass of @xmath58 , @xmath61 , and @xmath62 gev is the mass of the sm higgs @xcite . we note that the @xmath49 symmetry is softly broken by some other sector of lagrangian . the gauge - invariant yukawa couplings of vltqs to the sm quarks , the sm higgs doublet , and the new higgs singlet are expressed as : -l^y_vltq & = & tr(|f_2l f_2r ) s + & + & m_f_1 tr(|f_1l f_1r ) + m_f_2 tr(|f_2l f_2r)+ h.c . , [ eq : yukawa ] where @xmath63 is the left - handed sm quark doublet , all flavor indices are hidden , @xmath64 , and @xmath65 is the @xmath66 vltq with hypercharge @xmath67 , whose representations of @xmath68 are : f_1 = ( cc u_1/ & x + d_1 & -u_1/ ) , f_2 = ( cc d_2/ & u_2 + y & -d_2/ ) . under @xmath49 transformation , @xmath69 . the electric charges of @xmath70 , @xmath71 , @xmath34 , and @xmath35 are @xmath72 , @xmath37 , @xmath73 , and @xmath74 , respectively . therefore , @xmath75 can mix with up ( down)-type sm quarks . the masses of vltqs do not originate from the electroweak symmetry breaking . due to the gauge symmetry , vltqs in a given multiplet state are degenerate , and denoted by @xmath76 . since the mass terms of vltqs do not involve the @xmath58 field and the associated operators are dimension-3 , the discrete @xmath49 symmetry is softly broken by @xmath77 terms . it is worth mentioning that @xmath78 results in the mixture of the sm quarks and vltqs ; consequently , the @xmath56 coupling to the top quark is modified and the @xmath56 couplings to vltqs are induced . as a result , the sm higgs production cross section via gluon - gluon fusion ( ggf ) and its decays will be modified . in the next subsection , we discuss the modifications in detail . we note that the @xmath49 breaking effects will induce @xmath79 term through one - loop diagrams in the scalar potential . however , in addition to the suppression factor @xmath80 , the loop effects are suppressed by the small yukawa couplings @xmath78 ( see the detailed discussions later ) . as a result , the induced vev of @xmath58 field and the induced mixing between @xmath56 and @xmath58 are small , and the br for @xmath81 decay is a factor of two smaller than that for @xmath82 decay @xcite . next , we discuss the weak interactions of vltqs . as usual , we write the covariant derivative of @xmath25 as : d_= _ + i ( t^+ w^+_+t^- w^- _ ) + i ( t^3 - s^2_w q ) z_+ i e q a _ , where @xmath83 , @xmath84 , and @xmath85 are the gauge bosons in the sm , @xmath86 is the gauge coupling of @xmath87 , @xmath88 , @xmath89 is the weinberg angle , @xmath90 , and the charge operator @xmath91 , where @xmath35 is the hypercharge of the particle . thus , the gauge interactions of vltqs are written as @xcite : _ vff & = & -g + & - & , [ eq : vff ] where we express the triplet vlqs as @xmath92 and @xmath93 , diag@xmath94 , diag@xmath95 , and diag@xmath96 . to further understand the weak interactions in terms of physical states , we have to investigate the structures of flavor mixings when @xmath78 effects in eq . ( [ eq : yukawa ] ) are involved . the introduced two @xmath87 triplet vlqs contain the quarks with electric charges of @xmath97 and @xmath37 . from the new higgs yukawa couplings to the sm higgs and vltqs , the mixture between the sm quarks and vltqs is generated after ewsb . in order to get the physical mass eigenstates of quarks and the new flavor mixings , we have to diagonalize the mass matrices of the sm quarks and vltqs . with the yukawa couplings @xmath98 and @xmath99 ( i=1 - 3 ) in eq . ( [ eq : yukawa ] ) , the quark mass terms are given by : -l_mass = |*q*_l * m*_q * q*_r + |*q*_l * y*^q v * f*_r + |*f*_l * m*_f * f*_r + h.c . , where @xmath100 or @xmath101 denotes the sm up- or down - type quarks . we have chosen the basis such that @xmath102 is a @xmath103 diagonal matrix , @xmath104 or @xmath105 is the vltq with charge @xmath97 or @xmath37 , diag@xmath106 ) , and =( cc y_11/2 & y_21/ + y_12/2 & y_22/ + y_13/2 & y_23/ ) , * y^d*= ( cc y_11/ & -y_21/2 + y_12/ & -y_22/2 + y_13/ & -y_23/2 ) . [ eq : yud ] we do not have @xmath107 terms due to gauge invariance . the quark mass matrices for electric charges @xmath97 and @xmath37 now become @xmath108 matrices . one can introduce the @xmath109 unitary matrices @xmath110 and @xmath111 to diagonalize the mass matrices , namely @xmath112 . in order to obtain the information of @xmath113 , we consider the multiplications of mass matrices to be @xmath114 and @xmath115 , where @xmath116 and @xmath117 are expressed as : @xmath118 with @xmath119 , and @xmath120 . it is clear that the off - diagonal matrix elements in @xmath116 are related to @xmath121 while those in @xmath117 are @xmath122 . due to @xmath123 , the unitary matrices @xmath124 can be expanded with respect to @xmath125 and @xmath126 ; at the leading order approximation , they can be formulated as : v^q _ ( cc _ 33 & -(^q_)_32 + ( ^q _ ) _ 23 & _ 22 ) , [ eq : vqlr ] where @xmath127 , @xmath128 , and @xmath129 . we find that the effects of @xmath130 are suppressed by @xmath131 while those of @xmath132 are associated with @xmath133 . since the top and bottom quarks are much heavier than other sm quarks , in this study we keep the contributions from @xmath134 and @xmath135 , and ignore other @xmath136 that involve the light quark masses . we use the flavor mixing matrices of eq . ( [ eq : vqlr ] ) to investigate the new flavor couplings of the higgs and the weak gauge bosons below . from the yukawa couplings in eq . ( [ eq : yukawa ] ) , the sm higgs couplings to the quarks in the flavor space are written as : -l_hqq & = |q_l v^q q_r h + h.c . , [ eq : hqq ] where @xmath137 or @xmath138 , @xmath139 , and @xmath140 are the physical states of vltqs and carry the electric charges of @xmath72 and @xmath37 , respectively , and @xmath141 is the mixing matrix for the @xmath142-type quark and is given by : @xmath143 the small effects , such as @xmath144 , @xmath145 , and @xmath146 , have been dropped . according to eq . ( [ eq : vq ] ) , the @xmath56-mediated fcncs for the sm quarks ( e.g. , @xmath56-@xmath142-@xmath147 ) are proportional to @xmath148 . if the mass effects of the first two generations of quarks are neglected , we have the flavor - changing higgs interactions : @xmath149 where @xmath150 quark , @xmath151 quark , the definition of @xmath152 in eq . ( [ eq : yud ] ) is applied , and @xmath153 . the @xmath154 and @xmath155 oscillations can be induced via the tree - level higgs mediation in the vltq model . additionally , the brs for the flavor - changing processes @xmath156 , which are highly suppressed in the sm , become sizable . in addition to the new fcnc couplings , the flavor - conserving couplings are also modified : -l_hqq = |t_l t_r h + quark will affect the sm higgs production and decays in the @xmath7 collisions at the lhc . if we take @xmath157 tev , @xmath158 , and @xmath159 gev , the @xmath56 production cross section by the top - quark loop will be reduced by @xmath160 of the sm prediction . that is , the influence of new effects can not be ignored arbitrarily . from the flavor mixing matrix in eq . ( [ eq : vq ] ) , we can also obtain the sm higgs interactions with the vltqs as : @xmath161 with @xmath162 . since vltqs are color triplet states in @xmath163 and carry the same color charges as those of the sm quarks , the new couplings @xmath164 also contribute to the @xmath56 production cross section via the ggf channel . we will study their influence on the process @xmath165 in the numerical analysis . by combining the charged weak interactions of the sm quarks with those of vltqs in eq . ( [ eq : vff ] ) , the charged current interactions of quarks can be formulated by : _ w & = & - |*u*_l ^v^l_ckm * d*_l w^+ _ - |*u*_r ^v^r_ckm * d*_r w^+_+h.c . , [ eq : wud ] where @xmath166 and @xmath167 are respectively the physical up- and down - type quarks , and @xmath168 is the @xmath109 ckm matrix for left ( right)-handed quarks , defined by : v^l_ckm & = & v^u_l ( cc ( v_ckm ) _ 33 & 0_32 + 0_23 & _ 22 ) v^d_l , v^r_ckm = v^u_r ( cc 0_33 & 0_32 + 0_23 & _ 22 ) v^d_r . the @xmath103 matrix @xmath169 is associated with the sm ckm matrix . since the weak isospin of a triplet quark differs from that of a doublet quark , the new @xmath109 ckm matrices @xmath170 are non - unitary . by using the results of eq . ( [ eq : vqlr ] ) , the ckm matrix elements for the three - generation sm quarks are modified to be : ( v^sm_ckm)_i j ( v_ckm)_i j + ( _ 1i _ 1j - _ 2i _ 2j ) . [ eq : mckm ] with @xmath171 and @xmath172 tev , the changes of the sm ckm matrix elements are roughly estimated as @xmath173 . as indicated by experiments @xcite , the value of @xmath174 has the same order of magnitude as @xmath175 and is larger than @xmath176 . to satisfy the constraints of @xmath176 , the possible schemes are : ( a ) @xmath177 is less than @xmath178 , the smallest ckm matrix element , ( b ) @xmath179 so that @xmath180 and ( c ) @xmath181 which leads to @xmath180 . moreover , if we adopt @xmath182 @xmath1831 - 3 ) , all ckm matrix elements return to the sm ones . with the leading - order approximation for @xmath184 , the @xmath185-boson interactions with the sm quarks and vltqs are given by @xcite : @xmath186w^+_\mu \non \\ & - \frac{g}{2 } \left [ \zeta_{2i } \bar d_{il } \gamma^\mu y_l + \frac{m_b \zeta_{23}}{m_{f_2 } } \bar b_r \gamma^\mu y_r - \zeta_{1i } \bar x_l \gamma^\mu u_{il } - \frac{m_t \zeta_{13}}{m_{f_1 } } \bar x_r \gamma^\mu t_r \right ] w^+_\mu + h.c . \label{eq : wfq } \end{aligned}\ ] ] the charged weak interactions of vltqs can be directly read from eq . ( [ eq : vff ] ) . we next discuss the neutral weak interactions . it is known that the left - handed and right - handed quarks in the sm are @xmath187 doublets and singlets , respectively ; however , the vltqs are @xmath87 triplets . since the isospin of a triplet is different from those of doublets and singlets , in order to combine the vltqs with the sm quarks into the same representation in the flavor space , we need to rewrite the vertex structure of the @xmath1-boson , @xmath188 , in eq . ( [ eq : vff ] ) to fit the cases of doublets and singlets , such as @xmath189 , where @xmath190 for doublets and @xmath191 for singlets . due to the isospin difference , @xmath1-mediated fcncs are induced at the tree level . since vltqs @xmath34 and @xmath35 carry the electric charges of @xmath73 and @xmath192 , respectively , they can not mix up with other quarks in the neutral current interactions . in terms of weak eigenstates , we write the weak neutral current interactions in eq . ( [ eq : vff ] ) as : @xmath193\ , , \label{eq : zff } \end{aligned}\ ] ] where @xmath194 and @xmath195 are composed of vltqs with electric charges of @xmath72 and @xmath37 , respectively , @xmath196 , @xmath190 for @xmath197 , @xmath198 , and @xmath199 . we succeed in expressing the @xmath1 couplings to vltqs by using the sm @xmath1 couplings . it is clear that the first two terms in eq . ( [ eq : zff ] ) lead to the flavor - conserving couplings when the sm quarks and vltqs form a representation in the dimension-5 flavor space . since the sm quarks do not have the interaction structures , as shown in the last three terms of eq . ( [ eq : zff ] ) , as a result , fcncs via @xmath1 mediation are generated . hence , the @xmath1-boson interactions with quarks , which carry electric charges of @xmath72 and @xmath37 , can be formulated as : _ zqq & = & - c^q_l_ij |q_il ^q_j l z_- c^q_r_ij |q_i r ^q_jr z _ , + [ eq : zqq ] c^q_l_ij & = & ( i^q_3 -s^2_w q_q ) _ ij + ( -v^q_li4 v^q*_lj4 + v^q_li5 v^q*_lj5 ) , + c^q_r_ij & = & -s^2_w q_q _ ij + _ q ( v^q_r)_i _ q ( v^q*_r)__q j where @xmath200 or @xmath138 , @xmath201 are defined in eq . ( [ eq : vqlr ] ) , @xmath202 , and @xmath203 . using eq . ( [ eq : vqlr ] ) and the leading - order approximation , the new gauge couplings of the @xmath1-boson to the sm quarks are given by : _ zq_iq_j = - ( a_q _ 1i _ 1j - b_q _ 2i _ 2j ) |q_il ^q_jl z _ , [ eq : zqiqj ] where @xmath204 denote the up- or down - type sm quarks , @xmath205 , and @xmath206 . it can be seen that the fcnc effects can contribute to @xmath30 neutral meson mixings . a comparison with the results in eq . ( [ eq : mckm ] ) indicates that the induced new coupling structures in charged and neutral currents are different . it is interesting to investigate the possible schemes that can simultaneously satisfy the constraints from the ckm matrix elements and the data of neutral meson oscillations . the interactions of the @xmath1-boson couple to one vltq and one sm quark are shown as : @xmath207 one can get the @xmath1 couplings to vltqs from eq . ( [ eq : vff ] ) . in this section , we discuss the constraints from low - energy @xmath30 processes and from the data of the sm higgs production and decay into diphotons . from eqs . ( [ eq : hqq ] ) and ( [ eq : zqiqj ] ) , we know that the @xmath56- and @xmath1-mediated fcncs appear and contribute to the @xmath30 processes , such as @xmath209 and @xmath210 mixings , where the current experimental data can give strict constraints on the free parameters . since the fcnc couplings in the up - type quarks are the same as those in the down - type quarks and the hadronic effects in the @xmath211-meson system are dominated by unclear non - perturbative effects , we focus on @xmath212 and @xmath213 processes . following the notations in previous studies @xcite , the transition matrix elements for @xmath209 and @xmath210 mixings are given by : @xmath214\ , , \\ m^{k}_{12}(z ) & = \frac{(\delta^{sd}_l(z))^2}{2 m^2_z } c^{\rm vll}_1 ( \mu_z ) \bar p^{\rm vll}_1(k,\mu_z)\ , , \\ m^{b_q}_{12}(z ) & = \frac{(\delta^{bd}_l(z))^2}{2 m^2_z } c^{\rm vll}_1 ( \mu_z ) \bar p^{\rm vll}_1(b_q , \mu_z)\ , . \end{aligned}\ ] ] @xmath215 is the wilson coefficient with @xmath216 qcd corrections , and @xmath217 denotes the hadronic effects that include the renormalization group ( rg ) evolution from high energy to low energy , whose expressions are @xcite : @xmath218_{\rm sll } r_{b_q } b^{\rm sll}_{1}(\mu_b ) -\frac{3}{2 } [ \eta_{21}(\mu_b)]_{\rm sll } r_{b_q } b^{\rm sll}_{2}(\mu_b ) \ , , \non \\ p^{\rm sll}_2(b_q,\mu_b ) & = - \frac{5}{8 } [ \eta_{12}(\mu_b ) ] _ { \rm sll } r_{b_q } b^{\rm sll}_{1}(\mu_b ) -\frac{3}{2 } [ \eta_{22}(\mu_b)]_{\rm sll } r_{b_q } b^{\rm sll}_{2}(\mu_b ) \ , , \end{aligned}\ ] ] @xmath219 , where @xmath220 and @xmath221 are the mass and decay constant of the @xmath222-meson , respectively , @xmath223 gev for the @xmath224-meson , @xmath225 , and the values of other hadronic effects and rg evolution effects are given in table [ tab : values ] . @xmath226 are from the short - distance interactions of eqs . ( [ eq : hqq ] ) and ( [ eq : zqiqj ] ) and are written as : @xmath227 since we have ignored the effects of light quark masses , the @xmath56-mediated fcnc has no contribution to @xmath209 mixing . to constrain the parameters , we assume that the obtained @xmath228 in the model should be less than the experimental measurements . to understand the individual influences of @xmath56 mediation and @xmath1 mediation , we show their constraints separately . with @xmath229 , @xmath230 , and the inputs of table [ tab : values ] , we obtain the constraints as : @xmath209 mixing : @xmath231 @xmath154 mixing : @xmath232 @xmath155 mixing : @xmath233 from these results , we find that the constraint from @xmath234 is only a factor of 2 stronger than that from @xmath235 . since the ratio @xmath236 in experiments is very close to the wolfenstein s parameter @xmath237 @xcite , the difference of a factor of @xmath238 between eq . ( [ eq : bdc ] ) and eq . @xmath239 is reasonable . . [ cols="^,^,^,^,^",options="header " , ] finally , we briefly discuss the new physics in connection to the flavor physics . in this study , we do not introduce new couplings to the lepton sector , therefore , the contributions to the lepton flavor - changing processes are similar to the sm predictions . however , the introduced vlqs lead to fcncs at the tree level in the quark sector , where the strict constraints from @xmath30 processes have been considered in section iii . besides the rare decays @xmath240 and @xmath241 that were discussed earlier , it is also interesting to investigate the fcnc effects in the low energy physics . for instance , the coupling @xmath242 can contribute to the @xmath243 and @xmath244 decays , where the sm predicted brs are of @xmath245 , both are sensitive to the new physics effects , and the theoretical uncertainties are well - controlled @xcite . furthermore , the na62 experiment at cern can achieve the @xmath246 to be a precision of @xmath2 @xcite ; and the koto experiment at j - parc for @xmath247 decays can reach the sm sensitivity . thus , it is important to search for new physics in rare @xmath248 decays . in @xmath249-meson physics , the tree - level couplings @xmath250 with @xmath251 can contribute to @xmath252 decays . although the measured @xmath253 is consistent with the sm prediction @xcite , a @xmath254 deviation from the sm prediction in the angular analysis of @xmath255 is observed @xcite . it is worthy to explore the excess in our model . since the detailed analysis of flavor physics is beyond the scope of this paper , a complete analysis will be studied elsewhere @xcite . we have studied the phenomenology of which two triplet vlqs with @xmath0 and a higgs singlet are embedded in the sm . because the isospin of vlqs is different from that of the sm quarks , higgs- and @xmath1-mediated fcncs are generated at the tree level and the new ckm matrix becomes a non - unitary matrix . we find that the modifications of the ckm matrix elements coupled to the sm quarks can be smeared out if two triplet vlqs are introduced and the scheme @xmath256 is adopted , where @xmath257 are the parameters from flavor mixings . although the tree - level fcncs can not be removed , it was found that when the constraints from @xmath30 processes are applied , the upper limits of brs for @xmath258 decays are @xmath259 , which is two orders of magnitude smaller than the current experimental bounds . with the values of constrained parameters , we examined the influence of the model on the sm higgs production and its diphoton decay ; we found that @xmath260 and @xmath261 can have @xmath262 and @xmath31 deviations from the sm results , respectively . as a result , the signal strength for @xmath165 is thus changed by @xmath2 . the main purpose of this work was to explore the single production of exotic vlqs @xmath34 and @xmath35 in the @xmath7 collisions at @xmath8 tev . we gave a detailed analysis for each possible @xmath6 scattering , where @xmath204 and @xmath263 are the possible initial quarks . it was found that the contributions of @xmath264-channel annihilations are much smaller than those of @xmath265-channel annihilations . from this study , we comprehend the contribution of each subprocess to the production cross section of a specific vlq . the interesting production channels are @xmath266 , @xmath267 , and @xmath268 , where the corresponding production cross sections for @xmath12 tev are @xmath13 , @xmath14 , and @xmath15 fb , respectively . from our analysis , it is clear to see that the single production cross sections of vlqs are much larger than the pair production cross sections , which are through qcd processes . the dominant decay modes of the vlqs are @xmath16 and @xmath17 . each br can be 1/2 in our chosen scheme . for illustration , we estimate the significances for the channels proposed in eq . ( [ eq : signal ] ) . it is found that the significance for @xmath18 channel can be over @xmath19 . + * acknowledgments * g. aad _ et al . _ [ atlas collaboration ] , `` observation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc '' , phys . b * 716 * , 1 ( 2012 ) [ arxiv:1207.7214 [ hep - ex ] ] . s. chatrchyan _ et al . _ [ cms collaboration ] , `` observation of a new boson at a mass of 125 gev with the cms experiment at the lhc '' , phys . b * 716 * , 30 ( 2012 ) [ arxiv:1207.7235 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , jhep * 1512 * , 055 ( 2015 ) doi:10.1007/jhep12(2015)055 [ arxiv:1506.00962 [ hep - ex ] ] . v. khachatryan _ et al . _ [ cms collaboration ] , jhep * 1408 * , 173 ( 2014 ) [ arxiv:1405.1994 [ hep - ex ] ] ; v. khachatryan _ et al . _ [ cms collaboration ] , jhep * 1408 * , 174 ( 2014 ) [ arxiv:1405.3447 [ hep - ex ] ] ; v. khachatryan _ et al . _ [ cms collaboration ] , phys . b * 740 * , 83 ( 2015 ) [ arxiv:1407.3476 [ hep - ex ] ] . v. khachatryan _ et al . _ [ cms collaboration ] , phys . b * 749 * , 337 ( 2015 ) [ arxiv:1502.07400 [ hep - ex ] ] . the atlas collaboration , atlas - conf-2015 - 081 . m. aaboud _ et al . _ [ atlas collaboration ] , arxiv:1606.03833 [ hep - ex ] . cms collaboration [ cms collaboration ] , cms - pas - exo-15 - 004 . v. khachatryan _ et al . _ [ cms collaboration ] , arxiv:1606.04093 [ hep - ex ] . a. arhrib , r. benbrik , c. h. chen , m. gomez - bock and s. semlali , eur . j. c * 76 * , no . 6 , 328 ( 2016 ) doi:10.1140/epjc / s10052 - 016 - 4167 - 9 [ arxiv:1508.06490 [ hep - ph ] ] . f. del aguila , m. perez - victoria and j. santiago , jhep * 0009 * , 011 ( 2000 ) [ hep - ph/0007316 ] . a. atre , m. carena , t. han and j. santiago , phys . d * 79 * , 054018 ( 2009 ) [ arxiv:0806.3966 [ hep - ph ] ] . j. mrazek and a. wulzer , phys . d * 81 * , 075006 ( 2010 ) [ arxiv:0909.3977 [ hep - ph ] ] . g. cacciapaglia , a. deandrea , d. harada and y. okada , jhep * 1011 * , 159 ( 2010 ) [ arxiv:1007.2933 [ hep - ph ] ] . s. gopalakrishna , t. mandal , s. mitra and r. tibrewala , phys . d * 84 * , 055001 ( 2011 ) [ arxiv:1107.4306 [ hep - ph ] ] . f. j. botella , g. c. branco and m. nebot , jhep * 1212 * , 040 ( 2012 ) [ arxiv:1207.4440 [ hep - ph ] ] . y. okada and l. panizzi , adv . high energy phys . * 2013 * , 364936 ( 2013 ) [ arxiv:1207.5607 [ hep - ph ] ] . h. cai , jhep * 1302 * , 104 ( 2013 ) [ arxiv:1210.5200 [ hep - ph ] ] . g. cacciapaglia , a. deandrea , l. panizzi , s. perries and v. sordini , jhep * 1303 * , 004 ( 2013 ) [ arxiv:1211.4034 [ hep - ph ] ] . a. atre , m. chala and j. santiago , jhep * 1305 * , 099 ( 2013 ) [ arxiv:1302.0270 [ hep - ph ] ] . j. a. aguilar - saavedra , r. benbrik , s. heinemeyer and m. perez - victoria , phys . d * 88 * , no . 9 , 094010 ( 2013 ) [ arxiv:1306.0572 [ hep - ph ] ] . s. beauceron , g. cacciapaglia , a. deandrea and j. d. ruiz - alvarez , phys . d * 90 * , no . 11 , 115008 ( 2014 ) [ arxiv:1401.5979 [ hep - ph ] ] . a. k. alok , s. banerjee , d. kumar and s. u. sankar , arxiv:1402.1023 [ hep - ph ] . d. karabacak , s. nandi and s. k. rai , phys . b * 737 * , 341 ( 2014 ) [ arxiv:1405.0476 [ hep - ph ] ] . a. k. alok , s. banerjee , d. kumar , s. u. sankar and d. london , phys . d * 92 * , no . 1 , 013002 ( 2015 ) [ arxiv:1504.00517 [ hep - ph ] ] . n. vignaroli , phys . d * 91 * , no . 11 , 115009 ( 2015 ) [ arxiv:1504.01768 [ hep - ph ] ] . c. h. chen and t. nomura , phys . d * 92 * , no . 11 , 115021 ( 2015 ) [ arxiv:1509.02039 [ hep - ph ] ] . g. aad _ et al . _ [ atlas collaboration ] , phys . b * 718 * , 1284 ( 2013 ) [ arxiv:1210.5468 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , jhep * 1411 * , 104 ( 2014 ) [ arxiv:1409.5500 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , jhep * 1508 * , 105 ( 2015 ) [ arxiv:1505.04306 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , phys . d * 91 * , no . 11 , 112011 ( 2015 ) [ arxiv:1503.05425 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , jhep * 1510 * , 150 ( 2015 ) [ arxiv:1504.04605 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , phys . d * 92 * , no . 11 , 112007 ( 2015 ) [ arxiv:1509.04261 [ hep - ex ] ] . g. aad _ et al . _ [ atlas collaboration ] , arxiv:1510.02664 [ hep - ex ] . g. aad _ et al . _ [ atlas collaboration ] , arxiv:1602.06034 [ hep - ex ] . s. chatrchyan _ et al . _ [ cms collaboration ] , phys . b * 729 * , 149 ( 2014 ) [ arxiv:1311.7667 [ hep - ex ] ] . s. chatrchyan _ et al . _ [ cms collaboration ] , phys . * 112 * , no . 17 , 171801 ( 2014 ) [ arxiv:1312.2391 [ hep - ex ] ] . v. khachatryan _ et al . _ [ cms collaboration ] , arxiv:1507.07129 [ hep - ex ] . v. khachatryan _ et al . _ [ cms collaboration ] , phys . d * 93 * , no . 1 , 012003 ( 2016 ) [ arxiv:1509.04177 [ hep - ex ] ] . v. khachatryan _ et al . _ [ cms collaboration ] , jhep * 1506 * , 080 ( 2015 ) [ arxiv:1503.01952 [ hep - ex ] ] . olive et al . ( particle data group ) , chin . c , 38 , 090001 ( 2014 ) . a. j. buras and j. girrbach , jhep * 1203 * , 052 ( 2012 ) [ arxiv:1201.1302 [ hep - ph ] ] . g. aad _ et al . _ [ atlas collaboration ] , arxiv:1507.04548 [ hep - ex ] . s. chatrchyan et al . . [ cms collaboration ] , cms - pas - hig-14 - 009 g. aad _ et al . _ [ atlas collaboration ] , arxiv:1508.05796 [ hep - ex ] . s. chatrchyan _ et al . _ [ cms collaboration ] , phys . lett . * 112 * , no . 17 , 171802 ( 2014 ) [ arxiv:1312.4194 [ hep - ex ] ] . a. belyaev , n. d. christensen and a. pukhov , comput . phys . commun . * 184 * , 1729 ( 2013 ) [ arxiv:1207.6082 [ hep - ph ] ] . m. nadolsky , h. l. lai , q. h. cao , j. huston , j. pumplin , d. stump , w. k. tung and c .- p . yuan , phys . d * 78 * , 013004 ( 2008 ) [ arxiv:0802.0007 [ hep - ph ] ] . j. alwall _ et al . _ , jhep * 1407 * , 079 ( 2014 ) [ arxiv:1405.0301 [ hep - ph ] ] . a. alloul , n. d. christensen , c. degrande , c. duhr and b. fuks , comput . phys . commun . * 185 * , 2250 ( 2014 ) [ arxiv:1310.1921 [ hep - ph ] ] . c. s. deans [ nnpdf collaboration ] , arxiv:1304.2781 [ hep - ph ] . t. sjostrand , s. mrenna , p. z. skands , jhep * 0605 * , 026 ( 2006 ) . a. j. buras , d. buttazzo and r. knegjens , jhep * 1511 * , 166 ( 2015 ) [ arxiv:1507.08672 [ hep - ph ] ] . f. newson _ et al . _ , arxiv:1411.0109 [ hep - ex ] . a. romano , arxiv:1411.6546 [ hep - ex ] . v. khachatryan _ et al . _ [ cms and lhcb collaborations ] , nature * 522 * , 68 ( 2015 ) [ arxiv:1411.4413 [ hep - ex ] ] . r. aaij _ [ lhcb collaboration ] , jhep * 1602 * , 104 ( 2016 ) [ arxiv:1512.04442 [ hep - ex ] ] . c.h . chen and t. nomura , study of rare @xmath248 , @xmath211 , and @xmath249 meson decays in this model is in progress .

two triplet vector - like quarks ( vlqs ) with hypercharges of @xmath0 and one singlet scalar boson are embedded in the standard model ( sm ) to resolve the 750 gev diphoton excess . the constraints on the tree - level higgs- and @xmath1-mediated flavor - changing neutral currents are discussed in detail . besides the resolution of excess , it is found that the signal strength of diphoton higgs decay can have a @xmath2 deviation from the sm prediction and that the upper limits of the branching ratios for rare top - quark decays are @xmath3 . we find that the production cross section of a single vlq by electroweak processes is larger than that of vlq - pair by qcd processes . to explore the signals of the heavy vlqs at the lhc , we throughly analyze the production of single @xmath4 and @xmath5 via @xmath6 annihilations in @xmath7 collisions at @xmath8 tev . it is found that the electroweak production cross sections for @xmath9 , @xmath10 , and @xmath11 channels with @xmath12 tev can be @xmath13 , @xmath14 , and @xmath15 fb , respectively ; and the dominant decay modes are @xmath16 and @xmath17 . with adopting kinematic cuts , the significance for @xmath18 channel can be over @xmath19 . kias - p16026

congenital syngnathia ( cs ) is an unusual condition characterized by fusion of the jaw with inability to open the mouth at birth . fusion can be unilateral or bilateral or complete and range from simple mucosal bands ( synechiae ) to complete bony fusion ( synostosis ) . we present a case of a 2-day - old neonate with fusion of the maxillary and mandibular alveolar complex ( laster 's type 1b congenital maxillomandibular syngnathia ) along with tracheoesophageal fistula ( tef ) probably the first of its kind . a 2-day - old male neonate , preterm ( 36 weeks ) , normal delivery , weighing 2.0 kg , presented with a history of severely restricted mouth opening and frothing from mouth and nose and abdominal distention . the mother was healthy without any history of illness , trauma , or drug exposure . the baby was the first child , and there was no incidence of similar kind of anomalies in close family members . the child had a slit - like space of 56 mm between the upper and lower arches in the region of the central incisors with rest of the alveolar areas showing fusion preventing detailed intraoral examination [ figure 1 ] . radiological examination showed fusion of the upper and lower alveolar arches [ figure 2 ] . preoperative frontal view x - ray showing fusion of the maxillary and mandibular arches the patient was being given parenteral nutrition in view of reduced mouth opening and inability to pass infant feeding tube . the child had signs of aspiration pneumonitis ( rattling respiration , cough , and cyanosis ) and was rushed to emergency or to release the syngnathia under general anesthesia . a fiberoptic intubation through nasal route was performed using 2.2 mm ultrathin fiberoptic bronchoscope permitting passage of a 3.0 mm endotracheal tube ( ett ) . syngnathia was released transorally ; fusion on the left side was bony which was released by osteotome and mallet whereas scalpel blade was used to release the soft - tissue fusion on the right side . hemostasis was attained , and a collagen membrane dressing was given to cover the raw area . tongue , palate , and floor of the mouth were found to be anatomically normal after the release . no attempt at repair of tef repair was done in this surgical appointment which was subsequently repaired after 48 h under general anesthesia . unfortunately , the child developed septicemia likely due to previous aspiration pneumonitis and succumbed after 7 days . cs is a rare anomaly which presents as fusion of the jaws with inability to open the mouth at the time of birth . it can have varied presentations in maxillofacial complex ranging from simple fibrous union of alveolar ridges to bony fusion involving maxilla , mandible , temporomandibular joint , and even zygoma . have classified cs based on site and extent of fusion and its association with other craniofacial anomalies [ table 1 ] . the case discussed previously had fusion of the upper and lower alveolus without any craniofacial anomaly , i.e. , cleft , temporomandibular joint ( tmj ) ankylosis , or other hence was classified under laster 's type 1b congenital syngnathia . however , he had neck abnormality , i.e. , ctef . in our literature search ( pubmed central ( pmc ) , and google scholar ) , we did not come across any case of cs associated with ctef making this case a rare entity . laster 's classification of congenital syngnathia various theories have been proposed to explain the etiology of this anomaly . these include : persistence of buccopharyngeal membrane ( gorlin and goldman)oropharyngeal atresia secondary to persistence of buccopharyngeal membrane ( longacre)amniotic constriction bands which lead to pressure in the region of the developing first branchial arch ( burket)increasing period of contact between the alveoli due to the small jaw and decreased swallowing reflex ( walker and frase , humphrey)antenatal exposure to drugs such as meclizine , large dose vitamin a , which cause edema of the embryo and upsets skeletal growth ( king , kalter and warkaney ) . persistence of buccopharyngeal membrane ( gorlin and goldman ) oropharyngeal atresia secondary to persistence of buccopharyngeal membrane ( longacre ) amniotic constriction bands which lead to pressure in the region of the developing first branchial arch ( burket ) increasing period of contact between the alveoli due to the small jaw and decreased swallowing reflex ( walker and frase , humphrey ) antenatal exposure to drugs such as meclizine , large dose vitamin a , which cause edema of the embryo and upsets skeletal growth ( king , kalter and warkaney ) . therefore , a careful clinical and radiological examination forms an essential part in diagnosing cs . treatment of congenital intermaxillary syngnathia is surgical release under general or local anesthesia depending on the site and extent of fusion . blind nasal intubation is not preferred because of the risk of laryngeal edema and its sequelae . the use of interalveolar soft wedges has been recommended as a part of jaw physiotherapy to prevent the recurrence of the condition . parental counseling and periodic recall to assess the craniofacial growth and possible recurrences form an essential part in the management of such anomaly . a thorough literature search revealed that this is the first case of cs associated with tef . there is no established treatment protocol for such anomaly considering the relative rarity of the condition . the management team should be aware of the wide range of severity of syngnathia along with other possible congenital deformities and adopt a treatment plan according to the situation and general condition of the patient . furthermore , the parents must be counseled and informed about the surgical outcomes and associated comorbidities .

congenital syngnathia ( cs ) , first reported by burket in 1936 , is a rare condition , with < 50 reported cases and is associated with other conditions and syndromes . cs restricts mouth opening , causing difficulty in feeding , swallowing , and respiration . this report puts forth the clinical findings and management of this challenging condition in association with tracheoesophageal fistula in a neonate .

transplantation cures end - stage renal disease , and the only limitation to curing many more patients , some of whom die on the waiting list , is the lack of available organs . more than 100,000 patients require a kidney transplant , but the number of deceased donors has not risen to match the demand . the gap between potential recipients and organs available could be addressed either by listing fewer patients or by increasing the supply of donor organs . limiting access is not acceptable since any change in this direction would affect well - established listing indications . there would be strong resistance from patients and doctors , if we attempted to exclude individuals from the waiting list for kidneys based on age , race , level of illness , or the etiology of kidney failure . efforts to increase organ availability using deceased donors have been minimally effective , and the limited success has been achieved only by reducing the quality of the organs accepted for transplantation . various proposals to increase the number of deceased donors , including presumed consent , reimbursement to donor families , use of donors after cardiac death , and more liberal criteria for donor acceptance , have not substantially increased the existing number of deceased donors . to address these problems , we propose that living kidney donation , rather than deceased donation , becomes the first and preferred choice of patients and transplantation physicians for the treatment of end - stage renal disease ( esrd ) . we would recommend that living kidney donation be encouraged and promoted by the government and the transplantation community . the principal reasons for increasing the use of living kidney donors are as follows : the gap between supply and demand for organs continues to grow , that living kidney donors represent a much larger potential source of organs ( possibly even in the millions ) than deceased organ donors , and the outcomes of living donor kidney transplantation are significantly better than the ones of deceased organ transplantation . the maximum numbers of deceased organ donors have previously been estimated to be 12,000 to 15,000 per year . in the last decade , however , the number of living donors has decreased and that number remains below 6000 per year . these barriers include the unwillingness of donors to give an organ to strangers and the general reluctance of healthy people to accept health risks and undergo surgery and anesthesia to benefit others . we believe a further reason why the number of living donations is not increasing relates to the ambivalence within the transplantation community about whether living donation is ethical . dr francis moore , in whose program in 1954 the first successful kidney transplant was performed using a living donor , highlighted this ambivalence toward living donors when he wrote in 1964 : is it ever morally right and ethically acceptable to injure one person to help another ? because of these persistent ethical concerns , the prevailing consensus view in the transplantation community has been that living donation should be a second choice and should be considered only when no deceased organs are readily available or when there is an almost zero incidence of donor complications and a very low risk of mortality . a corollary is that living donation should never be openly promoted ahead of deceased donation but instead should be used as a last resort and often only if the donor volunteers without encouragement from the transplantation team . we believe the time has come to rethink this strategy of relying on deceased donation , an approach which is not meeting the increasing demand for kidney transplantation . but before we can move to the alternative strategy of encouraging living kidney donation , we must consider again the central question . is it ethical to use living unrelated kidney donors as the principal source of kidneys for transplantation ? and further , is it ethical to promote the use of living kidney donors ? further , living kidney donation is practiced widely in north america , europe , and especially in asia where deceased donation is not heavily relied upon . since 1954 , we estimate that more than 250,000 living kidney transplantations have been performed in more than 30 countries . this suggests that after 60 years , living kidney donation has been accepted on ethical grounds and on legal grounds by all of the world 's medical systems and societies . nevertheless , as we noted , living donation continues to be regarded by most western world centers , especially in europe , as a second choice ( except in asia ) compared to deceased organ donation . it is also clear that the lack of enthusiasm for living donation is not related to the benefits from the procedure . in almost all cases , in fact , the superior benefits of living compared to deceased donation are clear and proven . these benefits include decreased waiting time , better graft quality , the almost complete absence of the risk of disease transmission , the elective nature of the surgery , and most importantly , substantially better organ and recipient survival . according to data from the scientific registry of transplant recipients , the half - life of a kidney from a living donor is , on average , about 10 years longer than that of a kidney from a deceased donor . it is striking that deceased donor kidney transplantation is perhaps the only treatment we currently offer that has a demonstrated worse outcome than an alternative available therapy , living donor kidney transplantation . for those who continue to question the ethics of living donation , the central issue is donor risk . as dr thomas starzl wrote in 1985 commenting on the then high reported rate of complications : in view of such clinical information , is it ever ethical to encourage relatives to donate organs ? since the first successful living donor kidney transplant in 1954 , donor risks have decreased as donor nephrectomy has evolved from an open procedure to a laparoscopic procedure , as anesthesia and pain management have improved , and as safety measures for the donor have been regulated and implemented . in addition , donor coercion has decreased as informed consent and the use of donor advocates have become standards of care , and clinical outcomes have improved as data on donor morbidity and mortality have become publicly available . based on data from the scientific registry of transplant recipients , among 27,850 us living kidney donors between 2007 and 2011 , 32 ( 0.11% ) died within 2 years of donating . twelve of these deaths were attributed to medical reasons , 8 to suicide , 6 to homicide or accidental death , 4 to malignancy , and 2 from unknown causes . it seems reasonable to exclude the deaths due to malignancy and homicide / accidents and possibly suicide as well . with these exclusions , whether the deaths from suicide are related to the act of donation would require a careful analysis of the clinical and psychiatric history of these donors before and after donation . in a study published in 2010 , segev et al showed an even lower incidence of mortality among living donors : 0.03% in a population of 80,347 individuals with a median follow - up of 6.3 years . this mortality incidence was similar to that of a matched cohort of 9364 healthy individuals . the mortality rate in living organ donation is comparable to that of liposuction or scuba diving , both of which have a mortality of about 0.02% . while the mortality risk for living donors is not zero , it is low enough that the public , government regulators , and the professional community in every country have found the risk acceptable . immediate and long - term post - operative complications are the two components of donor morbidity risk . there is consistency in the reported incidence and type of perioperative and early post - operative morbidity . in a large , multi - center us study analyzing 3074 donors , major complications such as intra - operative injuries , pneumothorax , pulmonary embolus , myocardial infarction , acute renal failure , rhabdomyolysis , and congestive heart failure these data are very similar to those from large studies in norway and japan and single - center studies in the us . for long - term morbidity , the most essential component is the number of living donors who develop end - stage renal disease and require chronic dialysis or a kidney transplantation . specifically , is the number of esrd cases greater than would be expected from an age- and disease - matched cohort ? until very recently , the answer to this question was no . however , a recent publication compared the risk of esrd in 96,000 kidney donors with the risk in a healthy cohort of 93,000 non - donors . this recent study found an estimated lifetime risk of esrd to be 6.5 times higher in donors than in non - donors . the paper concluded that kidney donors had an increased relative risk of esrd although the magnitude of the absolute increased risk remained small , from 14 per 10,000 in healthy non - donors to 90 per 10,000 in healthy donors to 326 per 10,000 in unscreened non - donors . methodological problems with the study were commented on by gill and tonelli who concluded : the findings by muzaale and colleagues demonstrating the low absolute risk of esrd , also an analysis of donors in the us , should reassure future donors of the safety of living kidney donation . it is known that focusing on relative increases in risk ( rather than absolute increases in risk ) can unduly influence treatment decisions , especially for rare outcomes . given the limitations of the comparative analysis in the study by muzaale et al , it would be prudent for clinicians to emphasize the absolute risk of esrd in discussions with prospective living donors , ideally using a decision aid that will facilitate the process of obtaining informed consent . the other components of long - term morbidity after donation include the risk of developing hypertension , diabetes , or other health issues . several studies indicate that when the donor is carefully selected and existing morbidities , including high blood pressure , higher body mass index , or family history of renal disease , are firm exclusion criteria , the risk of developing any significant life - altering health problem is not different from that of any age - matched non - donor individual . other long - term studies raise the question of possible increase in cardiovascular risk and end - stage renal disease when different control groups are chosen . on the other hand , there is growing and clear evidence that hypertension , proteinuria , diabetes , and lower post - donation glomerular filtration rate are more common in african - american donors and in donors with a body mass index > 30 kg / m or with existing glucose intolerance . the studies cited in this paper support the view that in a properly selected donor , the quality of life and long - term health are not greatly affected by the act of donation . living donation is not associated with zero mortality but with an extremely low mortality and is not associated with no increased risk of esrd but with a small absolute risk of esrd in kidney donors . living questions have been raised about whether african - american donors had a higher risk of esrd than white donors . the recent paper cited above , by muzaale and his colleagues , reached the following conclusion : this difference [ in esrd ] was observed in both black and white individuals , with an estimated risk of 74.7 per 10,000 versus 23.9 per 10,000 black non - donors and an estimated risk of 22.7 per 10,000 white donors versus 0.0 white non - donors . in addition to recipient benefit , there are several other reasons that support living donor organ transplantation . living donor transplantation may prove to be more cost - effective than deceased organ transplantation , by consistently providing immediate graft function and lower organ acquisition fees . the fact that a living donor kidney has significantly longer half - life will decrease the number of patients requiring retransplantation increasing the number of organs for first time recipients . moreover , since kidney transplant becomes cost - effective compared to dialysis in the management of end - stage renal disease within 2 years of the transplant , the more kidney transplants performed , the greater the economic and clinical benefit for society . an increase in living donor transplantation in the united states also might have positive global effects . transplant tourism has deleterious effects on other countries health systems and has its own set of serious ethical issues . if the number of living donors increases in the us , the number of patients with end - stage renal disease who would seek surgical intervention outside the us would also decrease . we recommend re - examining the ethics of living donation so that we resolve our ambivalence and stop equivocating about its ethical acceptability . after 60 years of performing living kidney donor operations , and after more than a quarter of a million such operations , transplant centers around the world have affirmatively answered the question of whether they think living donor organ transplantation is ethical . we also recommend that health resources and services administration and united network for organ sharing modify their policies , policies that generally do not openly promote living kidney donation and consider making living donation rather than deceased donation the preferred and encouraged choice . we would urge expanding the process of paired living donor kidney exchanges and donor chains that involve both deceased and living kidney donors . since the seminal article on the ethics of paired kidney exchanges in 1997 there is already a system in place that aims to minimize risk and complications and that protects the donor at each step in the transplantation process . we recommend strengthening the consent process by using a uniform data - driven consent form valid for all centers . we also recommend that uniform clinical and psychological acceptance criteria for living donors be applied in all centers . these criteria should be based on the clinical characteristics of the donor for whom the safety profile is proven and known . it is essential that precise and up - to - date information about the risk of living donation continue to be gathered and provided to potential donors . clearly , we need a living donor registry to get the best data in the future . we should now initiate measures to promote living donation and to recruit more unrelated organ donors . this could be done through national advertising campaigns and by providing ethically acceptable incentives for living donation , including , for example , paid time off during evaluation and recovery , insurance coverage for all donor - related expenses , and free annual checkups . these would be simple , ethically acceptable steps to make living donation more widely used , convenient , and affordable . for those who continue to question the ethics of living donation , the central issue is donor risk . as dr thomas starzl wrote in 1985 commenting on the then high reported rate of complications : in view of such clinical information , is it ever ethical to encourage relatives to donate organs ? since the first successful living donor kidney transplant in 1954 , donor risks have decreased as donor nephrectomy has evolved from an open procedure to a laparoscopic procedure , as anesthesia and pain management have improved , and as safety measures for the donor have been regulated and implemented . in addition , donor coercion has decreased as informed consent and the use of donor advocates have become standards of care , and clinical outcomes have improved as data on donor morbidity and mortality have become publicly available . based on data from the scientific registry of transplant recipients , among 27,850 us living kidney donors between 2007 and 2011 , 32 ( 0.11% ) died within 2 years of donating . twelve of these deaths were attributed to medical reasons , 8 to suicide , 6 to homicide or accidental death , 4 to malignancy , and 2 from unknown causes . it seems reasonable to exclude the deaths due to malignancy and homicide / accidents and possibly suicide as well . with these exclusions , whether the deaths from suicide are related to the act of donation would require a careful analysis of the clinical and psychiatric history of these donors before and after donation . in a study published in 2010 , segev et al showed an even lower incidence of mortality among living donors : 0.03% in a population of 80,347 individuals with a median follow - up of 6.3 years . this mortality incidence was similar to that of a matched cohort of 9364 healthy individuals . the mortality rate in living organ donation is comparable to that of liposuction or scuba diving , both of which have a mortality of about 0.02% . while the mortality risk for living donors is not zero , it is low enough that the public , government regulators , and the professional community in every country have found the risk acceptable . immediate and long - term post - operative complications are the two components of donor morbidity risk . there is consistency in the reported incidence and type of perioperative and early post - operative morbidity . in a large , multi - center us study analyzing 3074 donors , major complications such as intra - operative injuries , pneumothorax , pulmonary embolus , myocardial infarction , acute renal failure , rhabdomyolysis , and congestive heart failure were reported in 4.2% of donors and minor complications in 6.4% . these data are very similar to those from large studies in norway and japan and single - center studies in the us . for long - term morbidity , the most essential component is the number of living donors who develop end - stage renal disease and require chronic dialysis or a kidney transplantation . specifically , is the number of esrd cases greater than would be expected from an age- and disease - matched cohort ? until very recently , the answer to this question was no . however , a recent publication compared the risk of esrd in 96,000 kidney donors with the risk in a healthy cohort of 93,000 non - donors . this recent study found an estimated lifetime risk of esrd to be 6.5 times higher in donors than in non - donors . the paper concluded that kidney donors had an increased relative risk of esrd although the magnitude of the absolute increased risk remained small , from 14 per 10,000 in healthy non - donors to 90 per 10,000 in healthy donors to 326 per 10,000 in unscreened non - donors . methodological problems with the study were commented on by gill and tonelli who concluded : the findings by muzaale and colleagues demonstrating the low absolute risk of esrd , also an analysis of donors in the us , should reassure future donors of the safety of living kidney donation . it is known that focusing on relative increases in risk ( rather than absolute increases in risk ) can unduly influence treatment decisions , especially for rare outcomes . given the limitations of the comparative analysis in the study by muzaale et al , it would be prudent for clinicians to emphasize the absolute risk of esrd in discussions with prospective living donors , ideally using a decision aid that will facilitate the process of obtaining informed consent . the other components of long - term morbidity after donation include the risk of developing hypertension , diabetes , or other health issues . several studies indicate that when the donor is carefully selected and existing morbidities , including high blood pressure , higher body mass index , or family history of renal disease , are firm exclusion criteria , the risk of developing any significant life - altering health problem is not different from that of any age - matched non - donor individual . other long - term studies raise the question of possible increase in cardiovascular risk and end - stage renal disease when different control groups are chosen . on the other hand , there is growing and clear evidence that hypertension , proteinuria , diabetes , and lower post - donation glomerular filtration rate are more common in african - american donors and in donors with a body mass index > 30 kg / m or with existing glucose intolerance . the studies cited in this paper support the view that in a properly selected donor , the quality of life and long - term health are not greatly affected by the act of donation . living donation is not associated with zero mortality but with an extremely low mortality and is not associated with no increased risk of esrd but with a small absolute risk of esrd in kidney donors . living questions have been raised about whether african - american donors had a higher risk of esrd than white donors . the recent paper cited above , by muzaale and his colleagues , reached the following conclusion : this difference [ in esrd ] was observed in both black and white individuals , with an estimated risk of 74.7 per 10,000 versus 23.9 per 10,000 black non - donors and an estimated risk of 22.7 per 10,000 white donors versus 0.0 white non - donors . mortality is the most feared complication from the act of donation . based on data from the scientific registry of transplant recipients , among 27,850 us living kidney donors between 2007 and 2011 twelve of these deaths were attributed to medical reasons , 8 to suicide , 6 to homicide or accidental death , 4 to malignancy , and 2 from unknown causes . it seems reasonable to exclude the deaths due to malignancy and homicide / accidents and possibly suicide as well . with these exclusions , whether the deaths from suicide are related to the act of donation would require a careful analysis of the clinical and psychiatric history of these donors before and after donation . in a study published in 2010 , segev et al showed an even lower incidence of mortality among living donors : 0.03% in a population of 80,347 individuals with a median follow - up of 6.3 years . this mortality incidence was similar to that of a matched cohort of 9364 healthy individuals . the mortality rate in living organ donation is comparable to that of liposuction or scuba diving , both of which have a mortality of about 0.02% . while the mortality risk for living donors is not zero , it is low enough that the public , government regulators , and the professional community in every country have found the risk acceptable . immediate and long - term post - operative complications are the two components of donor morbidity risk . there is consistency in the reported incidence and type of perioperative and early post - operative morbidity . in a large , multi - center us study analyzing 3074 donors , major complications such as intra - operative injuries , pneumothorax , pulmonary embolus , myocardial infarction , acute renal failure , rhabdomyolysis , and congestive heart failure these data are very similar to those from large studies in norway and japan and single - center studies in the us . for long - term morbidity , the most essential component is the number of living donors who develop end - stage renal disease and require chronic dialysis or a kidney transplantation . specifically , is the number of esrd cases greater than would be expected from an age- and disease - matched cohort ? until very recently , the answer to this question was no . however , a recent publication compared the risk of esrd in 96,000 kidney donors with the risk in a healthy cohort of 93,000 non - donors . this recent study found an estimated lifetime risk of esrd to be 6.5 times higher in donors than in non - donors . the paper concluded that kidney donors had an increased relative risk of esrd although the magnitude of the absolute increased risk remained small , from 14 per 10,000 in healthy non - donors to 90 per 10,000 in healthy donors to 326 per 10,000 in unscreened non - donors . methodological problems with the study were commented on by gill and tonelli who concluded : the findings by muzaale and colleagues demonstrating the low absolute risk of esrd , also an analysis of donors in the us , should reassure future donors of the safety of living kidney donation . it is known that focusing on relative increases in risk ( rather than absolute increases in risk ) can unduly influence treatment decisions , especially for rare outcomes . given the limitations of the comparative analysis in the study by muzaale et al , it would be prudent for clinicians to emphasize the absolute risk of esrd in discussions with prospective living donors , ideally using a decision aid that will facilitate the process of obtaining informed consent . the other components of long - term morbidity after donation include the risk of developing hypertension , diabetes , or other health issues . several studies indicate that when the donor is carefully selected and existing morbidities , including high blood pressure , higher body mass index , or family history of renal disease , are firm exclusion criteria , the risk of developing any significant life - altering health problem is not different from that of any age - matched non - donor individual . other long - term studies raise the question of possible increase in cardiovascular risk and end - stage renal disease when different control groups are chosen . on the other hand , there is growing and clear evidence that hypertension , proteinuria , diabetes , and lower post - donation glomerular filtration rate are more common in african - american donors and in donors with a body mass index > 30 kg / m or with existing glucose intolerance . the studies cited in this paper support the view that in a properly selected donor , the quality of life and long - term health are not greatly affected by the act of donation . living donation is not associated with zero mortality but with an extremely low mortality and is not associated with no increased risk of esrd but with a small absolute risk of esrd in kidney donors . living questions have been raised about whether african - american donors had a higher risk of esrd than white donors . the recent paper cited above , by muzaale and his colleagues , reached the following conclusion : this difference [ in esrd ] was observed in both black and white individuals , with an estimated risk of 74.7 per 10,000 versus 23.9 per 10,000 black non - donors and an estimated risk of 22.7 per 10,000 white donors versus 0.0 white non - donors . in addition to recipient benefit , there are several other reasons that support living donor organ transplantation . living donor transplantation may prove to be more cost - effective than deceased organ transplantation , by consistently providing immediate graft function and lower organ acquisition fees . the fact that a living donor kidney has significantly longer half - life will decrease the number of patients requiring retransplantation increasing the number of organs for first time recipients . moreover , since kidney transplant becomes cost - effective compared to dialysis in the management of end - stage renal disease within 2 years of the transplant , the more kidney transplants performed , the greater the economic and clinical benefit for society . an increase in living donor transplantation in the united states also might have positive global effects . transplant tourism has deleterious effects on other countries health systems and has its own set of serious ethical issues . if the number of living donors increases in the us , the number of patients with end - stage renal disease who would seek surgical intervention outside the us would also decrease . we recommend re - examining the ethics of living donation so that we resolve our ambivalence and stop equivocating about its ethical acceptability . after 60 years of performing living kidney donor operations , and after more than a quarter of a million such operations , transplant centers around the world have affirmatively answered the question of whether they think living donor organ transplantation is ethical . we also recommend that health resources and services administration and united network for organ sharing modify their policies , policies that generally do not openly promote living kidney donation and consider making living donation rather than deceased donation the preferred and encouraged choice . we would urge expanding the process of paired living donor kidney exchanges and donor chains that involve both deceased and living kidney donors . since the seminal article on the ethics of paired kidney exchanges in 1997 there is already a system in place that aims to minimize risk and complications and that protects the donor at each step in the transplantation process . we recommend strengthening the consent process by using a uniform data - driven consent form valid for all centers . we also recommend that uniform clinical and psychological acceptance criteria for living donors be applied in all centers . these criteria should be based on the clinical characteristics of the donor for whom the safety profile is proven and known . it is essential that precise and up - to - date information about the risk of living donation continue to be gathered and provided to potential donors . clearly , we need a living donor registry to get the best data in the future . we should now initiate measures to promote living donation and to recruit more unrelated organ donors . this could be done through national advertising campaigns and by providing ethically acceptable incentives for living donation , including , for example , paid time off during evaluation and recovery , insurance coverage for all donor - related expenses , and free annual checkups . these would be simple , ethically acceptable steps to make living donation more widely used , convenient , and affordable . at the present time , increasing the use of living donors offers the best solution to the organ shortage problem . the clinical questions raised when the first living donor kidney transplant was performed , involving donor risk , informed consent , donor protection , and organ quality , have been largely answered , thanks to the work of many physicians and surgeons , medical organizations such as the american society of transplant surgeons , and the federal government through the centers for medicare and medicaid services and the united network for organ sharing . we acknowledge that for certain categories of living donors the long - term follow - up data are incomplete or inconclusive , for example , for certain african - american donors . in this regard , we suggest that these donors will not be accepted until proper prospective long - term studies are concluded . we strongly encourage a wider utilization of living donation and recommend that living donation , rather than deceased donation , becomes the first choice for kidney transplantation . we believe that it is ethically sound to have living kidney donation as the primary source for organs when the mortality and morbidity risks to the donor are known and kept extremely low , when the donor is properly informed and protected from coercion , and when accepted national and local guidelines for living donation are followed .

abstractat the present time , increasing the use of living donors offers the best solution to the organ shortage problem . the clinical questions raised when the first living donor kidney transplant was performed , involving donor risk , informed consent , donor protection , and organ quality , have been largely answered . we strongly encourage a wider utilization of living donation and recommend that living donation , rather than deceased donation , become the first choice for kidney transplantation.we believe that it is ethically sound to have living kidney donation as the primary source for organs when the mortality and morbidity risks to the donor are known and kept extremely low , when the donor is properly informed and protected from coercion , and when accepted national and local guidelines for living donation are followed .

their copies numbers can rapidly increase by retrotransposition and serve as substrate for homologous recombinations in various categories of dna rearrangements including deletions , inversions , translocations , duplications and amplifications noted by ozouf - costaz et al . knowledge of the origin and function of these retrotransposons and of their role in the structure and organization of chromosomes in the teleost fish genomes is still very scarce and fragmented . two classes of transposable elements ( te ) are acknowledged among vertebrates : retrotransposons and transposons . the first class , known as retrotransposon , moves through the genome by the action of reverse transcriptase , an enzyme that can promote the synthesis of a dna strand from a rna primer , and is divided into autonomous , i.e. , ltr ( long - terminal repeat ) and non - ltr , in which lines ( long interspersed elements ) are part of the genome , and non - autonomous , in which the sines ( short interspersed elements ) are the representatives . fish genome contains all known types of transposable elements , and some of these have been mapped at the chromosome level . the retrotransposable elements of the retrotransposon class ( ltr ) in which can be highlighted the ty3/gypsy , ty1/copy , dirs1 retrotransposon and bel , are the most studied in fish species . retrotransposons described above , include 10 elements that display data regarding the location in fish chromosomes . among these are the elements rex ( rex1 , rex3 and rex6 ) which are retrotransposable elements characterized for the first time in the genome of the fish xiphophorus maculatus and appears to be the most abundant in different teleostei . in the order characiformes , little is known about the organization of the retrotransposon rex , and available data are only for erythrinus erythrinus . the rex1 element , represents a non - long - terminal - repeat ( non - ltr ) retrotransposons , related to the group cr1 ( chicken repeat ) , comprising a lines , and encodes a reverse transcriptase and an endonuclease apurnica / pyrimidine required for cleavage of the target sequence . thus , the objective of the present research is to isolate and map the retrotransposable element rex1 in the genome of five species of the genus prochilodus ( prochilodus argenteus , prochilodus brevis , prochilodus costatus , prochilodus lineatus and prochilodus nigricans ) by fluorescent in situ hybridization ( fish ) by studying occurrence of rex 1 retrotransposon in prochilodus genome and chromosomes and compare the obtained results with others teleost fish groups . all specimens of prochilodus ( p. argenteus , p. brevis , p. costatus , p. lineatus and p. nigricans ) cytogenetically analyzed exhibited a karyotypic constitution of 2n = 54 chromosomes . the amplification of the retrotransposable element rex1 in the genome of the species of prochilodus produced a band of approximately 600 bp for all analyzed species ( data not shown ) . analysis through the fluorescent in situ hybridization ( fish ) technique using the rex1 retrotransposons probes in chromosome preparations of the five prochilodus species ( fig . 1a e ) showed a dispersed pattern of the retrotransposable element rex1 throughout the genome of analyzed individuals . furthermore , the presence of small clusters in the telomeric and centromeric regions was regarded as a common feature in these prochilodus . the presence of these clusters , mainly in the centromeric regions , is coincident with the constitutive heterochromatin distribution pattern previously observed by c - banding for all specimens of these species . distribution pattern of the retrotransposable element rex1 in genome of ( a ) p. argenteus ; ( b ) p. brevis ) ; ( c ) p. costatus ; ( d ) p. nigricans and ( e ) p. lineatus species . chromosomal information on representatives of the genus prochilodus have revealed a conserved karyotypic structure of 2n = 54 chromosomes . all prochilodus cytogenetically analyzed in this study exhibited conserved chromosomal characteristics regarding the diploid number of 2n = 54 in accordance with literature data reported for these species . the evolutionary dynamics of the transposable elements in various groups , such as insects , fish , birds and mammals are extremely distinct . mammals genomes contain a large variety of transposable elements lineage types , while fish and drosophila lineages show various strains of these genomic elements , which are typically less abundant , but apparently more deleterious . in many insect and fish species , families of different strains of transposable elements with this variation in diversity and activity of transposable elements among various animal genomes is caused by the difference of the defense mechanisms of the host genome in opposition to the activities of the transposable elements . generally , the transposons have a sufficiently distinct organization among the species and are dispersed across the genome , usually occupying euchromatic regions , as already observed in humans and insects . this scattered pattern was also observed in this study in the five species of prochilodus analyzed with the rex1 retrotransposable element , as well as in species of the subfamily hypoptopomtinae using rex1 and rex3 ; in erythrinus erythrinus with rex3 ; in astatotilapia latifasciata with rex 1 and in some antarctic perciformes using the rex1 and rex3 elements . moreover , fish derived from the group of tetraodontiformes ( t. nigroviridis ) have an extremely compact genome , and the separation between poor and rich regions of gene segments is much evident according to fischer et al . and da silva et al . transposable elements in heterochromatin are apparently used as shelter , because the selection pressure is smaller in these regions noted by lippman , et al . as previously mentioned , rex elements are present in the genome of different species of teleosts . according to a review of retrotransposable use in fish genome mapping performed by ferreira et al . , it was observed that the rex elements exhibit different organizations among fish species . these elements were physically mapped in 28 species of fish . however , in 11 species , rex elements were organized in heterochromatic regions and in the other remaining 17 species , were scattered across the genome , as observed in the present study . a noteworthy example of rex presence in fish heterochromatic regions is attributed to cichlidae family , which different rex elements analysis revealed a compartmentalization in pericentric heterochromatic regions described by gross et al . similar to that observed in representatives of the antarctic fish species notothenia coriiceps . additionally , in cichlidae family , more specifically in oreochromis niloticus ( in nile tilapia genome ) , transposable elements were generally found scattered throughout the genome . this pattern , preferably scattered across the euchromatic regions , was also found in five species of the genus prochilodus ( p. argenteus , p. brevis , p. costatus , p. lineatus and p. nigricans ) , subject of this study , using the retrotransposable element rex1 ( fig . however , some small clusters were found in the heterochromatic regions , such as in the centromeres of some chromosome pairs , in the telomeric regions of all samples analyzed . the distribution pattern of the retrotransposons rex1 in prochilodus enabled one to observe a scattered pattern common among the five species ( fig . 1a e ) , i.e. , the rex 1 retrotransposable element displays a conserved characteristic for this genus , as previously proposed by pauls and bertollo using other cytogenetic markers . oftentimes , rex retrotransposable elements were found scattered throughout the genome of the species and more intensely in the chomosome euchromatic regions . however , some blocks of these transposable elements are coincident with heterochromatic regions , suggesting that the distribution pattern of these retroelements may be distinct in different orders of fish , which corroborates with the observed in prochilodus , where such retrotransposable elements were scattered throughout the genome , but featured a preferential accumulation in the constitutive heterochromatin regions . transposable elements are generally more abundant in the heterochromatin of several genomes and their presence in these regions seems to be common among multicellular eukaryotes . despite some discrepancies , plausible explanations about the relationship between the retrotransposable elements and heterochromatin become reasonable : tes tend to accumulate in regions with low recombination rates as a consequence of their removal from the region with high recombination rates , whereas ectopic recombination could have more deleterious effects ; there are more tes eliminations in gene - rich regions because of their potential deleterious effects when inserted within genes ; the high expression of te - encoded products might have negative consequences for the genome due to cell cost . thus , these tes would be eliminated from the region with high expression levels ; tes could accumulate in the heterochromatin as a consequence of their functional involvement in the maintenance of specific genomic regions , such as the pericentromeric and telomeric region . although the currently available information on the structural organization , evolution and functional behavior of tes in the fish genome are still very fragmented and restricted to few species , the data contribute to clarify the understanding of transposable elements distributions in prochilodus genome comparing the results with those obtained in teleostei order fish groups . it was collected 20 specimens of p. lineatus from wild populations of mogi - guau river , parana basin , pirassununga , sp , brazil , and also 17 specimens of p. nigricans from the araguaia river ( to ) , tocantins - araguaia basin , brazil . for the present study , it was also purchased 30 specimens of p. costatus from the tropical aquaculture fish farm , municipality of propri , ( se ) , brazil ; 6 individuals of p. argenteus from the so francisco river ( mg ) , brazil ; and finally , 5 specimens of p. brevis ( collected in the dnocs dam ( departamento de obras contra a seca ) ( rn ) , brazil . the chromosome preparations were obtained by mitotic stimulation method , direct in vitro preparations of anterior kidney , and direct in vivo preparations of anterior kidney . fluorescence in situ hybridization ( fish ) was performed according to pinkel et al . using the retrotransposon probe rex1 obtained by pcr ( polymerase chain reaction ) from amplifications of the genomic dna of p. lineatus utilizing the primers 1 : rtx1-f1 ( 5-ttc tcc agt ggc ctt caa cac c-3 ) and rtx1r1 ( 5-ttc ctt aaa aaa tag agt ctg ctc-3 ) . the rex1 probe was labeled with digoxigenin-11-dutp later detected with an antibody conjugated with rhodamine , providing the red color by the pcr ( polymerase chain reaction ) technique , according to the roche manufacturer s instructions . dna was hybridized at 37c overnight in a moist chamber ( 0.3 g of denatured probe , 50% formamide , 10 mg ml of dextran sulfate ; 2xssc , 5 mg / ml of salmon sperm dna ) . afterwards , slides were counterstained with dapi ( 4,6-diamidino-2-phenylindole ) and examined under a fluorescence photomicroscope ( bx 61 , olympus ) equipped with the olympus dp70 cooled digital camera .

transposable elements are repetitive dna sequences comprising a group of segments able to move and carry sequences within the genome . studies involving comparative genomics have revealed that most vertebrates have different populations of transposable elements with significant differences among species of the same lineage . few studies have been conducted in fish , the most diverse group of vertebrates , with the objective to locate different types of transposable elements . therefore , this study proposed to map the retrotransposable element rex1 applying fluorescent in situ hybridization ( fish ) in five species of the genus prochilodus ( prochilodus argenteus , prochilodus brevis , prochilodus costatus , prochilodus lineatus and prochilodus nigricans ) . after the application of the rex1 probe , scattered markings were found throughout the genome of analyzed species , and also the presence of small clusters located in the centromeric and telomeric regions coincident with the heterochromatin distribution pattern . this was the first description of the retrotransposable element rex1 in prochilodus genome seeking for a better understanding of the distribution pattern of these retrotransposons in the genome of teleost fish .

SECTION 1. ENTRIES OF CERTAIN HIGH-DENSITY FIBERBOARD-CORE, LAMINATE PANELS EXCEEDING 0.8 GRAMS PER CUBIC CENTIMETER ENTERED FROM 2001 THROUGH 2002. (a) In General.--Notwithstanding section 514 of the Tariff Act of 1930 (19 U.S.C. 1514) or any other provision of law, the Bureau of Customs and Border Protection shall, not later than 90 days after the receipt of the request described in subsection (b), liquidate or reliquidate the entries described in subsection (d) at a rate of duty of 1.9 cents per kilogram plus 1.5 percent ad valorem. (b) Request.--Liquidation or reliquidation may be made under subsection (a) with respect to an entry described in subsection (d) only if a request is filed with the Bureau of Customs and Border Protection not later than 90 days after the date of the enactment of this Act. (c) Refund of Amounts Owed.--Any amounts owed by the United States pursuant to the liquidation or reliquidation of an entry described in subsection (d) (including interest from the date of entry) shall be refunded not later than 90 days after the date of such liquidation or reliquidation. (d) Affected Entries.--The entries referred to in subsection (a) are as follows: Entry number Date of entry 101-6067581-4........................ 12/06/01 101-6072768-0........................ 12/17/01 101-6076465-9........................ 12/26/01 101-6078268-5........................ 12/28/01 112-9204436-8........................ 11/08/01 112-9207122-1........................ 11/14/01 112-9212066-3........................ 11/23/01 112-9217748-1........................ 11/29/01 112-9222234-5........................ 12/07/01 112-9222322-8........................ 12/14/01 112-9232908-2........................ 12/28/01 101-6042267-0........................ 10/20/01 101-6046215-5........................ 10/26/01 101-6049709-4........................ 11/01/01 101-6053384-9........................ 11/08/01 101-6056568-4........................ 11/15/01 101-6060617-3........................ 11/26/01 101-6065845-5........................ 12/04/01 101-4318096-5........................ 08/30/01 101-6019565-6........................ 08/31/01 101-6024049-4........................ 09/14/01 101-6027091-3........................ 09/20/01 101-6032267-2........................ 10/01/01 101-6033874-4........................ 10/05/01 101-6038184-3........................ 10/12/01 112-9029349-6........................ 03/10/01 112-9015640-4........................ 02/20/01 112-8980633-1........................ 01/30/01 112-9029854-5........................ 03/19/01 112-8971889-0........................ 01/13/01 112-8965535-7........................ 01/09/01 112-8970083-1........................ 01/09/01 AN9-0023828-6........................ 12/21/01 AN9-0023712-2........................ 12/14/01 AN9-0021265-3........................ 04/21/01 AN9-0023459-0........................ 11/27/01 AN9-0021028-5........................ 03/27/01 AN9-0020680-4........................ 03/08/01 AN9-0020627-5........................ 02/27/01 AN9-0023628-0........................ 12/10/01 112-9244755-3........................ 01/24/02 101-6089106-4........................ 01/24/02 112-9228782-7........................ 12/23/01 112-9102227-4........................ 06/24/01 112-9107614-8........................ 07/02/01 112-9114175-1........................ 07/05/01 112-9125239-2........................ 07/14/01 112-9132858-0........................ 07/28/01 112-9147711-4........................ 08/22/01 112-9157821-8........................ 09/08/01 112-9237227-2........................ 01/05/02 112-9166917-3........................ 09/16/01 112-9177774-5........................ 10/01/01 112-9178097-0........................ 09/29/01 112-9182039-6........................ 10/06/01 112-9183096-5........................ 10/13/01 112-9186179-6........................ 10/19/01 112-9196504-3........................ 10/27/01 112-9199438-1........................ 11/03/01 112-9199781-4........................ 11/05/01 112-9206482-0........................ 11/16/01 112-9208738-3........................ 11/16/01 112-9214038-0........................ 11/30/01 112-9214117-2........................ 11/25/01 112-9226168-1........................ 12/15/01 112-9055805-4........................ 04/21/01 112-9066463-9........................ 05/06/01 112-9071158-8........................ 05/12/01 112-9076192-2........................ 05/19/01 112-9082389-6........................ 05/26/01 112-9086554-1........................ 06/02/01 112-9097310-5........................ 06/16/01 112-9230980-3........................ 12/23/01 112-9237490-6........................ 01/04/02 101-6100047-5........................ 02/16/02 112-9259037-8........................ 02/16/02 112-9252990-5........................ 02/08/02 101-6108076-6........................ 02/27/02 112-9265107-1........................ 02/21/02 101-6104454-9........................ 02/22/02 112-9260622-4........................ 02/21/02 101-6107515-4........................ 02/28/02 112-9267793-6........................ 02/28/02 112-9268578-0........................ 03/07/02 101-6115432-2........................ 03/14/02 101-6115850-5........................ 03/14/02 101-6115854-7........................ 03/14/02 112-9273372-1........................ 03/14/02 101-6123042-9........................ 03/28/02 112-9281901-7........................ 03/28/02 101-6127822-0........................ 04/05/02 112-9285248-9........................ 04/04/02 112-9290639-2........................ 04/11/02 112-9251613-4........................ 02/02/02 112-9251643-1........................ 02/02/02 112-9255395-4........................ 02/09/02 AN9-0024441-7........................ 03/04/02 AN9-0024512-5........................ 03/09/02 112-9270377-3........................ 03/09/02 112-9266286-2........................ 02/25/02 112-9269399-0........................ 03/02/02 112-9256164-3........................ 02/18/02

Directs the Bureau of Customs and Border Protection to provide for the liquidation or reliquidation of certain entries relating to high-density fiberboard-core, laminate panels exceeding 0.8 grams per cubic centimeter entered from 2001 through 2002.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Community Development Investment Enhancements Act of 2006''. SEC. 2. ENHANCING THE AUTHORITY FOR NATIONAL BANKS TO MAKE COMMUNITY DEVELOPMENT INVESTMENTS. (a) National Banks.--The last sentence in the paragraph designated as the ``Eleventh.'' of section 5136 of the Revised Statutes of the United States (12 U.S.C. 24) is amended-- (1) by striking ``10 percent'' each place such term appears and inserting ``15 percent''; and (2) by adding at the end the following new sentence: ``The preceding standards and limitations apply to each investment under this paragraph made by a national bank directly and by its subsidiaries.''. (b) State Member Banks.--The last sentence of the 23rd undesignated paragraph of section 9 of the Federal Reserve Act (12 U.S.C. 338a) is amended-- (1) by striking ``10 percent'' each place such term appears and inserting ``15 percent''; and (2) by adding at the end the following new sentence: ``The preceding standards and limitations apply to each investment under this paragraph made by a State member bank directly and by its subsidiaries.''. SEC. 3. INVESTMENTS BY FEDERAL SAVINGS ASSOCIATIONS AUTHORIZED TO PROMOTE THE PUBLIC WELFARE. (a) In General.--Section 5(c)(3) of the Home Owners' Loan Act (12 U.S.C. 1464(c)) is amended by adding at the end the following new subparagraph: ``(D) Direct investments to promote the public welfare.-- ``(i) In general.--A Federal savings association may make investments designed primarily to promote the public welfare, including the welfare of low- and moderate- income communities or families through the provision of housing, services, and jobs. ``(ii) Direct investments or acquisition of interest in other companies.--Investments under clause (i) may be made directly or by purchasing interests in an entity primarily engaged in making such investments. ``(iii) Prohibition on unlimited liability.--No investment may be made under this subparagraph which would subject a Federal savings association to unlimited liability to any person. ``(iv) Single investment limitation to be established by director.--Subject to clauses (v) and (vi), the Director shall establish, by order or regulation, limits on-- ``(I) the amount any savings association may invest in any 1 project; and ``(II) the aggregate amount of investment of any savings association under this subparagraph. ``(v) Flexible aggregate investment limitation.--The aggregate amount of investments of any savings association under this subparagraph may not exceed an amount equal to the sum of 5 percent of the savings association's capital stock actually paid in and unimpaired and 5 percent of the savings association's unimpaired surplus, unless-- ``(I) the Director determines that the savings association is adequately capitalized; and ``(II) the Director determines, by order, that the aggregate amount of investments in a higher amount than the limit under this clause will pose no significant risk to the affected deposit insurance fund. ``(vi) Maximum aggregate investment limitation.--Notwithstanding clause (v), the aggregate amount of investments of any savings association under this subparagraph may not exceed an amount equal to the sum of 15 percent of the savings association's capital stock actually paid in and unimpaired and 15 percent of the savings association's unimpaired surplus. ``(vii) Investments not subject to other limitation on quality of investments.--No obligation a Federal savings association acquires or retains under this subparagraph shall be taken into account for purposes of the limitation contained in section 28(d) of the Federal Deposit Insurance Act on the acquisition and retention of any corporate debt security not of investment grade. ``(viii) Applicability of standards to each investment.--The standards and limitations of this subparagraph shall apply to each investment under this subparagraph made by a savings association directly and by its subsidiaries.''. (b) Technical and Conforming Amendments.--Section 5(c)(3)(A) of the Home Owners' Loan Act (12 U.S.C. 1464(c)(3)(A)) is amended to read as follows: ``(A) [Repealed]''. Passed the House of Representatives September 27, 2006. Attest: KAREN L. HAAS, Clerk.

Community Development Investment Enhancements Act of 2006 - Amends the Revised Statues of the United States and the Federal Reserve Act to increase from 10% to 15% of its capital stock actually paid in and unimpaired, and from 10% to 15% of its unimpaired surplus fund, the maximum aggregate community development investments of a national banking association or a state member bank, including its subsidiaries. Applies such limits to each such investment. Amends the Home Owners' Loan Act to authorize a federal savings association to make investments designed primarily to promote the public welfare, including the welfare of low- and moderate-income communities or families through the provision of housing, services, and jobs (community development investments). Permits such investments to be made directly or by purchase of interests in an entity primarily engaged in making such investments. Prohibits a federal savings association from making an investment which would subject it to unlimited liability to any person. Requires the Director of the Office of Thrift Supervision to establish: (1) the amount any savings association may invest in any one project; and (2) the aggregate amount of investment of any savings association. Restricts the aggregate amount of investment of any savings association, subject to specified determinations made by the Director. Prohibits the maximum aggregate amount of investments of any savings association from exceeding the same 15% of its capital stock actually paid in and unimpaired and 15% of its unimpaired surplus as imposed by this Act on national banking associations and state member banks.

let the single missing scalar of the standard model ( sm ) be called the higgs " , to stick to a debatable misdeed . because the idea is so venerable , one may have grown insensitive to how special a higgs boson would be . its quantum numbers must be those of the vacuum , which its field permeates . the boson itself would be the vibrational quantum * of * the vacuum , not a mere quantum * in * the vacuum , or in some other substance . the couplings of the higgs to quarks and leptons are proportional to their masses . so are its couplings to @xmath0 and @xmath1 , a fact that , within the sm , is in a sense verified . a significantly precise direct measurement of the higgs couplings to fermions is not an easy task . even for the heaviest of them , the top quark , the required integrated luminosity is large , as illustrated by the atlas collaboration on the left of fig . [ brsdisco ] . decays into @xmath2 , @xmath1 , @xmath3 and @xmath4 pairs as functions of @xmath5 . right : an example of discovery and scrutiny plot of a sm scalar with @xmath6 gev , not specially chosen for effect . @xmath7 as in fig . [ cmvariables ] . [ brsdisco],scaledwidth=100.0% ] in the past , given a newly discovered particle , one had to figure out its @xmath8 quantum numbers ( or its disrespect of the super - indexed ones ) to have it appear in the particle data book . publication in the new york times was not considered that urgent , nor was it immediate for bad news . times have changed . yet , two groups @xcite have thoroughly studied the determination of the quantum numbers and coupling characteristics of a putative signal at the lhc , that could be the elementary scalar of the sm , or an _ impostor _ thereof , both dubbed @xmath9 here . the golden channel " for this exercise is @xmath10 or @xmath11 , where @xmath12 is an @xmath13 or a @xmath14 , and @xmath15 denotes that , for @xmath16 , one of the @xmath1s is off - shell " . for a review of previous work on the subject , see e.g. @xcite . to be realistic ( ? ) let me consider two competing teams . they are working at a @xmath17 collider of energy @xmath18 tev , luminosity @xmath19 @xmath20 s@xmath21 and snowmass factor of 3 ( on average , things work well 1/3 of the time ) . the sm is correct , @xmath6 gev and the estimates of signals and backgrounds are reliable . as the number of events increases , team 2 would then gather evidence for an @xmath22 peak at the rate shown on the right of fig . [ brsdisco ] . team 1 is additionally checking that , indeed , the object has @xmath23 . t1 reaches discovery " ( @xmath24 significance ) some three months before t2 . the horizontal error bars , dominated by fluctuations in the expected background , tell us that the two teams are * only * @xmath25 apart ( iff from two different experiments ! ) . but that means the probability of t1 ( from experiment @xmath26 ) being 3 months ahead of t2 ( from experiment @xmath27 ) is @xmath28% ( @xmath29% for @xmath30 ) . the odds for winning with dice , if your competitor lets you win for 4 out of the 6 faces are also 66% . if the stakes are this high , would you not play ? it is interesting to compare the two @xmath9-identity - revealing integrated luminosities in figs . [ brsdisco ] , more so since event numbers on its right refer to the chain @xmath31 and are approximately quadrupled when all @xmath32 channels are considered . standard signal and background cross sections times branching ratios , @xmath33 , were used in fig . [ brsdisco ] . in discussing @xmath9 impostors we accept that they should not be distinguished from a sm @xmath9 on @xmath33 grounds , which , for all impostors , are hugely model - dependent . the technique to be used to measure @xmath8 for a putative @xmath9 signal has some pedigree . its quantum - mechanical version ( called nowadays the matrix element " method ) capitalizes on the entanglement of the two @xmath1 polarizations and dates back at least to the first ( correct ) measurements of the correlated @xmath34 polarizations in parapositronium ( @xmath35 ) decay @xcite . the technique is even older , as it actually consists in comparing theory and observations . the art is in exploiting _ a maximum of the information _ from both sides . pair - production and leptonic decay . [ cmvariables],scaledwidth=60.0% ] gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] + gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] gev , for all relevant angles and @xmath37 . the trigger and energy thresholds , resolutions and angular coverage are those of a typical " detector . [ shaping],title="fig:",scaledwidth=30.0% ] the event - by - event information on the channel at hand is very large , some of it is illustrated in fig . [ cmvariables ] , for the decay chain @xmath31 , with @xmath9 brought to rest . the angular variables @xmath38 describe @xmath1-pair production relative to the annihilating @xmath39 or @xmath40 pair . the variables @xmath41 are the @xmath1-pair decay angles . for fixed @xmath38 , @xmath41 , and @xmath37 ( the mass of a lepton pair if its parent @xmath1 is off - shell ) that is all there is : none less than six beautifully entangled variables ( @xmath42 $ ] is also measured event by event , @xmath5 is traditionally extracted from a fit to the @xmath42 $ ] distribution ) . real detectors have limited coverage in angles and momenta , they mis - shape " the theoretical distributions in the quantities just described . an example for a realistic detector and an unrealistic flat expectation is illustrated on the right of fig . [ shaping ] . for an @xmath9 with @xmath43 , the distribution in @xmath38 is flat , so that its inclusion ( in this case ) would seem like an overkill . not so ! detector - shaping effects and the correlations between the angular variables conspire to make the use of the full machinery a necessity @xcite . distribution . middle : splot of the @xmath44 distribution of the signal " events , compared with the montecarlo truth and the ( detector - shaped ) expected distribution , for @xmath23 . right : same as middle , for the background " events . [ splots],scaledwidth=100.0% ] there is a wonderful s - weighing " method for ( much of ) the exercise of ascertaining the lhc s potential to select the preferred hypothesis for an observed @xmath9 candidate . consider an @xmath42 $ ] distribution with an @xmath9 peak at 250 gev , constructed with the standard expectations for signal and background , as in fig . [ splots ] . performing a maximum - likelihood fit to this distribution one can ascertain the probability of events in each @xmath42 $ ] bin to be signal or background . next one can astutely ( and even statistically optimally ) reweigh the events into signal " and background " categories , to study their distributions in other variables @xcite , such as @xmath45 or @xmath46 in fig . [ splots ] . in this pseudo - experiment one knows the montecarlo truth " , compared in the figure with the impressive s - outcomes and the detector - shaped expectation . we use the full ( correlated ) distributions in all mentioned variables , but @xmath5 , to confront data " with different hypothesis . the astute reader has noticed that i have not mentioned the @xmath47 and @xmath48 distributions of the @xmath49 or @xmath50 pair ( be it an @xmath9 signal or the irreducible background ) . event by event , one can undo the corresponding boost but , to ascertain the detector - shaping effects , as in fig . [ shaping ] , for all the various sm or impostor @xmath9 objects , one has to use a specific event generator . we have done it @xcite , but we chose to pessimize " our results in this respect , _ not _ exploiting the ( @xmath51 ) distributions as part of the theoretical expectations ( which for impostors would be quite model - dependent ) . one reason is that the relevant parton distribution functions ( pdfs ) will be better known by the time a higgs hunt becomes realistic . another is that one can use the s - weigh technique to extract and separately plot the ( @xmath52 ) distribution for signal and background . the production of a sm @xmath9 but not that of most conceivable impostors is dominated by an extremely theory - laden process : gluon fusion via a top loop . as a first step it is preferable * to see * whether or not the ( @xmath52 ) distribution of the s - sieved signal events is that expected for @xmath39 fusion , as opposed to @xmath40 annihilation . the answer would be fascinating . the most general lorentz - invariant couplings of @xmath53 particles to the polarization vectors @xmath54 and @xmath55 of two @xmath1s of four - momenta @xmath56 and @xmath57 are given by the expressions : @xmath58 the vertex for @xmath59 is cumbersome . the quantities @xmath60 can be taken to be real , but for small absorptive effects . the expressions can be used to derive the distribution functions @xmath61 allowing one to determine the spin of an @xmath9 and the properties of the @xmath62 coupling . to give some @xmath43 examples : in the sm only @xmath63 is nonvanishing . for @xmath64 only @xmath65 . if @xmath66 and @xmath67 ( or @xmath68 ) @xmath69 , the @xmath62 vertex violates @xmath70 ( or @xmath71 ) . for a composite scalar " @xmath72 . while team 1 members are trying to establish the significance of the discovery of an object of specified properties ( as in fig . [ brsdisco ] , right ) , they may , with a few extra lines of code , be extracting much more information from the same data set , by asking leading questions , nlqs , nnlqs ... , whose answers are decreasingly statistically significant . , the sm in this case ) in favour of the right one ( @xmath73 ) . left and right : @xmath73 is @xmath74 , for @xmath75 and 350 gev . middle : @xmath73 is @xmath76 , @xmath6 gev . [ results1],scaledwidth=100.0% ] , with the hypotheses @xmath77 and @xmath78 , once interchanged . [ results2],scaledwidth=100.0% ] the quintessential lq is which of two hypothesis describes the data best , assuming that one of them is right . if the hypotheses are simple " ( contain no parameters to be fit ) the neyman - pearson lemma guarantees that the test is _ universally most powerful_. three examples are given in fig . [ results1 ] . on its left and right it is seen that it is easy " ( it takes a few tens of events ) to rule out the sm , if the observed resonance is an @xmath75 or 350 gev vector . on its middle , we see that , if the object is an axial vector , it would be much harder . this it is not due to the differing @xmath79 , but to the choice @xmath6 gev . for masses close to the @xmath80 threshold , the level arm provided by the lepton three - momenta is short , and the differences between _ pdfs _ is diminished . in fact , as an answer to a nlq , we have shown that , except close to threshold , it is easy " to tell any @xmath43 from any @xmath81 object , no matter how general their @xmath62 couplings are @xcite . in fig . [ results2 ] we see that it is easy , if the sm is right , to exclude @xmath82 at @xmath83 gev , but not at 200 . we also see that the interchange of right and wrong hypotheses leads to very similar expectations . [ result],scaledwidth=100.0% ] on the right of fig . [ result ] is the answer to a nnlq . we have assumed that a composite @xmath23 higgs has been found and parametrized its @xmath49 coupling by an angle @xmath84 . the measured value of @xmath85 is seen to be the input one , but for 50 events the uncertainties on what the input was , to be read horizontally , are large . for this case of a specific @xmath8 , but a complicated coupling , the various terms in the @xmath86 are not distinguishable on grounds of their properties under @xmath70 and @xmath71 . they do strongly interfere for specific values of @xmath85 , and the results of fig . [ result ] are not easy to obtain , requiring a full feldman - cousins belt construction @xcite . given a small data set constituting an initial discovery , one might settle for a stripped - down analysis . the cost of such a sub - optimal choice is shown on the left of fig . [ result ] for @xmath5@xmath87@xmath88 gev , illustrating the discrimination between the @xmath89 and @xmath90 hypotheses for likelihood definitions that exploit different sets of variables . n - dimensional _ pdfs _ in the variables @xmath91 are denoted @xmath92 , while @xmath93 is constructed from one - dimensional _ pdfs _ for all variables , ignoring ( erroneously ) their correlations . @xmath94 are _ pdfs _ including the variables @xmath95 and their correlations , but with the hypothesis @xmath90 represented by a _ pdf _ in which the variables @xmath96 have been integrated out . the likelihood @xmath97 performs badly even relative to @xmath98 , which uses fewer angular variables . the two differ only in that the first construction implicitly assumes a uniform @xmath99 coverage of the observed leptons ( an assumption customary in the literature ) as if the muon @xmath100 and @xmath47 analysis requirements did not depend on the @xmath38 angular variables . gev , integrated in all variables but @xmath101 and @xmath46 . left : the correct @xmath102 . right : the approximation " @xmath103 . [ results3],scaledwidth=100.0% ] treating the correlated angular variables as uncorrelated , as in the @xmath93 example of fig . [ result ] , not only degrades the discrimination significance but would lead to time - dependent , ultimately wrong conclusions . assume , for example , the sm with @xmath104 gev . let the data be fit to either a fully correlated _ pdf _ or an uncorrelated one . the projections of the corresponding theoretical _ pdfs _ , involving only the variables cos@xmath105 and cos@xmath106 , are illustrated in fig . [ results3 ] . on the left ( right ) of the figure we see @xmath107 $ ] ( @xmath108$]@xmath109@xmath110 $ ] ) . with limited statics insufficient to distinguish between the correlated and uncorrelated distributions the correct conclusion will be reached : the data are compatible with the sm . but , as the statistics are increased , the data will significantly deviate from the @xmath108\times p[{\rm cos}\,\theta_2]$ ] distribution , and a false rejection of the sm hypothesis would become increasingly supported . the difference between @xmath107 $ ] and @xmath108$]@xmath109@xmath110 $ ] is _ precisely _ what an unbelieving einstein called _ spooky action at a distance_. but , mercifully for physicists , the lord is subtle * and * perverse . i have alleged , by way of example , that for a fixed detector performance and integrated luminosity ( and no extra swiss francs ) it pays to have _ ab initio _ an analysis combining discovery and scrutiny . this is arguably true for many physics items other than @xmath111 . they readily come to mind .

consider the day when an invariant mass peak , roughly compatible with the higgs " , begins to emerge , say at the lhc , ... and may you see that day . there will be a difference between discovery and scrutiny . the latter would involve an effort to ascertain what it is , or is not , that has been found . it turns out that the two concepts are linked : scrutiny will naturally result in deeper knowledge is * this * what you were all looking for ? but may also speed up discovery . = 1 [ 1999/12/01 v1.4c il nuovo cimento ]

UPDATED: Video emerges showing taser used by Tuscaloosa Police on UA student Video has emerged of an apparent arrest of a University of Alabama student that ended in use of a taser and police club last night. According to multiple sources, the incident took place at an apartment complex near Buffalo Phil's last night after police were summoned to respond to a noise complaint. In the videos, a Tuscaloosa Police officer stands in the door of an apartment, speaking with several people located in the apartment. Many are filming the officer. The officer is asked multiple times whether anyone is being arrested or detained, and eventually indicates that one male is under arrest, but does not say under what charges. The Crimson White reached out to the tased individual. He declined comment. Multiple videos can be viewed here, here, here and here. The Crimson White has reached out to the Tuscaloosa Police Department for comment. If you have any information on this incident, please email [email protected]. UPDATE: The City of Tuscaloosa tweeted that videos of the arrest have been forwarded to internal affairs. UPDATE: The Tuscaloosa Police Department released a statement saying the incident occurred Nov. 8 at 3:19 a.m. and was a result of a loud music call. "A full investigation of the circumstances that are depicted in these videos will be conducted and all appropriate measures taken to ensure the integrity of the Tuscaloosa Police Department in serving the citizens of Tuscaloosa," the statement read. UPDATE(12:25 p.m., 11/09/15): The University released a statement saying they are aware of the incident and are concerned for the welfare of all students, particularly those who were arrested. "We have reached out to provide support to them, and we will continue to provide services they need," the statement read. The statement confirmed that three UAPD officers responded to a TPD officer's call for emergency assistance. They are reviewing the officers' actions. Students who have been impacted, the statement said, should call the University's Counseling Center at 205-348-3863. UPDATE(3:14 p.m., 11/09/15) In a press conference held at 2 p.m. Monday, TPD Chief of Police Steven Anderson confirmed that the department would be conducting an internal investigation into the events of the tasing incident on Saturday. "There was a lot of video that came from the individuals that were inside the apartment, and several of the officers have body cameras, and so we're going over a lot of video footage and so it's gonna take us a while," Anderson said. Three of the responding officers have already been placed on paid administrative leave in response to the event and will remain on leave until the completion of the investigation, Anderson said. He declined to name the three officers but confirmed that they were the officer who initially responded to the call and the officers who tased and clubbed the male individual in the video. Anderson asked that the public be patient and allow the department to conduct the investigation. "What I want [the public] to understand is that we've got a long way to go on this investigation," Anderson said. "Just because we've initially put three officers on administrative leave, by no means means that we're at the end of the investigation, we're done... We're going to be taking a look at the actions of each and every officer that responded to that location to determine if those officers are operating outside of our policies and procedures or outside of law, and that's what we feel like we need to do." Anderson was unable to give details as to how many officers responded to the incident or how many were wearing body cameras. UPDATE(5:40 p.m., 11/09/15) Lt. Teena Richardson of the Tuscaloosa Police Department released a statement naming Matthew Gimlin Macia, 22, Brandon James Williford, 21, and Caroline Elizabeth Giddis, 22, as the students arrested in the incident. Macia is charged with obstructing governmental operations and resisting arrest, Williford is charged with obstructing governmental operations, harrassment and resisting arrest, and Giddis is charged with obstructing governmental operations and harassment. UPDATE(11:19 a.m., 11/10/15) Chief Steven D. Anderson of the Tuscaloosa Police Department released a statement naming Officer James Kent, Officer Phillip Champion and Officer Gregory Pimm as the officers placed on administrative leave pending further investigation into their actions. "For the safety and security of the officers and their families only their names are being released at this time," the release read. ||||| TUSCALOOSA, Ala. (AP) — Three police officers were suspended with pay Monday after videos posted online showed officers using a stun gun and baton to break up a post-football game party and arrest three University of Alabama students. This Nov. 8, 2015 photo provided by Tuscaloosa Police Department shows Caroline Elizabeth Giddis. Several police officers were suspended with pay Monday, Nov. 9, after videos posted online showed officers... (Associated Press) This Nov. 8, 2015 photo provided by Tuscaloosa Police Department shows Brandon James Williford. Several police officers were suspended with pay Monday, Nov. 9, 2015, after videos posted online showed... (Associated Press) This Nov. 8, 2015 photo provided by Tuscaloosa Police Department shows Matthew Gimlin Macia. Several police officers were suspended with pay Monday, Nov. 9, after videos posted online showed officers... (Associated Press) Tuscaloosa police Chief Steve Anderson said he was "deeply disturbed" by what he saw in the videos and disappointed in the response of the officers, who were responding to a noise complaint. The incident occurred at an apartment building about a block from Bryant-Denny Stadium, where Alabama defeated Louisiana State University a few hours before the arrests. Residents said fans celebrated into the early morning hours. The videos, from varying angles, show a Tuscaloosa officer at the apartment's door, arguing for several minutes with occupants who refuse to exit. "Please let go of him. You are illegally entering," one of the young men says while an officer tries to lead another person out of the apartment, located within yards of a row of off-campus bars popular with Alabama students. The person gets away from the officer and goes back inside, and the officer follows him inside as voices get louder. After nearly two minutes of discussion and arguing, officers enter the residence and drag out two young men and a screaming woman. An officer uses a stun gun on at least one of the men; another officer hits him repeatedly with what appears to be a baton. Anderson told a news conference the officers on paid leave include one who used a stun gun on a student. The second officer hit a person with a police baton, and the third was the officer who responded to the initial call, the chief said. Their names haven't been released. A police statement identified the three students as 21-year-old Brandon James Williford, of Collierville, Tennessee; and two 22-year-olds, Matthew Gimlin Macia, of John Creeks, Georgia, and Caroline Elizabeth Giddis, of Collierville, Tennessee. All three are charged with obstructing governmental operations. Williford is also charged with harassment and resisting arrest; Macia also is charged with resisting; and Giddis is also charged with harassment. Williford and Giddis did not immediately respond to email messages. An email address for Macia could not be found. Officers were called on the noise complaint about 3:20 a.m. Sunday. Discarded beer cans, bottles and a pair of underwear still littered the building's walkways Monday afternoon. Residents of the apartment building said partiers were out late celebrating Alabama's win when police arrived. "We were downstairs when the first officer rolled up, and then they cut the music and everyone's like 'Oh, looks like they're about to tell us to shut it down,'" said Devin McDade, 22. McDade said he and his friends were in another apartment on the second floor of the building and opened the door when they heard a commotion outside. "We thought it was someone getting in a fight, then we just see all these cops yanking them out. As soon as we opened the door we heard the Taser going off," McDade said. The university said three of its officers responded after a Tuscaloosa officer requested emergency assistance. The school said it was reviewing whether its officers acted properly and was offering unspecified services to students who were involved. ||||| Updated at 3:55 p.m. to include the names of the students and the charges they face. Three Tuscaloosa police officers are on paid leave after they were seen using a Taser stun gun and baton on students during a noise complaint early Sunday morning in what the chief called a "black eye" for the department and the city. Chief Steve Anderson today said more officers could be placed on leave as what promises to be an exhaustive and lengthy investigation continues. The officers placed on leave are the first officer to arrive on the scene, the officer who used the Taser on a student and the officer who used the nightstick, he said. The first officer who arrived on the scene and was seen at the doorway in the multiple videos made public is an eight-year veteran. The officer who used the Taser has 12 years on the force, and the officer who repeatedly struck the student with the baton has two years on the TPD. The officers' names have not been released. Police were reportedly called to 12th Avenue Place Apartments on Frank Thomas Avenue about 3 a.m. Sunday on a noise complaint. What happened next is unclear, but multiple videos taken from both inside and outside of the apartment made their way across social media. The video shows an officer talking to those inside the apartment at the front door, and those inside refusing to exit the apartment. The students questioned whether they were being arrested or detained, and whether the officers were within their rights to search the apartment. Officers ended up going into the apartment. In one of the videos, one of the officers tells those inside the apartment to "Shut the (expletive) up." When told the incident was being videotaped, he replied, "I don't give a (expletive)." At least a dozen officers quickly responded to the scene. A witness told AL.com the scene was chaotic. "They had a girl and two boys on the ground,'' she said. "They were all screaming and everybody was videoing it." "It all happened extremely quickly, and I'm still shaken by the images that will forever be on my mind," said Patrick Weaver, a student who witnessed the events from a nearby apartment. "I've always been taught to respect authorities, but I believe that respect should be extended. "I believe in professionalism, and I don't believe that those police officers displayed that when they were screaming profane statements at those involved and us that were just bystanders that observed this awful incident. It's very concerning and most UA students would agree that we are very anxious and nervous to be around police right now. I'm praying for all involved and that justice would be served regardless of who side that is that wins. There needs to be a revolution in how the public and the police officers in our country interact with each other," Weaver said. One of the young men was taken outside the apartment and then hit with a Taser stun gun, and struck repeatedly with an officer's nightstick. Matthew Gimlin Macia, 22, of Johns Creek, Ga. was arrested on charges of obstructing governmental operations and resisting arrest; Brandon James Williford, 21, of Tennessee was arrested on charges of obstructing governmental operations, harassment and resisting arrest. Caroline Elizabeth Giddis, 22, of Tennessee was arrested on charges of obstructing governmental operations and harassment. All three are students. The officers were from the Tuscaloosa Police Department and The University of Alabama Police Department. Anderson released this statement Sunday night: "The City of Tuscaloosa and the Tuscaloosa Police Department have been made aware of videos regarding an incident that occurred on November 8, 2015 at 3:19 a.m. that were a result of a loud music call. A full investigation of the circumstances that are depicted in these videos will be conducted and all appropriate measures taken to ensure the integrity of the Tuscaloosa Police Department in serving the citizens of Tuscaloosa." University officials released a statement on Monday: "We are aware of the incident and we remain very concerned about the welfare of all students who were there, especially those who were arrested. We have reached out to provide support to them, and will continue to provide services they need. We can confirm that three UAPD officers responded to a TPD officer's call for emergency assistance that morning, and we are reviewing their actions to verify they acted appropriately. We encourage other students who have been impacted by this matter to contact the university's Counseling Center at 205-348-3863." At today's press conference, Anderson said he immediately ordered an investigation. "Needless to say, once I started watching watching it, I was deeply disturbed by what I saw,'' the chief said. The police staff met first thing Monday morning. He said Internal Affairs investigators will review all of the video submitted to them from the incident, as well as body camera video from the officers on the scene. He said he didn't have an exact count of how many officers responded to the apartment, but said the majority were wearing body cameras. He said police have already conducted some interviews, but added, "We've got a long way to go." "We're going to take a look at each and every officer's actions,'' Anderson said. "We're going to do an open and honest investigation and be transparent." "We take this very seriously. I take it very personally," he said. Anderson said he's spent 21 years helping to make the Tuscaloosa Police Department one that is respected. "I don't want to see that reputation destroyed by a careless or sensesless act,'' he said. The chief pleaded for patience. "This investigation does not move at the speed of the Internet,'' he said. "With a little bit of patience, we're going to get there. We're going to do everything we can to rebuild the public trust." "Do not be afraid of calling the Tuscaloosa Police Department,'' he said. "Do we always get it right? No, but there's no need to fear us or fear our officers." Anderson said if a police officer knocks on your door and you come to the door, it becomes a consensual contact. However, he said, "No the officer cannot just go in." He said he plans to add more training for his officers, including how to deal with escalating confrontation and what is, and isn't, allowed under the Fourth Amendment. "I take it personal,'' he said. "I ask myself if as a leader, have I failed my department?"

– The chief of police in Tuscaloosa, Ala., says the department and the city have a "black eye" after what he sees as the deeply disturbing arrest of three University of Alabama students early Sunday morning. Video posted online shows a city police officer standing in an apartment doorway arguing with a student before police drag two men and a woman out of the apartment, using a Taser and a baton on one man, the Crimson White reports. Chief Steven Anderson says there will be an internal investigation, and three officers, including the man first seen in the video and the man who used the Taser, have been suspended with pay. The incident happened hours after Alabama defeated Louisiana State University, and police say they were following up a noise complaint. The three students, Brandon Williford, Matthew Macia, and Caroline Giddis, face charges that include obstructing governmental operations, reports the AP. Anderson says complaints about the heavy-handed treatment of the students are being taken very seriously and he doesn't want the department's reputation to be ruined by a "careless or [senseless] act," AL.com reports. "Do not be afraid of calling the Tuscaloosa Police Department,'' he says. "Do we always get it right? No, but there's no need to fear us or fear our officers." (A student violently arrested for smoking on campus is suing a college in Illinois.)

SECTION 1. SHORT TITLE. This Act may be cited as the ``Veterans Appeals Assistance and Improvement Act of 2015''. SEC. 2. PROGRAM OF FINANCIAL ASSISTANCE FOR SUPPORT OF PROGRAMS THAT FURNISH LEGAL ASSISTANCE TO VETERANS SEEKING REVIEW BY UNITED STATES COURT OF APPEALS FOR VETERANS CLAIMS. (a) In General.--Chapter 59 of title 38, United States Code, is amended by adding at the end the following new section: ``Sec. 5906. Program of financial assistance for support of programs that furnish legal assistance to veterans seeking review by United States Court of Appeals for Veterans Claims ``(a) In General.--The United States Court of Appeals for Veterans Claims shall establish a program for the provision of financial assistance (through grant or contract made, to the maximum extent feasible) to facilitate the furnishing of legal and other assistance, without charge, through programs described in subsection (b), for veterans and other persons who are unable to afford the cost of legal representation in connection with decisions to which section 7252(a) of this title may apply or with other proceedings in the United States Court of Appeals for Veterans Claims. ``(b) Programs Described.--Programs described in this subsection are programs that furnish case screening and referral, training and education for attorney and related personnel, and encouragement and facilitation of pro bono representation by members of the bar and law school clinical and other appropriate programs, such as veterans service organizations, and through defraying expenses incurred in providing representation to persons described in subsection (a). ``(c) Legal Services Corporation.--(1) The United States Court of Appeals for Veterans Claims shall carry out subsection (a) by entering into an interagency agreement with the Legal Services Corporation. The agreement shall specify that the Corporation shall carry out the financial assistance program described in subsection (a). ``(2) Grants or contracts awarded under the financial assistance program described in subsection (a) shall be made by the Legal Services Corporation pursuant to a reimbursable payment from the Court in accordance with this section. ``(3) The Legal Services Corporation may receive a reimbursable payment from the Court for the purpose of providing the financial assistance described in subsection (a). ``(d) Limitation on Use of Funds.--No funds appropriated or otherwise made available to carry out this section may be used for the payment of attorney's fees. ``(e) Authorization of Appropriations.--There is authorized to be appropriated to carry out this section $3,000,000 for each of fiscal years 2015 through 2018.''. (b) Clerical Amendment.--The table of sections at the beginning of chapter 59 is amended by inserting after the item relating to section 5905 the following new item: ``5906. Program of financial assistance for support of programs that furnish legal assistance to veterans seeking review by United States Court of Appeals for Veterans Claims.''. SEC. 3. PROGRAM OF FINANCIAL ASSISTANCE FOR SUPPORT OF PROGRAMS THAT FURNISH LEGAL ASSISTANCE TO VETERANS SEEKING REVIEW BY BOARD OF VETERANS' APPEALS. (a) In General.--Chapter 59 of title 38, United States Code, as amended by section 2(a), is further amended by adding at the end the following new section: ``Sec. 5907. Program of financial assistance for support of programs that furnish legal assistance to veterans seeking review by Board of Veterans' Appeals ``(a) In General.--The Secretary shall establish a program for the provision of financial assistance (through grant or contract made, to the maximum extent feasible) to facilitate the furnishing of legal and other assistance, without charge, through programs described in subsection (b), to veterans and other persons who are unable to afford the cost of legal representation in connection with decisions to which section 7104 of this title may apply or with other proceedings of the Board of Veterans' Appeals. ``(b) Programs Described.--Programs described in this subsection are programs that furnish case screening and referral, training and education for attorney and related personnel, and encouragement and facilitation of pro bono representation by members of the bar and law school clinical and other appropriate programs, such as veterans service organizations, and through defraying expenses incurred in providing representation to persons described in subsection (a). ``(c) Legal Services Corporation.--(1) The Secretary shall carry out subsection (a) by entering into an interagency agreement with the Legal Services Corporation. The agreement shall specify that the Corporation shall carry out the financial assistance program described in subsection (a). ``(2) Grants or contracts awarded under the financial assistance program described in subsection (a) shall be made by the Legal Services Corporation pursuant to a reimbursable payment from the Secretary in accordance with this section. ``(3) The Legal Services Corporation may receive a reimbursable payment from the Secretary for the purpose of providing the financial assistance described in subsection (a). ``(d) Limitation on Use of Funds.--No funds appropriated or otherwise made available to carry out this section may be used for the payment of attorney's fees. ``(e) Authorization of Appropriations.--There is authorized to be appropriated to carry out this section $3,000,000 for each of fiscal years 2015 through 2018.''. (b) Clerical Amendment.--The table of sections at the beginning of chapter 59, as amended by section 2(b), is further amended by inserting after the item relating to section 5906 the following new item: ``5907. Program of financial assistance for support of programs that furnish legal assistance to veterans seeking review by Board of Veterans' Appeals.''. SEC. 4. EXPEDITED TREATMENT OF UNREASONABLY DELAYED CLAIMS. (a) In General.--Section 7112 of title 38, United States Code, is amended to read as follows: ``Sec. 7112. Expedited treatment of remanded or unreasonably delayed claims ``(a) In General.--The Secretary shall take such actions as may be necessary to provide for the expeditious treatment by the Board of any claim that-- ``(1) is remanded to the Secretary by the Court of Appeals for Veterans Claims; or ``(2) has been subjected to unreasonable or excessive delay. ``(b) Unreasonable or Excessive Delay.--For purposes of this section, a claim shall be presumed to have been subjected to unreasonable or excessive delay if the claim has been pending before the Board for eight years or more.''. (b) Clerical Amendment.--The table of sections at the beginning of chapter 71 of such title is amended by striking the item relating to section 7112 and inserting the following new item 7112: ``7112. Expedited treatment of remanded or unreasonably delayed claims.''. SEC. 5. COMPTROLLER GENERAL OF THE UNITED STATES REVIEW OF APPEALS OF DECISIONS OF SECRETARY OF VETERANS AFFAIRS REGARDING CLAIMS FOR DISABILITY COMPENSATION. (a) In General.--Not later than 180 days after the date of the enactment of this Act, the Comptroller General of the United States shall-- (1) complete a review of the processing of appeals of decisions of the Secretary of Veterans Affairs regarding claims for compensation under chapters 11 and 13 of title 38, United States Code; and (2) submit to Congress a report on the review completed under paragraph (1). (b) Elements.--The review required by subsection (a)(1) shall include the following: (1) Assessment of the regional offices of the Department of Veterans Affairs, the Board of Veterans' Appeals, and the United States Court of Appeals for Veterans Claims. (2) Examination of prolonged delays in processing appeals described in subsection (a)(1) and assessment of whether reviews of such appeals are meeting statutory requirements for timeliness. (3) Recommendations for such legislative and administrative action as the Comptroller General considers appropriate to improve the processing of such appeals.

Veterans Appeals Assistance and Improvement Act of 2015 This bill directs the U.S. Court of Appeals for Veterans Claims to establish a financial assistance program to provide legal and other assistance without charge for veterans and other persons seeking Court review who are unable to afford legal representation costs. (Programs include case screening and referral, training for attorney and related personnel, and facilitation of pro bono representation by members of the bar and law school clinical and other programs.) The Department of Veterans Affairs (VA) shall establish a financial assistance program to provide legal and other assistance without charge to veterans and other persons seeking review by the Board of Veterans' Appeals who are unable to afford legal representation costs. The Court and the VA shall each carry out such programs through an interagency agreement with the Legal Services Corporation. The Corporation may receive a reimbursable payment from the Court or VA for providing such financial assistance. Funds may not be used for the payment of attorney's fees. VA shall provide for the expeditious treatment by the Board of any claim that: (1) is remanded to VA by the Court, or (2) has been pending before the Board for eight years or more. The Government Accountability Office shall review the processing of appeals of VA decisions regarding service-connected disability and dependency and indemnity compensation claims.

chiral eft describes the interactions between nucleons at momentum scales of the order of the pion mass @xmath4 based on the symmetries of qcd @xcite . the resulting nuclear forces are organized in a systematic expansion in powers of @xmath5 , where @xmath6 denotes the breakdown scale , leading to a typical expansion parameter @xmath7 for nuclei . at a given order this includes contributions from one- or multi - pion exchanges that govern the long- and intermediate - range parts and from short - range contact interactions . the short - range couplings are fit to few - body data and thus capture all short - range effects relevant at low energies . in particular , chiral eft provides a systematic basis to investigate many - body forces and their impact on few- and many - body systems @xcite . in addition , it is possible to estimate theoretical uncertainties in the eft . an important feature of chiral eft is the consistency of two - nucleon ( nn ) and three - nucleon ( 3n ) interactions . this predicts the two - pion - exchange parts of the leading ( n@xmath8lo ) 3n forces , leaving only two low - energy couplings @xmath9 , @xmath10 that encode pion interactions with short - range nn pairs and short - range three - body physics . at the next - order , all many - body interactions are predicted parameter - free with many new structures @xcite . this makes the application of n@xmath0lo 3n and 4n forces very exciting . this is especially the case , because 3n forces have been found to be key for neutron matter @xcite and for neutron - rich nuclei @xcite , see , e.g. , the recent work on the calcium isotopes @xcite . the physics of neutron matter ranges from universal properties at low densities @xcite to the densest matter in neutron stars . for neutrons , the @xmath11 parts of n@xmath8lo 3n forces do not contribute due to the pauli principle and the pion coupling to the nucleon spin ( also the @xmath12 two - pion - exchange part does not contribute due to the isospin structure ) @xcite . therefore , all three- and four - neutron forces are predicted to n@xmath0lo . to study these , we recently presented the first calculation of the neutron - matter energy that includes all nn , 3n , and 4n interactions consistently to n@xmath0lo @xcite . the largest contributions to the neutron - matter energy arise from nn interactions . in refs . @xcite we studied the perturbative convergence of all existing nn potentials at n@xmath8lo and at n@xmath0lo of epelbaum , glckle , and meiner ( egm ) @xcite with cutoffs @xmath13 , @xmath14 , @xmath15 , @xmath16 , and @xmath17 , where @xmath18 and @xmath19 denote the cutoff in the lippmann - schwinger equation and in the two - pion - exchange spectral - function regularization , respectively ; as well as the available n@xmath0lo nn potentials of entem and machleidt ( em ) @xcite with cutoffs @xmath20 and @xmath21 . to study the perturbative convergence of the different nn potentials , we calculated the hartree - fock as well as second- and third - order energies , only including particle - particle diagrams , with both free and hartree - fock single - particle energies . the results for nn and n@xmath8lo 3n forces are shown in fig . [ fig : convergence ] for the perturbative nn interactions for a 3n cutoff @xmath22 and a particular choice of @xmath23 , @xmath24 , although the general picture is unchanged for other coupling values . the bands result from using a free to a hartree - fock single - particle spectrum . the n@xmath0lo egm potentials with cutoffs @xmath25 and @xmath26 exhibit only small energy changes from second to third order . this indicates that these potentials are perturbative for neutron matter . for the em @xmath27 potential the difference between second and third order is larger compared to the egm potentials . since this potential is most commonly used in nuclear structure calculations , we include it in our complete n@xmath0lo calculation . the perturbative convergence for these potentials in neutron matter is similar to renormalization - group - evolved interactions in nuclear matter @xcite . we have also studied in fig . [ fig : convergence ] the pounders n@xmath8lo nn potential @xcite , which is found to be perturbative as well . in addition , there are in - medium chiral perturbation theory schemes that treat the fermi momentum as an explicit scale @xcite . the larger - cutoff n@xmath0lo egm @xmath28 and @xmath29 potentials as well as the em @xmath21 potential are not used in our calculations because they show large changes from second to third order @xcite . this demonstrates that these interactions are nonperturbative . the n@xmath0lo egm @xmath29 potential is not used because it breaks wigner symmetry ( @xmath30 ) at the interaction level ( as discussed in ref . @xcite ) . the subleading n@xmath0lo 3n forces have been derived recently @xcite . they can be grouped into five topologies , where the latter two depend on the nn contacts @xmath31 : @xmath32 @xmath33 , @xmath34 , and @xmath35 denote the long - range two - pion - exchange , the two - pion one - pion - exchange , and the pion - ring 3n interactions , respectively @xcite . the terms @xmath36 and @xmath37 are the short - range two - pion - exchange contact 3n interaction and 3n relativistic corrections @xcite . the n@xmath0lo 4n forces have been derived in refs . @xcite and in general depend on the contact @xmath38 , but in neutron matter the @xmath38-dependent parts do not contribute . there are seven 4n topologies that lead to non - vanishing contributions . in neutron matter only two three - pion - exchange diagrams ( in ref . @xcite named @xmath39 and @xmath40 ) and the pion - pion - interaction diagram ( @xmath41 ) contribute @xcite . the n@xmath0lo many - body interactions are evaluated in the hartree - fock approximation , which is expected to be reliable for neutron matter @xcite . we show the individual contributions of the 3n and 4n forces in fig . [ fig : individualnm ] , where the bands correspond to the 3n/4n cutoff variation @xmath42 . the n@xmath0lo two - pion - exchange expectation value ( panel 1 ) sets the expected scale of n@xmath0lo 3n interactions . compared to this , we find relatively large expectation values in the @xmath34 , @xmath35 , and @xmath36 topologies . this could indicate that in these topologies @xmath43 contributions shifted to n@xmath44lo are expected to be important @xcite . the 3n relativistic corrections and the contributions from n@xmath0lo 4n forces are small ( see also ref . however , also for 4n forces additional larger contributions from @xmath43 excitations may arise at n@xmath44lo @xcite . the complete n@xmath0lo result for neutron matter is shown in the left panel of fig . [ fig : n3lo ] , which includes all nn , 3n , and 4n interactions to n@xmath0lo @xcite . at saturation density , we obtain for the energy per particle @xmath45 . this range is based on different nn potentials , a variation of the couplings @xmath46 , @xmath47 @xcite , which dominates the total uncertainty , a 3n/4n - cutoff variation @xmath48 , and the uncertainty in the many - body calculation . the neutron - matter energy in fig . [ fig : n3lo ] is in very good agreement with nlo lattice results @xcite and qmc simulations @xcite at very low densities ( see also the inset ) . at nuclear densities , we compare our n@xmath0lo results with variational calculations based on phenomenological potentials ( apr ) @xcite , which are within the n@xmath0lo band , but do not provide theoretical uncertainties . in addition , we compare the density dependence with results from auxiliary field diffusion mc ( afdmc ) calculations ( gcr ) @xcite based on nuclear force models adjusted to a symmetry energy of @xmath49 . we also compare the convergence from n@xmath8lo to n@xmath0lo in the same calculational setup . for this comparison , we only consider the egm potentials with cutoffs @xmath25 and @xmath26 . this leads to an n@xmath0lo energy range of @xmath50 per particle at @xmath51 . for the n@xmath8lo band in the right panel of fig . [ fig : n3lo ] , we have estimated the theoretical uncertainties in the same way , and find an energy of @xmath52 per particle at @xmath51 . the two bands overlap but the range of the band is only reduced by a factor of @xmath53 in contrast to the @xmath54 expected from the eft power counting . we attribute this to @xmath43 effects ( see the discussion in refs . quantum monte carlo methods have not been used with chiral eft interactions due to nonlocalities in their present implementation in momentum space . nonlocalities are difficult to handle in qmc @xcite . in the momentum - space interactions , there are two sources of nonlocalities : first , due to regulator functions that lead to nonlocal interactions upon fourier transformation , and second , due to contact interactions that depend on the momentum transfer in the exchange channel @xmath55 and from @xmath55-dependent parts in pion - exchange contributions beyond n@xmath8lo . for applications in qmc , we have developed local chiral eft interactions in ref . @xcite . to avoid regulator - generated nonlocalities for the long - range pion - exchange parts , we use the local coordinate - space expressions for the lo one - pion - exchange as well as nlo and n@xmath8lo two - pion - exchange interactions @xcite and regulate them directly in coordinate space using the function @xmath56 , which smoothly cuts off interactions at short distances @xmath57 while leaving the long - range parts unchanged @xcite . so , @xmath58 takes over the role of the cutoff @xmath18 in momentum space . to remove the @xmath55-dependent contact interactions to n@xmath8lo , we make use of the freedom to choose a basis of short - range operators in chiral eft interactions ( similar to fierz ambiguities ) . at lo , one usually considers the two momentum - independent contact interactions @xmath59 . however , it is equivalent to choose any two of the four operators @xmath60 , and @xmath61 , with spin and isospin operators @xmath62 , because there are only two s - wave channels due to the pauli principle . it is a convention in present chiral eft interactions to neglect the isospin dependence , which is then generated from the exchange terms @xcite . we use this freedom to keep at nlo ( order @xmath63 ) an isospin - dependent @xmath64 contact interaction and an isospin - dependent @xmath65 tensor part in favor of a nonlocal @xmath66 contact interaction and a nonlocal @xmath67 tensor part . this leads to the following seven linearly independent contact interactions at nlo that are local @xcite , @xmath68 where the only @xmath55-dependent contact interaction ( @xmath69 ) is a spin - orbit potential . the low - energy couplings @xmath70 at lo plus @xmath71 at nlo and n@xmath8lo are fit in ref . @xcite for different @xmath58 to the nn phase shifts of the nijmegen partial - wave analysis @xcite at laboratory energies @xmath72 and @xmath73 , using a local regulator . the reproduction of the isospin @xmath74 s- and p - waves is shown order by order in fig . [ fig : phases ] , where the bands are obtained by varying @xmath58 between @xmath75 and provide a measure of the theoretical uncertainty . at n@xmath8lo , an isospin - symmetry - breaking contact interaction ( @xmath76 for neutrons ) is added , which is fit to @xmath77 . as shown in fig . [ fig : phases ] , the comparison with nn phase shifts is very good for @xmath78 . this is similar for higher partial waves and isospin @xmath79 channels . in cases where there are deviations for higher energies ( such as in the @xmath0p@xmath80 ) , the width of the band signals significant theoretical uncertainties due to the chiral eft truncation at n@xmath8lo . the nlo and n@xmath8lo bands nicely overlap or are very close , but it is also apparent that the bands at n@xmath8lo are of a similar size as at nlo . this is because the width of the bands at both nlo and n@xmath8lo shows effects of the neglected order-@xmath81 contact interactions . since nuclear forces contain quadratic spin , isospin , and tensor operators ( of the form @xmath82 ) , the many - body wave function can not be expressed as a product of single - particle spin - isospin states . all possible spin - isospin nucleon - pair states need to be explicitly accounted for , leading to an exponential increase in the number of possible states . however , the afdmc method @xcite is capable of efficiently handling spin - dependent hamiltonians . afdmc rewrites the green s function by applying a hubbard - stratonovich transformation using auxiliary fields to change the quadratic spin - isospin operator dependences to linear . for the case of neutrons , it is also possible to include spin - orbit interactions and 3n forces in afdmc nonperturbatively @xcite . in the left panel of fig . [ fig : eos_qmc ] we show first afdmc calculations for the neutron - matter energy with local chiral eft nn interactions at lo , nlo , and n@xmath8lo @xcite . at each order , the full interaction is used both in the propagator and when evaluating observables . the bands in fig . [ fig : eos_qmc ] give the range of the energy obtained by varying @xmath58 between @xmath75 , where the softer @xmath83 interactions yield the lower energies . at lo , the energy has a large uncertainty . the overlap of the bands at different orders in fig . [ fig : eos_qmc ] is very systematic . in addition , the result that the nlo and n@xmath8lo bands are comparable is expected from the discussion of the phase - shift bands in fig . [ fig : phases ] and from the large @xmath84 entering at n@xmath8lo . our afdmc results provide first nonperturbative benchmarks for chiral eft interactions at nuclear densities . we have performed perturbative calculations as in the previous section based on the same local n@xmath8lo nn interactions . the perturbative energies are compared in the right panel of fig . [ fig : eos_qmc ] to the afdmc n@xmath8lo results . for the softer @xmath83 ( @xmath85 ) interaction , the third - order corrections are small and the perturbative third - order energy is in excellent agreement with the afdmc results , while for the harder @xmath86 ( @xmath87 ) interaction , the convergence is clearly slow . this is the first nonperturbative validation for neutron matter of the possible perturbativeness of low - cutoff @xmath85 interactions @xcite . the symmetry energy @xmath88 and its density derivative @xmath89 provide important input for astrophysics @xcite . to calculate these , we follow ref . @xcite . the predicted ranges for @xmath88 and @xmath89 at saturation density are @xmath90 and @xmath91 . the @xmath88 and @xmath89 ranges are in very good agreement with experimental constraints from nuclear masses @xcite and from the dipole polarizability of @xmath92pb @xcite , see the left panel of fig . in addition , they also overlap with the results for rg - evolved nn interactions with n@xmath8lo 3n forces @xcite , but due to the additional density dependences from n@xmath0lo many - body forces , the correlation between @xmath88 and @xmath89 is not as tight . the neutron - matter results also provide constraints for equations of state for core - collapse - supernova simulations . in the right panel of fig . [ svl ] , we compare the n@xmath0lo neutron - matter band ( red band ) to the lattimer - swesty ( ls ) equation of state @xcite ( with different incompressibilities 180 , 220 , and @xmath93mev ) , which is most commonly used in simulations , and to different relativistic mean - field - theory equations of state based on the density functionals dd2 @xcite , fsu2.1 @xcite , nl3 @xcite , sfho , sfhx @xcite , and tm1 @xcite . at low densities only the dd2 , fsu2.1 and sfhx equations of state are consistent with the n@xmath0lo neutron - matter band . the nl3 and tm1 equations of state have a too strong density dependence , which leads to unnaturally large @xmath88 and @xmath89 values . in addition , fig . [ svl ] exhibits a strange density dependence of sfhx . next , we use the n@xmath0lo neutron - matter results to provide constraints for the structure of neutron stars . we follow refs . @xcite for incorporating beta equilibrium and for the extension to high densities using piecewise polytropes that are constrained by causality and by the requirement to support a @xmath94 neutron star @xcite ( see also the recent @xmath95 discovery @xcite ) . in addition , we consider the case , if a @xmath96 neutron star were to be observed . the resulting constraints on the neutron star mass - radius diagram are shown in fig . [ fig : nstar ] by the red bands . the bands represent an envelope of a large number of individual equations of state reflecting the uncertainties in the n@xmath0lo neutron - matter calculation and in the polytropic extensions to high densities @xcite . the combination with the @xmath97 neutron star ( left panel ) predicts a radius range of @xmath98 km for a @xmath99 star @xcite . the maximal neutron star mass is found to be @xmath100 , with a corresponding radius of about @xmath101 km . we also find very good agreement with the mass - radius constraints from the neutron - matter calculations based on rg - evolved nn interactions with n@xmath8lo 3n forces @xcite , which are shown by the thick dashed blue lines in the left panel of fig . [ fig : nstar ] . in addition , we show in fig . [ fig : nstar ] the mass - radius relations obtained from equations of state for core - collapse supernova simulations @xcite . the inconsistency in fig . [ svl ] of many of the equations of state with the n@xmath0lo neutron - matter band at low densities results in a large spread of very low mass / large radius neutron stars , where the red band is considerably narrower in fig . [ fig : nstar ] . for typical neutron stars , our calculations rule out the nl3 and tm1 equations of state , which produce too large radii . finally , we have also explored the constraints from n@xmath0lo calculations for the chiral condensate in neutron matter @xcite . all the very best for your 70th birthday , james , lots of good health and energy for fun in life and physics ( and many days like the one we enjoyed in capri ) ! we would like to thank e. epelbaum , s. gandolfi , j. m. lattimer , a. nogga , and c. j. pethick , who contributed to the results presented in this talk . this work was supported by the dfg through grant sfb 634 , the erc grant no . 307986 strongint , the helmholtz alliance ha216/emmi , and nserc .

neutron matter presents a unique system in chiral effective field theory ( eft ) , because all many - body forces among neutrons are predicted to next - to - next - to - next - to - leading order ( n@xmath0lo ) . we discuss perturbative and first quantum monte carlo ( qmc ) calculations of neutron matter with chiral eft interactions and their astrophysical impact for the equation of state and neutron stars . + * keywords : * _ chiral eft ; three - body forces ; qmc ; neutron matter ; neutron stars _ * * neutron matter with chiral eft interactions : + perturbative and first qmc calculations + @xmath1__institut fr kernphysik , technische universitt darmstadt , 64289 darmstadt , germany _ _ + @xmath2__extreme matter institute emmi , gsi helmholtzzentrum fr schwerionenforschung gmbh , 64291 darmstadt , germany _ _ + @xmath3__department of physics , university of guelph , guelph , ontario n1 g 2w1 , canada _ _

Slain CPD Officer Kim's Family Fund On the morning of June 19, 2015 Cincinnati Police Department Officer Sonny Kim responded to a call in the Madisonville neighborhood, not far from his home, for a man erratically waving a gun in the street. After coming into contact with the armed individual, Officer Kim, 49 years old and a respected 27 year veteran was shot and killed. Officer Kim leaves behind a wife and three children, as well as a community that mourns the loss of a true public servant and honorable man. This fund has been set up to help the family through this difficult time with any expenses that they may have or as a college fund for the three Kim boys. On behalf of the Mason, OH Police Association, we ask that you consider any donation, large or small, to help the Kim family through this unthinkably difficult time. Gratefully, Officer Derek Bauman President Mason Police Association 12K SHARES Share Tweet Donate COPY, PASTE & SHARE: https://www.gofundme.com/sonnykim What is GoFundMe? ||||| 3333.26 Waiving tuition for child or spouse of public service officer killed in line of duty. (A) Any citizen of this state who has resided within the state for one year, who was in the active service of the United States as a soldier, sailor, nurse, or marine between April 6, 1917, and November 11, 1918, and who has been honorably discharged from that service, shall be admitted to any school, college, or university that receives state funds in support thereof, without being required to pay any tuition or matriculation fee, but is not relieved from the payment of laboratory or similar fees. (B) (1) As used in this division: (a) "Volunteer firefighter" has the meaning as in division (B)(1) of section 146.01 of the Revised Code. (b) "Public service officer" means an Ohio firefighter, volunteer firefighter, police officer, member of the state highway patrol, employee designated to exercise the powers of police officers pursuant to section 1545.13 of the Revised Code, or other peace officer as defined by division (B) of section 2935.01 of the Revised Code, or a person holding any equivalent position in another state. (c) "Qualified former spouse" means the former spouse of a public service officer, or of a member of the armed services of the United States, who is the custodial parent of a minor child of that marriage pursuant to an order allocating the parental rights and responsibilities for care of the child issued pursuant to section 3109.04 of the Revised Code. (d) "Operation enduring freedom" means that period of conflict which began October 7, 2001, and ends on a date declared by the president of the United States or the congress. (e) "Operation Iraqi freedom" means that period of conflict which began March 20, 2003, and ends on a date declared by the president of the United States or the congress. (f) "Combat zone" means an area that the president of the United States by executive order designates, for purposes of 26 U.S.C. 112, as an area in which armed forces of the United States are or have engaged in combat. (2) Any resident of this state who is under twenty-six years of age, or under thirty years of age if the resident has been honorably discharged from the armed services of the United States, who is the child of a public service officer killed in the line of duty or of a member of the armed services of the United States killed in the line of duty during operation enduring freedom or operation Iraqi freedom, and who is admitted to any state university or college as defined in division (A)(1) of section 3345.12 of the Revised Code, community college, state community college, university branch, or technical college shall not be required to pay any tuition or any student fee for up to four academic years of education, which shall be at the undergraduate level. A child of a member of the armed services of the United States killed in the line of duty during operation enduring freedom or operation Iraqi freedom is eligible for a waiver of tuition and student fees under this division only if the student is not eligible for a war orphans scholarship authorized by Chapter 5910. of the Revised Code. In any year in which the war orphans scholarship board reduces the percentage of tuition covered by a war orphans scholarship below one hundred per cent pursuant to division (A) of section 5910.04 of the Revised Code, the waiver of tuition and student fees under this division for a child of a member of the armed services of the United States killed in the line of duty during operation enduring freedom or operation Iraqi freedom shall be reduced by the same percentage. (3) Any resident of this state who is the spouse or qualified former spouse of a public service officer killed in the line of duty, and who is admitted to any state university or college as defined in division (A)(1) of section 3345.12 of the Revised Code, community college, state community college, university branch, or technical college, shall not be required to pay any tuition or any student fee for up to four academic years of education, which shall be at the undergraduate level. (4) Any resident of this state who is the spouse or qualified former spouse of a member of the armed services of the United States killed in the line of duty while serving in a combat zone after May 7, 1975, and who is admitted to any state university or college as defined in division (A)(1) of section 3345.12 of the Revised Code, community college, state community college, university branch, or technical college, shall not be required to pay any tuition or any student fee for up to four years of academic education, which shall be at the undergraduate level. In order to qualify under division (B)(4) of this section, the spouse or qualified former spouse shall have been a resident of this state at the time the member was killed in the line of duty. (C) Any institution that is not subject to division (B) of this section and that holds a valid certificate of registration issued under Chapter 3332. of the Revised Code, a valid certificate issued under Chapter 4709. of the Revised Code, or a valid license issued under Chapter 4713. of the Revised Code, or that is nonprofit and has a certificate of authorization issued under section 1713.02 of the Revised Code, or that is a private institution exempt from regulation under Chapter 3332. of the Revised Code as prescribed in section 3333.046 of the Revised Code, which reduces tuition and student fees of a student who is eligible to attend an institution of higher education under the provisions of division (B) of this section by an amount indicated by the chancellor of higher education shall be eligible to receive a grant in that amount from the chancellor. Each institution that enrolls students under division (B) of this section shall report to the chancellor, by the first day of July of each year, the number of students who were so enrolled and the average amount of all such tuition and student fees waived during the preceding year. The chancellor shall determine the average amount of all such tuition and student fees waived during the preceding year. The average amount of the tuition and student fees waived under division (B) of this section during the preceding year shall be the amount of grants that participating institutions shall receive under this division during the current year, but no grant under this division shall exceed the tuition and student fees due and payable by the student prior to the reduction referred to in this division. The grants shall be made for four years of undergraduate education of an eligible student. Amended by 131st General Assembly File No. TBD, HB 64, §101.01, eff. 9/29/2015. ||||| CINCINNATI — The University of Cincinnati will give the three children of fallen Cincinnati police officer Sonny Kim a free education if they choose to attend the college. “As a small token of gratitude to Officer Sonny Kim, UC will cover full undergraduate tuition for his 3 sons should they matriculate at UC,” UC President Santa J. Ono tweeted Monday morning. As a small token of gratitude to Officer Sonny Kim, UC will cover full undergraduate tuition for his 3 sons should they matriculate at UC — Santa J. Ono (@PrezOno) June 22, 2015 The average cost for a four-year degree at UC is about $50,000, Ono said. Ono said UC's offer goes beyond what is covered by an Ohio law that states "the child of a public service officer killed in the line of duty" and "who is admitted to any state university or college" "shall not be required to pay any tuition or any student fee for up to four academic years of education, which shall be at the undergraduate level." "Our scholarship to the Kim children we will be on top of any support from the Ohio Safety Officers fund," he said. "They can use it for room and board, books and study abroad." Kim, 48, a husband and father of three boys, died after being shot while responding to a call of a gunman acting erratically Friday morning. Police said Kim's shooter, 21-year-old Trepierre Hummons, called 911 at 9:03 a.m. to report a black man in his early 20s "walking around, getting belligerent with a gun" at the corner of Whetsel Avenue and Roe Street in Madisonville. They said he called again a few minutes later. Kim was the first officer on the scene at 9:19 a.m. Hummons started a fire fight with Kim, Cincinnati Police Chief Jeffrey Blackwell said. Both men died in the encounter. Kim, a 27-year veteran of the Cincinnati Police Department, also worked as the owner and main karate instructor at the Japanese Karate-Do dojo in Symmes Township. One of Kim’s sons left a powerful message left on Instagram Saturday telling his father goodbye. In it, Kim's son remembers riding bikes, running 5Ks and laughing at his dad's "stupid jokes that (he) would purposefully make a straight face at even though they were actually funny." UC's offer of free college educations isn't the only thing being offered to the Kim family. Mason Police Association President Derek Bauman started a GoFundMe page that topped $100,000 in donations for the family Monday morning. A public viewing and visitation for Kim will be held from 2 to 8 p.m. Thursday at the Cintas Center at Xavier University for Officer Kim. The Queen City Fraternal Order of Police Lodge 69 will hold services at 7 p.m. The funeral service will be held at the Cintas Center at 11 a.m. Friday, followed by a procession to the Gate of Heaven Cemetery for burial. UC Public Safety tweeted on Wednesday that they will coordinate shuttle rides to Kim's funeral services in conjunction with Cincinnati Police. They said that campus late night shuttles may be delayed due to this effort.

– When Cincinnati officer Sonny Kim was shot to death in the line of duty last week, he left behind three sons. But while his family is still dealing with the grief from his death, there's one thing they won't have to worry so much about anymore: college for the boys. University of Cincinnati President Santa Ono tweeted out a generous offer on Monday that ensures Kim's sons get the four-year education their father would have wanted them to have, WCPO reports. "As a small token of gratitude to Officer Sonny Kim, UC will cover full undergraduate tuition for his 3 sons should they matriculate at UC," Ono wrote. Ono notes that this offering stretches beyond a law on Ohio's books that waives tuition for spouses and kids of public service officers slain in the line of duty. "Our scholarship to the Kim children ... will be on top of any support from the Ohio Safety Officers fund," Ono says, per WCPO. "They can use it for room and board, books, and study abroad." The station also points out that there's been even more of an outpouring of goodwill: The president of a local police association started a GoFundMe page for the Kim family that's already raised nearly $134,000. (A California university is offering scholarships to sex-trafficking survivors.)

WASHINGTON—The National Security Agency ended a program used to spy on German Chancellor Angela Merkel and a number of other world leaders after an internal Obama administration review started this summer revealed to the White House the existence of the operation, U.S. officials said. Officials said the internal review turned up NSA monitoring of some 35 world leaders, in the U.S. government's first public acknowledgment that it tapped the phones of world leaders. European leaders have joined international outrage over... ||||| It's a prime site, a diplomat's dream. Is there any better location for an embassy than Berlin's Pariser Platz? It's just a few paces from here to the Reichstag. When the American ambassador steps out the door, he looks directly onto the Brandenburg Gate. When the United States moved into the massive embassy building in 2008, it threw a huge party. Over 4,500 guests were invited. Former President George H. W. Bush cut the red-white-and-blue ribbon. Chancellor Angela Merkel offered warm words for the occasion. Since then, when the US ambassador receives high-ranking visitors, they often take a stroll out to the roof terrace, which offers a breathtaking view of the Reichstag and Tiergarten park. Even the Chancellery can be glimpsed. This is the political heart of the republic, where billion-euro budgets are negotiated, laws are formulated and soldiers are sent to war. It's an ideal location for diplomats -- and for spies. Research by SPIEGEL reporters in Berlin and Washington, talks with intelligence officials and the evaluation of internal documents of the US' National Security Agency and other information, most of which comes from the archive of former NSA contractor Edward Snowden, lead to the conclusion that the US diplomatic mission in the German capital has not merely been promoting German-American friendship. On the contrary, it is a nest of espionage. From the roof of the embassy, a special unit of the CIA and NSA can apparently monitor a large part of cellphone communication in the government quarter. And there is evidence that agents based at Pariser Platz recently targeted the cellphone that Merkel uses the most. The NSA spying scandal has thus reached a new level, becoming a serious threat to the trans-Atlantic partnership. The mere suspicion that one of Merkel's cellphones was being monitored by the NSA has led in the past week to serious tensions between Berlin and Washington. Hardly anything is as sensitive a subject to Merkel as the surveillance of her cellphone. It is her instrument of power. She uses it not only to lead her party, the center-right Christian Democratic Union (CDU), but also to conduct a large portion of government business. Merkel uses the device so frequently that there was even debate earlier this year over whether her text-messaging activity should be archived as part of executive action. 'That's Just Not Done' Merkel has often said -- half in earnest, half in jest -- that she operates under the assumption that her phone calls are being monitored. But she apparently had in mind countries like China and Russia, where data protection is not taken very seriously, and not Germany's friends in Washington. Last Wednesday Merkel placed a strongly worded phone call to US President Barack Obama. Sixty-two percent of Germans approve of her harsh reaction, according to a survey by polling institute YouGov. A quarter think it was too mild. In a gesture of displeasure usually reserved for rogue states, German Foreign Minister Guido Westerwelle summoned the new US ambassador, John Emerson, for a meeting at the Foreign Ministry. The NSA affair has shaken the certainties of German politics. Even Merkel's CDU, long a loyal friend of Washington, is now openly questioning the trans-Atlantic free trade agreement. At the Chancellery it's now being said that if the US government doesn't take greater pains to clarify the situation, certain conclusions will be drawn and talks over the agreement could potentially be put on hold. "Spying between friends, that's just not done," said Merkel on Thursday at a European Union summit in Brussels. "Now trust has to be rebuilt." But until recently it sounded as if the government had faith in its ally's intelligence agencies. In mid-August Merkel's chief of staff, Ronald Pofalla, offhandedly described the NSA scandal as over. German authorities offered none of their own findings -- just a dry statement from the NSA leadership saying the agency adhered to all agreements between the countries. Now it is not just Pofalla who stands disgraced, but Merkel as well. She looks like a head of government who only stands up to Obama when she herself is a target of the US intelligence services. The German website Der Postillon published a satirical version last Thursday of the statement given by Merkel's spokesman, Steffen Seibert: "The chancellor considers it a slap in the face that she has most likely been monitored over the years just like some mangy resident of Germany." Merkel has nothing to fear domestically from the recent turn of affairs. The election is over, the conservatives and the center-left Social Democrats are already in official negotiations toward forming a new government. No one wants to poison the atmosphere with mutual accusation. Nevertheless, Merkel must now answer the question of how much she is willing to tolerate from her American allies. Posing as Diplomats A "top secret" classified NSA document from the year 2010 shows that a unit known as the "Special Collection Service" (SCS) is operational in Berlin, among other locations. It is an elite corps run in concert by the US intelligence agencies NSA and CIA. The secret list reveals that its agents are active worldwide in around 80 locations, 19 of which are in Europe -- cities such as Paris, Madrid, Rome, Prague and Geneva. The SCS maintains two bases in Germany, one in Berlin and another in Frankfurt. That alone is unusual. But in addition, both German bases are equipped at the highest level and staffed with active personnel. The SCS teams predominantly work undercover in shielded areas of the American Embassy and Consulate, where they are officially accredited as diplomats and as such enjoy special privileges. Under diplomatic protection, they are able to look and listen unhindered. They just can't get caught. Wiretapping from an embassy is illegal in nearly every country. But that is precisely the task of the SCS, as is evidenced by another secret document. According to the document, the SCS operates its own sophisticated listening devices with which they can intercept virtually every popular method of communication: cellular signals, wireless networks and satellite communication. The necessary equipment is usually installed on the upper floors of the embassy buildings or on rooftops where the technology is covered with screens or Potemkin-like structures that protect it from prying eyes. That is apparently the case in Berlin, as well. SPIEGEL asked British investigative journalist Duncan Campbell to appraise the setup at the embassy. In 1976, Campbell uncovered the existence of the British intelligence service GCHQ. In his so-called "Echelon Report" in 1999, he described for the European Parliament the existence of the global surveillance network of the same name. Campbell refers to window-like indentations on the roof of the US Embassy. They are not glazed but rather veneered with "dielectric" material and are painted to blend into the surrounding masonry. This material is permeable even by weak radio signals. The interception technology is located behind these radio-transparent screens, says Campbell. The offices of SCS agents would most likely be located in the same windowless attic. No Comment from the NSA This would correspond to internal NSA documents seen by SPIEGEL. They show, for example, an SCS office in another US embassy -- a small windowless room full of cables with a work station of "signal processing racks" containing dozens of plug-in units for "signal analysis." On Friday, author and NSA expert James Bamford also visited SPIEGEL's Berlin bureau, which is located on Pariser Platz diagonally opposite the US Embassy. "To me, it looks like NSA eavesdropping equipment is hidden behind there," he said. "The covering seems to be made of the same material that the agency uses to shield larger systems." The Berlin-based security expert Andy Müller Maguhn was also consulted. "The location is ideal for intercepting mobile communications in Berlin's government district," he says, "be it technical surveillance of communication between cellphones and wireless cell towers or radio links that connect radio towers to the network." Apparently, SCS agents use the same technology all over the world. They can intercept cellphone signals while simultaneously locating people of interest. One antenna system used by the SCS is known by the affable code name "Einstein." When contacted by SPIEGEL, the NSA declined to comment on the matter. The SCS are careful to hide their technology, especially the large antennas on the roofs of embassies and consulates. If the equipment is discovered, explains a "top secret" set of classified internal guidelines, it "would cause serious harm to relations between the United States and a foreign government." According to the documents, SCS units can also intercept microwave and millimeter-wave signals. Some programs, such as one entitled "Birdwatcher," deal primarily with encrypted communications in foreign countries and the search for potential access points. Birdwatcher is controlled directly from SCS headquarters in Maryland. With the growing importance of the Internet, the work of the SCS has changed. Some 80 branches offer "thousands of opportunities on the net" for web-based operations, according to an internal presentation. The organization is now able not only to intercept cellphone calls and satellite communication, but also to proceed against criminals or hackers. From some embassies, the Americans have planted sensors in communications equipment of the respective host countries that are triggered by selected terms. ||||| Agency says report in German press that president was briefed on monitoring of chancellor's phone is 'not true' The US National Security Agency was forced on Sunday to deny that its director ever discussed a surveillance operation against the German chancellor with President Barack Obama, as the White House tried to contain a full-scale diplomatic crisis over espionage directed at allied countries. The Obama administration appeared in disarray as it struggled with the fallout over the disclosure that the National Security Agency monitored the phone conversations of at least 35 world leaders, and that the phone of the German chancellor, Angela Merkel, had been monitored. Early on Sunday, the White House refused to comment on an overnight report in the German tabloid Bild, which alleged that Obama was personally briefed about by the operation to target Merkel's phone by the NSA's director, Keith Alexander, and allowed it to continue. That appeared to conflict with a second report, in the German newspaper Frankfurter Allgemeine Sonntagszeitung. It said that when Obama spoke to Merkel over the phone on Wednesday, he assured the German leader he had not previously known her phone had been monitored. Caitlin Hayden, the White House's national security council spokeswoman, declined to comment on the reports, telling the Guardian: "We are not going to comment publicly on every specific alleged intelligence activity." However just over three hours later, that position appeared to have been reversed, when the NSA said in a statement that Alexander "did not discuss with President Obama in 2010 an alleged foreign intelligence operation involving German Chancellor Merkel, nor has he ever discussed alleged operations involving Chancellor Merkel. News reports claiming otherwise are not true". Bild cited "a secret intelligence employee who is familiar with the NSA operation against Merkel" in its story, which was widely-picked up by global media. The intervention by the NSA was unusual – the agency rarely comments publicly on specific allegations about its surveillance activities. However the White House and NSA are coming under intense pressure to reveal the extent to which Obama and senior administration officials knew about US surveillance operations targeting the leaders of allied countries. The agency did not dispute another report in Germany, based on documents disclosed by the whistleblower Edward Snowden, that the NSA's Special Collection Service (SCS) had listed Merkel's phone number since 2002. The report, in Der Spiegel, said the phone number was still on the list – marked as "GE Chancellor Merkel" – weeks before Obama visited Berlin in June, raising the possibility that the German leader had been under surveillance for more than a decade. In an SCS document cited by the magazine, the agency said it had a "not legally registered spying branch" in the US embassy in Berlin, the exposure of which would lead to "grave damage for the relations of the United States to another government". A delegation of German intelligence officials are due to arrive in the US to meet counterparts in the coming days. They are expected to demand clarity on the nature and scope of NSA activities in their country. 'A greater focus' NSA headquarters in Fort Meade, Maryland. Photograph: Getty Images However in Washington, the first signs are emerging that Obama's administration may seek to distance itself from the NSA, concluding that the spy-agency has strayed beyond its remit and overreached. Many senior figures in Congress have already said the NSA failed to properly inform them of the nature and scope of its surveillance activities. Lisa Monaco, a homeland security advisor to the White House, called on Friday for a "greater focus" to ensure the US was balancing "security needs with the privacy concerns all people share". Her op-ed piece in USA Today was widely interpreted as a signal of growing concern within the administration. Monaco wrote: "We want to ensure we are collecting information because we need it and not just because we can." In August, announcing a review of US intelligence activities in the aftermath of the first disclosures based on documents leaked by whistleblower Edward Snowden, Obama gave the impression that the NSA was solely focused on counter-terrorism measures. "I don't have an interest and the people at the NSA don't have an interest in doing anything other than making sure that where we can prevent a terrorist attack, where we can get information ahead of time, that we're able to carry out that critical task," he said. "We do not have an interest in doing anything other than that." The Spiegel report said the NSA's Berlin-based surveillance hub, adjacent to the Brandenburg gate, was one of several in Europe, citing a 2010 document that referred to branches existing in about 80 locations across the world, including Paris, Madrid, Rome, Prague, Geneva and Frankfurt. The article said it was not clear whether the monitoring of Merkel's phone included actual telephone conversations or was restricted to call data, but raised the question over whether a surveillance operation, which began three years before she became chancellor, was initially intended to gather intelligence ahead of the Iraq War, which Germany opposed. Merkel, then in opposition, was critical of Germany's anti-war stance. Bild reported that the then-chancellor, Gerhard Schröder, was also the target of surveillance, at the behest of the George Bush administration. A new dimension The Republican Mike Rogers is the chair of the House intelligence committee. Photograph: AP Revelations about the NSA monitoring foreign leaders – particularly allies – have blown open a dimension of the NSA scandal which, until now, has proven relatively uncontroversial in the US: surveillance conducted abroad. The US debate over NSA surveillance has focused almost exclusively on operations that may involve US citizens – such as a program to collect the phone records of millions of Americans. Until the recent revelations, there was virtually no concern raised over surveillance involving foreign citizens, even among vocal critics of the NSA on Capitol Hill. Legislation to reform the NSA, which is being introduced in both houses of Congress this week, focuses almost entirely upon surveillance activities that might involve US citizens. Few in Washington are challenging the administration's claim that "all nations" engage in similar forms of espionage. However diplomatic sources have told the Guardian that the White House's declarations that its practices do not differ from those employed by "all nations" are deeply misleading. The sources said that while the US, Russia, China, Britain and France are well-known to engage in aggressive cyber espionage, including against allies, many other countries do not have anywhere near the same surveillance infrastructure – and concentrate their more limited resources on counter-terrorism and serious crime. The revelations about NSA activity in Germany were discussed on the US Sunday morning political talkshows. Speaking on Face the Nation, on CBS, the Republican Darrell Issa, the chairman of the House oversight and government reform committee was asked if he thought Obama had known about the surveillance of Merkel's phone. He said: "Remember, the NSA works for the president. Through his national security advisers he knew or should have known." Asked about the propriety of such surveillance, Issa answered: "If what you do in Germany helps the Germans, then fine. But you don't spy on a head of state." Mike Rogers, the Republican chair of the House intelligence committee, was more bullish in defending surveillance practices, criticising press coverage of the latest NSA revelations and arguing that Europeans were unaware of the extent of surveillance conducted by their own governments and had been misled by incorrect media reports about the nature of NSA activities. He told CNN recent reports in France about the NSA's monitoring of millions of phone calls in the country were "100% wrong". "I would argue by the way, if the French citizens knew exactly what that was about, they would be applauding and popping champagne corks," he said. "It's a good thing – it keeps the French safe." Going further, Rogers claimed that the emergence of fascism in Europe in the early 20th century could be partly explained by a conscious decision by the US not to monitor its allies. "We said: 'We're not going to do any kinds of those things, that would not be appropriate," he said. "Look what happened in the 30s: the rise of fascism, the rise of communism, the rise of imperialism. We didn't see any of it. And it resulted in the deaths of tens of millions of people." Rogers added: "Remember: sometimes our friends have relationships with our adversaries." • This article was amended on 28 October 2013. An earlier version misspelled the Brandenburg Gate as the Brandenberg Gate.

– US officials (though unnamed ones) have for the first time owned up to tapping the phones of 35 world leaders—an admission made in the course of issuing a denial: They tell the Wall Street Journal that President Obama had no knowledge of that monitoring until after the Edward Snowden leaks this year. Further, those leaks led Obama to request a review of surveillance activities; he ultimately ordered an end to the snooping on some—but not all—of the leaders after that summertime review, according to the officials. The Journal doesn't know which leaders remain on the list, though it notes that Angela Merkel is definitely not being monitored, and that those who are still under surveillance have not been removed because they are providing useful intelligence. More on the subject: Merkel's conversations still could be occasionally overheard, though, point out the officials. That's because leaders who have been crossed off the NSA's list communicate with ones who remain on it. Officials say Obama was briefed on intelligence-gathering "priorities" but wasn't involved in choosing targets. "These decisions are made at NSA," one official says. "The president doesn't sign off on this stuff." That arrangement is now under review, however. The White House says it won't "comment publicly on every specific alleged intelligence activity," but the NSA issued a statement yesterday to deny a report that Obama had been briefed on the surveillance of Merkel back in 2010, reports the Guardian. A database entry in the Snowden documents suggests the surveillance began in 2002, well before she became chancellor. But German-American woes may be far from over: Der Spiegel claims that a spy outfit tied to the CIA and NSA has set up an illicit "listening station" atop the roof of the US Embassy in Berlin. Relying on documents leaked by Snowden, it reports that the "Special Collection Service" operates devices that can intercept everything from cell signals to satellite communications, and Der Spiegel believes those devices are possibly in operation behind "window-like indentations on the [embassy's] roof ... veneered with 'dielectric' material and are painted to blend into the surrounding masonry." The NSA had no comment. Cue Spanish outrage: El Mundo today claims that the NSA tracked more than 60 million phone calls in the country between December 2012 and January 2013. More on that story here.

guillain - barr syndrome ( gbs ) has a worldwide annual incidence of 1.3 cases/100,000 . the incidence is lower in children ( age < 15 years ) , 0.38 and 0.91 cases/100,000 with a mortality rate of 35% . a 5-month - old girl presented with cough , loose stools for 5 days , breathing difficulty , and listlessness for 3 days . child was treated as pneumonia ; however , due to worsening respiratory distress , she was referred to our center . at arrival a working diagnosis of pneumonia with respiratory failure was made , and child started on intravenous piperacillin - tazobactam . investigations revealed hemoglobin 9.2 g / dl , white blood count 15,200/cum , neutrophil - 62% , lymphocytes - 32% , platelet count - 288000/cmm , c - reactive protein - 1.08 mg / l , and procalcitonin - 0.27 ng / ml . chest x - ray was normal . a detailed neuromuscular examination revealed areflexia , marked hypotonia , and reduced power in all four limbs . in the light of minimal ventilator requirements , normal chest radiograph , and neuromuscular weakness with areflexia possibilities of spinal muscular atrophy ( sma ) , poliomyelitis , and serum potassium was 3.70 mmol / l , and serum calcium was 9.03 mg / dl . nerve conduction velocity showed absent compound muscle action potential ( cmap ) in both common peroneal nerves and increased distal latency and decreased cmap amplitude and conduction velocity in the left median , left ulnar , and both tibial nerves . f - wave was absent in left median , left ulnar , both common peroneal , and posterior tibial nerves . sensory nerve action potential was also absent in left median , left ulnar , and both sural nerves , suggestive of mixed sensory - motor , severe axonal , and demyelinating polyradiculoneuropathy . child was given two doses of intravenous immunoglobulin at 1 g / kg / day . there was a gradual improvement in power in all limbs over next 4 weeks , child was weaned off from the ventilator and tracheostomy tube was decannulated before discharge . a review of literature revealed only two reported cases of gbs in infants until date worldwide . on follow - up after 1 month , the child was doing well and attained age appropriate milestones . the classical presentation is characterized by an acute monophasic , nonfebrile , postinfectious illness manifesting as ascending weakness , and areflexia . the clinical suspicion of gbs in our case was based on the presence of a weakness , flaccidity , and areflexia . the age of the patient was the cause of diagnostic dilemma with only two younger children reported until date with postnatally acquired gbs on an extensive literature search . differential diagnoses such as poliomyelitis , sma , congenital myopathies , and muscular dystrophies had to be considered . we would wish to reemphasize and underline the importance of having a high index of suspicion of gbs in critically sick and ventilated infants with acute flaccid paralysis , irrespective of the age . a preceding history suggestive of etiology may or may not be available . hence , a thorough clinical examination , lumbar puncture for csf analysis , and electrophysiological studies to confirm the diagnosis are recommended .

guillain - barr syndrome ( gbs ) is a rare entity in infants . we report a case of gbs in a 5-month - old girl . the child presented with cough , loose stools , breathing difficulty , and listlessness . the child was treated as pneumonia with respiratory failure . due to difficulty in weaning from ventilation with areflexia , marked hypotonia , and reduced power in all four limbs ; possibilities of spinal muscular atrophy , poliomyelitis , and myopathies were kept . nerve conduction velocity study was suggestive of mixed sensory - motor , severe axonal , and demyelinating polyradiculoneuropathy . cerebrospinal fluid study revealed albuminocytological dissociation . child was diagnosed as gbs and treated with intravenous immunoglobulin . child recovered completely on follow - up . gbs should be considered as a differential diagnosis in acute onset respiratory failure with neuromuscular weakness in infants .

the triplet superconducting proximity effect@xcite in half - metals ( fully polarized ferromagnets , conducting only for one spin direction ) has received a considerable attention recently , both theoretically@xcite and experimentally.@xcite the mechanism behind the effect is the process of triplet andreev reflection at the half - metal superconductor interface.@xcite the key ingredient that allows and influences this reflection process is provided by the magnetic properties of the interface between the half - metal and the superconductor : it should have a magnetization that is misaligned from that of the half - metal.@xcite the role of such an interface is to break all the symmetries in spin - space , thereby allowing for the spin rotations necessary for the triplet andreev reflection . the properties of the interface , however , are not easy to manipulate in experiments , which is the reason why only a low proportion of half - metal superconductor samples show behavior consistent with triplet andreev reflection.@xcite here we study triplet andreev reflection in a setup that is free of this difficulty . the setup consists of an andreev quantum dot@xcite ( i.e. , a quantum dot in contact with a superconductor ) , coupled to a normal , source reservoir via a single - mode quantum point contact ( qpc ) , see fig . [ fig : setup ] . spin - orbit scattering in the quantum dot is assumed to be strong enough that the direction of the spin is randomized in much shorter time than the typical time @xmath0 of the escape from the dot . this allows the dot to effectively play the role of the interface . the role of the half metal is played by the qpc , which is set to the spin - selective @xmath1 conductance plateau using a parallel magnetic field.@xcite ( for simplicity , we assume that the andreev conductance of the contact to the superconductor is much larger than @xmath1 , which makes the transport properties insensitive to the details of this contact . ) a surprising feature of triplet andreev reflection is that despite the randomized spin in the quantum dot , the conductance of such a fully phase coherent , single - channel system vanishes in the zero temperature , linear response regime.@xcite while current can be passed through the system using finite voltages or temperature , it is natural to ask , whether there is still a possibility for transport in the zero temperature , linear response limit . in this paper we show that there is : relaxing the condition of full phase coherence enables the zero - bias triplet andreev conductance to take nonzero values . in the remaining sections , our goal is to demonstrate this statement by studying the behavior of the triplet andreev conductance in the presence of dephasing in detail . , via a single - mode , spin - filtering qpc . dephasing is introduced by coupling the dot to a voltage probe ( vp ) via a contact supporting @xmath2 modes with a tunnel barrier ( black rectangle ) of transparency @xmath3 per mode.,height=170 ] we introduce dephasing by coupling the quantum dot to an additional normal reservoir , which acts as a voltage probe.@xcite a voltage probe draws no net current , but it absorbs and reinjects quasiparticles without a phase relationship , thereby destroying phase coherence . dephasing due to a voltage probe in normal - superconducting structures at zero temperature was studied in refs . , for systems where no triplet andreev reflection could occur . the contact to the voltage probe is characterized by the number of modes ( including the spin degrees of freedom ) @xmath2 and the tunnel probability per mode @xmath3 , which together determine the dephasing rate as @xmath4 , where @xmath5 denotes the mean level spacing of the quantum dot . we consider two limits , a voltage probe with a single mode , spin - filtering contact , @xmath6 , and a voltage probe with macroscopic number of modes , @xmath7 . in the first case the dephasing rate is controlled by the tunnel probability . in the second case , for @xmath8 , which will turn out to be the regime where the conductance behaves nontrivially , the transport properties depend on @xmath2 and @xmath3 only through their product , i.e. , the dephasing rate.@xcite the two limits considered here represent two types of voltage probes that appear in the context of spin dependent quantum transport.@xcite the probe @xmath6 is a spin - conserving probe , while without further specification , the @xmath7 can be either a spin - conserving or a spin - nonconserving voltage probe . for the systems studied in this paper , there is no need for further specification , as the type of the voltage probe is unimportant due to the strong spin - orbit scattering in the quantum dot . we formulate our problem within the framework of the scattering matrix approach . the transport quantities of interest are expressed in terms of the scattering matrix @xmath9 at the fermi energy ( the chemical potential of the superconductor ) , relating incoming and outgoing modes ( including the electron - hole degrees of freedom ) in the contacts to the normal reservoirs . the currents at the contact to the source ( @xmath10 ) and the voltage probe ( @xmath11 ) are given by@xcite @xmath12v_\beta\\ { \cal r}^{ij}_{\alpha\beta}&={{\rm tr}}\left[(s^ { ij}_{\alpha\beta})^\dagger s^ { ij}_{\alpha\beta}\right],\end{aligned}\ ] ] where @xmath13 , and the index @xmath14 refers to electron and hole modes , respectively . the voltages @xmath15 are measured from the chemical potential of the superconductor , which is assumed to be grounded . the voltage @xmath16 is determined by demanding that no current is drawn to the voltage probe , @xmath17 . the conductance , defined by @xmath18 is given by @xmath19 where we substituted @xmath20 . equation is the starting point for our calculations . in what follows , we concentrate on systems where the motion inside the quantum dot is chaotic . we are interested in the statistics of the conductance , which we obtain using random matrix theory@xcite for the scattering matrix @xmath9 . we first discuss the case voltage probe with @xmath6 . the calculational advantage of this case is that it allows for a problem with minimal dimension , with the single mode source contact and a single mode voltage probe contact resulting in a @xmath21 scattering matrix . the parallel magnetic field together with the strong spin - orbit scattering places the quantum dot in the unitary symmetry class.@xcite consequently , the dot - superconductor system belongs to class @xmath22 in the symmetry classification of altland and zirnbauer,@xcite which translates to @xmath23 as the only constraint for the scattering matrix , besides unitarity . ( @xmath24 denotes the @xmath25-th pauli matrix in electron - hole space . ) assuming that the contact to the source reservoir is ideal , the two single - mode qpc - s can be characterized by the reflection matrix @xmath26 where the block structure reflects a grading according to the normal contacts and @xmath27 is the reflection phase shift for electrons at the voltage probe contact . the statistical properties of the conductance follow from the distribution of the scattering matrix , which is given by the generalization of the poisson kernel,@xcite @xmath28 the probability distribution is understood with respect to the invariant measure @xmath29 on the manifold @xmath30 defined by @xmath23 in the space of @xmath31 matrices . we parametrize @xmath9 as @xmath32 where @xmath33 , @xmath34 , @xmath35 su@xmath36 and @xmath37 . ( @xmath38 denotes the @xmath25-the pauli matrix in spin - space . ) the matrix structure in corresponds to electron - hole grading . the above parametrization can be obtained from the polar decomposition introduced in the appendix . . implies that @xmath39 and that the matrix @xmath40 has a twofold degenerate eigenvalue @xmath41 . this is true for the generic setups with vanishing linear conductance in the fully phase coherent limit , i.e. , if the closed andreev quantum dot has no energy level at the fermi energy.@xcite ( for a detailed discussion of this point we refer to the appendix . ) using the euler angle parametrization for @xmath42 , @xmath43\times [ 0,4 \pi]\times [ 0,\pi ] , \end{array}\ ] ] the invariant measure on @xmath30 is given by @xmath44 , and the conductance in units of @xmath1 is @xmath45 the distribution of the conductance is given by , which can be reduced to @xmath46 for @xmath47 and @xmath48 otherwise . a closed form expression can be given for @xmath49 , of the conductance for @xmath6 , for various values of the dephasing rate @xmath50 . the curves , in order of decreasing maximum , correspond to @xmath51 , @xmath52 , @xmath53 , @xmath54 , respectively . the empty squares represent smoothed histograms obtained from 3000 numerically generated scattering matrices for each value of @xmath3 , for a system where the superconducting contact supports 50 propagating modes . lower panel : the average ( solid line ) and the standard deviation ( dashed line ) of the conductance as a function of @xmath55 . the crosses are results of the numerical simulation.,title="fig:",height=207 ] of the conductance for @xmath6 , for various values of the dephasing rate @xmath50 . the curves , in order of decreasing maximum , correspond to @xmath51 , @xmath52 , @xmath53 , @xmath54 , respectively . the empty squares represent smoothed histograms obtained from 3000 numerically generated scattering matrices for each value of @xmath3 , for a system where the superconducting contact supports 50 propagating modes . lower panel : the average ( solid line ) and the standard deviation ( dashed line ) of the conductance as a function of @xmath55 . the crosses are results of the numerical simulation.,title="fig:",height=207 ] @xmath56 for @xmath57 , we evaluated the integral numerically . the resulting distribution is shown in the top panel of fig . [ fig : contrdeph ] for several values of @xmath3 . in the absence of dephasing , the conductance vanishes , corresponding to @xmath58 . with the gradual introduction of dephasing , @xmath59 is enabled to take nonzero values , leading to a widening of the conductance distribution with increasing dephasing rate , eventually reaching the distribution for @xmath49 . in the bottom panel of fig . [ fig : contrdeph ] we show the dependence of the average and the variance of the conductance on @xmath3 . while the average conductance increases monotonically with increasing dephasing rate , the variance increases to a maximum at @xmath60 , which is followed by a slight decrease . the finite value of the conductance fluctuations at @xmath49 ( corresponding to the maximal dephasing for @xmath6 ) indicates that a single channel voltage probe can not lead to a complete loss of phase coherence as we will see below , without phase coherence , the conductance fluctuations are suppressed back to zero . for weak dephasing , @xmath61 , the conductance distribution is rapidly decaying away from @xmath62 and it has the scaling form @xmath63 . this results in the dependence @xmath64 for the @xmath65-the moment of the conductance . now we turn to the case of the voltage probe with macroscopic number of channels , @xmath7 . while it might be possible to make some analytical progress using the poisson kernel distribution of ref . and following similar steps to the calculation of ref . , we resort to a simpler approach and obtain the statistics of the conductance by generating an ensemble of scattering matrices numerically . the scattering matrix @xmath9 is expressed in terms of the electron scattering matrix @xmath66 of the normal region . here @xmath67 is describes reflection from the dot through the normal contacts , @xmath68 describes reflection through the superconducting contacts , @xmath69 corresponds to transmission to the superconducting , and @xmath70 to the normal contacts . the necessary blocks of @xmath9 in electron - hole grading are given by@xcite [ eq : reereh ] @xmath71 the scattering matrix @xmath72 can be expressed using the statistical mapping@xcite @xmath73 where @xmath74 is unitary and @xmath75 is a diagonal matrix containing the transmission probabilities of the contacts with @xmath76 corresponding to perfect transmission through the single mode qpc and @xmath77 for @xmath78 describing tunneling at the voltage probe . we took @xmath79 for @xmath80 , corresponding to the contact to the superconductor . the results do not depend on this choice , as long as the andreev conductance of the contact is much greater than @xmath1 . using the mapping , the distribution of @xmath72 is obtained by taking @xmath74 from the circular unitary ensemble,@xcite which we generated numerically.@xcite for a mutual test of the program and the calculations , we first show results for @xmath6 in fig . [ fig : contrdeph ] . as it is seen , the agreement between the calculation and the numerics is perfect . the conductance distribution in the limit @xmath7 is shown in the top panel of fig . [ fig : intrdeph ] for several values of the dephasing rate @xmath55 . the distribution @xmath81 initially widens from @xmath82 with increasing @xmath55 and then it gradually narrows again to @xmath83 , where @xmath84 is conductance of the single mode qpc and the andreev conductance of the superconducting contact in series , in units of @xmath1 . the dependence of the average and the variance of the conductance on @xmath55 is shown in bottom panel of fig . [ fig : intrdeph ] . while the average conductance increases monotonically to its classical value , the conductance fluctuations display nonmonotonic behavior , corresponding to the initial widening and the final re - narrowing of the conductance distribution . fig . [ fig : intrdeph ] also shows a comparison between the limits @xmath6 and @xmath7 . for a given value of @xmath55 , the conductance distribution close to @xmath62 is suppressed for @xmath7 , in contrast to the single channel case , where @xmath85 is finite . the average conductance increases faster for @xmath7 towards its classical value , while the conductance fluctuations are suppressed compared to @xmath86 . , for different values of the dephasing rate @xmath55 . the solid curves , in order of increasing position @xmath59 of the maximum , correspond to @xmath87 , @xmath88 , @xmath89 , @xmath90 , respectively . the curves are obtained by smoothing histograms from 3000 numerically generated scattering matrices for each value of @xmath55 , with @xmath91 , for a system where the superconducting contact supports 50 propagating modes . for comparison , we show the distribution for @xmath6 , @xmath92 ( dashed line ) . lower panel : the average ( solid line ) and the standard deviation ( dashed line ) of the conductance as a function of @xmath55 . for comparison , the dotted lines show the corresponding functions for @xmath6.,title="fig:",height=207 ] , for different values of the dephasing rate @xmath55 . the solid curves , in order of increasing position @xmath59 of the maximum , correspond to @xmath87 , @xmath88 , @xmath89 , @xmath90 , respectively . the curves are obtained by smoothing histograms from 3000 numerically generated scattering matrices for each value of @xmath55 , with @xmath91 , for a system where the superconducting contact supports 50 propagating modes . for comparison , we show the distribution for @xmath6 , @xmath92 ( dashed line ) . lower panel : the average ( solid line ) and the standard deviation ( dashed line ) of the conductance as a function of @xmath55 . for comparison , the dotted lines show the corresponding functions for @xmath6.,title="fig:",height=207 ] in summary , we have studied in detail how dephasing due to a voltage probe enables a nonzero value for the zero temperature , zero - bias triplet andreev conductance in andreev quantum dots with a single - channel spin - filtering source point contact . we focused on systems where the quantum dot is chaotic , and obtained the full distribution of the conductance as a function of the dephasing rate for two limiting cases for the number of modes @xmath2 in the voltage probe contact , @xmath6 , and @xmath7 . compared to chaotic quantum dots in other transport situations , our findings for the conductance are quite unusual . dephasing is known to monotonically suppress the conductance fluctuations , in general.@xcite in contrast , as dephasing gradually enables transport , the fluctuations of the triplet andreev conductance are initially enhanced , which is followed by a suppression for strong dephasing , i.e. , the overall dependence on the dephasing rate is nonmonotonic . it is worthwhile to point out that in the @xmath7 case , unlike ref . , we did not intend to use the voltage probe to model dephasing processes intrinsic to the quantum dot , since accounting for the temperature dependence of such processes would necessitate considering the effect of thermal smearing.@xcite instead , our results apply to the situation where the dephasing rate is controlled by a real , physically present voltage probe . experimental control of the dephasing rate using a voltage probe was demonstrated very recently in the work of roulleau _ et al_.@xcite this makes us believe that , in principle , it is realistic to test our predictions in experiments . this work originated from discussions with p. w. brouwer . the author has also benefited from discussions with c. w. j. beenakker . this research was supported by the dutch science foundation nwo / fom . the andreev reflection eigenvalues @xmath93 are the eigenvalues of the matrix @xmath40 . we prove here the consequences of electron - hole symmetry on these quantities , and relate them to the condition of the absence of energy level of the closed andreev quantum dot at the fermi energy . + * theorem : * at the fermi energy , the degeneracy @xmath94 of the andreev reflection eigenvalue @xmath93 is even if , and @xmath95 , where @xmath96 is the degeneracy of the unit andreev reflection eigenvalue , if present , @xmath97 otherwise . furthermore , the scattering matrix at the fermi energy can be decomposed in electron - hole grading as @xmath98 where @xmath99 and @xmath100 are unitary matrices , and @xmath102 , where @xmath103 + _ proof : _ following from the electron - hole symmetry , the scattering matrix has the block decomposition @xmath104 we start with the singular value decomposition @xmath105 where @xmath106 are unitary matrices . using @xmath107 and @xmath108 , one finds that @xmath109 here @xmath110 is a block diagonal unitary matrix , @xmath111 substituting and into @xmath112 leads to @xmath113 for @xmath114 , @xmath115 is antisymmetric , and due to its unitarity @xmath116 , from which it follows that @xmath94 is even . being antisymmetric and unitary , @xmath115 can be decomposed as@xcite @xmath117 where @xmath118 is unitary . for @xmath119 , eqn . is automatically satisfied , without further requirements for @xmath115 . for the zero andreev reflection eigenvalue , if present , we can set @xmath120 with an arbitrary unitary matrix @xmath121 , as for @xmath122 , @xmath123 drops out from . for the unit andreev reflection eigenvalue , if present , we write @xmath124 with @xmath121 , @xmath125 unitary . taken together , the matrix @xmath110 can be written as @xmath126 where @xmath127 for @xmath128 . writing @xmath129 and @xmath130 as which gives the decomposition upon substitution in eq . . the decomposition satisfies the unitarity and electron - hole symmetry requirements , therefore there are no further relations between the matrices @xmath99 and @xmath100 . the result @xmath95 follows straightforwardly . @xmath133 note that in eq . , we assumed @xmath39 , however only @xmath134 follows from @xmath135 . we show below that this is a valid assumption in the generic situation that there is no energy level of the closed andreev quantum dot at the fermi energy . using the channel coupled model employed in ref . , the scattering matrix can be expressed as@xcite @xmath136 here the hermitian matrix @xmath137 is a projection of @xmath138 , where @xmath139 models the closed andreev quantum dot . if @xmath139 has no zero eigenvalues , i.e. , there is no level at the fermi energy , the matrix @xmath140 can be taken at @xmath141 without complications . following from the symmetry of @xmath142 , the eigenvalues of @xmath9 come in complex conjugate pairs , therefore , @xmath39 . ( if there is a level at the fermi energy , an eigenvalue of @xmath140 can diverge as @xmath143 while an other can tend to zero , leading to a @xmath144 eigenvalue pair of @xmath9 , and thereby to @xmath145 . ) this result , together with @xmath95 , contains as a special case the finding of ref . , that for a single mode system , @xmath146 at the fermi level , if the closed andreev quantum dot has no level at the fermi energy . indeed , for such a system , @xmath9 is a @xmath147 matrix , i.e. , there is a single andreev reflection eigenvalue . as it is singly degenerate , it can be only zero or unity , and @xmath39 guarantees that it is zero . for the @xmath21 matrix in eq . , the degeneracy of the andreev reflection eigenvalue also follows from @xmath39 . if there was no degeneracy , the eigenvalues could be only a zero and a unit eigenvalue . this would mean @xmath145 .

we study the conductance of normal - superconducting quantum dots with strong spin - orbit scattering , coupled to a source reservoir using a single - mode spin - filtering quantum point contact . the choice of the system is guided by the aim to study triplet andreev reflection without relying on half metallic materials with specific interface properties . focusing on the zero temperature , zero - bias regime , we show how dephasing due to the presence of a voltage probe enables the conductance , which vanishes in the quantum limit , to take nonzero values . concentrating on chaotic quantum dots , we obtain the full distribution of the conductance as a function of the dephasing rate . as dephasing gradually lifts the conductance from zero , the dependence of the conductance fluctuations on the dephasing rate is nonmonotonic . this is in contrast to chaotic quantum dots in usual transport situations , where dephasing monotonically suppresses the conductance fluctuations .

from childhood we see a mysterious play of light and shadow which is really a manifestation of diffraction phenomena . it turns out that diffraction phenomena take place in the processes with particles and nuclei as well . at present time it is well established that the fundamental dynamics of particles and nuclei contains the dynamics of diffraction phenomena as a special case . everybody who works in diffraction ( high - energy ) physics has learned that profiles of shadows are related to the fundamental dynamics . so , our intuition suggests that there are very deep relationships between three blocks shown on the diagram below @xmath0 @xmath1 @xmath2 0.2 true in @xmath3 0.2 true in @xmath4 here i d like to discuss some aspects of these relationships in the framework of general structures in the relativistic quantum theory . it will be shown that the diffraction phenomena with a shadow dynamics in the scattering of a high - energy particle from composite systems , like nuclei , will be characterized by the scaling laws with a quite clear physical meaning . deuteron is the simplest composite nuclear system , that s why it may serve as the best laboratory to study shadow dynamics . i ll also attempt to demonstrate new structures of the shadow dynamics in the light of existing experimental data on proton(antiproton)-deuteron total cross sections . therefore , above all , let me remind you some well - known facts to restore what was many years ago . first of all , experimental and theoretical studies of high - energy particle interaction with deuterons have shown that the total cross section in scattering from deuteron can not be treated as equal to the sum of total cross sections in scattering from free proton and neutron even in the range of asymptotically high energies . glauber was the first to propose the explanation of this effect . using the methods of diffraction theory , the quasiclassical picture for scattering from composite systems and eikonal approximation for high - energy scattering amplitudes , he found long ago @xcite that the total cross section in scattering from deuteron could be expressed by the formula _ d = _ p + _ n - , [ 1 ] where = _ g = < > _ d.[2 ] here @xmath5 are the total cross sections in scattering from deuteron , proton and neutron , @xmath6 is the average value for the inverse square of the distance between the nucleons inside a deuteron , @xmath7 is the glauber shadow correction describing the effect of eclipsing or the screening effect in the recent terminology . the glauber shadow correction has quite a clear physical interpretation . this correction originates from elastic rescattering of an incident particle on the nucleons in a deuteron and corresponds to the configuration when the relative position of the nucleons in a deuteron is such that one casts its shadow " on the other @xcite . it was soon understood that in the range of high energies the shadow effects may arise due to inelastic interactions of an incident particle with the nucleons of a deuteron @xcite . therefore , an inelastic shadow correction had to be added to the glauber one . a simple formula for the total ( elastic plus inelastic ) shadow correction had been derived by gribov @xcite in the assumption of pomeron dominance in the dynamics of elastic and inelastic interactions however , it was observed that the calculations performed by the gribov formula did not meet the experimental data : the calculated values of the inelastic shadow correction over - estimated the experimental values . the idea , that the pomeron dominance is not justified at the recently available energies , has been explored in papers @xcite . the authors of refs . @xcite argued that the account of the triple - reggeon diagrams for six - point amplitude in addition to the triple - pomeron ones allowed them to obtain a good agreement with the experiment . alberi and baldracchini replied @xcite and pointed out that discrepancy between theory and experiment could not be eliminated by taking into account the triple - reggeon diagrams : in fact , it is needed to modify the dynamics of the six - point amplitude with more complicated diagrams than the triple regge ones . this means that up to now we had not , in the framework of regge phenomenology , a clear understanding for the shadow corrections in elastic scattering from deuteron . the theoretical understanding of the screening effects in scattering from any composite system is of fundamental importance , because the structure of shadow corrections is deeply related to the structure of the composite system itself . at the same time the structure of the shadow corrections displays new aspects for the fundamental dynamics . here we are concerned with the study of shadow dynamics in scattering from deuteron in some details . a new simple formula for the shadow corrections to the total cross - section in scattering from deuteron will be presented and new scaling characteristics with a clear physical interpretation will be established . furthermore , the effect of weakening the inelastic screening at super - high energies is theoretically discovered here . we also made a preliminary comparison of the obtained structure for the shadow corrections with the experimental data on proton(antiproton)-deuteron total cross sections . it will be shown that there is quite a remarkable correspondence of the theory with the experimental data . in our papers @xcite the problem of scattering from two - body bound states was treated with the help of dynamic equations obtained on the basis of single - time formalism in qft @xcite . now i shall briefly sketch the basic results of our analysis of high - energy particle scattering from deuteron . as has been shown in @xcite , the total cross - section in the scattering from deuteron can be expressed by the formula _ = _ hp^tot(s ) + _ hn^tot(s ) - ( s ) , [ 3 ] where @xmath8 are the total cross - sections in scattering from deuteron , proton and neutron , @xmath9 @xmath10 @xmath11 is the slope of the forward diffraction peak in the elastic scattering from nucleon , @xmath12 is defined by the deuteron relativistic formfactor @xcite , q , [ 6 ] @xmath13 is the shadow correction describing the effect of eclipsing or screening effect during the elastic rescatterings of an incident hadron on the nucleons in a deuteron . the quantity @xmath14 in our approach represents the contribution of the three - body forces to the total cross - section in the scattering from deuteron . for the definition of three - body forces in relativistic quantum theory see recent paper @xcite and references therein . for this quantity paper @xcite provides the following expression : ^inel(s ) = - imr(s;-,,q ; , -,q ) , [ 7 ] where @xmath15 is the incident particle momentum in the lab system ( rest frame of deuteron ) , @xmath16 is the deuteron relativistic formfactor , normalized to unity at zero , @xmath17 @xmath18 is the nucleon mass . the function @xmath19 is expressed via the amplitude of the three - body forces @xmath20 and the amplitudes of elastic scattering from the nucleons @xmath21 by the relation @xmath22 a physical reason for the appearance of @xmath14 is directly connected with the inelastic interactions of an incident particle with the nucleons of deuteron . it can be shown that the contribution of three - body forces to the scattering amplitude from deuteron is related to the processes of multiparticle production of inclusive type in the inelastic interactions of the incident particle with the nucleons of deuteron @xcite . this can be done with the help of the unitarity equation . to understand the quantity @xmath14 more clearly we may consider an elementary model for three - body forces . for simplicity , let us consider the model proposed in @xcite where the imaginary part of the three - body forces scattering amplitude has the form imf_0(s ; p_1 , p_2 , p_3 ; q_1 , q_2 , q_3 ) = f_0(s ) \{- ^3_i=1 ( p_i - q_i)^2},[9 ] where @xmath23 , @xmath24 are free parameters which , in general , may depend on the total energy of three - body system . this model assumption is not so significant for our main conclusions but allows one to make some calculations in a closed form . indeed , calculating all the integrals , we obtain for the quantity @xmath14 @xcite ^inel(s ) = , [ 10 ] where |(s ) = -1,[11 ] ^2_0(s)=r^2_0(s)(1- ) , = , [ 12 ] and we suppose that asymptotically @xmath25 from the analysis of the problem of high - energy particle scattering from deuteron we have derived the formula relating one - particle inclusive cross - section with the imaginary part of the three - body forces scattering amplitude . this formula looks like @xcite , [ 13 ] @xmath26 @xmath27}{2\omega_{h}(\vec q + \vec{\delta}')2e_n ( \vec{\delta } - \vec{\delta}')}\times\ ] ] imf_hn(s ; , q ; - , q + )imf_0(|s;- , - , q + ; , - , q ) , [ 14 ] @xmath28 s = , |s = 2(s + m_n^2 ) - m_x^2,t = - 4 ^ 2 . [ 15 ] i d like to draw attention to the minus sign in the r.h.s . of eq . ( [ 13 ] ) . the simple model for the three - body forces considered above ( see eq . ( [ 9 ] ) ) gives the following result for the one - particle inclusive cross - section in the region of diffraction dissociation = ( |s)imf_0(|s;- , , q ; , - , q ) = ( |s)f_0(|s ) , [ 16 ] where ( |s ) = -1.[17 ] the configuration of particles momenta and kinematical variables are shown in fig . the variable @xmath29 in the r.h.s . of eq . ( [ 16 ] ) is related to the kinematical variables of one - particle inclusive reaction by eqs . ( [ 15 ] ) . we may call the quantity @xmath30 a renormalized flux a l goulianos . however , it should be pointed out that in our approach we have a flux of real particles and function @xmath31 has quite a clear physical meaning . the function @xmath31 originates from initial and final states interactions and describes the screening effect or the effect of eclipsing of the three - body forces by two - body ones @xcite . if we take the usual parameterization for one - particle inclusive cross - section in the region of diffraction dissociation = a(s.m_x^2 ) , [ 18 ] then we obtain for the quantities @xmath32 and @xmath33 a(s , m_x^2 ) = ( |s)f_0(|s ) , b(s , m_x^2 ) = [ 19 ] . ( [ 19 ] ) shows that the effective radius of three - body forces is related to the slope of diffraction cone for inclusive diffraction dissociation processes in the same way as the effective radius of two - body forces is related to the slope of diffraction cone in elastic scattering processes . moreover , it follows from the expressions r_0(|s ) = |s / s_0,|s = 2(s+m_n^2 ) - m_x^2 [ 20 ] that the slope of diffraction cone for inclusive diffraction dissociation processes at a fixed energy decreases with the growth of missing mass . this property agrees well qualitatively with the experimentally observable picture . actually , we have even a more remarkable fact : shrinkage or narrowing of diffraction cone for inclusive diffraction dissociation processes with the growth of energy at a fixed missing mass and widening of this cone with the growth of missing mass at a fixed energy is of universal character . as it follows from eq . ( [ 16 ] ) this property is the consequence of the fact that the one - particle inclusive cross - section depends on the variables @xmath34 and @xmath35 via one variable @xmath29 which is a linear combination of @xmath34 and @xmath35 . this peculiar scaling " is the manifestation of @xmath36-symmetry of the three - body forces ( [ 9 ] ) . it would be very desirable to experimentally study this new scaling law related to the symmetry of the new fundamental ( three - body ) forces . now let us take into account that the functions @xmath37 and @xmath38 are almost the same . in fact , @xmath39 if the condition @xmath40 is realized , because in that case @xmath41 , but in a general case we have a bound @xmath42 . therefore , we can eliminate one and the same combination @xmath43 entered into equations ( [ 10 ] ) , ( [ 16 ] ) and express it through experimentally measurable quantities . we obtain in this way a(s , m_x^2 ) = ^inel(|s ) . [ 21 ] eq . ( [ 21 ] ) establishes a deep connection of inelastic shadow correction with one - particle inclusive cross - section . this relation allows one to express the inelastic shadow correction via a total single diffractive dissociation cross - section . this will be done in the next section . we ll start the derivation of the desired expression with the definition of total single diffractive dissociation cross - section _ sd^(s ) = _ m_min^2^s_t_-(m_x^2)^t_+ ( m_x^2 ) dt . [ 22 ] here we have specially labeled the total single diffractive dissociation cross - section by the index @xmath44 . it s clear the parameter @xmath44 defines the range of integration in the variable @xmath35 . unfortunately , there is no common consent in the choice of this parameter today . however , we would like to point out an exceptional value for the parameter @xmath44 which naturally arises from our approach . namely , let us put ^ex = /2m_n r_d,[ex ] then we define the exceptional total single diffractive dissociation cross - section _ sd^ex(s ) = _ sd^(s)|_=^ex . the exceptional value ( [ ex ] ) for the parameter @xmath44 has a very deep physical meaning : it tells us that the range of integration in ( [ 22 ] ) in the variable @xmath35 is to be determined by internucleon distances where the two - nucleon bound state may be organized . the weaker ( the larger the internucleon distances ) two - nucleon bound state is , the smaller the range of integration in ( [ 22 ] ) in the variable @xmath35 and vice versa . as a result we immediately obtain from eqs . ( [ 18 ] , [ 21 ] , [ 22 ] ) @xcite ^inel(s ) = 2 _ sd^ex(s)a^inel(x_inel),[23 ] where a^inel(x_inel ) = , x^2_inel = , [ 24 ] reminding that @xmath45 @xcite . here is a convenient place to rewrite the elastic shadow correction ( [ 5 ] ) in a similar form ^el(s ) = 2 ^el(s)a^el(x_el ) , ^el(s ) , [ 25 ] where a^el(x_el ) = , x^2_el = , [ 26 ] and we suppose as above that @xmath46 the obtained expressions for the shadow corrections have quite a transparent physical meaning , both the elastic @xmath47 and inelastic @xmath48 scaling functions have a clear physical interpretation . the function @xmath47 measures out a portion of elastic rescattering events among of all the events during the interaction of an incident particle with a deuteron as a whole , and this function attached to the total probability of elastic interaction of an incident particle with a separate nucleon in a deuteron . correspondingly , the function @xmath48 measures out a portion of inelastic events of inclusive type among of all the events during the interaction of an incident particle with a deuteron as a whole , and this function attached to the total probability of single diffraction dissociation of an incident particle on a separate nucleon in a deuteron . the scaling variables @xmath49 and @xmath50 have quite a clear physical meaning too . the dimensionless quantity @xmath49 characterizes the effective distances measured in the units of fundamental length " , which the deuteron size is , in elastic interactions , but the similar quantity @xmath50 characterizes the effective distances measured in the units of the same fundamental length " during inelastic interactions . the functions @xmath47 and @xmath48 have quite different behaviour : @xmath47 is a monotonic function while @xmath48 has the maximum at the point @xmath51 where @xmath52 . the graph of @xmath48 is shown in fig . this graph displays an interesting physical effect of weakening the inelastic eclipsing ( screening ) at superhigh energies . the energy at the maximum of @xmath48 can easily be calculated from the equation @xmath53 and it will be done later on . account of the real part for the hadron - nucleon elastic scattering amplitude modifies the scaling function @xmath47 in the following way : a^el(x_el ) a^el(x_el,_el)=a^el(x_el),_el .[27 ] we see that nonzero value for @xmath54 violates the scaling behaviour of @xmath47 . however , @xmath54 has a small value at high energy and moreover @xmath55 at @xmath56 , therefore , the violation of the scaling law is small at high energy and we have the restoring scaling in the limit @xmath56 . the scaling function @xmath48 is not modified because all the information on the real parts of the amplitudes is contained in the function @xmath37 , which is eliminated in the derivation of formula ( [ 21 ] ) . however , if we would like to speculate in inessential but subtle distinction between the functions @xmath37 and @xmath38 , then the function @xmath48 should be modified to the form a^inel(x_inel ) a^inel(x_inel , x,,,)=a^inel(x_inel)r_(x , , , ) , where r_(x , , , ) = , @xmath57 it can easily be seen that r_(0,,,)=r_(x,0,,)=r_(x , , 0,)=r_(x,,,0)=1 . besides , we have 01/41r _ _ , _ = . from the froissart bound it follows @xmath58 . so , in the case that @xmath59 or @xmath60 , taking into account that @xmath61 , we obtain @xmath62 . of course , it would be desirable to compare the obtained new structure for the shadow corrections in elastic scattering from deuteron with the existing experimental data on hadron - deuteron total cross sections . the next section will be consecrated to this comparison . here we have tried to make a preliminary comparison of the new structure for the shadow corrections in elastic scattering from deuteron with the existing experimental data on proton - deuteron and antiproton - deuteron total cross sections . to make this comparison in a more transparent manner , let us rewrite formula ( [ 3 ] ) for the hadron - deuteron total cross section in a simplified form _ hd^tot = 2 _ hn^tot - , = ^el + ^inel,[28 ] ^el = 2 ^ela^el = , [ 29 ] ^inel = 2 _ sd^exa^inel , a^inel = , x^2_inel .[30 ] all the quantities entered in formulas ( [ 28 ] [ 30 ] ) are the functions of the energy per nucleon . in the first step we analysed the experimental data on antiproton deuteron total cross sections . we have used our theoretical formula describing the global structure of antiproton - proton total cross sections @xcite as @xmath63 . a new fit to the data on the total single diffraction dissociation cross sections in @xmath64 collision with our formula @xcite _ sd^tot(s ) = 2 _ sd^ex(s ) = [ 31 ] has been made as well using a wider set of the data ( see table [ tab ] ) . the new fit yielded @xmath65 the fit result is shown in fig . it is seen that the fitting curve , as in the previous fit @xcite , goes excellently over the experimental points of the cdf group at fermilab @xcite . we can substitute @xmath66 in eq . ( [ 30 ] ) for formula ( [ 31 ] ) , after that the expression for the total shadow correction may be rewritten in the form _ |p d(s ) = + , [ 32 ] where all the parameters are fixed according to our previous fits @xcite apart from @xmath67 , which is considered as a single free fit parameter . our fit yielded @xmath68 the fit result is shown in fig . [ fig4 ] . for completeness the theory prediction for antiproton - deuteron total cross section is plotted up to tevatron energies . at this place it should be make the following remark . it is known the latest experimental value for the deuteron matter radius @xmath69 @xcite . the fitted value for the @xmath67 satisfies with a good accuracy to the equality r_d^2 = r^2_d , m,(r^2_d , m = 3.853fm^2 = 98.96gev^-2 ) . now it would be very intriguing for us to make a comparison of theoretical formula ( [ 32 ] ) with the data on proton - deuteron total cross sections where @xmath67 has to be fixed by the previous fit to the data on antiproton - deuteron total cross sections . as in the previous fit we supposed @xmath70 and @xmath71 had been taken from our global description of proton - proton total cross sections @xcite . we also assumed that @xmath72 . so , in this case we have not any free parameters . the result of the comparison is shown in fig . as you can see the correspondence of the theory to the experimental data is quite remarkable apart from the resonance region . the resonance region requires a more careful consideration than that performed here . in this paper we have been concerned with a study of shadow corrections to the total cross section in scattering from deuteron . the dynamic apparatus based on the single - time formalism in qft has been used as a tool and subsequently applied to describe the properties of high - energy particle interaction in scattering from two - body composite system . as we have repeatedly emphasized in our previous works , the conceptual notion of the new fundamental forces i.e. three - body forces appeared as a consequence of consistent consideration of the dynamics for three particle system in the framework of relativistic quantum theory . in our previous investigation , we have provided the general framework and described some general properties of the three - body ( in general many - body ) forces to implement the crucial property of any theory such as the general requirements of unitarity and analyticity @xcite . within this framework we have established a profound relationship of the three - body forces to the dynamics of one - particle inclusive reactions . the main topic of our studies was to develop the methods which form the basis for both analytical calculations and phenomenological investigations . such developments are necessary for providing an understanding of the relation between the general structure of the relativistic quantum theory and relevant hadronic phenomena described , as a rule , in the frame of the phenomenological models . even though our motivation to construct the general formalism to study the dynamics of a relativistic three - particle system has been , in the main , a theoretical one , we have applied this formalism to investigate the properties of the resultant hadron - deuteron interaction . we have calculated explicitly the contribution of three - body forces to the total cross section in scattering from any two - body composite system and investigated the resulting strong interaction phenomena by applying our approach to the well - known relevant case , i.e hadron deuteron scattering . it seems that very weakly bound two - nucleon state , the deuteron , exhibits the dynamics which leaves the clustering of the quarks into hadrons essentially intact during the interaction with the incident hadron and therefore makes , in a natural way , the dynamical scheme accessible to a description in terms of nucleonic degrees of freedom only . in this way we found the new structures for the total shadow correction to the total cross section in scattering from deuteron . first of all , it has been observed that the total shadow correction inherits the general structure of total cross section and contains two inherent parts as well , an elastic part and inelastic one . this partitioning is performed explicitly in the framework of our approach . it turns out that the elastic part can be expressed through the elastic scaling ( structure ) function and the fundamental dynamical quantity , which is the total elastic cross section in scattering from an isolated constituent ( nucleon ) in the composite system ( deuteron ) . at the same time the inelastic part is expressed through the inelastic scaling ( structure ) function and the fundamental dynamical quantity , which is the total single diffractive dissociation cross section in scattering from an isolated constituent in the composite system too . thus , the general formalism in qft makes it possible to define properly the dynamics of particle scattering from a composite system and express this dynamics in terms of the fundamental dynamics of particle scattering from an isolated constituent in the composite system and the structure of the composite system as itself . we have restricted ourselves to the simplest composite system , which a two - body composite system ( deuteron ) is . however , our general formalism can be straightforwardly applied to any multiparticle system and may be used to specify the dynamics for any many - body composite system as well . there is no , in principle , difficulty in extending general formalism to more complex compound many - particle systems such as , for example , nuclei . we have not attempted to study such extension in this paper , hope , this will be the subject of our future studies . the main goal of this work is to gain some insight into hadronic phenomena resulting from compositeness in the presence of three - body ( in general many - body ) forces . the general formalism , which we have outlined , tells us that the obtained results are substantially more general because they have a reliable ground in the framework of the relativistic quantum theory . it is evident now that these results correspond to the very deep physical phenomena in the fundamental dynamics . what seems most important , which we have discovered in the work , is that the elastic and inelastic structure functions have quite different behaviour . the inelastic structure function has the maximum and tends to zero at infinity , while the elastic structure function is the monotonic function and tends to unity at infinity . this is the most significant difference between the elastic and inelastic structure functions and it has far reaching physical consequences . this difference manifests itself in the effect of weakening of inelastic eclipsing ( screening ) at super - high energies . what does it mean physically ? to understand it let s combine the elastic shadow correction and the first term in eq . ( [ 28 ] ) for the hadron - deuteron total cross section _ hd^tot = 2 _ hn^inel + 2 _ hn^el(1 - a^el ) - ^inel,1-a^el=. [ 34 ] we have in this way that asymptotically _ hd^tot = 2 _ hn^inel , s . probably the generalization of this result to any many - nucleon systems ( nuclei ) looks like _ ha^tot = a _ hn^inel , s . obviously , this result confirms theoretically the so called quark counting rules . moreover , it turns out that the total absorption ( inelastic ) cross section manifests itself as a fundamental dynamical quantity for the constituents in a composite system . we would also like to emphasize the different range of variation for the elastic and inelastic structure functions 0 a^el 1,0 a^inel 2/3 . the inelastic shadow correction in a wide range of energies ( up to planck scale ) is shown in figs . [ fig6],[fig7 ] . the energy , where the inelastic shadow correction has a maximum , has to be calculated from the equality @xmath73 . taking @xmath74 from the fit and @xmath75 from paper @xcite , we obtain @xmath76 . of course , such energies are not available at now working accelerators . however , we always have room for a speculative discussion . for example , let us consider a proton as a two - body ( quark - diquark ) composite system . from the experiment it is known that the value for the charge radius of the proton @xmath77 . if we put @xmath78 , then resolving the equation @xmath79 , we obtain @xmath80 . this is just the energy of tevatron . furthermore in the point @xmath81 of the minimum for proton - proton(antiproton ) total cross sections , we find @xmath82 . this is just one half of the proton charge radius . so , a realistic and fundamental property of our approach is that it exhibits two clearly distinct energy regions , associated with the energies where the range of three - body forces is small compared with the size of two - body composite system , on the one hand , and with the energies where the range of three - body forces is large compared with the two - body bound state size , on the other hand . the size of two - body compound system plays a role of fundamental scale " separating these two distinct energy regions . [ fig8 ] displays the significance of shadow corrections in elastic scattering from deuteron . the elastic and inelastic shadow corrections to the proton(antiproton)-deuteron total cross sections are plotted in fig . [ fig9 ] . our analysis shows that the magnitude of inelastic shadow correction is about 10 percent of elastic one at available energies . figuratively speaking , if we called the elastic shadow corrections a fine structure in the total cross sections , then we might call the inelastic shadow corrections a super - fine structure in the total cross sections . in this sense three - body forces make a fine tuning " in the dynamics of the relativistic three - body system . that is why the precise measurements of hadron - deuteron total cross - sections at high energies are most important . therefore , it would be very desirable to think about the creation of accelerating deuterons beams instead of protons ones at the now working accelerators and colliders . at last , let me remember a unique phenomenon in the history of human civilization related to pythagoras , a greek mathematician and philosopher , who lived in the sixth century b.c . gathering together a group of pupils in the greek sity of croton in southern italy , he organized a brotherhood devoted to both learning and virtuous living . the pythagorean brotherhoods remained active for several centuries . the great ideas of pythagoras and his followers exerted great influence on the intellectual development of human civilization and had a fundamental importance at all times . the well known pythagoras theorem , a major step in the devlopment of geometry , is that the square of the hypotenuse of a right - angle triangle equals the sum of squares of the two other sides , together with its corollary , namely , that the diagonal of a square is incommensurable with its side . the next theorem is that the sum of the angles within any triangle is 180 degrees . of great influence were the pythagorean doctrines that numbers were the basis of all things and possessed a mystic significance , in particular the idea that the cosmos is a mathematically ordered whole . pythagoras was led to this conception by his discovery that the notes sounded by stringed instrument are related to the length of the strings , he recognized that first four numbers , whose sum equals @xmath83 ( so called pythagorean quaternion @xmath84 ) , contained all basic musical intervals : the octave , the fifth and the fourth . in fact , all the major consonances , that is , the octave , the fifth and the fourth are produced by vibrating strings whose lengths stand to one another in the ratios of @xmath85 , @xmath86 and @xmath87 respectively . the resemblance which he perceived between the orderlines of music , as expressed in the ratios which he had discovered and the idea that cosmos is an orderly whole , made up of parts harmoniously related to one another , led him to conceive of the cosmos too as mathematically ordered . the pythagoreans supposed that the universe was a sphere in which the planets revolved . the revolving planets were thought to produce musical notes the music of the spheres " . the importance of this conception is very great , for example , it is the ultimate source of galileo s belief that the book of nature is written in mathematical symbols " and hence the ultimate source of modern physics in the form in which it came to us from galileo . the pythagoreans believed also in reincarnation , that is , the soul , after death , passes into another living thing , which presupposes the ability of the soul to survive the death of the body , and hence some sort of belief in its immortality . as it was established above in our study the inelastic structure function @xmath48 has the maximum and at the maximum this function equals @xmath88 . the number @xmath88 may be considered as a fundamental number calculated in the theory with a clear physical interpretation . we also found the relations @xmath89 and @xmath90 which looked like harmonic ratios mentioned above and hence might be considered as the music " produced by diffraction phenomena in high energy elementary particle physics . it seems , we come back to the great pythagorean ideas reformulated in terms of the objects living in the microcosmos . the great pythagorean idea applied to the microcosmos might be shown by the following diagram : 0.1 true in @xmath91 + 0.1 true in @xmath92 0.1 true in @xmath93 0.1 true in @xmath94 0.1 true in @xmath95 0.1 true in so , it appears that the study of diffraction phenomena in high energy elementary particle physics makes it possible to establish a missing link between cosmos and microcosmos , between the great ancient ideas and recent investigations in particle and nuclear physics and to confirm the unity of physical picture of the world . anyway , we believe in it . it is my great pleasure to express thanks to the organizing committee for the kind invitation to attend this wonderful workshop . i would like to especially thank v.i . savrin , v. keshek and all local organizers for warm and kind hospitality throughout the workshop . * * r.j . glauber , phys . rev . * 100 * , 242 ( 1955 ) ; lectures in theoretical physics , interscience , new york , v. 1 , p. 315 - 414 , 1959 . abers et al . , nuovo cim . * 42a * , 363 ( 1966 ) . j. pumplin , m. ross , phys.rev . * 21 * , 1778 ( 1968 ) . v.n . gribov , sov . jetp , * 56 * , 892 ( 1969 ) . anisovich , l.g . dakhno , p.e . volkovitsky , sov . jetp , * 61 * , 1576 ( 1972 ) ; phys.lett . * 42b * , 224 ( 1972 ) . + v.v . anisovich , preprint ihep 72 - 76 , serpukhov , 1972 . anisovich , l.g . dakhno , nucl . b*85 * , 208 ( 1975 ) . + l.g . dakhno , preprint ihep 76 - 117 , serpukhov , 1976 . g. alberi , f. baldracchini , preprint ref.th.2443-cern ; nucl . b*138 * , 164 ( 1978 ) . arkhipov , v.i . savrin , sov . * 16 * , 328 ( 1973 ) ; * 19 * , 320 ( 1974 ) ; * 24 * , 78 ( 1975 ) ; * 24 * , 303 ( 1975 ) . arkhipov , v.i . savrin , sov . * 24 * , 78 ( 1975 ) . arkhipov , sov . phys . * 49 * , 320 ( 1981 ) . arkhipov , what can we learn from the study of single diffractive dissociation at high energies ? talk presented at the international conference on elastic and diffracrive scattering , protvino , russia , june 28july 2 , 1999 , in the proceedings of viiith blois workshop ( world scientific , singapore , 2000 ) , p. 109 ; report ihep 99 - 43 , protvino , 1999 ; e - print hep - ph/9909531 . arkhipov , diffraction 2000 : new scaling laws in shadow dynamics , to be published in proceedings of the workshop diffraction 2000 " , cetraro , italy , september 27 , 2000 ; e - print hep - ph/0011220 . arkhipov , preprint ihep 99 - 44 , protvino , 1999 ; e - print hep - ph/9912202 . arkhipov , preprint ihep 99 - 45 , protvino , 1999 ; e - print hep - ph/9911533 . f. abe et al . , ( cdf ) phys . rev . d*50 * , 5535 ( 1994 ) . k. goulianos , j. montanha , phys . rev . d*59 * , 114017 ( 1999 ) ; eprint hep - ph/9805496 . ansorge et al . , z. phys . c*33 * , 175 ( 1986 ) . alner et al . , ( ua5 ) phys . rep . * 154 * , 247 ( 1987 ) . d. bernard et al . , ( ua4 ) phys . b*186 * , 227 ( 1987 ) . n.a . amos et al . , ( e710 ) phys . b*243 * , 158 ( 1990 ) ; n.a . amos et al . , ( e710 ) phys . b*301 * , 313 ( 1993 ) . f. schmidt - kaler et al . lett . * 70 * , 2261 ( 1993 ) . arkhipov , v.i . savrin , sov . j. theor * 49 * , 3 ( 1981 ) . arkhipov , rep . on math . phys . * 20 * , 303 ( 1984 ) .

the relationships between the fundamental dynamics and diffraction phenomena in scattering from two - body composite system are discussed . a new simple formula for the shadow corrections to the total cross - section in scattering from deuteron has been derived and new scaling characteristics with a clear physical interpretation have been established . the effect of weakening the inelastic screening at super - high energies is theoretically discovered . a comparison of the obtained structure for the shadow corrections with the experimental data on proton(antiproton)-deuteron total cross sections has been performed . it is shown that there is quite a remarkable correspondens of the theory with the experimental data . -2.0 cm -2.0 cm * three - body forces , single diffraction dissociation and shadow corrections to hadron - deuteron total cross - sections * + a.a . arkhipov + _ institute for high energy physics + 142284 protvino , moscow region , russia _

special relativity ( sr ) and general relativity ( gr ) are at the basis of our understanding of space and time and thus are fundamental for the formulation of physical theories . without sr we can not explain the phenomena in high energy physics and in particle astrophysics , without gr there is no understanding of the gravitational phenomena in our solar system , of the dynamics of galaxies and of our universe , and , finally , of the physics of black holes . both theories are linked by the fact that the validity of st is necessary for gr . due to the overall importance of these theories , a persistent effort to improve the experimental tests of their foundations is mandatory . modern tests of sr and gr using ultrastable oscillators have been performed on earth @xcite , and an experiment is planned on the international space station @xcite . furthermore , new results from quantum gravity theories predict small deviations from sr and gr giving additional motivation to improve tests on sr and gr . for example , loop gravity and string theory predict modifications of the maxwell equations @xcite . these modifications lead to an anisotropic speed of light and to a dispersion in vacuum , thus violating the postulates of sr . quantum gravity also predicts , besides a violation of the weak equivalence principle @xcite , a violation of the universality of the gravitational red shift @xcite . although the amount of sr violations predicted by quantum gravity are too small to be in the range of experimental capabilities in the near future , these predictions open up the window for violations for such basic principles . since we do not know the true quantum gravity theory we also do not know the true parameters of the theory and therefore the predicted range of violations of sr and gr is no final prediction , but merely a hint . ( -5,-3)(7,5)(-4.6,-3.5)(7,5 ) ( -3,0)0.47 ( -3,0),title="fig:",width=37 ] ( -0.5,1.5)(0,0)(4.5,1.7 ) ( -3,-1.5)perigee @xmath0 10000 km ( 3.7,4.4)apogee @xmath0 40000 km ( -0.5,3.4)(4.8,2.2 ) ( -0.5,3.3)(1.5,-1.7 ) ( -1.7,3.3)(0,0.3)(0.6,0.2 ) ( -0.3,0.3)(0.3,1 ) ( 0.4,0.42)(0.3,0.45 ) ( -0.5,3.3 ) ( -1.5,0.5)(-0.5,1.5)(-3.5,1.5)(-4.5,0.5)(-1.5,0.5 ) ( 0,0)(1,0.5 ) ( -1,0)(1,2 ) ( -1,0)(-1,2 ) ( 1,0)(1,2 ) ( 0,2)(1,0.5 ) ( 0.5,0.5)(1.5,1.5)(4.5,1.5)(3.5,0.5)(0.5,0.5 ) ( 0,2)(0,9 ) ( -1.4,3.5)@xmath1 ( -2,4.3)(-4,4.3 ) ( -3,4.6)to sun ( 4,-0.45)2.8 ( 4.75,-0.15 ) ( 3.2,4.2)(3.2,-1.2)(1.2,-3.2)(-4.2,-3.2)(-6.2,-1.2)(-6.2,4.2)(-4.2,6.2)(1.2,6.2)(3.2,4.2 ) ( 0,-0.8)(0.8,0 ) ( 1.2,-0.8)(2,0 ) ( 0,-2)(0.8,-1.2 ) ( 1.2,-2)(2,-1.2 ) ( 0,-0.8)(0,0)(0.8,0 ) ( 1.2,0)(2,0)(2,-0.8 ) ( 0,-1.2)(0,-2)(0.8,-2 ) ( 1.2,-2)(2,-2)(2,-1.2 ) ( 2,-1.2)(2,-0.8 ) ( 0.8,-2)(1.2,-2 ) ( 0,-1.2)(0,-0.8 ) ( 0.8,0)(1.2,0 ) ( -5.5,-1.3)(-4,-0.7 ) ( -4,-0.9)(-4,-0.7)(-5.5,-0.7)(-5.5,-1.3)(-4,-1.3)(-4,-1.1 ) ( 0.7,3)(1.3,4.5 ) ( 0.9,3)(0.7,3)(0.7,4.5)(1.3,4.5)(1.3,3)(1.1,3 ) ( -6,0.7)(-4.5,1.3 ) ( -6,2.7)(-4.5,3.3 ) ( -5.25,1.3)(-5.25,2.7 ) ( -1,4.2 ) ( 0,0)0.30180 ( 0,0)0.30180 ( 0,0.3)(0,1.2 ) ( -1.9,1 ) ( 0,0)0.30180 ( 0,0)0.30180 ( 0.5,0.5)(1.5,1.5 ) ( -1.5,-1.5)(-0.5,-0.5 ) ( -0.5,0.5)(-1.5,1.5 ) ( -1.5,2.5)(-0.5,3.5 ) ( -4,-1)(-2.5,-1 ) ( -2.5,-1)(1.6,-1 ) ( 2,-1)(0.4,-1 ) ( -1,-1)(-1,0 ) ( -1,0)(-1,2 ) ( -1,2)(-1,4.2 ) ( -4.5,3)(-2.75,3 ) ( -2.75,3)(-1,3 ) ( 1,3)(1,1.25 ) ( 1,2.5)(1,-1.6 ) ( 1,-2)(1,-0.4 ) ( 1,1)(0,1 ) ( 0,1)(-1,1 ) ( -1,1)(-1.9,1 ) ( -2.2,1)(-3,1 ) ( -4.5,1)(-3.64,1 ) ( -3.34,1.3)(-3.34,2.9 ) ( -3.34,3.1)(-3.34,5.4 ) ( -3.34,1)@xmath2 ( -4.5,-1.6)laser 1 ( 1.6,3.75)laser 2 ( 0,-2.3 ) ( 0,-2.7 ) ( -2.2,5.7)to data recording ( 2.7,1.5)thermal isolation ( -5.1,0.4)atomic ( -5.2,-0.1)clock ( -5,4.1)comb ( -4.9,3.6)generator by means of the proposed mission optis an improvement of three tests of sr and gr by up to three orders of magnitude is projected : llc experiment & present accuracy & projected accuracy + [ 1ex ] ' '' '' michelson morley experiment ( mm ) & @xmath3 @xcite & @xmath4 + kennedy thorndike experiment ( kt ) & @xmath5 @xcite & @xmath6 + universality of gravitat . red shift ( lpi ) & @xmath7 @xcite & @xmath8 + [ 1ex ] the main features of the optis mission can be seen in fig.[optisprinzip ] : a spinning drag free satellite orbits the earth . the satellite payload consists of two lasers , two orthogonal optical cavities , a femtosecond laser comb generator , and an atomic clock . the two cavities are used for the mm experiment which searches for differences in the velocity of light in different directions . the atomic clock represents an independent clock of different physical nature . a comparison between the atomic clock and an optical cavity can be performed by means of the comb generator . a search for a dependence of their frequency ratio with respect to a change of the velocity of the satellite or with respect to a change of the gravitational potential amounts to a kt test and to a test of the universality of the gravitational red shift , respectively . the most precise experiments testing the constancy of the speed of light use cavities . the wave vector magnitude @xmath9 of an electromagnetic wave in a cavity of length @xmath10 is given by @xmath11 and the frequency @xmath12 of an outcoupled wave by @xmath13 . if the velocity of light depends on the orientation of the cavity and on the velocity @xmath14 of the laboratory , @xmath15 , so will the frequency @xmath16 . fig.[fig : schemetest ] shows a schematic setup for a search of an orientation and velocity dependence of the frequency . since sr is based on an orientation and velocity _ in_dependent speed of light , the search for an orientiation and velocity dependence of the frequency amounts to a test of sr . ( 1,-2)(9,7)(5,1.4)(0,0.02)10(0,0)(4,1 ) ( 4.4,1.6)(5.2,1.4)(5.7,2.3)(4.9,2.5)(4.4,1.6 ) ( 5.2,1.4)(5.7,2.3)(5.7,1.7 ) ( 2.7,1.3)(5,2 ) ( 5,2)(5,4 ) ( 5,4)(5,5 ) ( 3.7,1.6)(-0.05,-0.015)20(0,0)(0.25,0.4 ) ( 5,-1)(5,0.36 ) ( 5,5)(0,0)0.30180 ( 0,0)0.30180 ( 0,0.3)(0,1.8)(0.7,-0.2)(0.7,1.3 ) ( 7.3,5.1 ) ( 6.5,1.8)mirror ( 3,2.8)cavity ( -0.3,1.2)turn table ( 5,0.8)(0.5,-0.992157)(1,-0.968246)(1.5,-0.927025)(2,-0.866025)(2.5,-0.780625)(3,-0.661438)(3.5,-0.484123)(3.7,-0.379967)(3.9,-0.222205 ) ( 8.3,-0.2)@xmath17 ( 4,-2)(7,-1 ) ( 7,-1.4)@xmath18 according to common test theories @xcite , the orientation and velocity dependence of the velocity of light is parametrized according to @xmath19 this means that all anomalous terms vanish for vanishing velocity @xmath14 . here @xmath17 is the angle between the velocity with respect to the cosmic preferred frame @xmath18 and the cavity axis . in addition , an expansion with respect to @xmath20 has been used , for simplicity . if special relativity is valid , then @xmath21 . the parameters @xmath22 and @xmath23 in the mansouri sexl and robertson test theories are given by [ cols="<,<,<",options="header " , ] in order to test the isotropy of space , or the isotropy of the velocity of light , one has to mount the cavity on a turn table and look for a variation of the frequency as the turn table is rotated . this setup has been used in experiments since 1955 , see fig.[fig : historymm ] . in terms of the relative variation of the velocity of light , of the robertson parameter , and of the mansouri sexl parameter , the most accurate result is @xcite @xmath24 for more interpretation see @xcite . a hypothetical dependence of the velocity of light on the velocity @xmath14 of the laboratory can be tested by changing the velocity of the cavity and looking for a variation of the frequency . in earth based experiments , the rotation of the earth around its axis ( @xmath25 ) or around the sun ( @xmath26 ) can be used , where @xmath27 is the velocity with respect to the cosmic microwave background , the cosmologically preferred frame . because of technical reasons only the rotation of the earth around its own axis has been used so far . in terms of the same parameters as above , the most accurate result is @xcite @xmath28 in the framework of einstein s gr , the comparison of two identical clocks of frequency @xmath29 located in different gravitational potentials @xmath30 and @xmath31 yields @xmath32 . the gravitational red shift does not depend on the type of clock . this is the universality of the gravitational red shift , an aspect of local position invariance . if einstein s theory is not correct , then the red shift may depend on the clock @xmath33 with @xmath34 . in einstein s gr @xmath35 . if two different clocks are displaced together in a gravitational potential , a relative frequency shift @xmath36 may occur , which is proportional to the difference of the gravitational potential relative to the uinitial position . ( 0,-1)(16,11)(1,-1.5)(16,-1.5 ) ( 1,-1.5)(1,10 ) ( 0.1,10)@xmath37 ( 1,-1.5)(1,0)15(0,0)(0,0.2 ) ( 2,-2)1880 ( 3,-2)1890 ( 4,-2)1900 ( 5,-2)1910 ( 6,-2)1920 ( 7,-2)1930 ( 8,-2)1940 ( 9,-2)1950 ( 10,-2)1960 ( 11,-2)1970 ( 12,-2)1980 ( 13,-2)1990 ( 14,-2)2000 ( 0.3,-1)@xmath38 ( 1,-1)(15,-1 ) ( 0.3,0)@xmath39 ( 1,0)(15,0 ) ( 0.3,1)@xmath40 ( 1,1)(15,1 ) ( 0.3,2)@xmath41 ( 1,2)(15,2 ) ( 0.3,3)@xmath42 ( 1,3)(15,3 ) ( 0.3,4)@xmath43 ( 1,4)(15,4 ) ( 0.3,5)@xmath44 ( 1,5)(15,5 ) ( 0.3,6)@xmath45 ( 1,6)(15,6 ) ( 0.3,7)@xmath46 ( 1,7)(15,7 ) ( 0.3,8)@xmath47 ( 1,8)(15,8 ) ( 0.3,9)@xmath48 ( 1,9)(15,9 ) ( 2,8)(0,0 ) ( 4.4,7)(0,0)@xmath49 morley & miller 1904 ( 6.4,7.2)(0,0)@xmath49 tomaschek 1924 ( 6.6,5.5)(0,0)@xmath49 kennedy 1926 ( 6.7,6.8)(0,0)@xmath49 illingworth 1927 ( 7,6.5)(0,0)@xmath49 joos 1930 ( 9.5,4)(0,0)@xmath49 essen 1955 ( 9.8,3.2)(0,0)@xmath49 cedarholm et al 1958 ( 10.4,3.2)(0,0)@xmath49 jaseja et al 1964 ( 11.9,2.5)(0,0)@xmath49 brillet & hall 1979 ( 14.3,-1)(0,0)@xmath49 optis ( proposed ) for the hydrogen maser @xmath50 ( gp - a experiment , @xcite ) , verifying the gravitational red shift . for a test of the universality of the gravitational red shift by means of a comparison between a microwave cavity and an atomic cesium clock , the best result is @xmath51 @xcite . the advantages of a sattelite mission for doing experiments for testing sr and gr are the following : * the high orbital velocity ( see eq.([genansatz ] ) . for the proposed ( elliptic ) orbit , @xmath14 varies between @xmath52 and @xmath53 over half the orbit period @xmath54 . this value is 20 times larger than the change of the velocity of the earth s surface over a period of 12 h. * the shorter period @xmath55 of the velocity modulation as compared to 24 h on earth . it relaxes the requirements on the optical resonators and is directly relevant for the kt and lpi tests . it is indirectly useful also for the elimination of systematic effects in the mm test . * the difference of the gravitational potential in the highly eccentric orbit is @xmath56 . this is about three orders of magnitude larger than the difference of the potential of the sun which an earth bound observer experiences . this is relevant for the lpi test . * the microgravity environment minimizes distortions of the optical resonators . this is relevant for the mm test . * a variable spin frequency of the satellite permits elimination of sytematic effects . * long integration times ( longer than 6 months ) . in this and the following section we discuss the science payload of the satellite , the relevant performance specifications and the resulting requirements for the orbit and the satellite bus structure . in order to perform the mm test , the satellite has to spin around its axis . a typical rotation period is @xmath57 . for the elimination of systematic errors , the rotation frequency @xmath1 can be varied . for the kt test the timescale is the orbit time @xmath58 . the main subsystems of the experimental payload are optical resonators , ultra stable lasers , an optical frequency comb generator and an ultra stable microwave oscillator . these components are interconnected and supplemented by the locking and stabilization electronics , the optical bench , the drag free control system ( discussed in the next section ) , and an advanced thermal control system . the lisa pre phase a report @xcite showed that a 3stage passive thermal isolation is sufficient to achieve a level of thermal fluctuations below @xmath59 at @xmath60 . this performance ( assuming no shadow phases ) would be sufficient for the optis random noise requirements . to supress the fluctuations correlated with the rotation of the satellite , an improvement of the thermal stability by one order of magnitude would be required . this could be achieved either by an additional stage of passive isolation , or by adding an active temperature stabilization . the optical resonators are the central part of the experimental setup . in the baseline configuration , two crossed standing wave resonators are implemented by optically contacting four highly reflective mirrors to a monolithic spacer block with two orthogonal holes made from a low expansion glass ceramic ( ule , zerodur ) . with a technically feasible finesse of @xmath61 and a length of @xmath62 each , these resonators should exhibit linewidths of @xmath63 . low expansion glass ceramics are designed for a minimal thermal expansion coefficient ( @xmath64 ) at room temperature and can be manufactured in many different shapes and dimensions . resonators made from these materials are well suited for laser stabilization , although aging effects cause a continuous shrinking of the material and thereby frequency drifts of typically @xmath65 . the monolithic construction of the resonator block serves to strongly reduce the effect of shrinking and of temperature fluctuations on the mm experiment : a high degree of common mode rejection ( two orders of magnitude ) in the differential frequency measurement of the lasers locked to the resonators is expected . for the kt and the redshift experiment , on the other hand , the aging related frequency drift is critical . it has to be modelled well enough to keep the unpredictable residual part below @xmath66 ( i.e. @xmath67 ) over the signal half period @xmath68 . this is feasible @xcite . for the projected measurement sensitivity the temperature stability requirements are as follows : a level @xmath69 for random fluctuations over the spin period time scale and a level @xmath70 for a temperature modulation correlated with the rotation of the satellite . for the kt as well as for the redshift experiment the requirements are @xmath71 for random temperature fluctuations on a time scale of the orbit period and @xmath72 for temperature modulation correlated with the orbital motion . the length of the reference resonators is affected by accelerations , with a typical sensitivity of @xmath73 for a resonator length of @xmath74 @xcite . this leads to a requirement of @xmath75 for random residual accelerations and @xmath76 for residual accelerations correlated with the rotation of the satellite . the drag - free control system ( see next section ) is designed to meet these requirements . the lasers used for the optis mission should have high intrinsic frequency stability , narrow linewidth and high intensity stability . these requirements are best fulfilled by diode pumped monolithic nd : yag lasers , which are also used in gravity wave detectors ( geo600 , ligo , virgo , lisa ) and many other high precision experiments @xcite . such lasers are already available in space qualified versions . locking the lasers to the reference resonators using the pound drever hall frequency modulation method requires fast , low noise photodetectors and an optimized electronic control system . the intrinsic noise of the photodetectors has to be sufficiently low to allow shot noise limited detection . the residual amplitude fluctuations of the lasers have to be actively suppressed . to prevent thermally induced length changes of the resonators by absorbed laser radiation , the intensity of the laser beams has to be actively stabilized to a relative level of @xmath77 in the frequency range @xmath78 to @xmath79 . the whole optical setup should be stable and isolated from vibrations to prevent frequency fluctuations caused by vibration induced doppler shifts . even very small displacements ( less then @xmath80 ) of the laser beams relative to the reference resonators are known to cause substantial frequency shifts @xcite . these requirements can be fulfilled by using a well designed monolithic optical bench on which all optical components are stably mounted as close together as possible . the kt and the universality of red shift experiments require an independent frequency reference . this reference should be based on the difference of two energy levels in an atomic or molecular system . atomic clocks based on hyperfine transitions in cesium or rubidium atoms are suited for this task . they are available in space qualified versions with relative instabilities of better than @xmath81 for the relevant time scale @xmath82 of several hours . the atomic clock can also serve as the reference for the microwave synthesizer required to mix down the beat signal between the two stabilized lasers in the mm experiment from typically 1 ghz to a lower frequency for data acquisition and analysis . the required relative instability @xmath83 on the timescale @xmath84 of @xmath85 is thereby satisfied . for the frequency comparison between the atomic clock and the lasers stabilized to the reference resonators it is necessary to multiply the microwave output of the atomic clock ( @xmath86 ) into the optical range ( @xmath87 ) . thanks to recent important progress in the field of frequency metrology , this can now be done reliably amd simply by using femtosecond optical comb generators @xcite . here the repetition rate of a mode locked femtosecond laser of @xmath88 is locked to an atomic clock . its optical spectrum ( a comb of frequencies spaced at exactly the repetition rate ) is broadened to more than one octave by passing the pulses through a special optical fiber . by measuring and stabilizing the beatnote between the high frequency part of the comb and the frequency doubled low frequency part , it is then possible to determine the absolute frequency of each component of the comb relative to the atomic clock . in a final step the frequency of the cavity stabilized lasers is then compared to the closest frequency component of the comb by measuring their beatnote with a fast photodetector . compact diode pumped comb generators with very low power consumption , as required for space applications , are already under development . the experimental requirements define an optimum mission profile . in particular , the requirements of attitude control , maximum residual acceleration , and temperature stability result in the following specifications : * the satellite needs a drag - free attitude and orbit control system for all 6 degrees of freedom . thrust control must be possible down to @xmath89n by means of ion thrusters ( field emission electical propulsion , feep ) . * for drag - free control the satellite needs an appropriate reference sensor . * feeps are not effective for orbit heights less than 1000 km , because of the high gas density in lower orbits . * to avoid charging of the capacitive reference sensor by interactions with high energy protons , highly eccentric orbits , where the satellite passes the van belt , are not appropriate . * the kt experiment requires a low orbit , because the experimental resolution depends directly on the satellite orbit velocity . * the precise attitude control requires a star sensor with a resolution of 10 arcsec . * mechanical components for attitude control ( e.g. fly wheel or mechanical gyros ) can not be used , because of the sensitivity of the experiment to vibrations . * temperature stability requirements during integration times of more than 100 s can only be realized on orbits without or with rare eclipse intervals . * the thermal control of the satellie structure must achieve a stabilioty of @xmath90 . * the mission time is 6 months minimum . optis is designed to be launched on a micro satellite with limited technological performance . considering all experimental requirements , technological feasibility , launch capability , and design philosophy the most feasible solution is to launch the satellite in a high elliptical orbit , attainable via a geo transfer orbit ( gto ) by lifting the perigee . in this scenario , the satellite is first launched as an auxiliary payload ( asap5 ) by an ariane 5 rocket into the gto with an apogee of 35800 km and a perigee of only 280 km . an additional kick motor on the satellite will lift the satellite in its final orbit with a perigee of about 10000 km , corresponding to @xmath91 . a minimum height of 10000 km enables one to use ion thrusters ( feeps ) and avoids flying through the van allen belt . also , the orbit eccentricity of @xmath92 is high enough to attain sufficient velocity differences for the kt experiment . although the relatively high orbit reduces the in orbit velocity of the satellite by a factor of 2.8 compared to a low earth circular orbit , it is still 20 times higher than for an earth based experiment . the satellite has cylindrical shape , with a height and a diameter of about 1.5 m. it spins around its cylindrical axis which is always directed to the sun . the front facing the sun is covered by solar panels . behind the front plate serving as thermal shield a cylindrical box for on board electronics and thruster control is located . the experimental box whose temperature is actively controlled is placed below the electronics . a stringer structure below the experimental box carries the kick motor and the fuel tank . 4 clusters of ion thrusters for fine ( drag free ) attitude control as well as 3 clusters of cold gas thrusters for coarse attitude control and first acquisition operation are mounted circumferentially . the structure elements of the entire bus have to satisfy the extreme requirement for passive thermal control . their thermal expansion coefficient has to be less than @xmath93 . the total satellite mass is about 250 kg including 90 kg of experimental payload . the total power budget is estimated to be less than 250 w. during experimental and safe mode coarse attitude and orbit control are based on a sun sensor ( 1 arcsec resolution ) and a star sensor ( 10 arcsec resolution ) . fiber gyros are used for spin and de spin maneuvers and serve to control the cold gas thrusters . the fine attitude control , also called the drag free control , must be carried out with an accuracy of @xmath94 within the signal bandwidth of @xmath95 to @xmath96 hz , depending on the satellite s spin rate . the general principle of drag free control is to make the satellite s trajectory as close as possible a geodesic . therefore , a capacitive reference sensor @xcite is used . the sensor unit consists of a test mass whose movements are measured capacitively with respect to all 6 degrees of freedom . apart from the sensing electrodes , electrodes for servo control surround the test mass and compensate its movement relative to the satellite structure . the signal is also used to control the satellite s movement via the ion thrusters . thus , the test mass falls quasi freely and is shielded against all disturbances by the satellite , in particular against solar pressure and drag . because the servo - control is influenced by back action effects , the test mass and the servo control form a spring mass system whose spring constant and eigenfrequnecy must be adapted to the signal bandwidth . therefore , electrode surfaces , charging by external sources as well as the precision of the test mass and the electrode alignments influence the measurement of @xmath97 directly and make necessary repeated in orbit calibration maneuvers @xcite . the chosen orbit avoids charging effects as much as possible . feep ion thrusters ( field emission electric propulsion ) must be used to overcome ( 1 ) solar radiation pressure acting on the satellite and disturbing its free fall behaviour , and ( 2 ) to control the residual acceleration down to @xmath98 in the signal bandwidth . the first requirement sets an upper limit for the thrust : linear forces acting on the satellite are less than @xmath99 in all 3 axes and maximum torques are about @xmath100 . the second condition determines the resolution of thrust control which have to be done with an accuracy of about @xmath101 . a feep able to satisfy these requirements is the indium liquid metal ion source ( lmis ) of the austrian research centers seibersdorf ( arcs ) @xcite . thrust is produced by accelerating indium ions in a strong electrical field . a sharpened tungsten needle is mounted in the centre of a cylindrical indium reservoir bonded to a ceramic tube which houses a heater element for melting the indium . ion emission is started by applying a high positive potential between the tip covered with a thin indium film and an accelerator electrode . to avoid charging a neutralizer emitting electones is installed . the feeps have a length of 2 cm , a diameter of 4 mm , and weigh only several grams sufficient for the entire mission . a continuous thrust of @xmath102 per thruster is available . for a satellite diameter of about 1.5 m ( the maximum asap 5 size ) , the solar radiation pressure of ca . @xmath103 and the radiation pressure of the earth albedo of @xmath104 sum up to a total drag of about @xmath105 . considering thruster noise , misalignments and other disturbing effects , a continuous thrust of @xmath106 would be sufficient . to control all 6 degrees of freedom a minimum of 3 clusters of 4 thrusters is necessary . to guarantee a continuous thrust with some redundancy 4 clusters are desirable . the power consumption is less than 3 w on average with peaks up to 25 w. the proposed optis mission is capable to make considerable improvements , up to three orders of magnitude , in the tests of sr and gr . it is designed to be a low cost mission . it is based on using ( i ) recent laboratory developments in optical technology and ( ii ) the advantages of space conditions : quit environment , long integration time , large velocities and large potential differences . the optical technology includes an optical comb generator , stabilized lasers and highly stable cavities . we remark that an alternative optical cavity system consisting of a monolithic silicon block operated at @xmath107 , the temperature where the thermal expansion coefficient vanishes , should be studied @xcite . the advantage of this approach could be a significantly reduced level of creep and therefore a corresponding improvement of the kt test .

a new satellite based test of special and general relativity is proposed . for the michelson morley experiment we expect an improvement of at least three orders of magnitude , and for the kennedy thorndike experiment an improvement of more than one order of magnitude . furthermore , an improvement by two orders of the test of the universality of the gravitational red shift by comparison of an atomic clock with an optical clock is projected . the tests are based on ultrastable optical cavities , an atomic clock and a comb generator .

this is the second in a series of papers devoted to investigate whether the maximum young cluster masses observed in a galaxy reflect physical processes that determine them or if , instead , they constitute an effect of random sampling statistics . a correlation between gas surface density and embedded maximum cluster mass ( i.e. , @xmath13 ) has been proposed as an ansatz to explain the existence of the h@xmath14 cut - off in disk galaxies , while at the same time , as can be inferred from uv data , there is no actual star formation cut - off @xcite . similarly , a correlation @xmath15 has been proposed by @xcite and @xcite , arising from the star formation law ( @xmath16 * ? ? ? * ) , in conjunction with the assumption of pressure equilibrium between the ambient ism and the cluster - forming cloud cores . in this case , @xmath17 , with the lower value expected for equal ( volume ) density clusters , and the higher one for clusters with equal size @xcite . in the first paper of the series @xcite , we analyzed radially averaged distributions of gas surface densities and of cluster masses in the flocculent galaxy m 33 . here , we study the grand - design galaxy m 51 . star cluster data are presented in section 1 , and ism data in section 2 ; both cluster and gas data are taken from the literature . the results and a comparison with m 33 are discussed in section 3 . section 4 contains our summary and conclusions . we rely on two catalogs of star clusters brighter than @xmath18 = 23 mag , detected by @xcite , based on hubble space telescope ( _ hst _ ) advanced camera for surveys ( acs ) observations acquired by the hubble heritage team . @xcite compiled two catalogs , one of 2224 class 1 " clusters , that appear circular and well isolated , and one with 1388 class 2 " clusters , which have elongated or irregular shapes and/or close neighbors . these original catalogs list , among other properties , cluster ra and dec , half - light radius @xmath19 , ( @xmath20 ) and ( @xmath21 ) colors , aperture corrected @xmath22 mag , and photometric errors , all in the _ hst _ equivalent of the johnson system . from the recovery of artificial clusters , @xcite determined that the completeness of clusters with @xmath23 mag is higher than 80% , regardless of the clustering properties of the field . subsequently , @xcite calculated masses , ages , and reddening for the clusters , via the comparison of their broad band , @xmath24 , and @xmath25 filters . @xcite complemented these with archival @xmath26 wide field planetary camera 2 ( wfpc2 ) data . ] spectral energy distributions ( seds ) with theoretical seds derived from the @xcite stellar population synthesis models . the models used by @xcite have a salpeter initial mass function ( imf ) , with lower and upper mass cutoffs of 0.1 @xmath27 and 100 @xmath27 , respectively ; ages between 1 myr and 15 gyr ; and solar metallicity . each one of the 182 model spectra was reddened by @xmath28 values between 0.0 and 0.6 in 40 0.015 mag steps . ] the age and reddening of each cluster were determined simultaneously , from a @xmath29 fit of the reddened model seds to the photometric data . the original catalogs were thus reduced to 1125 class 1 and 835 class 2 objects with acceptable fits . for each cluster , a mass was finally assigned from the mass to light ratio @xmath30 of the best - fit model and the @xmath22-band cluster magnitude , taking the measured extinction into account and adopting a distance to m 51 of 8.4 mpc @xcite . 40.7 pc ; @xmath31 , the galactocentric distance of the isophote with surface brightness in the @xmath32-band @xmath33 mag @xmath34 , is 13.7 kpc or @xmath35 . ] the @xcite catalogs list , for each cluster , log age and errors , log mass , color excess and errors , and @xmath29 value of the best - fit . these catalogs do not provide an error in the mass determination . one possible estimate is given by the @xmath30 ratios at the minimum and maximum ages ( the age minus and plus its error , respectively ) of each cluster . except for 24 ( out of 1960 ) clusters ( half of them less massive than @xmath36 ) , this error is smaller than 0.15 dex ( 35% of the mass ) in all cases . the dominant source of error is probably the uncertainty in the distance modulus ( 0.6 mag , or a factor of @xmath37 2 in mass ) . it would affect all the masses equally , though , so it would not change the exponent of any relationship between cluster mass and gas or sfr surface density . the age distribution of the clusters shows three peaks , that likely signpost bursts of enhanced star formation rate , respectively , at stellar ages of @xmath38 5 , 100 , and 200 myr . the two older starbursts are better traced by the detected class 1 objects , which have masses ranging from @xmath39 to @xmath40 . conversely , detected clusters in the recent burst belong mostly to class 2 , with significantly lower masses , between @xmath41 and @xmath42 . since m 51 is a grand - design spiral with large azimuthal variations of gas surface density , a two - dimensional approach is required , as opposed to a comparison of individual cluster masses with radial gas profiles , that was adequate for m 33 . we use the hi map of m 51 data from @xcite ; it was originally acquired with the very large array ( vla ) and has a spatial resolution of 13@xmath43 . we derive the molecular gas surface density distribution from the @xmath44co 21 mosaic obtained by @xcite with the iram-30 m telescope ; it has a resolution of 11@xmath43 . finally , to calculate the sfr surface density distribution we rely on the total power 20 cm radio continuum image published by @xcite ; it has a resolution of 15@xmath43 , and was produced from vla c- and d - array data . in order to get the h@xmath45 , hi , and sfr surface densities from the integrated intensity maps , we follow the same procedures as @xcite . at a given position in m 51 , the neutral gas surface density @xmath46(hi ) cos @xmath47 , where @xmath48 is the hydrogen atomic mass and @xmath49 is the inclination angle of m 51 ; assuming optically thin emission , @xmath50(hi ) = @xmath51/(k km s@xmath52)@xmath53 likewise , we obtain the molecular gas surface density as @xmath54(h@xmath45 ) cos @xmath47 . @xcite assume a co 2 - 1/1 - 0 intensity of 0.8 , and a constant co to h@xmath45 conversion factor , @xmath55 , 1/4 that of the milky way ( mw ) , with @xmath56 @xmath53 ( k km s@xmath52)@xmath52 , such that the molecular hydrogen column density is @xmath50(h@xmath45 ) = 0.25 @xmath57d@xmath58 , where @xmath59 is the main beam brightness temperature . the total gas surface density is @xmath60 , so as to include helium . again , following @xcite , we derive @xmath3 from the 20 cm radio continuum data . } m_\odot { \rm pc^{-2 } gyr^{-1}}$ ] . ] the 20 cm non - thermal radio continuum is due to synchrotron radiation by supernovae - accelerated cosmic rays ; it hence traces recent star formation , and has a strong correlation with the far - infrared ( fir ; e.g. , * ? ? ? * ) . can be readily derived from fir emission , given that a significant amount of it is due to reprocessing by dust of light from young stars ; fir emission also has the advantage that it does not need to be corrected for extinction . in fact , @xcite find that sfrs obtained at optical and uv wavelengths are often overcorrected for extinction , since stellar balmer absorption contaminates emission lines ; optical / uv and fir / mm sfr estimators agree well once this effect is taken into account . ] at the position of each star cluster , gas surface densities are obtained from the hi , h@xmath45 , and 20 cm mosaics averaging , respectively , the emission over @xmath61 ( @xmath62 pc@xmath63 ) , @xmath64 ( @xmath65 pc@xmath63 ) , and @xmath64 . on the side ; the smallest area over which we can average the flux is a subarray of 3@xmath663 pixels ( sides of subarrays must have an odd number of pixels ) , centered on the position of each cluster . we match the elements over which we average the hi and 20 cm fluxes to this @xmath67 footprint as closely as is allowed by the pixel sizes of the images , respectively , @xmath68 ( arrays with 5 pixels on the side ) and @xmath69 ( arrays of 9 @xmath66 9 square pixels ) . ] ninety - five of the clusters in the sample have coordinates that fall outside of the borders of the radio images , so that only 1865 objects can be compared with the gas and sfr densities at their location in the m 51 disk . @xcite find that the completeness distribution is quite similar for both class 1 and class 2 clusters . since cluster brightness in the optical diminishes with age , the completeness limit of the cluster mass function depends on cluster age . based on their photometric completeness limits , @xcite determine that conservative limits over which their mass functions are not affected by incompleteness are @xmath70 for clusters younger than 10@xmath71 , and at least 1@xmath72 for clusters between 100 and 250 myr . we will first work with the 167 clusters in the catalogs with at least @xmath73 , ages between 40 and 400 myr , yr old burst reaches 25 myr , but no cluster in this group that is younger than 40 myr makes the @xmath73 cut . ] and detected co , hi , and 20 cm emission at their present locations . @xcite and @xcite find that the cluster mass function is approximately independent of age ( and the age function independent of mass ) for clusters younger than @xmath74 yr in m 83 and m 51@xcite , respectively . similar results are found for the magellanic clouds @xcite and the antena galaxies @xcite . the implication is that the mass - dependent disruption timescale is @xmath75 2 gyr @xcite . we take care here to compare cluster mass with gas and sfr surface density always in bins with the same number of clusters , in order to test whether any change in maximum cluster mass is a statistical , size - of - sample effect . we search for correlations between cluster mass , and gas and sfr surface densities of the form : @xmath76 where @xmath77 is the mass of the @xmath47-th most massive star cluster , and @xmath78 stands for hi , h2 , total gas or sfr . figures [ m51_stot ] , [ m51_sh2 ] , [ m51_ssfr ] , and [ m51_shi ] show log of star cluster mass versus , respectively , log of total gas , molecular gas , star formation rate , and neutral gas surface densities . the comparison is performed in bins with equal number of clusters . bins increase from 2 ( upper left panel ) to 6 ( lower middle panel ) , and the number of clusters in each bin is indicated . instead of using the maximum cluster mass in each bin for the comparison , the median of the five most massive clusters ( or the third most massive cluster , @xmath5 ) in each bin is displayed as a filled circle ; the error bars represent the interquartile range , for both mass and gas / sfr surface density . since the uncertainty in the measurement of any individual mass is typically a factor of 2 - 3 , the median of the 5 most massive clusters in each bin should in general be a more statistically robust indicator of any existing trend ( in every bin there are always more than 5 clusters more massive than the completeness limit ) . there is no correlation of @xmath5 with the surface densities of total gas , @xmath0 , molecular gas , @xmath6 , or star formation rate , @xmath3 . conversely , there is a hint of a correlation with @xmath2 . the slopes ( @xmath79 ) and intercepts ( @xmath80 ) of the fits in the bins with 3 or more points , as well as their uncertainties , are listed in table 1 . the fits average can be expressed as log@xmath81 . lrrrrrr 3 & 55 - 56 & @xmath82 & @xmath83 & + 4 & 41 - 42 & @xmath84 & @xmath83 + 5 & 33 - 34 & @xmath85 & @xmath86 + 6 & 27 - 28 & @xmath87 & @xmath88 + in order to further explore whether the intrinsic mass distribution of clusters may be changing as a function of neutral gas surface density , we perform a kolmogorov - smirnov ( k - s ) test on the 6 different subsamples presented in the bottom middle panel of figure [ m51_shi ] . figure [ m51_ks ] shows the cumulative probability distributions and @xmath2 of each subsample , and the @xmath89 and @xmath90 values for every bin pair @xmath91 are given in table 2 ( higher bin number indicates larger surface density ) . assuming that sample pairs with @xmath92 are taken from different distribution functions with high significance , bin 1 ( _ red solid line _ ) , with the smallest surface density @xmath93 pc@xmath94 , seems to be different from bin 6 ( _ orange long dashed - dotted line _ ) , with the largest surface density @xmath95 pc@xmath94 ( @xmath96 ) . the mass distributions in bins 3 , 4 , and 5 appear to lie somewhere in between . no hard conclusion can be drawn , however , since bin 2 ( _ green dotted line _ ) , with the second lowest hi surface density , is in fact indistinguishable from bin 6 ( @xmath97 for the pair ) . + @c|cc|cc|cc|cc|cc@ & & & & & & & & & & + & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 + & & & & & & & & & & + & & & & & + 1 & 1.53 & 0.0187 & 0.69 & 0.7198 & 0.97 & 0.3003 & 0.83 & 0.4903 & 1.44 & 0.0318 + 2 & & & 1.11 & 0.1687 & 0.83 & 0.4903 & 0.83 & 0.4903 & 0.46 & 0.9823 + 3 & & & & & 0.83 & 0.4903 & 0.69 & 0.7198 & 1.04 & 0.2337 + 4 & & & & & & & 0.28 & 1.0000 & 0.76 & 0.6100 + 5 & & & & & & & & & 0.73 & 0.6530 + [ kstab ] we now analyze the 56 clusters younger than 10@xmath71 yr with mass at least 5@xmath100 and higher , and detected co , hi , and 20 cm emission at their positions . figures [ m51_young_stot ] , [ m51_young_sh2 ] , [ m51_young_ssfr ] , and [ m51_young_shi ] show log of star cluster mass versus , respectively , log of @xmath0 , @xmath6 , @xmath3 , and @xmath2 . bins with indicated , equal , number of clusters again increase from 2 to 6 ; points are the median of the 5 most massive clusters in each bin . as with clusters in the two older bursts , there is no correlation between @xmath5 , and @xmath6 or @xmath3 . the correlation with @xmath2 is tighter and has a slightly steeper slope , though , with average fit for all the bins with 3 or more points log@xmath101 . moreover , there is also a hint of a correlation of @xmath5 with the total mass surface density @xmath0 , with average fit log@xmath102 . fully aware that the statistical significance might be questionable , we show nontheless log@xmath103 of _ maximum _ cluster mass in the bin , @xmath104 , versus @xmath2 for clusters younger than 10@xmath71 yr in figure [ m51_young_max_shi ] . the error in log mass for each cluster was determined as described previously in section [ scd ] ; the error bar in @xmath2 shows the uncertainty in the measurement at the cluster s position . the average of the fits in the bins with more than 3 points is as tight as for @xmath5 , and consistent with it : log@xmath105 . the parameters of the fits for the younger burst can be found in table 3 . lrrrrrr + 3 & 18 - 19 & @xmath106 & @xmath107 & + 4 & 14 & @xmath108 & @xmath107 + 5 & 11 - 12 & @xmath109 & @xmath110 + 6 & 9 - 10 & @xmath111 & @xmath112 + + 3 & 18 - 19 & @xmath109 & @xmath113 + 4 & 14 & @xmath109 & @xmath113 + 5 & 11 - 12 & @xmath114 & @xmath115 + 6 & 9 - 10 & @xmath116 & @xmath117 + + 3 & 18 - 19 & @xmath118 & @xmath119 + 4 & 14 & @xmath120 & @xmath121 + 5 & 11 - 12 & @xmath87 & @xmath122 + 6 & 9 - 10 & @xmath123 & @xmath112 + + @c|cc|cc|cc|cc|cc@ & & & & & & & & & & + & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 & @xmath98 & @xmath99 + & & & & & & & & & & + & & & & & + 1 & 1.20 & 0.1108 & 0.91 & 0.3754 & 0.60 & 0.8646 & 0.83 & 0.4892 & 1.38 & 0.0438 + 2 & & & 1.12 & 0.1617 & 1.12 & 0.1617 & 0.81 & 0.5305 & 0.78 & 0.5732 + 3 & & & & & 0.51 & 0.9575 & 0.76 & 0.6030 & 1.27 & 0.0778 + 4 & & & & & & & 0.51 & 0.9575 & 1.27 & 0.0778 + 5 & & & & & & & & & 0.76 & 0.6030 + [ kstabyoung ] we perform once more a k - s test on the 6 different subsamples presented in the bottom middle panel of figure [ m51_young_shi ] . the test is illustrated with figure [ m51_young_ks ] , and its numerical results are given in table 4 . bin 1 ( _ red solid line _ ) , with the smallest surface density @xmath124 pc@xmath94 , seems to be different , with high statistical significance , from bin 6 ( _ orange long dashed - dotted line _ ) , with the largest surface density @xmath125 pc@xmath94 ( @xmath126 ) . the mass distibutions in all the other bins lie in between , although we notice that the distributions in bins 4 ( _ cyan long dashed line _ ) and 5 ( _ magenta dashed - dotted line _ ) are actually closer to bin 1 than to bin 6 ( @xmath127 ; @xmath128 ; @xmath129 ; @xmath130 ) . in a companion paper @xcite , we have performed a similar analysis on the flocculent galaxy m 33 , except that we have compared the _ radial _ profiles of cluster mass distribution and gas surface densities . since m 33 is a flocculent galaxy without a strong spiral perturbation , in general one can assume that the @xmath12 azimuthal averages provide a good estimate of the actual surface densities at any given point located at the same galactocentric distance . from the radial analysis , and both the average and median of the 5 most massive clusters in data bins , we derive for m 33 : log@xmath131 ; log@xmath132 ; log@xmath133 . one would also derive log@xmath134 , but there is a very small range of @xmath2 values in the disk of m 33 , as the radial distribution of neutral gas has @xmath135 ( exponential scale length @xmath136 ) , i.e. , it is more than twice as shallow as in m 51 , which has @xmath137 . here , we present the m 33 data in a way that is directly comparable to our analysis of m 51 . to this end , and since all ism phases have roughly exponential profiles , we use radius as a proxy for surface density , and produce plots for m 33 analogous to figures [ m51_stot ] , [ m51_sh2 ] , [ m51_ssfr ] , and [ m51_shi ] . we note that the log@xmath138 ranges indicated by the bars at the bottom of the panels sometimes overlap slightly , owing to the departures of the surface density profiles from a perfect exponential ; and ( 2 ) we omit in all cases the last bin , i.e. , the one at the largest galactocentric distance . as explained in @xcite , this bin is dominated by the most massive cluster in the galaxy , whose formation conditions are badly misrepresented by the azimuthally averaged gas surface density . moreover , the last bin always includes a radial range for which there is no gas data ; these stop at @xmath139 . the results of this exercise are shown in figures [ m33_stot ] , [ m33_sh2 ] , [ m33_ssfr ] , and [ m33_shi ] , and in table 3 . firstly , this fresh look at the data highlights that a correlation does not seem to exist between @xmath5 and @xmath2 . overlap more than a little , a sign that @xmath2 is far from changing monotonically with radius . ] as for the other ism components , we get : log@xmath140 ; log@xmath141 ; log@xmath142 . the 2-d correlation of log@xmath143 with total gas surface density , log@xmath144 , has a slightly shallower slope than the comparison between radial profiles . the radial and 2-d results for molecular gas and star formation rate densities , on the other hand , are consistent within 1 @xmath145 . lrrrrrr + 3 & 62 - 63 & @xmath146 & @xmath147 + 4 & 49 - 50 & @xmath110 & @xmath148 + 5 & 42 - 43 & @xmath149 & @xmath150 + + 3 & 62 - 63 & @xmath151 & @xmath152 + 4 & 49 - 50 & @xmath153 & @xmath154 + 5 & 42 - 43 & @xmath155 & @xmath156 + + 3 & 62 - 63 & @xmath157 & @xmath158 + 4 & 49 - 50 & @xmath118 & @xmath159 + 5 & 42 - 43 & @xmath160 & @xmath161 + we have analyzed the relationship between maximum cluster mass and gas surface density in m 51 , in order to explore the suggestion that maximum cluster mass is determined by physical processes , e.g. , the equilibrium pressure between cluster forming cores and the ambient interstellar medium @xcite , and since the existence of such a relationship can reconcile sfr measurements derived , respectively , from h@xmath14 and fuv emission in galaxy disks . furthermore , we have already found evidence in m 33 that star formation is not a stochastic process , and that the range of star cluster masses is driven by environmental physics . in our work , we have used published gas data of m 51 @xcite , and catalogs originally comprising more than 1800 young star clusters in its disk , also from the literature @xcite . among other information , these catalogs provide positions , ages , reddenings , and masses for the clusters . we have compared the 2-d distribution of the young star clusters with those of gas surface density and star formation rate . to test whether any trend is caused by random sampling from the cluster mass function as a size of sample effect , we have measured the distribution of maximum mass with gas surface density in 2 to 6 bins with an equal number of clusters in each bin . we examined two samples of clusters in m 51 : one of 167 clusters 25 to 400 myr old , and with a mass of at least 1@xmath72 , and another one of 56 clusters younger than 10 myr , with masses of 5000 @xmath27 and up . for the older sample , regardless of the number of bins , we find no correlation between the mass of the 3rd most massive cluster in each bin , @xmath5 , and the local surface densities of total gas , molecular gas , or star formation rate . there is , however , a hint of a correlation with local neutral gas surface density , such that log@xmath162 . for the younger sample , we find no correlation between @xmath5 , and either @xmath6 or @xmath3 . on the other hand , there is a correlation with @xmath2 that is tighter and with a slightly steeper slope than the one found for old sample ( although still consistent with it ) : log@xmath163 . a correlation may also exist for the most recent burst of @xmath5 with the total mass surface density @xmath0 : log@xmath102 . if true , the comparison between the correlations with the older and younger burst implies that the normalization depends on the cluster mass and/or age ranges . the results could not be more different from the ones obtained for the flocculent galaxy m 33 . from a 1-d radial analysis , we have previously derived for m 33 : @xmath164 @xmath165 @xmath166 with a treatment that mimicks the 2-d analysis of m 51 , we get for m 33 : @xmath9 @xmath167 @xmath168 in m 33 , the relation between @xmath5 and @xmath3 is consistent with the expectations from pressure equilibrium considerations . on the other hand , the slope of the correlation with @xmath0 is steeper than the value assumed by @xcite to explain the h@xmath14 cut - off in galaxy disks . there is no correlation with @xmath2 , but m 33 is known to have been interacting , and the hi distribution may not reflect the equilibrium configuration . the tight correlation with @xmath1 and @xmath3 , and the looser one with @xmath0 agree with the recent results of a study of 33 nearby spiral galaxies by @xcite , who find a tight and linear relation between @xmath3 and @xmath1 , with little dependence on @xmath0 . how can one understand the diametrically opposite results found for the grand - design spiral m 51 ? it is , of course , possible that stochastic sampling is at work in m 51 , such that the most massive cluster masses scale with the size of the sample . but then we would have to accept that stochastic sampling operates in some cases , like in m 51 , and not in others , like in m 33 . we propose a different hypothesis . the large azimuthal variations in gas and sfr surface densities in m 51 preclude a radial approach . instead , we compared star cluster masses with local surface densities . the problem then is that , typically , the clusters detected in the acs data with masses above the completeness limit of 10@xmath169 are older than 10@xmath170 yr ( only 24 out of 167 have ages between 40 and 90 myr ) . even if the cluster mass function is approximately independent of age over a timescale of a few hundred million years , clusters also complete between half and two full orbits around the galaxy in this time , and hence the local gas density around any given cluster probably has little to do with the gas density at the site and time of cluster formation . the two facts , that the correlation between @xmath5 and @xmath2 seems to be tighter for the younger sample , and that this latter group of clusters might also exhibit a correlation between cluster mass and total gas surface density @xmath0 , give some credibility to this hypothesis . unfortunately , the resolution of the radio data implies that we are comparing clusters with sizes of the order of 10 pc with gas surface densities averaged over an area of @xmath171 pc@xmath63 . even in the case of the younger sample , the measured @xmath12s are likely quite diluted compared to the actual densities relevant for the formation of the clusters . by contrast , 257 out of the 258 clusters kept for the final analysis in m 33 are younger than 2.5@xmath172 yr ( the age of the exception is 60 myr ) and , at any rate , the lack of a strong spiral perturbation means that the azimuthally averaged gas emission is in general representative of the star - forming conditions of clusters located at the same radii . to be able to perform a statistically significant analysis of clusters younger than 25 myr , still close to their birthsites and whose local gas densities resemble their star - forming environments , the depth and resolution of the cluster data need to be enough for the assembly of a sufficiently numerous sample above the mass function completeness limit . the gas data should also have a resolution comparable to the physical sizes of the clusters . the confirmation of the m 33 results will have to wait for the outcome of studies in closer targets , like the magellanic clouds , where the mass density distribution of clusters younger than a few @xmath172 yr can be probed with large numbers down to 100 - 1000 @xmath27 , and where the clusters physical sizes are well matched by the resolution achievable at radio wavelengths ; the data to do so already exist . ragl is grateful for the support received from dgapa , unam , and conacyt , mexico . n. hwang and m. g. lee generously provided the cluster catalogs used in this work . we thank a. rots , k. schuster , and r. beck for granting access to the hi , co , and 20 cm continuum images of m 51 , respectively . l. loinard helped with the nitty gritty details of the conversion of the reduced radio data to physical surface densities , and with the transformation of the hi image to coordinates j2000 . we acknowledge the positive and helpful comments of an anonymous referee .

we analyze the relationship between maximum cluster mass , and surface densities of total gas ( @xmath0 ) , molecular gas ( @xmath1 ) , neutral gas ( @xmath2 ) and star formation rate ( @xmath3 ) in the grand design galaxy m 51 , using published gas data and a catalog of masses , ages , and reddenings of more than 1800 star clusters in its disk , of which 223 are above the cluster mass distribution function completeness limit . by comparing the 2-d distribution of cluster masses and gas surface densities , we find for clusters older than 25 myr that @xmath4 , where @xmath5 is the median of the 5 most massive clusters . there is no correlation with @xmath0 , @xmath6 , or @xmath3 . for clusters younger than 10 myr , @xmath7 , @xmath8 ; there is no correlation with either @xmath1 or @xmath3 . the results could hardly be more different than those found for clusters younger than 25 myr in m 33 . for the flocculent galaxy m 33 , there is no correlation between maximum cluster mass and neutral gas , but we have determined @xmath9 @xmath10 @xmath11 . for the older sample in m 51 , the lack of tight correlations is probably due to the combination of the strong azimuthal variations in the surface densities of gas and star formation rate , and the cluster ages . these two facts mean that neither the azimuthal average of the surface densities at a given radius , nor the surface densities at the present - day location of a stellar cluster represent the true surface densities at the place and time of cluster formation . in the case of the younger sample , even if the clusters have not yet traveled too far from their birthsites , the poor resolution of the radio data compared to the physical sizes of the clusters results in measured @xmath12s that are likely quite diluted compared to the actual densities relevant for the formation of the clusters .

the study of transport properties of semiconductor structures with many occupied electronic subbands has attracted scientific interest for a long time , concerning especially with two - subband occupancy and screening effects in the scattering processes @xcite . moreover , until recently these studies were made in inversion layers of si - mos ( metal - oxide - semiconductor ) structures @xcite in gaas / al@xmath0ga@xmath1as selectively doped heterojunctions with two - subband occupied @xcite , where large - scale fluctuations of layers have small effect on the position of the energy levels and transport properties . recently , new types of quantum wells ( qw ) , e.g. , modulation - doped qw @xcite , wide parabolic qw @xcite , and stepped qw @xcite semiconductor structures with two occupied subbands , have been grown by tailoring the conduction - band edge of iii - iv semiconductors . it was shown that these novel heterostuctures with double subband occupancy exhibit a much stronger effect of large - scale disorder on transport properties than the previously studied one - subband systems . for the new systems , the screening is effective only on the average of the external changes of the bottoms of the two occupied subbands , which are different from each other , and caused by smooth variations of qw parameters on the scale of the bohr radius as illustrated in fig . . only essential unscreened large - scale fluctuations of the both occupied qw levels are present in these systems . this paper addresses the effect of such non - screened variations of both occupied energy levels on the electronic spectrum and the classical magnetotransport by employing different confinement models : hard wall qw ( fig . 1b ) , parabolic qw ( fig . 1c ) , and stepped qw ( fig . short - range and small - angle elastic scattering mechanisms , within a local response approximation , are included in the linearized kinetic equation . we obtain effective magnetotransport coefficients , which are evaluated from the components of the local conductivity tensor averaged over large - scale inhomogeneities , up to second order in the disorder contributions to the conductivity@xcite , for zero temperature . in addition , we calculate the modulation of the effective conductivity by the transverse voltage . we take into account the difference between intra - subband momentum scattering frequencies and the inter - subband contributions . we investigate also the spatial variations of these frequencies . we find an essential broadening of the peak of intersubband transitions due to the large - scale inhomogeneities and we provide numerical estimates of magnetotransport coefficients for the considered models . the organization of the paper is as follows . in sec . ii the energy spectrum , which takes into account non - screened variations of levels , and the general conductivity tensor within the linear response approach , are obtained . from the transition probability for a random potential model , we calculate , in sec . iii , the scattering frequencies and magnetotransport coefficients considering short - range and small - angle scattering mechanisms and after averaging the conductivity tensor over in - plane large - scale inhomogeneities . in sec . iv , we discuss the assumptions , on which the work described here is explicitly dependent , and we present our concluding remarks . we discuss now our model for the energy levels fluctuations due to random inhomogeneities and we obtain the general expressions of the conductivity tensor based on the local response approach for nonideal qws with two occupied subbands . electron energy levels in a qw with slowly varying width can be described in terms of @xmath2 along with the in - plane kinetic energy given by the parabolic dispersion law @xmath3 with effective mass @xmath4 . for instance , the influence of nonideal heterointerfaces in the hard - wall qw , formed by large band offsets , can be studied by assuming that the qw widths , @xmath5 , are randomly varied . then , the few lowest energy levels @xmath6 are given by @xmath7 where @xmath8 , @xmath9 is the mean width of the qw , and @xmath10 is its random fluctuation due to heterointerface roughness . the energy of an electron in the @xmath11-th subband is given as @xmath12 , where @xmath13 is the screening potential averaged over the @xmath11-th subband charge distribution @xmath14 along the @xmath15 direction . the potential @xmath16 is determined by the poisson s equation as @xmath17 where @xmath18 is the electron density in the @xmath11-th subband , @xmath19 is the 2d density of states , @xmath20 the fermi energy , @xmath21 is the electron density averaged over the random inhomogeneities , and @xmath22 is the dielectric constant , assumed independent of @xmath15 . hereafter , we consider only the case of two occupied subbands . the solution of eq . ( [ 2 ] ) is given as @xmath23 where @xmath24 is the 2d fourier transform of the nonuniform part of the electron density @xmath25 substituting eq . ( [ 4 ] ) in eq . ( [ 3 ] ) , we are led to the system of two linear inhomogeneous equations for the fourier transforms of screening potentials @xmath26 for @xmath27 and @xmath28 subbands : @xmath29 notice that inhomogeneity of eq . ( [ 5 ] ) comes from terms @xmath30 . hence the solutions are expressed in terms of the variations of the occupied levels , introduced by eq . ( [ 1 ] ) . assuming large - scale variations , @xmath31 , it follows from eq . ( [ 5 ] ) that only the fourier components with @xmath32 are essential . then @xmath33 in eq . ( [ 5 ] ) can be well approximated by the unity and we have @xmath34 where @xmath35 is the bohr radius . here the right - hand side is independent of @xmath11 , so @xmath36 . further , for @xmath37 from eq . ( [ 6 ] ) , it follows that @xmath38 i.e. , screening is relevant only on the average of the external variations @xmath39 and @xmath40 . as a result , the electron spectrum energy can be written in the form @xmath41 where @xmath42 is the non - screened part of potential . for further numerical estimates , we assume gaussian correlations for the qw width fluctuations @xmath43 here @xmath44 , @xmath45 is the typical height of the roughness interface and @xmath46 $ ] is the gaussian function with lateral correlation length @xmath47 . we can also write analogous expressions for the case of parabolic ( fig . 1c ) and stepped ( fig.1d ) qws but we do not give here the pertinent formulas considering further that @xmath48 is a given quantity . classical transport phenomena for electrons with spectrum , given by eq . ( [ 8 ] ) , are described by the distribution function @xmath49 within the linear response theory . here @xmath50 is the unperturbed fermi distribution and the field - induced distribution is determined from the linearized kinetic equation of @xmath11-th subband given by @xmath51\cdot \frac{\partial } { \partial { \bf p}}\right ) \delta f_{{\bf pr}}^{(s)}-i_{s}(\delta f|{\bf pr})=-e{\bf e}_{{\bf r}}\cdot \frac{% \partial f_{f}(e_{p{\bf r}}^{(s)})}{\partial { \bf p } } , \label{10}\ ] ] where @xmath52 is the electric field , which is zero in the absence of a net current density @xmath53 , @xmath54 is the magnetic field perpendicular to the qw s plane ( @xmath55 ) and the collision integral for the elastic scattering case is written as @xmath56 @xmath57 is the transition probability per second between states @xmath58 and @xmath59 . the total current density @xmath53 is given by the standard expression @xmath60 and satisfies the continuity equation @xmath61 . the contributions from the convection and random fields in the left - hand side of eq . ( [ 10 ] ) are estimated as @xmath62 and @xmath63 respectively . these contributions can be discarded when @xmath64 and @xmath65 , where @xmath66 is the characteristics electron energy , where we have used the relaxation time approximation to estimate the collision integral as @xmath67 under these assumptions , eq . ( [ 10 ] ) assumes the form @xmath68\frac{\partial } { \partial { \bf p}}\delta f_{{\bf pr}}^{(s)}-i_{s}(\delta f|{\bf pr})=-e({\bf e}_{{\bf r}}\cdot { \bf v}% ) f_{f}^{^{\prime } } ( e_{p{\bf r}}^{(s ) } ) , \label{13}\ ] ] where @xmath69 . we look for a solution in the form @xmath70\cdot { \bf v})\right\ } , \label{14}\ ] ] where the coefficients @xmath71 and @xmath72 depend only on @xmath73 . substituting eq . ( [ 14 ] ) into the kinetic equation ( [ 13 ] ) , we obtain the linear algebraic system ( see ref.@xcite for details ) @xmath74 the solution of eq . ( [ 15 ] ) for our two - level system is expressed through the transport relaxation frequency of @xmath11-th subband given by @xmath75 \label{16}\ ] ] and the intersubband relaxation frequencies are written as @xmath76 where @xmath77 . the solution of eqs . ( [ 15 ] ) is @xmath78-\tilde{\nu}_{12}[\tilde{\nu}_{12}\nu _ { 2}+\eta _ { 1}(\omega _ { c}^{2}+\tilde{\nu}_{12}^{2})]}{\delta } \nonumber \\ b_{1 } & = & \frac{\omega _ { c}^{2}+\nu _ { 2}^{2}+\tilde{\nu}_{12}^{2}+\eta _ { 1}% \tilde{\nu}_{12}(\nu _ { 1}+\nu _ { 2})}{\delta } , \label{18}\end{aligned}\ ] ] with the cyclotron frequency @xmath79 , @xmath80 , @xmath81 , and @xmath82 $ ] . in eq . ( [ 18 ] ) we have @xmath83 , where the momenta @xmath84 and @xmath85 are connected through @xmath86 from energy conservation . the expressions for @xmath87 and @xmath88 follows from the above expressions for @xmath89 and @xmath90 , respectively , by changing @xmath91 , @xmath92 everywhere in eq . ( [ 18 ] ) and taking @xmath93 where @xmath84 now satisfies @xmath94 . furthermore , for the zero - temperature , the coefficients @xmath71 and @xmath72 are calculated only at the fermi level . thus , we have to use @xmath95 ( @xmath96 ) in @xmath97,@xmath90 ( @xmath87,@xmath88 ) while @xmath98 and @xmath99 correspondingly . the induced current density , at zero temperature , is written as @xmath100\right\ } \equiv \hat{\sigma}({\bf r}){\bf e}_{{\bf r } } , \label{19}\ ] ] where the electron concentration for the @xmath11-th subband is given by @xmath101 @xmath102 is the mean concentration of the @xmath11-th level and @xmath103 is the total average concentration . from eq . ( [ 19 ] ) , the components of the @xmath104 conductivity tensor are @xmath105 where @xmath106 and @xmath107 . note , that the conductivity dependence on @xmath108 comes not only due to the spatial variations of @xmath109 but also because @xmath110and @xmath111 depends on @xmath112 . in this section , we study the peculiarities of the steady - state magnetotransport caused by unscreened fluctuations of the qw s energy levels . in the model of random potentials , the transition probability can be written as @xmath113|\left\langle s^{\prime } |e^{iqz}|s\right\rangle |^{2}\delta ( e_{{\bf p^{\prime } } , s^{\prime } , { \bf r}}-e_{{\bf p},s,{\bf r } } ) , \label{22}\ ] ] where @xmath114 is the gaussian correlation function for the random potential with characteristic scale @xmath115 ( note that @xmath116 ) , @xmath117 $ ] is a 3d wave vector , and @xmath118 is the normalization length . summing over @xmath119 in eq . ( [ 22 ] ) leads to @xmath120^{2 } } \label{23}\ ] ] and the transition probability transforms into @xmath121^{2}\}k_{ss^{\prime } } \delta ( e_{{\bf % p^{\prime } } , s^{\prime } , { \bf r}}-e_{{\bf p},s,{\bf r } } ) , \label{24}\ ] ] where the @xmath122-function depends on @xmath112 only for intersubband transitions , @xmath123 . notice that @xmath124 . the functions @xmath125 are calculated below for the cases of short - range ( @xmath126 ) and small - angle ( @xmath127 ) scattering . we consider three models of confinement potential : _ _ hard - wall qws ( see sec . iia ) , _ _ parabolic qws@xcite with effective width @xmath128 , @xmath129 is the characteristic frequency of the potential , and _ _ stepped qws@xcite with quite different well widths @xmath130 . the coefficients @xmath131 are shown in table i. consider next the relaxation frequencies for these cases . for short - range scattering , straightforward calculations of eqs . ( [ 16 ] ) , ( [ 17 ] ) , and ( [ 24 ] ) give @xmath132 and @xmath133 . for small - angle scattering , we obtain @xmath134 where we assumed that @xmath135 and @xmath136 is determined from @xmath137 . we point out that , in these conditions for small - angle scattering , we have @xmath138 due to the exponentially small factor . indeed , for instance , in the case of the parabolic qw , @xmath139 $ ] . for the maximum ratio @xmath140 , we estimate @xmath141 $ ] . so , if @xmath142\ll 10^{-1}$ ] , we obtain @xmath143 for hard - wall and parabolic qws . similar condition holds for the stepped qw . for small - angle scattering , we neglect further very small contributions related to @xmath144 and @xmath145 . then , as it is seen in the table i and eq . ( [ 26 ] ) , the transport coefficients do not depend essentially on the specific qw for small - angle scattering . in order to analyze the influence of non - uniform contributions , we have to average the local conductivity tensor , eqs . ( [ 21 ] ) , written in the form @xmath146 , where @xmath147 is the non - uniform contribution and @xmath148 is the conductivity tensor for an ideal qw with two occupied subbands given by @xmath149 here we assume that intersubband frequencies are negligible . following ref . @xcite , we obtain , up to the second order in the large - scale disorder , the effective conductivity tensor , from @xmath150 , as @xmath151 where @xmath152 denotes the average over the sample area , _ i.e_. , for distances @xmath153 , and @xmath154 @xcite . the average is performed using fourier transform of the gaussian correlation function , eq . ( [ 9 ] ) , @xmath155 $ ] with @xmath156 . before explicit calculation of the local magnetoconductivity tensor from the general eq . ( [ 21 ] ) , we present now standard expressions for magnetotransport coefficients of a qw with two occupied subbands . using the conductivity tensor , given by eq . ( [ 27 ] ) , we obtain the magnetoresistance @xmath157 } , \label{29}\ ] ] and the hall coefficient @xmath158}. \label{30}\ ] ] for strong ( @xmath159 ) and weak ( @xmath160 ) magnetic fields , the hall coefficient do not depend on @xmath161 leading to @xmath162 and @xmath163 $ ] . for short - range scattering , all frequencies do not depend on @xmath164 and as a consequence , the coefficients @xmath71 and @xmath72 are independent of @xmath112 . the non - uniform contribution to the conductivity tensor takes the form @xmath165 after substituting eq . ( [ 31 ] ) into eq . ( [ 28 ] ) and performing the averaging process , we obtain the components of the effective conductivity tensor as @xmath166 @xmath167 where @xmath168 gives the concentration fluctuation due to large - scale inhomogeneities . using eqs . ( [ 32 ] ) and ( [ 33 ] ) , the effective magnetoresistance @xmath169 , and the hall coefficient @xmath170 , can be easily obtained . in fig . 2 , we plot @xmath171 as a function of the magnetic field for @xmath172 . the solid and dot - dashed curves are @xmath173 times enlarged and correspond to parabolic qws where @xmath174 and @xmath175 and @xmath176 respectively , the dotted and dashed curves correspond to stepped qws for @xmath175 and @xmath177 , respectively , with @xmath178 , @xmath179 , @xmath180 ev , which leads to @xmath181@xmath182 , @xmath183 mev , and @xmath184@xmath185 . it follows that @xmath186 . notice that @xmath187 as well as @xmath188 for the hard - wall qw because @xmath189 for short - range scattering . then magnetoresistance is absent for hard - wall qws , while a positive magnetoresistance appears for the parabolic qw , which becomes larger by a factor of @xmath190 in the case of the stepped qw . in fig . 3 , we depict @xmath191 , where @xmath192 with @xmath193 using the same curves and conditions as in fig . 2 . similarly to fig . 2 , the solid and dot - dashed curves represent @xmath194 for the parabolic qw . in the case of the hard - wall qw , @xmath195 and @xmath196 because @xmath189 . hence for hard - wall qw @xmath197 , while an explicit dependence of @xmath161 is observed for parabolic and stepped qws . in addition , from figs . 2,3 it follows that unscreened effect of the large - scale inhomogeneities of a qw parameters is manifested through stronger magnetoresistance at @xmath198 and weaker at @xmath199 . while it leads to smaller hall coefficient for @xmath200 , for @xmath201 effect of such large - scale inhomogeneities on hall coefficient becomes negligible . notice that in experiment of ref . @xcite it was observed for magnetic fields , @xmath202 t , practically independent of @xmath203 magnetoresistance in gaas - based parabolic qw with two occupied subbands : which leads to @xmath204 very close to @xmath205 that in turn can be valid only when scattering is short - range . for small - angle scattering , large - scale fluctuations of the electron density and scattering frequencies play an important role . as we have seen , scattering frequencies , given by eq . ( [ 26 ] ) , depend on fluctuations of the fermi momenta . further , we can neglect contributions coming from @xmath206 and @xmath144 . using eqs . ( [ 18 ] ) , ( [ 21 ] ) , ( [ 26 ] ) , and ( [ 28 ] ) , the components of the effective conductivity tensor , for small - angle scattering , can be written as @xmath207 , \label{34}\ ] ] and @xmath208 where @xmath209 \right\ } , \label{36}\ ] ] @xmath210 \right\ } , \label{37}\ ] ] and @xmath211 @xmath212 here @xmath213 , where @xmath214 is independent of @xmath112 and is determined by @xmath102 , @xmath215 , and a typical scattering frequency @xmath216 is determined as @xmath217 . notice that @xmath218 is related to @xmath102 , while @xmath219 corresponds to @xmath220 . in figs . 4 and 5 we present our calculated effective conductivity tensor , given by eqs . ( [ 34])-([39 ] ) , magnetoresistance @xmath171 and the hall coefficient , @xmath170 . in fig 4 , we show @xmath171 for @xmath172 as a function of @xmath221 . the solid and dashed curves represent @xmath222 for small - angle scattering for @xmath223 and @xmath224 , respectively . and @xmath225 . for comparison , we plot the dotted curve for short - range scattering in the stepped qw as shown in fig . we observe in fig . 4 that , for small - angle scattering , large - scale inhomogeneities strongly modifies the effective magnetoresistance in the case of two occupied subbands . its behavior can be essentially different from the situation of short - range scattering . in this case , as it can be seen in fig . 2 , the magnetoresistance increases before reaching a plateau at @xmath226 . on the contrary , for small - angle scattering , this behavior is observed at @xmath227 . as it is seen in fig . 4 , there is a much larger region of classical magnetic fields in which the magnetoresistance increases in case of small - angle scattering than for short - range scattering . furthermore , in contrast with the short - range scattering case , we see that large - scale unscreened inhomogeneities lead to substantially smaller values of magnetoresistance at relatively weak magnetic fields , @xmath228 , while contributes to enhance the magnetoresistance at larger magnetic fields , @xmath229 . notice that according experimental results of ref . @xcite , where all data are given for @xmath230 , the rather small magnetoresistance was attributed to small - angle scattering , which is confirmed by our calculated @xmath169 given by the solid curve in fig . 4 . using the same parameters of fig . 4 , @xmath191 is depicted in fig . we now observe that large - scale unscreened inhomogeneities lead to a substantially weaker dependence of @xmath170 on @xmath161 in agreement with the experimental results of ref . @xcite . in conclusion , our theoretical results describe qualitatively well the experimental ones.@xcite we point out that the results , in the case of small - angle scattering , are independent of qw confinement model . now we consider the modulation of the effective conductivity under transverse voltage which causes intersubband redistribution of the electron population . from eq . ( [ 32 ] ) , for zero magnetic field , the effective conductivity , for short - range scattering , can be written as @xmath231 where @xmath232 , @xmath233 , @xmath234 , @xmath235 with @xmath236 and @xmath237 . for hard - wall qws , because @xmath238 , it follows that @xmath239 is independent of @xmath240 . in fig . 6 , we present @xmath241 as a function of @xmath242 . the dotted and dashed curves correspond to stepped qws with @xmath243 , for the same parameters used in fig . 2 , and @xmath223 and @xmath244 , respectively . the thin - solid curve corresponds to a parabolic qw , with @xmath245 , for @xmath246 which practically coincides with that for @xmath247 . we observe that all curves , plotted in fig . 6 , for short - range scattering , have a negative slope . for small - angle scattering , the effective conductivity , given by eq . ( [ 34 ] ) , transforms , for @xmath248 , into @xmath249 \right\ } \nonumber \\ \ast & & \times \left ( 1-\frac{25\overline{\delta n}^{2}}{2n^{2}}\frac{\left [ ( 1+\frac{\delta n}{n})^{3/2}-(1-\frac{\delta n}{n})^{3/2}\right ] ^{2}}{% \left\ { ( 1+\frac{\delta n}{n})^{5/2}+(1-\frac{\delta n}{n})^{5/2}+\frac{15% \overline{\delta n}^{2}}{2n^{2}}\left [ ( 1+\frac{\delta n}{n})^{1/2}+(1-\frac{% \delta n}{n})^{1/2}\right ] \right\ } ^{2}}\right ) . \label{41}\end{aligned}\ ] ] in fig . 6 , we show the results of @xmath250 as a function of @xmath242 , calculated from eq . ( [ 41 ] ) and represented by solid and dot - dot - dashed curves , which correspond to @xmath223 and @xmath251 , respectively . we see that in contrast with the short - range scattering , now the curves have a positive slope . we do not discuss here the relation between @xmath242 and the applied voltage . according to , for instance refs . @xcite , @xcite and electro - optical measurements ( for references see ref . @xcite ) , the population redistribution can be essential already for rather small voltages . more detailed behavior can be achieved by performing self - consistent calculations for band structures with diagrams shown in figs . 1(_b - d _ ) . we have shown that non - screened variations of the intersubband energy modify essentially the transport properties of quantum wells when two subbands are occupied . relative changes in the transport coefficients are determined by the degree of the random redistribution of the electron density and by the extent of the asymmetry of scattering processes that , for short - range scattering , are characterized by dimensionless parameters @xmath252 and @xmath253 , respectively . our model is founded on some assumptions , which we discuss below , and more detailed numerical calculations , which take into account peculiarities of the band structure and scattering mechanisms , are necessary for a full description of the electron transport . however , our results demonstrate that the kinetic coefficients change when we move from single to double subband occupancy in samples of similar quality . along with magnetotransport characteristics ( magnetoresistance , the hall coefficient , etc . ) and the field effect ( modulation of effective conductivity by transverse voltage ) , other transport phenomena like shubnikov - de haas oscillations and cyclotron resonance are influenced by non - screened variations of subbands . for instance , essential broadening of the peak of intersubband transitions of a qw , due to unscreened large - scale inhomogeneities,@xcite takes place also in the case of two occupied subbands . the effect of such inhomogeneities on intersubband optical transitions also requires special study . we discuss now the model assumptions . we have used the approximation of smooth inhomogeneities in several points : _ i ) _ dependence of qw energy levels upon the in - plane coordinate @xmath112 ; _ ii ) _ we have assumed that characteristic scale of smooth inhomogeneities @xmath254 , and the screened potential , given by eq . ( [ 7 ] ) , results only on the average of variations of the energy levels ; _ iii ) _ the condition that the transport scattering length @xmath64 mainly determines the regime of applicability of the treatment ; _ iv ) _ the approximation of small amplitudes for smooth inhomogeneities , which leads to conditions @xmath255 , reduces quantitatively the effects , but it allows to use theory applied to weakly large - scale inhomogeneous media @xcite . in addition , our calculations are based on simple qw spectra models instead of detailed self - consistent calculations of the band structure . however , we believe that the model assumptions , which are commonly used , do not change the overall behavior and numerical estimates of the magnetotransport coefficients . we hope our work can stimulate further experimental study of the transport properties of nonideal qws with multisubband occupancy in order to verify the effects of large - scale , unscreened inhomogeneities . this work was supported by grants nos . 95/0789 - 3 and 98/10192 - 2 from fundao de amparo pesquisa de so paulo ( fapesp ) . o. g. b and n. s. are grateful to conselho nacional de desenvolvimento cientfico e tecnolgico ( cnpq ) for research fellowship . r. fletcher , e. zaremba , m. diorio , c. t. foxon , and j. j. harris , phys . b * 41 * , 10649 ( 1990 ) ; d. r. leadley , r. fletcher , r. j. nicolas , f. tao , c. t. foxon , j. j. harris , phys . rev b * 46 * , 12439 ( 1992 ) . p. f. yuh , k. l. wang , j. appl . * 65 * , 4377 ( 1989 ) ; v. berger , semicond sci . technol . * 9 * , 1493 ( 1994 ) ; h. li , z. wang , j. liang , b. xu , j. xu , q. gong , c. jiang , f. liu , and w. zhou , j. appl . phys . * 82 * , 6107 ( 1997 ) . table i. coefficients @xmath125 , which appear in the transition probability given by eq . ( [ 24 ] ) . the columns labeled _ i _ and _ ii _ stand for the short - range and small - angle scatterings , respectively , and for ( _ b _ ) hard - wall , ( _ c _ ) parabolic and ( _ d _ ) stepped qws depicted in fig . 1 . @xmath256 with @xmath257 , @xmath258 , @xmath259 , and @xmath260 and @xmath261 . ( _ a _ ) schematic views of the spatial variations of two occupied energy levels in the qw along the @xmath262 direction with ( solid curve ) and without ( dotted curve ) screening . band diagrams for ( _ b _ ) hard - wall , ( _ c _ ) parabolic and ( _ d _ ) stepped qws with non - ideal heterointerfaces . magnetoresistance @xmath171 as a function of the magnetic field for short - range scattering . the solid and dash - dotted curves plot @xmath263 in case of parabolic qws , @xmath174 , with @xmath175 and @xmath176 , respectively . the dotted and dashed curves correspond to stepped qws , @xmath186 , with @xmath175 and @xmath264 , respectively . the ratio between average subband populations @xmath265 and @xmath266 is the typical value of the concentration fluctuations in both occupied subbands . magnetoresistance @xmath171 as function of magnetic field for small - angle scattering . the solid and dashed curves correspond to @xmath267 with @xmath223 and @xmath268 , respectively . for comparison with the @xmath171 behavior for short - range scattering , the dotted curve is the same as in fig . 2 . fig . 6 . conductivity @xmath269 , for zero magnetic field , as a function of @xmath270 showing the effect of intersubband population redistribution due to transverse electric field . the solid and dot - dot - dashed curves , with a positive slope , are for small - angle scattering and @xmath223 and @xmath251 , respectively . the thin solid ( parabolic qw with @xmath251 ) dotted ( stepped qw with @xmath271 , and dashed curves ( stepped qw with @xmath272 are for short - range scattering ; other parameters are the same as for the stepped qw in fig .

electron transport in nonideal quantum wells ( qw ) with large - scale variations of energy levels is studied when two subbands are occupied . although the mean fluctuations of these two levels are screened by the in - plane redistribution of electrons , the energies of both levels remain nonuniform over the plane . the effect of random inhomogeneities on the classical transport is studied within the framework of a local response approach for weak disorder . both short - range and small - angle scattering mechanisms are considered . magnetotransport characteristics and the modulation of the effective conductivity by transverse voltage are evaluated for different kinds of confinement potentials ( hard wall qw , parabolic qw , and stepped qw ) . pacs 73.20.dx ; 73.40.-c ; 72.10.fk

SECTION 1. SHORT TITLE. This Act may be cited as the ``Navajo-Hopi Land Dispute Settlement Act of 1996''. SEC. 2. FINDINGS. The Congress finds that-- (1) it is in the public interest for the Tribe, Navajos residing on the Hopi Partitioned Lands, and the United States to reach a peaceful resolution of the longstanding disagreements between the parties under the Act commonly known as the ``Navajo- Hopi Land Settlement Act of 1974'' (Public Law 93-531; 25 U.S.C. 640d et seq.); (2) it is in the best interest of the Tribe and the United States that there be a fair and final settlement of certain issues remaining in connection with the Navajo-Hopi Land Settlement Act of 1974, including the full and final settlement of the multiple claims that the Tribe has against the United States; (3) this Act, together with the Settlement Agreement executed on December 14, 1995, and the Accommodation Agreement (as incorporated by the Settlement Agreement), provide the authority for the Tribe to enter agreements with eligible Navajo families in order for those families to remain residents of the Hopi Partitioned Lands for a period of 75 years, subject to the terms and conditions of the Accommodation Agreement; (4) the United States acknowledges and respects-- (A) the sincerity of the traditional beliefs of the members of the Tribe and the Navajo families residing on the Hopi Partitioned Lands; and (B) the importance that the respective traditional beliefs of the members of the Tribe and Navajo families have with respect to the culture and way of life of those members and families; (5) this Act, the Settlement Agreement, and the Accommodation Agreement provide for the mutual respect and protection of the traditional religious beliefs and practices of the Tribe and the Navajo families residing on the Hopi Partitioned Lands; (6) the Tribe is encouraged to work with the Navajo families residing on the Hopi Partitioned Lands to address their concerns regarding the establishment of family or individual burial plots for deceased family members who have resided on the Hopi Partitioned Lands; and (7) neither the Navajo Nation nor the Navajo families residing upon Hopi Partitioned Lands were parties to or signers of the Settlement Agreement between the United States and the Hopi Tribe. SEC. 3. DEFINITIONS. Except as otherwise provided in this Act, for purposes of this Act, the following definitions shall apply: (1) Accommodation.--The term ``Accommodation'' has the meaning provided that term under the Settlement Agreement. (2) Hopi partitioned lands.--The term ``Hopi Partitioned Lands'' means lands located in the Hopi Partitioned Area, as defined in section 168.1(g) of title 25, Code of Federal Regulations (as in effect on the date of enactment of this Act). (3) Navajo partitioned lands.--The term ``Navajo Partitioned Lands'' has the meaning provided that term in the proposed regulations issued on November 1, 1995, at 60 Fed. Reg. 55506. (4) New lands.--The term ``New Lands'' has the meaning provided that term in section 700.701(b) of title 25, Code of Federal Regulations. (5) Secretary.--The term ``Secretary'' means the Secretary of the Interior. (6) Settlement agreement.--The term ``Settlement Agreement'' means the agreement between the United States and the Hopi Tribe executed on December 14, 1995. (7) Tribe.--The term ``Tribe'' means the Hopi Tribe. (8) Newly acquired trust lands.--The term ``newly acquired trust lands'' means lands taken into trust for the Tribe within the State of Arizona pursuant to this Act or the Settlement Agreement. SEC. 4. RATIFICATION OF SETTLEMENT AGREEMENT. The United States approves, ratifies, and confirms the Settlement Agreement. SEC. 5. CONDITIONS FOR LANDS TAKEN INTO TRUST. The Secretary shall take such action as may be necessary to ensure that the following conditions are met prior to taking lands into trust for the benefit of the Tribe pursuant to the Settlement Agreement: (1) Selection of lands taken into trust.-- (A) Primary area.--In accordance with section 7(a) of the Settlement Agreement, the primary area within which lands acquired by the Tribe may be taken into trust by the Secretary for the benefit of the Tribe under the Settlement Agreement shall be located in northern Arizona. (B) Requirements for lands taken into trust in the primary area.--Lands taken into trust in the primary area referred to in subparagraph (A) shall be-- (i) land that is used substantially for ranching, agriculture, or another similar use; and (ii) to the extent feasible, in contiguous parcels. (2) Acquisition of lands.--Before taking any land into trust for the benefit of the Tribe under this section, the Secretary shall ensure that-- (A) at least 85 percent of the eligible Navajo heads of household (as determined under the Settlement Agreement) have entered into an accommodation or have chosen to relocate and are eligible for relocation assistance (as determined under the Settlement Agreement); and (B) the Tribe has consulted with the State of Arizona concerning the lands proposed to be placed in trust, including consulting with the State concerning the impact of placing those lands into trust on the State and political subdivisions thereof resulting from the removal of land from the tax rolls in a manner consistent with the provisions of part 151 of title 25, Code of Federal Regulations. (3) Prohibition.--The Secretary may not, pursuant to the provisions of this Act and the Settlement Agreement, place lands, any portion of which are located within or contiguous to a 5-mile radius of an incorporated town or city (as those terms are defined by the Secretary) in northern Arizona, into trust for benefit of the Tribe without specific statutory authority. (4) Expeditious action by the secretary.--Consistent with all other provisions of this Act, the Secretary is directed to take lands into trust under this Act expeditiously and without undue delay. SEC. 6. ACQUISITION THROUGH CONDEMNATION OF CERTAIN INTERSPERSED LANDS. (a) In General.-- (1) Action by the secretary.-- (A) In general.--The Secretary shall take action as specified in subparagraph (B), to the extent that the Tribe, in accordance with section 7(b) of the Settlement Agreement-- (i) acquires private lands; and (ii) requests the Secretary to acquire through condemnation interspersed lands that are owned by the State of Arizona and are located within the exterior boundaries of those private lands in order to have both the private lands and the State lands taken into trust by the Secretary for the benefit of the Tribe. (B) Acquisition through condemnation.--With respect to a request for an acquisition of lands through condemnation made under subparagraph (A), the Secretary shall, upon the recommendation of the Tribe, take such action as may be necessary to acquire the lands through condemnation and, with funds provided by the Tribe, pay the State of Arizona fair market value for those lands in accordance with applicable Federal law, if the conditions described in paragraph (2) are met. (2) Conditions for acquisition through condemnation.--The Secretary may acquire lands through condemnation under this subsection if-- (A) that acquisition is consistent with the purpose of obtaining not more than 500,000 acres of land to be taken into trust for the Tribe; (B) the State of Arizona concurs with the United States that the acquisition is consistent with the interests of the State; and (C) the Tribe pays for the land acquired through condemnation under this subsection. (b) Disposition of Lands.--If the Secretary acquires lands through condemnation under subsection (a), the Secretary shall take those lands into trust for the Tribe in accordance with this Act and the Settlement Agreement. (c) Private Lands.--The Secretary may not acquire private lands through condemnation for the purpose specified in subsection (a)(2)(A). SEC. 7. ACTION TO QUIET POSSESSION. If the United States fails to discharge the obligations specified in section 9(c) of the Settlement Agreement with respect to voluntary relocation of Navajos residing on Hopi Partitioned Lands, or section 9(d) of the Settlement Agreement, relating to the implementation of sections 700.137 through 700.139 of title 25, Code of Federal Regulations, on the New Lands, including failure for reason of insufficient funds made available by appropriations or otherwise, the Tribe may bring an action to quiet possession that relates to the use of the Hopi Partitioned Lands after February 1, 2000, by a Navajo family that is eligible for an accommodation, but fails to enter into an accommodation. SEC. 8. PAYMENT TO STATE OF ARIZONA. (a) Authorization of Appropriations.--Subject to subsection (b), there are authorized to be appropriated to the Department of the Interior $250,000 for fiscal year 1998, to be used by the Secretary of the Interior for making a payment to the State of Arizona. (b) Payment.--The Secretary shall make a payment in the amount specified in subsection (a) to the State of Arizona after an initial acquisition of land from the State has been made by the Secretary pursuant to section 6. SEC. 9. 75-YEAR LEASING AUTHORITY. The first section of the Act of August 9, 1955 (69 Stat. 539, chapter 615; 25 U.S.C. 415) is amended by adding at the end the following new subsections: ``(c) Leases Involving the Hopi Tribe and the Hopi Partitioned Lands Accommodation Agreement.--Notwithstanding subsection (a), a lease of land by the Hopi Tribe to Navajo Indians on the Hopi Partitioned Lands may be for a term of 75 years, and may be extended at the conclusion of the term of the lease. ``(d) Definitions.--For purposes of this section-- ``(1) the term `Hopi Partitioned Lands' means lands located in the Hopi Partitioned Area, as defined in section 168.1(g) of title 25, Code of Federal Regulations (as in effect on the date of enactment of this subsection); and ``(2) the term `Navajo Indians' means members of the Navajo Tribe.''. SEC. 10. REAUTHORIZATION OF THE NAVAJO-HOPI RELOCATION HOUSING PROGRAM. Section 25(a)(8) of Public Law 93-531 (25 U.S.C. 640d-24(a)(8)) is amended by striking ``1996, and 1997'' and inserting ``1996, 1997, 1998, 1999, and 2000''. SEC. 11. EFFECT OF THIS ACT ON CASES INVOLVING THE NAVAJO NATION AND THE HOPI TRIBE. Nothing in this Act or the amendments made by this Act shall be interpreted or deemed to preclude, limit, or endorse, in any manner, actions by the Navajo Nation that seek, in court, an offset from judgments for payments received by the Hopi Tribe under the Settlement Agreement. SEC. 12. WATER RIGHTS. (a) In General.-- (1) Water rights.--Subject to the other provisions of this section, newly acquired trust lands shall have only the following water rights: (A) The right to the reasonable use of groundwater pumped from such lands. (B) All rights to the use of surface water on such lands existing under State law on the date of acquisition, with the priority date of such right under State law. (C) The right to make any further beneficial use on such lands which is unappropriated on the date each parcel of newly acquired trust lands is taken into trust. The priority date for the right shall be the date the lands are taken into trust. (2) Rights not subject to forfeiture or abandonment.--The Tribe's water rights for newly acquired trust lands shall not be subject to forfeiture or abandonment arising from events occurring after the date the lands are taken into trust. (b) Recognition as valid uses.-- (1) Groundwater.--With respect to water rights associated with newly acquired trust lands, the Tribe, and the United States on the Tribe's behalf, shall recognize as valid all uses of groundwater which may be made from wells (or their subsequent replacements) in existence on the date each parcel of newly acquired trust land is acquired and shall not object to such groundwater uses on the basis of water rights associated with the newly acquired trust lands. The Tribe, and the United States on the Tribe's behalf, may object only to the impact of groundwater uses on newly acquired trust lands which are initiated after the date the lands affected are taken into trust and only on grounds allowed by the State law as it exists when the objection is made. The Tribe, and the United States on the Tribe's behalf, shall not object to the impact of groundwater uses on the Tribe's right to surface water established pursuant to subsection (a)(3) when those groundwater uses are initiated before the Tribe initiates its beneficial use of surface water pursuant to subsection (a)(3). (2) Surface water.--With respect to water rights associated with newly acquired trust lands, the Tribe, and the United States on the Tribe's behalf, shall recognize as valid all uses of surface water in existence on or prior to the date each parcel of newly acquired trust land is acquired and shall not object to such surface water uses on the basis of water rights associated with the newly acquired trust lands, but shall have the right to enforce the priority of its rights against all junior water rights the exercise of which interfere with the actual use of the Tribe's senior surface water rights. (3) Rule of construction.--Nothing in paragraph (1) or (2) shall preclude the Tribe, or the United States on the Tribe's behalf, from asserting objections to water rights and uses on the basis of the Tribe's water rights on its currently existing trust lands. (c) Applicability of State Law on Lands Other Than Newly Acquired Lands.--The Tribe, and the United States on the Tribe's behalf, further recognize that State law applies to water uses on lands, including subsurface estates, that exist within the exterior boundaries of newly acquired trust lands and that are owned by any party other than the Tribe. (d) Adjudication of Water Rights on Newly Acquired Trust Lands.-- The Tribe's water rights on newly acquired trust lands shall be adjudicated with the rights of all other competing users in the court now presiding over the Little Colorado River Adjudication, or if that court no longer has jurisdiction, in the appropriate State or Federal court. Any controversies between or among users arising under Federal or State law involving the Tribe's water rights on newly acquired trust lands shall be resolved in the court now presiding over the Little Colorado River Adjudication, or, if that court no longer has jurisdiction, in the appropriate State or Federal court. Nothing in this subsection shall be construed to affect any court's jurisdiction: Provided, That the Tribe shall administer all water rights established in subsection (a). (e) Prohibition.--Water rights for newly acquired trust lands shall not be used, leased, sold, or transported for use off of such lands or the Tribe's other trust lands: Provided, That the Tribe may agree with other persons having junior water rights to subordinate the Tribe's senior water rights. Water rights for newly acquired trust lands can only be used on those lands or other trust lands of the Tribe located within the same river basin tributary to the main stream of the Colorado River. (f) Subsurface Interests.--On any newly acquired trust lands where the subsurface interest is owned by any party other than the Tribe, the trust status of the surface ownership shall not impair any existing right of the subsurface owner to develop the subsurface interest and to have access to the surface for the purpose of such development. (g) Statutory Construction with Respect to Water Rights of Other Federally Recognized Indian Tribes.--Nothing in this section shall affect the water rights of any other federally recognized Indian tribe with a priority date earlier than the date the newly acquired trust lands are taken into trust. (h) Statutory Construction.--Nothing in this section shall be construed to determine the law applicable to water use on lands owned by the United States, other than on the newly acquired trust lands. The granting of the right to make beneficial use of unappropriated surface water on the newly acquired trust lands with a priority date such lands are taken into trust shall not be construed to imply that such right is a Federal reserved water right. Nothing in this section or any other provision of this Act shall be construed to establish any Federal reserved right to groundwater. Authority for the Secretary to take land into trust for the Tribe pursuant to the Settlement Agreement and this Act shall be construed as having been provided solely by the provisions of this Act. Speaker of the House of Representatives. Vice President of the United States and President of the Senate.

Navajo-Hopi Land Dispute Settlement Act of 1996 - Ratifies the Settlement Agreement between the United States and the Hopi Tribe executed on December 14, 1995. Sets forth the conditions to be met prior to taking lands into trust for the Tribe pursuant to the Settlement Agreement. Authorizes the Secretary of the Interior to acquire: (1) private lands; and (2) through condemnation, with funds provided by the Tribe, certain interspersed lands that are owned by the State of Arizona in order to have both the private and the State lands taken into trust for the Tribe. Prohibits the Secretary, pursuant to the provisions of this Act and the Settlement Agreement, from placing lands, any portion of which are located within or contiguous to a five-mile radius of an incorporated town or city in Northern Arizona, into trust for the Tribe without specific statutory authority. Authorizes the Tribe, if the United States fails to discharge the obligation of voluntarily relocating Navajos residing on Hopi Partitioned Lands, to bring an action to quiet possession relating to use of such Lands after February 2002 by an eligible Navajo family that fails to enter into an accommodation. Authorizes an appropriation to the Department of the Interior of $250,000 for FY 1998 to be used for making a payment to the State of Arizona. Requires the Secretary to make such a payment to the State of Arizona after an initial acquisition of land from the State has been made by the Secretary. Amends Federal law to authorize leases by the Hopi Tribe to Navajo Indians residing on Hopi Partitioned Lands that may be for a 75-year term and extended at the conclusion of the lease term. Amends Public Law 93-531 to reauthorize the Navajo-Hopi Relocation Housing Program through FY 2000. Sets forth provisions concerning water rights on newly aquired trust lands.

the mhc class i antigen processing system is generally believed to have evolved as a result of selective pressures imposed by intracellular pathogens . new findings , however , have resurrected the idea that cancer immunosurveillance , a process that seeks and destroys cancers of nonviral origin , was a key factor in the evolution of the class i remarkably , lethal tumors can be transmitted in two mammalian species by direct transfer of tumor cells themselves and not by tumor viruses , as was generally assumed ( 2 , 3 ) . the need to reject such transmissible tumors may have provided a strong selective pressure in the evolution of immunosurveillance . indeed , the constitutive expression of class i molecules ( as opposed to their induction by infection ) may have evolved primarily to facilitate the detection of transmissible and spontaneously arising tumors ( 4 ) . detection of these tumors would be most efficient if active gene expression was monitored independently of mrna abundance and protein stability . this would prevent the overloading of class i molecules with peptides from the most abundant cellular proteins ( structural elements , chaperones , ribosomes , etc . ) , which are rarely altered in neoplasms . indeed , analysis of the class i immunopeptidome reveals little correlation between the abundance of mrnas and class i binding peptides ( 5 , 6 ) . rather , these peptides appear to be selected for presentation by some other metric that favors rare mrna species and peptides from gene products translated by nonstandard rules ( 7 ) , perhaps by a subset of ribosomes ( immunoribosomes ) whose products have privileged access to the class i processing pathway ( 8 , 9 ) . the possible evolution of this pathway for detecting peptides from tumor cell gene products that are rare or are rapidly degraded may have influenced the mechanisms used to monitor viral gene expression . studies in a variety of systems point to an intimate kinetic link between protein synthesis and the generation of viral and cellular peptides that bind to class i mhc ( 8) . this is expected for nonstandard gene products ( arfs , downstream or alternative initiation , stop codon read through ) , which misfold and are rapidly targeted for degradation . surprisingly , however , this also applies to peptides derived from standard viral and cellular orfs ( 10 ) . rapid degradation may result from unavoidable mistakes in transcription , translation , protein folding , or assembly of multi - subunit proteins . alternatively , immunoribosomes ( should they exist ) may directly target their translation products for rapid degradation to enable immunosurveillance . surveillance of drips may have evolved to facilitate tumor cell recognition . but this surveillance may also enable the immune system to rapidly detect viral infections by monitoring what is actively being translated , rather than what has already been translated . viral proteins are typically highly stable ( half - life in days , not minutes ) . antigenic peptides are thus unlikely to be derived from the standard turnover of these proteins , as it would take many hours to generate enough peptides from even the most abundant viral proteins to compete with those generated from the billions of cellular proteins present at the time of infection . additionally , using drips as a source of peptides provides a mechanism for monitoring the expression of 25% of cellular gene products ( and many viral proteins ) that are targeted to the er for secretion or cell surface display , and that are eventually degraded by extra - cytosolic proteases . although most cellular and viral peptide ligands appear to arise from drips encoded by standard reading frames , increasing numbers of arf - encoded peptides ( arfps ) have been reported ( 11 ) . is simply defined as an overlapping reading frame that does not encode a functional gene product . although some arfs are synthesized as errors in translation ( and are thus drips ) , proteins encoded by overlapping reading frames can be functional products of natural selection . many viruses , especially those with small genomes , use overlapping reading frames and/or multiple splice sites to create functional viral proteins . the influenza a virus protein , pb1-f2 , is the poster child for arfs that are really orfs . this 87-residue protein was serendipitously discovered in the first systematic survey for viral arfps and was identified as the source of a highly immunogenic peptide in influenza virus infected b6 mice ( 12 ) . pb1-f2 is encoded by the + 1 reading frame of the pb1 polymerase genes in > 90% of human and avian influenza viruses . pb1-f2 is an abundantly synthesized mitochondrial protein that plays an important role in viral pathogenesis ( 13 ) . had pb1-f2 been discovered before pb1 , it would have been considered the orf , and pb1 the ( very long ) pseudo - arf . the first viral arf that was reported to have cd8 t cell immunogenicity is probably also an orf with an important function in viral pathogenesis ( 14 ) . similarly , immunogenic arfs from the hepatitis c virus , which elicit cd4 t cell and antibody responses ( 15 ) , now have ascribed functions ( 16 ) , bestowing orfhood on these gene products . arfs created by genetic manipulation of viral ( 17 , 18 ) or plasmid orfs ( 19 ) have also been shown to demonstrate antigenicity and immunogenicity . several immunogenic arfps have been reported for tumor antigens ( 11 ) , but it is difficult to establish that their expression ( and immunogenicity ) is not based on legitimate splicing events that only occur in vivo . the best case for natural arfps comes from studies of immunodeficiency viruses . in a seminal study , 20 ) described six arfps encoded by human immunodeficiency virus ( hiv ) and provided evidence for their immunogenicity in humans . these six peptides were encoded by three arfs ranging from 33 to 52 residues , which is much shorter than is typically needed to generate a stably folded , functional protein . although it is impossible to prove the lack of function of an arf gene product , documenting that a translated gene product is rapidly degraded is a good start ( though perversely , a sizable fraction of pb1-f2 is rapidly degraded ; reference 12 ) . ( 1 ) use the rhesus macaque simian immunodeficiency virus ( siv ) model to establish the in vivo relevance of viral arfps . using computer algorithms to predict siv arfps with high affinity for the mamu b*17 class i molecule this peptide originates from an arf of the viral env protein ( or the incompletely spliced product of the viral protein rev , as these genes occupy overlapping reading frames ) . a synthetic version of the peptide , they show , binds to class i molecules with high affinity ( kd = 32 nm ) , and siv - infected mamu - b*17 macaques mount a strong b*17-restricted cd8 t cell response against this peptide . first , cd8 t cells specific for the peptide inhibited replication of virus in vitro in b*17-expressing cells . second , and most remarkably , 5 of 20 b*17 siv - infected animals selected for viral escape mutants with the identical point mutation , which recodes the c - terminal anchor residue of the peptide from w to k ( and is synonymous in env ) . this substitution caused a 30-fold reduction in the binding of the mutant peptide to b*17 and prevented peptide - specific cd8 t cells from recognizing cells infected with the escape mutant . as the first report of an arf - encoded determinant that facilitates viral evolution in response to immune pressure , these findings provide the smoking gun for the in vivo relevance of arfps . this undoubtedly reflects , in part , investigator bias in searching for immunogenic determinants in only the most obvious places . it is now possible to predict in silico high affinity class i binding peptides with an accuracy as high as 90% ( 21 ) . the success of maness et al . in using this approach should spur investigators to systematically search for arfps in other viruses . moreover , as improvements in mass spectroscopy enable more rapid and sensitive identification of peptides recovered from mhc class i molecules , spectroscopists should compare detected masses with all six possible reading frames for potential matches and not forget about nucleic acid or direct proteasome - mediated peptide splicing , which can even reorder peptide sequences ( 22 ) . alternative peptides recognized by virus - induced cd8 t cells may also be encoded by the host . the initial study that characterized hiv class i peptide ligands using mass spectroscopy identified three peptides that were not present on uninfected cells ( 23 ) . remarkably , however , each of these peptides was encoded by the human vinculin gene , whose expression is enhanced by hiv infection . even more remarkably , cd8 t cells obtained from several hiv - infected individuals , but not from uninfected hosts , recognized these self - determinants . similarly , measles virus infection induces human autoreactive cd8 t cells that recognize up - regulated self - peptides ( 24 ) . the latest mass spectrometric sequencing study of hiv - induced class i peptide ligands identified no fewer than 15 host - derived peptides that were absent in uninfected cells ( 25 ) . although acute viral infections are frequently suspected of initiating chronic autoimmune diseases ( with little supporting evidence to date ) , these findings raise the important but frequently overlooked question regarding the extent to which self - limited autoreactive cd8 t cells might contribute to antiviral responses . it is obvious ( but still needs to be stated ) that the induction of self - peptide specific cd8 t cell responses , regardless of their physiological function , is too dangerous to be considered in vaccine design . but what about viral arfps ? in theory , the most effective cd8 t cell based vaccines should encompass the widest possible range of viral peptides that are naturally displayed by class i molecules on infected cells . maness et al . clearly demonstrate that arf - derived peptides can generate robust , highly protective responses . it is possible to design vaccines that deliberately ( over)express all possible reading frames of viral proteins , even targeting them for rapid degradation in vectors designed for direct priming . unless further research demonstrates the ubiquitous targeting of viral arfps by cd8 t cells , however , it is probably best not to pursue this approach . to some extent , competition limits the immunogenicity of immunogens in individual lymphoid organs ( particularly via immunodomination ; reference 26 ) . therefore , generating cd8 t cells specific for peptides that are never actually produced during infection would be counterproductive . moreover , the findings of maness et al . uncover the achilles heel of arfps : if the source arfp is a genuine arf , it is under no selective pressure to maintain its function . an effective cd8 t cell response , therefore , will result in rapid mutation of the targeted peptides , particularly in rna viruses , which have extremely high mutation rates . it is important to note that this argument is much less relevant for tumor arfps , as tumor - specific determinants are both more difficult to identify and much more genetically stable than viral determinants . but doubts about practical uses for viral arfps should in no way dampen enthusiasm for their further discovery and characterization . understanding immunity to viruses requires the characterization of the full breadth of the immune response to viral peptides and , as maness et al . demonstrate , arfps can be crucial in controlling viral replication and in driving viral evolution . moreover , understanding the mechanisms for arfp generation will no doubt provide unique insights into the varied processes by which the information encoded by nucleic acids is converted into polypeptides . time and time again , such curiosity - driven explorations into basic cell biology have generated practical applications in diverse areas that extend beyond the immediate topic of interest .

cd8 + t cells rapidly recognize virus - infected cells due to the generation of antigenic peptides from defective ribosomal products ( drips ) that are encoded by standard open reading frames ( orfs ) . new data now show that alternative reading frame ( arf ) drips can also induce robust cd8 + t cell responses . arf - specific t cells control retroviral replication and select for viral escape in monkeys , providing the most compelling evidence to date for the biological relevance of arf immunosurveillance .

the website of ijp was searched for publications year and issue wise for contributing authors from pharmacy institutions during 20102015 . based on the geographical addresses , the publications were categorized as national and international and were further categorized to state wise if national , and country wise if international . the number / frequency of publications by these pharmacy institutes was counted issue wise and its percentage to total publications issue wise and year wise was calculated . articles were categorized as editorial , educational forum , research article and review article , letter to the editor , drug watch , short communication , and book review . research articles were further classified whether preclinical ( animal studies ) or clinical ( human ) . preclinical research was further categorized based on the investigational product whether a plant product / extract or chemical / synthetic product . a total of 1034 articles were published in ijp from 2010 to 2015 . of these , 189 ( 18% ) articles were published by pharmacy institutes [ table 1 ] of which 90% ( n = 170 ) were contributed from pharmacy institutes within india while 10% ( n = 19 ) publications were from countries such as china ( 4 ) , usa ( 3 ) , turkey and iraq ( 2 ) , iran , sri lanka , egypt , tanzania , indonesia , australia , malaysia , france ( 1 ) , respectively . within india , the top 5 contributing states included karnataka ( 43 ) , maharashtra ( 25 ) , gujarat ( 21 ) , madhya pradesh ( 18 ) , and tamil nadu ( 13 ) . year - wise publications in indian journal of pharmacology from pharmacy institutes articles were categorized as editorial , educational forum , research article and review article , letter to the editor , drug watch , short communication , and book review . a good percent of research manuscripts were published from pharmacy institutes [ table 2 ] . of 189 articles published from pharmacy institutes , 141 ( 74.60% ) articles were research manuscripts as compared to 46% from institutes other than pharmacy ; mostly medical and other biomedical institutes . contributions in drug watch ( 16.5% vs. 1.6% ) , and case reports were comparatively less from pharmacy institutes . distribution of articles published in indian journal of pharmacology research publications from pharmacy institutes were further classified into preclinical and clinical studies . preclinical studies were further categorized based on the type of investigational product whether of plant extract or synthetic / drug product [ table 3 ] . most of the publications from pharmacy institutes were researched on animals ( 92% ) while only 8% were clinical studies . most of the preclinical studies ( 64% ) researched screening of plant extracts for their pharmacological actions as compared to drug studies ( 36% ) . categorizing research publications in indian journal of pharmacology the preclinical studies screened the plant extracts for various activities such as immunosuppressive properties , antidiabetic activity hepatoprotective effects , for inflammatory bowel disease , antiurolithiatic and antioxidant activity , against neurotoxicity , cardiotoxicity , obesity , anti - inflammatory and antiulcer activity , in acute renal failure , antidiarrheal , antinociceptive / analgesic activity , antihyperlipidemic , antidepressant / anxiolytic , etc . articles were categorized as editorial , educational forum , research article and review article , letter to the editor , drug watch , short communication , and book review . a good percent of research manuscripts were published from pharmacy institutes [ table 2 ] . of 189 articles published from pharmacy institutes , 141 ( 74.60% ) articles were research manuscripts as compared to 46% from institutes other than pharmacy ; mostly medical and other biomedical institutes . contributions in drug watch ( 16.5% vs. 1.6% ) , and case reports were comparatively less from pharmacy institutes . preclinical studies were further categorized based on the type of investigational product whether of plant extract or synthetic / drug product [ table 3 ] . most of the publications from pharmacy institutes were researched on animals ( 92% ) while only 8% were clinical studies . most of the preclinical studies ( 64% ) researched screening of plant extracts for their pharmacological actions as compared to drug studies ( 36% ) . categorizing research publications in indian journal of pharmacology the preclinical studies screened the plant extracts for various activities such as immunosuppressive properties , antidiabetic activity hepatoprotective effects , for inflammatory bowel disease , antiurolithiatic and antioxidant activity , against neurotoxicity , cardiotoxicity , obesity , anti - inflammatory and antiulcer activity , in acute renal failure , antidiarrheal , antinociceptive / analgesic activity , antihyperlipidemic , antidepressant / anxiolytic , etc . scientific writing and publication mark the endpoint of research that has been performed , completed , peer - reviewed and accepted and complements teaching and training , clinical service and patient care . since 1969 ijp ( issn 02537613 ) is an official publication of the indian pharmacological society , a peer - reviewed open access biomedical specialty periodical from india . ijp s website was searched for publications by contributing authors from pharmacy institutes from 2010 to 2015 . a total of 1034 manuscripts were published in ijp in 6 years with an average of 172 publications per year . a total of 189 ( 18% ) were from pharmacy institutes both from and outside india with an average of 31 publications per year . in india as per aicte , there are 445 institutes offering pharmacy education to 24,672 students and as per mci , there are 462 institutes offering medical education to 63,535 students pharmacy institutes offering masters in pharmacology approximate to 239 while 257 medical institutes offer 789 seats in md pharmacology and dm clinical pharmacology . although number of pharmacy institutes have grown with time , the temporal trends in terms of the number of publications by pharmacy institutes has not increased . most of the manuscripts were contributed from pharmacy institutes located in the indian states such as karnataka , maharashtra , madhya pradesh , gujarat , and tamil nadu which also house more number of pharmacy institutes . although ijp charges no publication fees , international contributors stood to 10% only , possibly influenced by number of factors such as scope of research , marketing strategy of publication house , citations , indexing , and impact factor of the journal . although publication volumes are comparatively low from pharmacy institutes , number of research manuscripts from pharmacy institutes was higher ( 75% vs. 46% ) as compared to other biomedical institutes . the reasons may range from noble to base reasons including but not limited to postgraduate pharmacy curriculum , policies laid by regulators of pharmacy education , multi and interdisciplinary integration and collaboration , the pharmaceutical industry of the country , expanded role offered by pharmacists in healthcare , rich indigenous medical system , government policies supporting public - private partnerships and at the bottom of the list necessary evil for job or promotion . however , 64% of these research manuscripts studied in vitro , in vivo screening of phytochemical constituents of indigenous plant extracts or formulations for its pharmacological activity . the reason for this trend seems that phytochemical research is both cost and time effective . medicinal plants are resources of new drugs and pharmacological properties of an herbal formulation depend on phytochemical constituents present therein . however , in the present context , most of the plant research is limited to screening activity . very few of these researched plant activity undergoes characterization and standardization of well - defined active constituents to undergo reliable clinical trials . taking otherwise this trend may also translate not only as a cost and time effective mode of research but publication as well . molecular and cellular pharmacology studies still need to the forefront of research by pharmacy institutes since 92% research by pharmacy institutes is preclinical as per present data . pharmacy institutes with well - established animal house facilities can serve as research hubs in the drug development process . regulatory drugs and cosmetics act , schedule y preclinical studies can be integrated to pharmacy curricula . in the present study , with multi and interdisciplinary collaborations in the pharmacy profession , areas like clinical pharmacy can manipulate an accurate make use of medicines on before , during and after the prescription is written . thus , today s pharmacist will evolve to conduct research in pharmacovigilance , prescription patterns , antibiotic use and misuse , drug adherence , drug interaction , nuclear medicine , and specialized areas of treatment . this study has not made a comparative analysis between publications made by medical , pharmacy , and other biomedical institutes which could focus their relative contributory role . furthermore , publications from 2010 to 2015 by pharmacy institutes only have been incorporated . in conclusion , publication in ijp complements teaching and training , research and clinical service offered by biomedical community . temporal trends in pharmacology publications in ijp by pharmacy institutes infers that research by pharmacy institutes needs to be more science oriented with well - defined objectives leading to molecular and cellular pharmacology . with the increased responsibility and scope of pharmacy profession in health care , contributions in clinical studies this study has not made a comparative analysis between publications made by medical , pharmacy , and other biomedical institutes which could focus their relative contributory role . furthermore , publications from 2010 to 2015 by pharmacy institutes only have been incorporated . in conclusion , publication in ijp complements teaching and training , research and clinical service offered by biomedical community . temporal trends in pharmacology publications in ijp by pharmacy institutes infers that research by pharmacy institutes needs to be more science oriented with well - defined objectives leading to molecular and cellular pharmacology . with the increased responsibility and scope of pharmacy profession in health care , contributions in clinical studies

objective : publications in indian journal of pharmacology ( ijp ) are the face of contemporary pharmacology practices followed in health - care profession - a knowledge - based profession . it depicts trends in terms of quantity ( proportions ) , quality , type ( preclinical / clinical ) , thrust areas , etc . , of pharmacology followed by biomedical community professions both nationally and internationally . this article aims to establish temporal trends in pharmacology research by pharmacy institutes in light of its publications to ijp from 2010 to 2015.methodology:the website of ijp was searched for publications year and issue wise for contributing authors from pharmacy institutions and analyzed for types of publications , their source and the categories of research documented in these publications.results:a total of 1034 articles were published , of which 189 ( 18% ) articles were published by pharmacy institutes , of which 90% ( n = 170 ) were contributed from pharmacy institutes within india whereas 10% ( n = 19 ) from international pharmacy institutes . 75% of these were research publication , the majority of which ( 65% ) were related to preclinical screening of phytochemical constituents from plants.conclusion:with multi and interdisciplinary collaborations in pharmacy profession the trend needs to improve toward molecular and cellular pharmacology and clinical studies .

To commemorate the occasion, E! News exclusively caught up with the duo to chat about their marriage, what the future holds and, of course, Courtney's big move into adulthood. "It's been an adventurous ride so far, that's for sure," Courtney tells us regarding the past year and half with Doug. "It has been the most beautiful time of my life and there's more to come." Doug certainly seems to share that sentiment and notes that "one of the many reasons why I love and admire my wife is that she didn't ask for bling on her landmark 18th birthday. She didn't ask for expensive clothes or shoes, a flashy party, an extravagant vacation, a luxurious car or to be taken out on the town." ||||| Starting in 1996, Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the Wayback Machine after an embargo period.

– Remember Courtney Stodden, she of the totally bizarre tweets who married 51-year-old actor Doug Hutchison when she was just 16? Well, she's 18 now, and E! reports that her birthday gift was a dog that she named ... Dourtney. We can't make this stuff up. In Dourtney's honor, take a look at Fox News' list of "child stars turned child brides." Behold, a dozen celebrities who married as teens: Drew Barrymore: By 18, she'd called off two engagements. Then she married at 19, and filed for divorce less than two months later. Melanie Griffith: She started dating Don Johnson, who was then 22, when she was just 14. They wed when she turned 18, but broke up six months later. (They ended up marrying a second time, then splitting up yet again.) Demi Moore: She got her last name from her first marriage, to Freddy Moore, which took place two months after she turned 17 and lasted four years. Kim Kardashian: She actually managed to stay married four years the first time around. She married Damon Thomas when she was 19. Olivia Wilde: The House actress married an Italian prince, Tao Ruspoli, when she was 18. They broke up last year. Macaulay Culkin: When he married Rachel Miner at 17, they issued a statement saying how happy they were to have "found each other at such a young age." Unfortunately, they lost each other two years later. Click for the complete list.

SECTION 1. SHORT TITLE. This Act may be cited as the ``Public Good IRA Rollover Act of 2007''. SEC. 2. TAX-FREE DISTRIBUTIONS FROM INDIVIDUAL RETIREMENT ACCOUNTS FOR CHARITABLE PURPOSES. (a) In General.--Paragraph (8) of section 408(d) of the Internal Revenue Code of 1986 (relating to tax treatment of distributions) is amended to read as follows: ``(8) Distributions for charitable purposes.-- ``(A) In general.--No amount shall be includible in gross income by reason of a qualified charitable distribution. ``(B) Qualified charitable distribution.--For purposes of this paragraph, the term `qualified charitable distribution' means any distribution from an individual retirement account-- ``(i) which is made directly by the trustee-- ``(I) to an organization described in section 170(c), or ``(II) to a split-interest entity, and ``(ii) which is made on or after the date that the individual for whose benefit the account is maintained has attained-- ``(I) in the case of any distribution described in clause (i)(I), age 70\1/2\, and ``(II) in the case of any distribution described in clause (i)(II), age 59\1/2\. A distribution shall be treated as a qualified charitable distribution only to the extent that the distribution would be includible in gross income without regard to subparagraph (A) and, in the case of a distribution to a split-interest entity, only if no person holds an income interest in the amounts in the split-interest entity attributable to such distribution other than one or more of the following: the individual for whose benefit such account is maintained, the spouse of such individual, or any organization described in section 170(c). ``(C) Contributions must be otherwise deductible.-- For purposes of this paragraph-- ``(i) Direct contributions.--A distribution to an organization described in section 170(c) shall be treated as a qualified charitable distribution only if a deduction for the entire distribution would be allowable under section 170 (determined without regard to subsection (b) thereof and this paragraph). ``(ii) Split-interest gifts.--A distribution to a split-interest entity shall be treated as a qualified charitable distribution only if a deduction for the entire value of the interest in the distribution for the use of an organization described in section 170(c) would be allowable under section 170 (determined without regard to subsection (b) thereof and this paragraph). ``(D) Application of section 72.--Notwithstanding section 72, in determining the extent to which a distribution is a qualified charitable distribution, the entire amount of the distribution shall be treated as includible in gross income without regard to subparagraph (A) to the extent that such amount does not exceed the aggregate amount which would be so includible if all amounts were distributed from all individual retirement accounts otherwise taken into account in determining the inclusion on such distribution under section 72. Proper adjustments shall be made in applying section 72 to other distributions in such taxable year and subsequent taxable years. ``(E) Special rules for split-interest entities.-- ``(i) Charitable remainder trusts.-- Notwithstanding section 664(b), distributions made from a trust described in subparagraph (G)(i) shall be treated as ordinary income in the hands of the beneficiary to whom is paid the annuity described in section 664(d)(1)(A) or the payment described in section 664(d)(2)(A). ``(ii) Pooled income funds.--No amount shall be includible in the gross income of a pooled income fund (as defined in subparagraph (G)(ii)) by reason of a qualified charitable distribution to such fund, and all distributions from the fund which are attributable to qualified charitable distributions shall be treated as ordinary income to the beneficiary. ``(iii) Charitable gift annuities.-- Qualified charitable distributions made for a charitable gift annuity shall not be treated as an investment in the contract. ``(F) Denial of deduction.--Qualified charitable distributions shall not be taken into account in determining the deduction under section 170. ``(G) Split-interest entity defined.--For purposes of this paragraph, the term `split-interest entity' means-- ``(i) a charitable remainder annuity trust or a charitable remainder unitrust (as such terms are defined in section 664(d)) which must be funded exclusively by qualified charitable distributions, ``(ii) a pooled income fund (as defined in section 642(c)(5)), but only if the fund accounts separately for amounts attributable to qualified charitable distributions, and ``(iii) a charitable gift annuity (as defined in section 501(m)(5)).''. (b) Effective Date.--The amendment made by this section shall apply to distributions made in taxable years beginning after December 31, 2006.

Public Good IRA Rollover Act of 2007 - Amends the Internal Revenue Code to exclude from gross income distributions from individual retirement accounts for certain charitable purposes.

the transfusion of blood and blood products is an integral and essential part of hospital services . the blood requisition in elective and emergency procedures from surgery , trauma and obstetrics and gynaecology departments are often associated with excessive demand for cross matching of blood which is often more than the required blood and blood products . the transfusion services , thus , are burdened in terms of unnecessary reagent usage , time and manpower . over - ordering of blood leads to financial loss for the patient , increase in cost during the hospital stay and increase in demand for blood . this study aimed to investigate the blood ordering pattern for maximum utilisation of blood and pave the way for formulating maximum surgical blood ordering schedule ( msbos ) for procedures where a complete crossmatch appears mandatory . the msbos is a list of common elective surgical procedures for which the maximum numbers of units of blood are cross matched pre - operatively for each procedure . the elective surgeries utilise only 30% of cross matched blood and are viewed as one of the areas of hospital wastage of this vital resource . many studies have been conducted on blood ordering and transfusion practices in elective surgery and have demonstrated over - ordering and underutilisation of blood . a number of studies have shown meaningful reductions in crossmatch requests , number of units cross matched and units transfused after msbos was implemented and group and screen were introduced . units cross matched fell slightly more than the units transfused , resulting in the lower cross match : transfusion ratios ( ctrs ) and indicating more effective use of resources . therefore , the aim of the study was to investigate the blood ordering pattern and transfusion practices and subsequently incorporate a blood ordering schedule which streamlines the use of blood and blood products for elective and emergency surgical procedures and , therefore , decrease over - ordering of blood . an observational study was conducted over a period of 19 months from february 2014 to september 2015 in a 350-bedded tertiary care hospital . source of data was blood bank requisition forms and blood bank registers of patients who underwent elective or emergency procedures in the hospital , for which blood was ordered . patients age and sex , diagnosis , type of procedure performed , pre - procedure haemoglobin level and number of blood units required to be cross matched and transfused were obtained from blood bank requisition form . the number of units prepared , cross matched and transfused as well as the number of patients for whom cross matching and transfusion were done was collected from blood bank registers . the blood which was cross matched but not transfused was considered as wasted . for the purpose of analysis , ctr = number of units cross matched / number of units transfuseda ratio of 2.5 and below is considered indicative of significant blood usagetransfusion probability ( % t ) = number of patients transfused / number of patients cross matched 100 . a value of 30% and above was considered indicative of efficient blood usagetransfusion index ( ti ) = number of units transfused / number of patients cross matched . a value of 0.5 or more was considered indicative of significant blood utilisationmead 's criteria : msbos = 1.5 ticode numbers were used instead of personal identification nomenclatures and the data were kept locked to maintain confidentiality of the information . ctr = number of units cross matched / number of units transfuseda ratio of 2.5 and below is considered indicative of significant blood usage transfusion probability ( % t ) = number of patients transfused / number of patients cross matched 100 . a value of 30% and above was considered indicative of efficient blood usage transfusion index ( ti ) = number of units transfused / number of patients cross matched . a value of 0.5 or more was considered indicative of significant blood utilisation mead 's criteria : msbos = 1.5 ti code numbers were used instead of personal identification nomenclatures and the data were kept locked to maintain confidentiality of the information . during the study , the hospital blood bank was requested to prepare 10,594 units of blood for 2556 patients who underwent major elective and emergency procedures . the majority of the patients were females , 1507 ( 59.2% ) , who underwent procedures in the elective schedule , and blood for transfusion was arranged by replacement donation [ table 1 ] . the blood units prepared per patient ranged from one to six units . from 10,594 units prepared , 1700 ( 16.04% ) units thus , only 16.04% of total blood cross matched was utilised , leaving 83.9% of the units cross matched but not transfused to the patient for whom it was prepared , i.e. , wasted . surgery department had the highest number of patients cross matched , 988 ( 38.7% ) , as well as with the highest no of units reserved , 5056 ( 47.72% ) , but not transfused , 4608 ( 43.5% ) . on the other hand , obstetrics and gynaecology were the departments with the second highest number of units cross matched and reserved for transfusion , 2162 ( 20.4% ) , but not transfused 1714 ( 16.17% ) . socio demographic and other characteristics of patients ( n=10594 ) in the study that spanned over 19 months , a total of 10,594 blood requests were received . the department of surgery made 5056 ( 47.72% ) requests for cross matched blood products followed by department of obstetrics and gynaecology which made 2162 ( 20.4% ) requests . the blood crossmatch requests from the department of medicine were 1969 ( 18.58% ) , and the oncology department made 1407 ( 13.28% ) requests for blood . a total of 10,594 units were cross matched , and of these , 1700 ( 16.04% ) units were utilised , leading to 8892 ( 83.9% ) of units not utilised due to non - transfusion [ figure 1 ] . number of units ( cross matched versus transfused ) the comprehensive blood utilisation indices of the hospital were c / t ratio = 6.23 . however , the blood utilisation indices of patients in different departments revealed different values [ table 2 ] . comparison between number of units cross matched and transfused the most common reason for transfusion was anaemia , with haemoglobin of < 10 g / dl . overall number 1084 ( 63.2% ) of patients who were anaemic pre - operatively were transfused and had more transfusions as compared to patients with normal pre - operative haemoglobin [ table 3 ] . transfusion activity in relation to anaemia eleven out of thirteen procedures had a ctr higher than 2.5 . the majority of these procedures belonged to the department of obstetrics and gynaecology and surgery [ table 4 ] . blood cross - match and transfusion patterns for different procedures with high c : t ratio the study aimed to investigate the blood ordering pattern and transfusion practices . the study revealed that the blood products which are cross matched for the purpose of transfusion are not transfused , and this impacts the transfusion services by underutilisation or over - ordering of blood products . the ctr in some procedures in our study varied from 2 to 10.6 , and there is over - ordering of blood products in many procedures . the over - requisition of blood without subsequent utilisation has been reported by earlier workers . the reason of over - ordering for blood is frequently based on the subjective anticipation of blood loss instead of audit - based estimates of the requirement in a particular procedure . the practice of making blood ready before scheduling a surgery may also be responsible for such a scenario combined with the fact that there is a great tendency to request more units of blood for elective procedures than what is actually required . higher ctrs have also been reported by collins et al . among the surgical categories , wherein the percentage of cases where none of the issued red blood cells were transfused ranged up to 93% , suggesting that gross over - ordering of crossmatches are seen in certain surgeries . similar findings were observed in our study where the surgical procedures of caesarean section , postpartum haemorrhage , prolapse uterus and carcinoma of oral cavity had higher ctrs . further procedures such as ovarian cystadenomas , chronic subdural haematoma and incomplete abortions also had high ctrs . the ctr is used for evaluating blood transfusion practices . the overall ctr of 6.31 observed in the current study is considered to be indicative of inefficient blood usage . still , the ctr widely varied and was very high in many surgeries of the department of surgery and gynaecology and obstetrics . similar findings regarding certain surgeries are observed in another study by subramanian et al . , which revealed that certain surgeries such as cholecystectomy ( open / laparoscopic ) , thyroidectomy , ureterolithotomy , gastro / cysto - jejunostomy , vagotomy / pyloroplasty , incisional hernia repair , varicose vein surgery and omentopexy had none of the three indices showing optimum blood utilisation . the probability of transfusion for a given procedure ( % t ) , which signifies the probability of transfusion , and a value of 30% and above have been suggestive of significant blood usage . the results of the present study revealed an overall transfusion probability of 57.62% as % t is dependent on the number of patients transfused and indicates appropriate transfusion as compared to number of units crossmatched per patient which were in excess of those transfused . this finding is similar to the study by subramanian et al . , in which % t for laprotomy , vascular surgery , amputation , few neck procedures and orthopaedic procedures was > 50% . regarding ti , a value of 0.5 or more is indicative of significant blood utilisation . . reports of ti in the range of 0.1 to 0.4 has also been reported in various surgical procedures . this finding of higher blood ordering pattern , especially in the department of surgery and obstetrics and gynaecology , needs to be revised and over - ordering of blood should be minimised . the obstetrics and gynaecology and surgery unit had the highest consumption of requested blood with a ctr of 4.82 and 10.96 , respectively , and % t of 41.26% and 48.98% , respectively . although the overall ctr is raised , still the % ti reflects appropriate blood usage for the respective departments as this finding may reflect the anticipated transfusion requirement of patients with caesarean section , postpartum haemorrhage , prolapsed uterus and debulking surgery for carcinomas which lead to more number of blood units being cross matched per patient and less number of units transfused per patient . furthermore , low incidence of prophylactic patient blood management in the aforementioned conditions may have contributed to high ctr . ineffectual transfusion practice with a high ctr and % t as observed in the present study has led to unnecessary wastage of blood and unavailability of blood for patients in need as cross matched blood is usually held in reserve . a similar pattern of over - ordering of blood leading to holding up of blood bank reserve as cross matched blood is considered reserved blood has been observed by bashawri et al . this also leads to increase in the workload of blood bank personnel as well as wastage of reagents , workforce and time with financial implications to both the patient and blood bank . the factors predictive of pre- and peri - operative blood transfusion are anaemia as rbc transfusion is the only way to rapidly treat severe anaemia . in the absence of an explicit msbos , ordering for blood transfusion is frequently based on the subjective anticipation of blood loss instead of audit - based estimates of the requirement in a particular procedure . the current deficiency of explicit msbos in our hospital is the major factor responsible for this . based on the findings in our study , a maximal surgical blood order schedule calculation by the formula 1.5 ti has been suggested to the hospital transfusion committee . the formulation of data - driven msbos and adhering to transfusion guidelines and prospective audit allied to educational programmes may be effective in modifying clinician 's behaviour in ordering transfusions and , therefore , reduce the number of unused units and generate considerable cost savings . however , transfusion requirements are subjective , and there is no fool proof way which can estimate blood loss or intraoperative modifications . other measures with proven improvement in ctr and % t are type and screen ( t and s ) , save and abbreviated crossmatch . the msbos specifies the number of blood units to be routinely cross matched for elective surgical procedures based on retrospective analysis of actual blood usage for these procedures . the t and s is determination of the patient 's abo group and rh type and screening for unexpected , clinically significant allo - antibodies . if the screen is negative , abo - compatible blood from the local inventory can be used with a quick spin crossmatch . by contrast , if the antibody screen is positive , then workup is necessary to determine the target antigen and identifying antigen - negative units for transfusion . the limitation of our study is that data was collected and catogorized into four broad specialities , however data on use of blood in ot / critical care , surgical speciality may have provided more useful insights . developing a blood ordering policy , which is a guide to expect normal blood usage for surgical procedures , can decrease over - ordering of blood , thereby reducing unnecessary compatibility testing , returning of unused blood and wastage due to outdating . it also allows for a more efficient management of blood inventory . in this respect , the hospital blood transfusion committee has to implement msboss for selected surgical procedures , conduct regular auditing about the effectiveness of the blood requesting policy using the ctr and offer periodic feedbacks to improve blood ordering , handling , distribution and utilisation practices of this scarce resource .

background and aims : excessive requests for cross matching blood which is more than the blood required for transfusion are usually based on worst case assumptions leading to overestimation of blood usage . we investigated the blood ordering pattern and transfusion practices so as to incorporate a blood ordering schedule for streamlining the use of blood in various hospital departments.methods:the study was conducted over a period of 19 months in a 350 bedded tertiary teaching hospital . source of data was blood bank requisition forms and blood bank registers of patients who underwent elective or emergency procedures in the hospital , for which blood was ordered . data were entered in ms excel and analysed using spss version 20.results:the blood bank was requested to prepare 10,594 units of blood for 2556 patients . the blood utilised was 16.04% of total cross matched blood , leaving 83.9% of units cross matched but not transfused to patient for whom it was prepared , i.e. , wasted . the surgery department had the highest number of units cross matched and transfused . the least number of units cross matched and wasted due to non - transfusion were from the department of oncology.conclusion:the current deficiency of explicit maximum blood order schedule in our hospital is the major factor responsible for high cross match : transfusion ratio . therefore , a maximal surgical blood order schedule has been suggested to the hospital transfusion committee to implement maximum surgical blood order schedules for selected procedures .

scattering at center - of - mass ( cm ) energies exceeding the quantum gravity scale ( transplanckian scattering , or _ t - scattering _ , for short ) is an exotic process of significant theoretical interest . in particular , it provides a laboratory to study the black hole information loss paradox . microscopic black hole formation and its subsequent evaporation is expected for impact parameters @xmath0 of the order of the schwarzschild radius @xmath1 of a black hole of mass @xmath2 @xcite,@xcite,@xcite,@xcite . the detailed description of how this happens depends on the unknown underlying theory of quantum gravity and is at present out of reach . on the other hand , large impact parameters @xmath3 correspond to elastic small - angle scattering , whose amplitude can be predicted on the basis of general relativity alone . it is given by eikonalized single - graviton exchange @xcite,@xcite,@xcite,@xcite . computing the corrections in @xmath4 to the elastic scattering , one hopes to learn about the strong inelastic dynamics at @xmath5 @xcite,@xcite,@xcite,@xcite,@xcite . t - scattering is also interesting phenomenologically . if large extra dimension scenarios of tev - scale gravity @xcite are realized in nature , this process could be observed at the lhc and other future colliders @xcite,@xcite , as well as in collisions of high - energy cosmic neutrinos with atmospheric nucleons @xcite,@xcite . in these scenarios the total t - scattering cross section is finite , grows with energy , and is dominated by calculable small - angle scattering between partonic constituents @xcite,@xcite , see fig . [ fig : dispp ] . the subleading black hole production cross section at present can only be estimated from geometrical arguments . in spite of the small scattering angle , the typical momentum transfer in these scattering events is well above the qcd scale , and the typical impact parameter is much smaller than the proton size , which sets the typical distance between two uncorrelated partons inside the proton . it is unlikely that a multiple parton interaction , fig . [ fig : pp ] , will occur in the same t - scattering . thus it is clear that the partonic picture should be applicable at leading order in the qcd coupling . in other words , we can compute the total cross section via a convolution of the partonic cross section and the parton distribution functions ( pdf ) @xmath6 . several interesting questions arise when one tries to think what happens beyond the leading order . for example , it s not known how to treat events of the type shown in fig . [ fig : disg ] , where one of the colliding partons ( say a quark ) radiates a gluon just before the collision . now the quark - gluon separation is not necessarily large , and the pair may scatter coherently . what is the correct description of such _ rescattering _ processes , and what is the resulting effect on the total t - scattering cross section ? a related question is : which factorization scale @xmath7 should we choose in the computation of the total cross section ? as is well known , qcd - initiated processes have significant higher - order logarithmic corrections , associated with the collinear qcd radiation off initial partons . by choosing @xmath7 appropriately , these corrections can and should be reabsorbed into the pdf . as we will see below , the familiar choice @xmath8 is likely not the right one for the t - scattering . if so , we would like to see this explicitly . the purpose of this paper is to answer the above - mentioned questions . we will be focusing on the qcd radiation since it is the dominant phenomenological effect due to the relative largeness of @xmath9 . however , our methods are equally applicable to the radiation of photons or any other spin 1 gauge bosons . we also hope that these methods may later prove useful in the more complicated problem of _ gravitational _ radiation emitted in t - scattering , and in particular to provide an alternative to the existing computations which are limited to the case when the emitted radiation is _ soft _ @xcite,@xcite . the paper is organized as follows . in section [ sec : review ] we review the eikonalization of small - angle @xmath10 partonic scattering amplitude , following @xcite,@xcite . to keep close contact with phenomenology , we work in the context of large extra dimension scenarios with the quantum gravity scale around a tev . a key feature of the extra - dimensional situation with @xmath11 compactified dimensions is the appearance of a new length scale @xmath12 , which sets the range of a typical t - scattering interaction . in @xmath13-dimensional planck units , @xmath14 we have @xmath15},\ ] ] so that @xmath16 in the deep transplanckian regime @xmath17 . we also present an alternative computation of the @xmath10 amplitude , based on generalizing to @xmath13 dimensions the early idea of t hooft @xcite , who considered the small - angle t - scattering by solving the klein - gordon equation for one particle propagating in the classical gravitational field of the other particle . in section [ sec : hadronic ] we start discussing small - angle t - scattering with hadronic initial states , as in fig . [ fig : dispp ] , in which qcd effects are expected to play a role . according to the existing proposal of emparan , masip and rattazzi @xcite , the total cross section for these processes must be computed with the following prescription for the pdf scale @xmath7 : @xmath18{l}q\,\quad\text{if}\quad q < b_{c}^{-1}\,,\\ q^{\frac{1}{n+1}}\left ( b_{c}^{-1}\right ) ^{\frac{n}{n+1}}\,\text{\quad if\quad}q > b_{c}^{-1}\ , , \end{array } \right . \label{eq : mu}\ ] ] where @xmath19 . for sufficiently high momentum transfers this deviates from the familiar prescription @xmath20 . an intuitive justification for this scale in terms of the typical impact parameter was given in @xcite , but we would like to check it via a direct computation . the first step is to be able to evaluate the amplitude for small - angle t - scattering accompanied by collinear qcd radiation . in the resummation approach @xcite,@xcite , this computation seems prohibitively difficult even for one - gluon emission . indeed , the eikonal amplitude for quark - quark t - scattering is a sum of an infinite number of crossed ladder gravition exchanges . the outgoing gluon may be attached anywhere on the quark lines , both external and internal . moreover , in the @xmath21 splitting , the emitted near - collinear gluon is not necessarily soft , and thus may also exchange gravitons . the number of diagrams to resum skyrockets . t hooft s approach is a much better starting point . as we point out , it can be easily ` upgraded ' to the case when radiation is present , provided that only one of the two colliding particles radiates . this covers completely lepton - quark scattering and is an important special case for quark - quark scattering . the idea is very simple . in the @xmath10 scattering , t hooft treated one particle classically , the other one quantum mechanically . the only new twist is to allow the quantum particle to radiate . in other words , we should treat the non - radiating parton classically , while the radiating parton _ and the gluonic radiation field with which it interacts _ quantum mechanically . this trick reduces the problem to a quantum field theory computation in the classical gravitational background produced by a relativistic point particle , the aichelburg - sexl ( as ) shock wave @xcite . in section [ sec : qft ] we develop the necessary formalism . we first consider the simplest perturbative quantum field theory in the as background : a scalar field with cubic self - interactions . we introduce a diagram technique for computing arbitrary transition amplitudes in this theory , which turns out to be closely related to the standard rules of light - cone perturbation theory in flat space . we then explain the changes necessary for the gluon field and for the scalar - gluon interactions , and compute the one - gluon emission amplitude as an example . notice that while fermionic matter fields can be considered analogously , we do not include them in this work in order to keep technical details to a minimum . thus we stick to a toy model in which the partonic constituents of colliding hadron(s ) are scalars . armed with the knowledge of gluon emission amplitudes , in section [ sec : qcdeffects ] we attack the question of qcd corrections to t - scattering . for definiteness and simplicity , we consider the gravitational analogue of the dis : a transplanckian electron - proton collision . the observable is the total cross section as a function of the bjorken @xmath22 and the transverse momentum transfer @xmath23 , in the small - angle region @xmath24 . at leading order ( lo ) in the qcd coupling @xmath9 , the partons scatter elastically on the electron ( no gluon emission ) . at next - to - leading order ( nlo ) , we demonstrate the appearance of logarithmic corrections whose scale is precisely the @xmath25 from eq . ( [ eq : mu ] ) . we find that the cross section factorizes , in the sense that these logarithms appear multiplied by the dglap splitting functions , and can be reabsorbed into the pdfs . finally , we are able to show that this factorization holds to all orders in @xmath9 , in the leading - logarithm approximation ( lla ) . our computation gives an explicit check for the validity of the partonic picture for the t - scattering . moreover , it gives an interesting and unexpected explanation for why the pdf scale deviates from the usual @xmath26 . it turns out that rescatterings like in fig . [ fig : disg ] _ suppress the initial state qcd radiation at transverse momenta _ @xmath27 . as a result the transverse momentum distribution of emitted gluons has the form:@xmath28 where @xmath29 is the standard distribution without rescattering , and @xmath30 is a function interpolating between @xmath31 for @xmath32 and @xmath33 for @xmath34 . logarithmic corrections to the cross section are obtained , as usual , by integrating eq . ( [ eq : dn ] ) over the gluon phase space , and the scale of these logarithms is a geometric mean of @xmath35 and @xmath36 as in eq . ( [ eq : mu ] ) . notice that one could imagine other distributions giving rise to @xmath37 , for example the standard @xmath38 with a sharp cutoff at @xmath39 . in this sense eq . ( [ eq : dn ] ) contains more information than the identification of the correct factorization scale . the predicted suppression of the initial state radiation is @xmath11-dependent and could in principle be used to determine the number of extra dimensions . a crucial insight into the physics of radiative processes is obtained by going into the impact parameter representation . in this picture , we find that the scattering is described via a multi - particle wavefunction of the virtual state ( parton@xmath40radiated quanta ) , which is multipled by individual eikonal factors when crossing the shock wave . this interpretation suggests a possible generalization of our formalism to the case when both colliding partons radiate , which we discuss in section [ sec : simul ] . in conclusion , this work shows that factorization holds for qcd effects in t - scattering , and that the factorization scale has a nontrivial dependence on @xmath41 , in agreement with the earlier proposal of ref . the novelty is that we arrive at these results by a concrete computation , and that we derive the modified distribution of the initial state radiation due to rescattering effects . the new distribution should be now incorporated into a ` transplanckian parton shower algorithm ' , to be used in monte - carlo simulations of t - scattering . we will come back to this issue in a future publication . in this section we review the basics of small angle t - scattering in the eikonal approximation . we will work within the large flat extra dimensions scenario of tev - scale gravity @xcite , see @xcite for the current experimental constraints . consider then two transplanckian massless standard model ( sm ) particles , thus confined to the sm 3-brane , which scatter due to the @xmath13-dimensional gravitational field , @xmath42 , @xmath11 being the number of large extra dimensions , @xmath43 for phenomenological reasons . for now we ignore all interactions except for gravity . in particular , we suppose that the colliding particles are not charged , and thus can not emit photons or gluons . we are interested in the scattering amplitude for small momentum transfer @xmath44 in this regime gravitational radiation is also suppressed ( see @xcite ) , and we have elastic @xmath10 scattering . the most direct way to compute the amplitude is by resumming the crossed ladder graviton exchange diagrams @xcite,@xcite , see fig . [ fig : eik ] . for small momentum transfer , exchanged gravitons are soft , and well - known simplifications occur in the vertices and the intermediate state propagators , allowing the resummation . the first term in the series , the one - graviton exchange , is given by@xmath45 where @xmath23 is the momentum transfer , which lies mostly in the direction transverse to the beam : @xmath46 . the @xmath13-dimensional planck scale @xmath47 tev is normalized as in @xcite,@xcite . the divergent integral over the extra dimensional momentum @xmath48 needs to be treated properly ; see below . the second term in the series , the sum of two one - loop diagrams , turns out to be equal to a convolution of two born amplitudes:@xmath49 and this pattern continues to higher orders . as a result the series can be summed by going to the impact parameter representation . the amplitude acquires the eikonal form:@xmath50 with the eikonal phase @xmath51 given by the fourier transform of the born amplitude in the transverse plane:@xmath52 to evaluate the eikonal phase , we need to regulate the divergent born amplitude ( [ eq : born ] ) . in @xcite , dimensional regularization was used , and it was argued that since the subtracted divergent terms are local , they do not affect the small angle scattering amplitude ) a physical regulator @xmath53 , with @xmath54 interpreted as an effective width of the sm brane , @xmath55tev@xmath56 . it was found that the resulting eikonal phase coincides with ( [ eq : eikr ] ) for @xmath57 , while for @xmath58 it varies slowly ( logarithmically ) . the eikonal amplitude then indeed agrees with ( [ eq : fn ] ) in the small scattering angle region . the same conclusion was also reached in @xcite using a sharp cutoff . ] . the eikonal phase was found to be:@xmath59 ^{1/n}\left ( \frac{s}{m_{d}^{2}}\right ) ^{1/n}\ , . \label{eq : eikr}\ ] ] the corresponding amplitude is then given by:@xmath60\ , . \label{eq : fn}\ ] ] the functions @xmath61 are plotted in fig . [ fig : fn ] ( see also fig . 2 of @xcite ) . their most salient features are as follows . at moderate @xmath62 , we have @xmath63 , @xmath64 the integral ( [ eq : fn ] ) receiving contributions from @xmath65 . on the other hand , for @xmath66 the integral has a saddle point at @xmath67 , and the amplitude decays:@xmath68 the appearance of the scale @xmath12 is a peculiar feature of t - scattering for @xmath69 . since the amplitude is the largest in the region @xmath62 , a typical scattering will have @xmath70 . yet a classical particle trajectory for these @xmath23 is undefined , all impact parameters @xmath71 contributing to the scattering . on the other hand , for @xmath72 @xmath73 the scattering is dominated by a characteristic impact parameter @xmath74 , corresponding to the above saddle point . in this case the particle trajectory is well defined and the t - scattering is truly semiclassical , with many gravitons being exchanged . an alternative computation of the small angle t - scattering amplitude can be given using a method due to t hooft @xcite , originally formulated in four dimensions . in this approach , particle @xmath75 scatters on the classical gravitational field created by particle @xmath76 . in other words , particle @xmath76 is treated as a classical point particle , while particle @xmath75 is treated quantum - mechanically . consider then the gravitational field of a relativistic classical point particle @xmath76 of energy @xmath77 propagating in the positive @xmath78 direction . this field is the @xmath13-dimensional generalization of the as @xcite shock wave:@xmath79 here @xmath80 while @xmath81 denotes @xmath82 transverse directions . einstein s equations with the lightlike source@xmath83 reduce to one linear equation for the shock wave profile @xmath84:@xmath85 the solution of this equation coincides with the eikonal phase ( [ eq : eikr ] ) per unit of particle @xmath75 energy : @xmath86 the right - moving particle @xmath75 is confined to the sm 3-brane , and its wavefunction solves the klein - gordon equation in the metric induced on the brane by the shock wave ( [ eq : as ] ) . at @xmath87 the wavefunction is a standard plane wave @xmath88 the metric ( [ eq : as ] ) has a strong discontinuity at @xmath89 . to solve the klein - gordon equation across the discontinuity , it is convenient to make a coordinate transformation @xcite,@xcite@xmath90 in the @xmath91 coordinates the metric is continuous across @xmath89 . when crossing the shock wave , the wavefunction remains continuous in these coordinates . this means that for small positive @xmath92 we have:@xmath93\ , . \label{eq : after}\ ] ] the @xmath94-dependent shift of the @xmath95 coordinate has a well - known classical origin : it is related to the time delay experienced by geodesics crossing the as shock wave , see fig . [ fig : as ] . coordinates , in which the metric is not manifestly flat for @xmath96 , nor even manifestly asymptotically flat , which makes these coordinates unsuitable for defining asymptotic outgoing states . the asymptotic states should be described in the @xmath22 coordinates , that s why in the last equation in ( [ eq : after ] ) we reverted to them . ] we now see from ( [ eq : after ] ) that the wavefunction immediately before and after the collision is related by a pure phase factor @xmath97 ) , which via ( [ eq : chiphi ] ) is identical with the eikonal phase factor in ( [ eq : eikr ] ) . an alternative derivation , by directly solving the klein - gordon equation , is given in appendix [ sec : gluonas ] . thus , t hooft s method is equivalent to the resummation . this is not surprising , because the external field approximation in quantum field theory resums precisely crossed ladder diagrams @xcite . the as shock wave is a solution to both linearized gravity and the full nonlinear einstein s equations . in retrospect , this explains why the diagrams in which gravitons emitted by particles @xmath76 and @xmath75 interact did not have to be taken into account in the resummation method . see @xcite for a detailed discussion and comparison of the two methods in @xmath98 . still , an attentive reader will notice two small differences between the two results . first , eq . ( [ eq : eikr ] ) contains @xmath99 under the integral sign , while t hooft s method gives a pure phase . this is the usual difference between the s- and t - matrices , @xmath100 . second , the amplitude ( [ eq : eikr ] ) is relativistically normalized , while in the new derivation normalization needs yet to be determined . modulo the normalization issue ( which will be resolved in section [ sec : scalar ] below ) , the power of t hooft s method relative to the resummation is quite evident . the eikonal phase is given a simple physical interpretation it is related to the time delay experienced by geodesics upon crossing the shock wave . the exponential factor @xmath101 emerges as a whole rather than by summing infinitely many individually large terms . if tev - scale gravity is the way of nature , then transplanckian collisions may be within the energy reach of the lhc . moreover , transplanckian collisions may be constantly happening in the atmosphere , between the atmospheric nucleons and high - energy cosmic rays ( @xmath102 gev for @xmath103 gev of the order of the gzk cutoff ) . in case of cosmic ray neutrinos this signal could actually be observable . since protons are not elementary particles , the theory of small angle t - scattering from section [ sec : review ] should be applied instead to @xmath10 collisions between the partonic constituents . notice that since we are dealing with cm energies well over a tev , the typical momentum transfers will be hard compared to the qcd scale , even though the scattering angle has to be small for the eikonal approximation to be valid . thus the collision resolves the internal structure of the proton(s ) , and the partonic picture is applicable @xcite . viewed another way , when two protons collide , there is a phase factor @xmath104 for each pair of partons moving in the opposite directions , see fig . [ fig : pp ] . this factor tends to zero rapidly at transverse separations @xmath105 , where @xmath106 gev)@xmath56 for t - scattering at the lhc energies . since partons are distributed in the disk of radius @xmath107gev@xmath108 , it is unlikely that more than one pair will undergo a hard collision . we would like to briefly mention which observables one usually computes in phenomenological studies . in @xmath109 collisions one is mostly interested in the total interaction cross section as a function of the energy transfer to the proton @xcite,@xcite,@xcite . we will discuss a similar observable in section [ sec : qcdeffects ] below . on the other hand , in the @xmath110 collisions at the lhc one studies two jet final states of high invariant mass , produced at a small angle to the beam @xcite,@xcite , see fig . [ fig : dispp ] . these jets originate from all possible parton pairs @xmath111 ) with the same partonic cross section , the eikonal amplitude being independent of the particle spin . for @xmath112 not much above a tev , the dijet t - scattering signal turns out to be visible over the qcd background . so far it may look that from the point of view of qcd , the t - scattering is just like any other hard process . let us however discuss which parton distribution factorization scale @xmath7 one should use when evaluating the t - scattering cross sections a necessary prerequisite for any practical computation . for the usual hard processes , we are accustomed to the choice @xmath113 , but for the t - scattering this turns out to be more subtle . as we discussed in section [ sec : resum ] , t - scattering becomes semiclassical in the region of large momentum transfers @xmath114 . in this regime , the transverse distance characterizing the process is the typical impact parameter @xmath115 which is _ parametrically larger _ than @xmath116 . it is for this reason that ref . @xcite advocated a hybrid prescription : one should use @xmath113 for @xmath117 and switch to @xmath118 for @xmath119 see eq . ( [ eq : mu ] ) . for t - scattering at the lhc energies , the factorization scale @xmath25 will be hard with respect to the qcd scale as long as the momentum transfer @xmath35 is hard . this gives a self - consistency check on the proposed picture . is a _ decreasing _ function of the cm energy , since the typical impact parameter grows with @xmath2 . even for hard momentum transfers , for sufficiently high @xmath2 the factorization scale will come down to a gev , signalling a breakdown of the partonic picture . at even higher cm energies ( which are well beyond the range of lhc or even cosmic ray collisions ) , the proton should interact gravitationally as a point particle . ] the above is a summary of the current understanding of qcd effects in t - scattering . clearly , it is based mostly on intuition . we would like to develop a systematic theory of these phenomena . in particular , such a theory should allow to check the factorization scale proposal by a concrete computation . we have to evaluate the leading log corrections to the t - scattering cross section due to the initial state radiation emission , and to show that they can be absorbed into a shift of the pdf factorization scale . since @xmath7 is conjectured to have a nontrivial dependence on @xmath35 , some nontrivial physics is likely to come out . two equivalent methods were given in section [ sec : review ] to describe t - scattering without radiation . which one shall we try to generalize to the case when radiation is present ? for the resummation method , generalization does not seem to be easy , not even for the one - gluon emission . think about infinitely many crossed - ladder diagrams , infinitely many places to attach the gluon line , and the necessity to take into account the gravitational exchanges of the emitted gluon ! for t hooft s method , on the other hand , the situation looks hopeful : if only particle @xmath75 radiates , it is quite clear how to include its radiation . namely , we should keep working in the classical gravitational background created by particle @xmath76 , but switch from relativistic quantum mechanics ( wavefunctions , the klein - gordon equation ) to quantum field theory ( green s functions and interaction vertices ) . we will follow this path and will see that it allows relatively straightforward computations of the gluon emission amplitudes . physically , the assumption that particle @xmath76 does not qcd - radiate is realized if @xmath76 is a lepton . if both @xmath76 and @xmath75 are strongly interacting , one could first compute the radiation off @xmath75 ( taking @xmath76 classical ) , then off @xmath76 ( taking @xmath75 classical ) . such an approximation of independent emission is valid for the dominant , collinear , radiation in the usual perturbative processes . for the t - scattering , we will be able to partially justify it below . but first we have to understand well the case of non - radiating @xmath76 . to compute the qcd radiation accompanying a transplanckian collision , we will replace particle @xmath76 with the classical background it generates , but will keep particle @xmath75 and the gluons as quantum fields . thus we will be doing perturbative qft computations in the shock wave background . we start with the simplest interacting qft , the massless @xmath120 theory:@xmath121 we will describe how to compute transition amplitudes in this theory , and how these are related to the amplitudes in the full theory ( i.e. before particle @xmath76 was replaced by a classical gravitational field ) . the @xmath122 in ( [ eq : lphi ] ) is the 4-dimensional metric obtained by restricting the @xmath13-dimensional as shock wave ( [ eq : as ] ) to the sm brane on which both particles and the radiation propagate . we will continue using the coordinates as in ( [ eq : as ] ) , only restricting the number of @xmath81 components from @xmath82 to @xmath123 . two features make this theory much simpler than it would be for generic curved backgrounds treated in @xcite : 1 . the metric is invariant under @xmath95 shifts . the conjugate momentum @xmath124 is conserved . this leads in particular to the absence of spontaneous particle creation . 2 . the spacetime is flat except on the @xmath89 plane . the feynman rules are simplified by using the flat - space coordinates . we start by canonically quantizing the quadratic part of the lagrangian . the scalar field modes are found by solving the equations of motion ( eom ) in the shock wave background with the plane wave conditions in the asymptotic past @xmath87 : we denote the 2-dimensional , transverse to the beam , part of 4-dimensional lorentz vectors . the minkowski space signature is @xmath125.]@xmath126.x}+\theta(x^{-})\int\frac{d^{2}\mathbf{q}}{(2\pi)^{2}}\,i(p^{-},\mathbf{q})\,e^{i[p+\mathbf{q}].x}\,,\label{eq : modes}\\ i(p^{-},\mathbf{q } ) & \equiv\int d^{2}\mathbf{x}\,e^{-i\mathbf{q}.\mathbf{x}}e^{i\frac{1}{2}p^{-}\phi(\mathbf{x})}\,.\nonumber\end{aligned}\ ] ] the compact vector in square brackets notation denotes an on - shell 4-vector whose @xmath40 component is computed in terms of the known @xmath127 and @xmath128 , i.e. @xmath129\equiv((\mathbf{p+q})^{2}/p^{-},p^{-},\mathbf{p+q}),$ ] etc . the function @xmath130 is identical to the eikonal amplitude ( [ eq : eikr ] ) , up to the normalization and the absence of @xmath99 under the integral sign ( which means that it contains an extra @xmath131-function piece ) . the modes ( [ eq : modes ] ) solve the klein - gordon equation both for @xmath87 and for @xmath132 across the shock wave , they satisfy the matching condition of section [ sec : thooft ] : @xmath133 we proceed to quantize the field by expanding in oscillators:@xmath134^{\ast}\right\ } \,,\\[5pt ] \lbrack a_{p_{1}^{-}\mathbf{p}_{1}},a_{p_{2}^{-}\mathbf{p}_{2}}^{\dagger } ] = ( 2\pi)^{3}\delta(p_{1}^{-}-p_{2}^{-})\delta^{(2)}(\mathbf{p}_{1}-\mathbf{p}_{2})\,.\end{gathered}\ ] ] such normalization of the creation / annihilation operators is standard for quantizing on the light cone ; it differs from the usual one by a simple rescaling . equivalently , we can quantize using the outgoing modes , which reduce to plane waves for @xmath135:@xmath136.x}+\theta ( -x^{-})\int\frac{d^{2}\mathbf{q}}{(2\pi)^{2}}\,i(p^{-},\mathbf{q})\,e^{i[p-\mathbf{q}].x}\ , . \label{eq : modes1}\ ] ] the in and out modes are related by a unitary bogoliubov transformation , which acts only on the transverse momentum @xmath137 but not on @xmath124 . thus there is no spontaneous particle creation in this background ; the vacuum is unambiguously defined . let us now build a perturbation theory for transition amplitudes . the logic is simplest in the position space . even though the metric is singular at @xmath138 it is easy to see that@xmath139 : the metric determinant drops out of the interaction lagrangian . thus the feynman diagrams will be given by flat space integrals , with no singular contribution from the shock wave . for instance , the @xmath140-channel diagram contributing to the @xmath141 transition amplitude will be given by:@xmath142{phi3.pdf}}=(-i\lambda)^{2}\int d^{4}x\,d^{4}y\,[\phi_{3}^{\text{out}}(x)]^{\ast}\,[\phi_{4}^{\text{out}}(y)]^{\ast}\,g(x , y)\,\phi_{1}^{\text{in}}(x)\,\phi_{2}^{\text{in}}(y)\ , . \label{eq : exf}\ ] ] the @xmath143 and @xmath144 enter as the in and out state wavefunctions . the propagator @xmath145 must be @xmath92-ordered : @xmath146 in ( [ eq : exf ] ) we have to integrate in all possible @xmath92 orderings of @xmath22 and @xmath147 with respect to each other and to the shock wave sitting at @xmath89 . the propagator will take different forms depending on the ordering . for @xmath92 and @xmath148 on the same side of the shock , we get the flat space result:@xmath149.(x - y)}+(x\leftrightarrow y)\,.\ ] ] on the other hand , across the shock wave we [email protected] - i[p].y}+(x\leftrightarrow y)\,.\ ] ] the momentum - space feynman rule can now be found by straightforward fourier transformation ; they are as follows . the in and out states are specified by the @xmath124 and @xmath137 of all incoming and outgoing particles . the transition amplitude @xmath151 in the external gravitational field of particle @xmath76 is then given by:@xmath152 the @xmath153 is a function of the external momenta computed as a series in @xmath154 according to the following rules . to obtain the @xmath155 term : * draw the feynman diagrams with @xmath156 @xmath120 vertices , considering all possible @xmath92-orderings of these vertices with respect to each other and to the shock wave at @xmath89 . * consider all shock wave crossings as additional vertices , with entering transverse momenta @xmath157 representing momentum exchange with the shock wave . * assign @xmath124,@xmath137 internal lines momenta by using their conservation in all vertices ( @xmath120 and shock wave crossings ) . momentum flow is in the direction of increasing @xmath92 . the internal @xmath158 momenta are not conserved but are assigned by using the on - shell condition @xmath159 * for each @xmath120 vertex multiply by @xmath160 * for each shock wave crossing vertex multiply by @xmath161 , where @xmath124 is conserved in the crossing . * for each internal line ( i.e. a line connecting two vertices , @xmath120 or shock wave crossing ) carrying momentum @xmath124 , multiply by @xmath162 * the @xmath120 vertices and the shock wave at @xmath89 divide the @xmath92 axis into two unbounded and @xmath156 bounded intervals . for each bounded interval , we define an _ intermediate state _ , consisting of all the particles whose internal lines traverse this interval . for each intermediate state at _ negative _ @xmath92 , the amplitude is multiplied by@xmath163 for each intermediate state at _ positive _ @xmath92 , it is multiplied by@xmath164 the sums are over all particles in the initial ( @xmath165 ) , intermediate , and final ( @xmath166 ) state . * integrate over the momenta @xmath157 exchanged with the shock wave:@xmath167 * for loop diagrams , integrate over all undetermined momenta @xmath168:@xmath169 the reader will notice a striking similarity to the usual light - cone perturbation theory ( pt ) rules @xcite . notice in particular the light - cone energy denominators , and the @xmath170 factors , which eliminate some of the diagrams present in the time - ordered ` old ' perturbation theory . new features in our case are the shock wave crossing vertices , and that there are two types of energy denominators , depending on the ordering with respect to the shock wave . we thus have ` light - cone pt in presence of an instantaneous interaction ' . many years ago , bjorken , kogut and soper @xcite have developed light - cone pt in external electromagnetic field , and argued that at sufficiently high energies interaction with the external field can be represented as an instantaneous eikonal scattering . in our case , the eikonal factor has gravitational origin , but the formalism is the same . the formalism of @xcite has found application in the dipole scattering approach to the dis at small @xmath22 : an almost - real photon splits into two quarks which then undergo eikonal scattering in the gluon field of the proton @xcite . the difference is that the gluon field of the proton is not really known , while in our case the eikonal phase can be computed exactly . we will now demonstrate the rules by computing a couple of amplitudes . the elastic one - particle amplitude @xmath171 is given by just one diagram with a shock wave crossing vertex ( denoted by a cross):@xmath172{phi3-simplest.pdf}\nonumber\\ \mathcal{m}(p\rightarrow p^{\prime})=p^{-}i(p^{-},\mathbf{p}-\mathbf{p}^{\prime})\qquad(p^{2}=p^{\prime2}=0,\,p^{-}=p^{\prime-})~. \label{eq : mael}\ ] ] as a more complicated example , let us compute one of the diagrams appearing in the computation of the amplitude @xmath141:@xmath173{phi3-o1.pdf}\ ] ] we have two @xmath120 vertices and three shock wave crossings . the dotted lines stress the @xmath92 ordering of the vertices . the @xmath174 are the internal line momenta , whose @xmath127 and @xmath175 components are fixed via momentum conservation , while the @xmath40 components are determined by being on shell . there are two intermediate states : one before the shock wave @xmath176 , and one after @xmath177 . the value of this diagram is thus:@xmath178 finally , we have to discuss the relation between the transition amplitude @xmath153 and the full relativistic scattering amplitude @xmath179 , i.e. the one obtained when we reinstate particle @xmath76 as a quantum particle as opposed to replacing it with its classical field . we have:@xmath180 the incoming ( outgoing ) momenta of particle @xmath76 are assigned as follows:@xmath181 in other words , particle @xmath76 absorbs the total transverse momentum exchanged with the shock wave . as long as the momentum transfer is small compared to @xmath182 , @xmath183 is almost on shell and the approximation is justified . the relative factor @xmath184 in ( [ eq : mma ] ) is related to the normalization of the particle @xmath76 state , which is lost when we replace it with a classical field . this factor is thus process - independent . for instance one can extract it from the external field approximation in qed @xcite . the extra @xmath185 can be traced back to the external field creation vertex , which carries a factor of @xmath185 . this settles the question of relativistic normalization of the amplitudes computed via t hooft s method . we can now complete the comparison with the resummation method . using eqs . ( [ eq : mael ] ) , ( [ eq : mma ] ) we have@xmath186 which agrees with the eikonal amplitude from eq . ( [ eq : aeikr ] ) including the normalization , modulo the difference between the s- and t - matrices already discussed in section [ sec : thooft ] . in order to keep technical details to a minimum , we will not consider fermionic fields in the shock wave background . instead , we will stick to a toy model in which charged matter ( partonic constituents of the colliding hadrons ) consists of massless scalars . this will be sufficient given our general goals . on the other hand , since the coupling constant of the @xmath120 lagrangian has dimension of mass , the cubic self - interaction is not a good model for the qcd radiation . we do have to introduce gauge fields . thus we switch from ( [ eq : lphi ] ) to a different microscopic lagrangian , describing the su(3 ) yang - mills theory and a massless complex scalar in the fundamental representation , propagating in the shock wave background:@xmath187)\ , . \label{eq : lsg}\ ] ] most of the @xmath120 formalism is carried over with trivial changes . instead of repeating the whole discussion , we will introduce the necessary modifications on a concrete example . namely , let us consider the one - gluon emission : particle @xmath75 , while scattering in the gravitational field of particle @xmath76 , emits a gluon . the amplitude is given by the sum of the following two diagrams:@xmath188{mg+.pdf}}\quad(\text{ii)}{\includegraphics [ natheight=2.171600 in , natwidth=2.987300 in , height=1.4563 in , width=1.9975 in ] { mg-.pdf } } \label{eq:1g}\ ] ] the new objects are the gluon emission and the gluon shock wave crossing vertices . to simplify the computations , we will impose the lorenz and light - cone gauge conditions:@xmath189 the treatment in a general gauge and demonstration of gauge invariance is given in appendix [ sec : gluonas ] . gluon emission in curved space is described by the cubic term in the lagrangian:@xmath190 here @xmath191 is the strong coupling constant , and the su(3 ) generators are normalized by tr@xmath192 . in the light - cone gauge the singular component @xmath193 drops out ( see appendix [ sec : gluonas ] for a more detailed discussion ) . the gluon emission vertex is thus the same as in flat space:@xmath194{scalar - gauge - vertex.pdf}}\nonumber\\ g_{s}t_{ij}^{a}(p_{1}+p_{2}).\varepsilon\quad\longrightarrow\quad~g_{s}t_{ij}^{a}(\mathbf{p}_{1}+\mathbf{p}_{2}-\frac{p_{1}^{-}+p_{2}^{-}}{l^{-}}\mathbf{l}).\boldsymbol{\upepsilon\qquad(}\varepsilon_{+}=0,\,l.\varepsilon = 0)\ , , \label{eq : gluonv}\ ] ] where we used the lorenz gauge to eliminate the @xmath195 component . the gluon shock wave crossing vertex contains the same factor @xmath196 as in the scalar case . a new feature is that the @xmath195 polarization component changes in the crossing according to:@xmath197{gauge - vertex.pdf}}\quad\varepsilon_{2-}=\varepsilon_{1-}-\frac { \boldsymbol{\upepsilon}_{1}.\mathbf{q}}{p_{1}^{-}},~\boldsymbol{\upepsilon}_{2}=\boldsymbol{\upepsilon}_{1}\quad(\varepsilon_{+}\equiv0)\ , , \label{eq : gluoncross}\ ] ] this rule is easy to guess from consistency with the imposed gauge ; see appendix [ sec : gluonas ] for an explicit derivation . notice however that we do nt have to keep track of this change in @xmath195 if we use the simplified gluon emission vertex in ( [ eq : gluonv ] ) . we are now ready to evaluate the above two diagrams . working for simplicity in the frame where @xmath198 , we get:@xmath199^{+}}\boldsymbol{\,},\nonumber\\ \mathcal{m}^{(\text{ii } ) } & = ig_{s}t_{ij}^{a}\int\frac{d^{2}\mathbf{k}}{(2\pi)^{2}}i(l^{-},\mathbf{k})\,i(p^{\prime-},\mathbf{q}-\mathbf{k})\frac{(\mathbf{k}-\mathbf{l}-\frac{2p^{-}-l^{-}}{l^{-}}(\mathbf{l}-\mathbf{k})).\boldsymbol{\upepsilon}}{-[p - l+\mathbf{k}]^{+}-[l-\mathbf{k}]^{+}+i\varepsilon}\boldsymbol{\,}. \label{eq : m1geval}\ ] ] physical consequences of the derived expressions will be discussed below . as a final comment , we note that lagrangian ( [ eq : lsg ] ) contains also a cubic gluon self - interaction vertex , which could be discussed analogously to ( [ eq : gluonv ] ) , as well as two quartic vertices ( @xmath200 and @xmath201 ) . the quartic vertices do not contribute to the amplitudes in the collinearly enhanced region , and we will not need their precise expressions . the dominant qcd radiation effects in the usual perturbative hard scattering processes are the collinear initial and final state radiation . we now proceed to see how these effects manifest themselves in the t - scattering . we will focus on the initial state radiation and its effect on the parton distribution scale . final state radiation , which happens after the partons cross the shock wave , is expected to be as usual . to discuss radiative corrections to the pdfs , we need to choose a process and an observable which can be defined and computed beyond lo . the simplest such process is the t - scattering analogue of the dis . in other words , we will consider an electron - proton t - scattering @xmath202+anything at a fixed momentum transfer . this is like in fig . [ fig : dispp ] with an electron instead of a neutrino . the scattering is characterized by @xmath203 and @xmath204 , the energy transfer to the proton . these can be measured by observing the electron . as usual , we assume small angle scattering : @xmath205 . we will also assume that the relative electron energy loss is small , @xmath206 . under these conditions , and also since the electron does not qcd - radiates , we can represent it by a classical relativistic point particle of fixed energy . this is our ` particle @xmath76 ' . using the @xmath183 on shell condition @xmath207 , it is easy to show that the momentum transfer is mostly in the transverse plane , as expressed by the relation:@xmath208 like in the dis , we are interested in the differential cross section with respect to @xmath23 and the bjorken @xmath22 : @xmath209 as is customary , we will first analyze the partonic cross section @xmath210 between the electron and a quark ( particle @xmath75 ) . we will work in a toy model of scalar quarks . at lo ( no gluon emission ) , the amplitude is ( [ eq : nog ] ) and the partonic cross section is given by @xmath211 armed with the formalism from section [ sec : qft ] , we can easily write down the gluon emission amplitudes . at the nlo we have diagrams with real gluon emission , as in eq . ( [ eq:1 g ] ) , as well as virtual corrections to the external legs and the vertices in the elastic amplitude . as usual , the latter diagrams do not have to be computed explicitly , since they only correct the coefficient of @xmath212 we thus focus on the real emission . the partonic cross section with one gluon emitted is given by a phase space integral ( see appendix [ sec : phase])@xmath213 q^{+}=\mathbf{l}^{2}/l^{-}+(\mathbf{q}-\mathbf{l})^{2}/p_{b^{\prime}}^{-}\,.\nonumber\end{gathered}\ ] ] here @xmath179 is the relativistic scattering amplitude @xmath214 , related to the transition amplitude in the external field @xmath215 via eq . ( [ eq : mma ] ) . the amplitude @xmath216 is in turn the sum of the two diagrams ( [ eq:1 g ] ) , evaluated in eq . ( [ eq : m1geval ] ) . we are using notation from ( [ eq:1 g ] ) with @xmath217 , @xmath218 . the @xmath204 is the total + momentum of the quark - gluon system after the collision . the @xmath78 is the @xmath124 momentum fraction carried off by quark @xmath219:@xmath220 let us first analyze which region of the @xmath221 plane contributes to the integral ( [ eq:1gpart ] ) . for which @xmath221 is there a @xmath78 saturating the @xmath131-function ? the relevant function ( see fig . [ fig : xz ] ) @xmath222 has a maximum value@xmath223 thus , the integrand of ( [ eq:1gpart ] ) is nonzero for @xmath221 belonging to the ellipse:@xmath224 in other words , phase space limits the transverse momentum of the emitted gluon to be at most @xmath225 . let us now examine the amplitude , whose two parts are given in eq . ( [ eq : m1geval ] ) . by analogy with the usual dis , we expect that part ( i ) , corresponding to the gluon emission _ after _ the hard scattering , gives only a finite correction to the cross section , while part ( ii ) contains a logarithmic ir divergence which has to be absorbed by redefining the pdfs . let us see formally how this happens . notice that part ( i ) of the amplitude is non - singular in the @xmath221 plane . in particular , the intermediate state denominator is completely fixed at @xmath226 . omitting the @xmath22 dependent factors , the amplitude is thus @xmath227 and its square is @xmath228 after integrating over the ellipse in the @xmath221 plane ( area @xmath229 we get a finite contribution to the differential cross section of the relative order @xmath230 this is as expected . interesting physics is associated with part ( ii ) , whose expression can be simplified as follows:@xmath231 \mathbf{m}_{i } & = \int\frac{d^{2}\mathbf{k}}{(2\pi)^{2}}\frac{(\mathbf{k}-\mathbf{l})_{i}}{(\mathbf{k}-\mathbf{l})^{2}}\,i(zp^{-},\mathbf{q}-\mathbf{k})\,i((1-z)p^{-},\mathbf{k})\,\label{eq : mi0}\\ & \equiv\frac{-\mathbf{l}_{i}}{\mathbf{l}^{2}}\,\widetilde{i}(zp^{-},\mathbf{q})+\,\frac{(\mathbf{q}-\mathbf{l})_{i}}{(\mathbf{q}-\mathbf{l})^{2}}\widetilde{i}((1-z)p^{-},\mathbf{q})\nonumber\\ & + \int\frac{d^{2}\mathbf{k}}{(2\pi)^{2}}\frac{(\mathbf{k}-\mathbf{l})_{i}}{(\mathbf{k}-\mathbf{l})^{2}}\,\widetilde{i}(zp^{-},\mathbf{q}-\mathbf{k})\,\widetilde{i}((1-z)p^{-},\mathbf{k})\ , . \label{eq : mi}\ ] ] here we separated the regular part @xmath232 of the @xmath130 from the @xmath131-function piece describing the propagation without scattering:@xmath233 \widetilde{i}(p^{-},\mathbf{q})=2\pi b_{c}^{2}f_{n}(b_{c}|\mathbf{q}|)\,,\end{gathered}\ ] ] where @xmath61 are the same functions as in eq . ( [ eq : fn ] ) . we omitted a total @xmath234 piece from ( [ eq : mi ] ) . the physical meaning of the decomposition ( [ eq : mi ] ) is as follows . in the first two terms , only one of the two splitting products of quark @xmath75 participates in the gravitational interaction , the other one passing the shock wave without scattering . the last term instead describes their coherent gravitational scattering , as in fig . [ fig : disg ] . we call it the _ rescattering _ term , since it corresponds to the situation when the emitted qcd radiation changes its direction in the field of the shock wave . we now proceed to studying corrections to the cross section . consider first the case @xmath235 in this case all the entering @xmath232 functions are @xmath236 the rescattering term can be estimated by integrating up to @xmath237 beyond which point the @xmath232 decrease faster than @xmath238 , and the integral converges . we get@xmath239 we see that rescattering is subleading to the first two terms in ( [ eq : mi])@xmath240 concentrating on the first two terms , the dominant contribution to the cross section comes from the singularities at @xmath241 and @xmath242 . squaring the amplitude and integrating we get : @xmath243 here we used that in the relevant regions of integration ( see fig . [ fig : xz])@xmath244 eq . ( [ eq : nlo ] ) has the standard factorized form expected from an nlo qcd correction to a hard scattering @xcite . the ir divergent logarithm multiplies the quark - electron and gluon - electron lo cross sections , with the _ scalar _ quark dglap splitting functions @xmath245 and @xmath246 as coefficients . as usual , we can absorb the ir divergence into the quark ( first term ) and gluon ( second term ) pdfs . if we fix the parton distribution scale at the upper cutoff , @xmath247 , then the whole logarithmic correction is absorbed . it is of course not surprising that we managed to recover the standard factorization for @xmath70 : rescattering was not important in this case , and without rescattering there is no difference between transplanckian and any other hard scattering . let us proceed to the case @xmath248 . the situation here is more complicated since the rescattering is no longer subleading . consider for example the region @xmath249 . the rescattering integral is dominated by @xmath250 , where @xmath251 is maximal , and not , say , by the region of @xmath252 where @xmath253 is maximal . the reason is that @xmath254 decreases faster than @xmath238 for @xmath255 . we get an estimate : @xmath256 which is comparable to the first term without rescattering in ( [ eq : mi ] ) . in a situation when rescattering can not be neglected , the separation into three terms in eq . ( [ eq : mi ] ) becomes artificial , and we should treat the whole amplitude as given in ( [ eq : mi0 ] ) . substituting the definitions of @xmath257 , we can transform this expression into a transverse plane integral:@xmath258 this simple equation provides a key insight into the physics of the process . namely , we can view the factor @xmath259 as the coordinate - space wavefunction of the gluon - quark state into which quark @xmath75 splits . upon crossing the shock wave , this two - particle wavefunction is multiplied by the eikonal factors @xmath260 and @xmath261 , depending on the transverse plane position of each particle . finally , to compute the s - matrix element , one takes the overlap with the outgoing state wavefunction @xmath262 . pair in the field of an incoming nucleus . ] the completely general expression ( [ eq : miimp ] ) can be further simplified if @xmath263 . in this case , the typical @xmath264 contributing to the integral are much larger than the typical @xmath265 . approximating @xmath266 , the amplitude takes a factorized form:@xmath267 where the gluon emission factor @xmath268 is given by@xmath269\,,\label{eq : f}\\[5pt ] c_{n}(u)\equiv\int_{0}^{\infty}dy\,j_{1}(y)\,e^{i(\frac{u}{y})^{n}}\,.\nonumber\end{gathered}\ ] ] this factor has a nontrivial dependence on @xmath221 . for @xmath270 the integral is dominated by large @xmath271 , so that the second term in the exponent can be dropped , giving @xmath272 thus we recover the first term in eq . ( [ eq : mi ] ) , which in this limit dominates the amplitude . on the other hand , in the opposite limit the integral can be evaluated by stationary phase , with the result:@xmath273 remember that precisely in this case we expected a non - negligible contribution from rescattering , see eq . ( [ eq : mresc ] ) . we now see that its effect is indeed important : rescattering leads to an @xmath274 reduction of the gluon emission amplitude ! physically , this can be explained as follows . to scatter with large @xmath221 , the emitted gluon must cross the shock wave in the region of small impact parameters . in this region , the eikonal factor in ( [ eq : f ] ) distorts the gluon wavefunction , which leads to suppression of the amplitude via destructive interference . it is however remarkable that , up to an @xmath221-dependent phase , the suppressed amplitude still goes as @xmath275 . in terms of the function @xmath276 , the above asymptotics can be stated as follows:@xmath277 as can be seen from fig . [ fig : cn ] , the large @xmath278 behavior sets in already for @xmath279 . we are now ready to derive the logarithmic correction to the cross section for @xmath248 . we square eq . ( [ eq : miappr ] ) and integrate in @xmath263 , taking into account the suppression for @xmath280 . schematically , we get : @xmath281 in other words , due to the @xmath33 suppression of the second term , the arguments of the two logs combine into a geometric mean which coincides exactly with eq . ( [ eq : mu ] ) ! the final result is as follows : for @xmath248 , the nlo correction to the cross section is given by the same eq . ( [ eq : nlo ] ) as for @xmath70 with the following simple replacement:@xmath282 let us discuss what we have achieved . first , we have shown that the emission amplitude of near - collinear gluons has a factorized form , eq . ( [ eq : miappr ] ) . physically , it means that we can first consider the hard scattering process , and worry about adding additional gluons later . if a parton splits in two before crossing the shock wave , one and only one of the splitting products absorbs most of the momentum transfer in a typical event . this is actually an important check of validity of the partonic picture . second , we found explicitly the gluon emission factor @xmath268 . the probability distribution of emitted gluons is given by @xmath283 . we found that for large relative transverse momenta @xmath284 ( but still @xmath263 ) this distribution is suppressed by a factor @xmath33 relative to the standard qcd distribution @xmath285 . this is a new effect , which could be used to measure the number of extra dimensions . finally , as a consequence of this suppression , the logarithmic nlo correction to the partonic cross section involves , for @xmath248 , a scale which interpolates between the usual @xmath286 and @xmath36 in agreement with eq . ( [ eq : mu ] ) . in fact , as we show in appendix [ sec : multi ] , such logarithms occur in every order of perturbation theory . thus , as usual , they can be exponentiated and removed by shifting the parton distribution scale to @xmath287 . this , then , provides a formal justification for the proposal of emparan , masip , and rattazzi @xcite , that this scale is the one minimizing higher - order corrections . our derivation of the scale ( [ eq : mu ] ) has an added advantage that we now know the gluon distribution . this distribution could not be easily guessed : for example the standard @xmath38 with a sharp @xmath39 cutoff would give rise to the same log . at the same time , the very fact that we found agreement with ref . @xcite may seem like a mistery . remember that they _ fixed _ this scale to be equal to @xmath39 ( see section [ sec : hadronic ] ) . where , then , does the typical impact parameter @xmath288 hide in our computation ? in fact , if we are not interested in the gluon distribution , we can reformulate our derivation so that it will conform with the original intuition of @xcite . the idea is to compute the lhs of eq . ( [ eq : fint ] ) not from the asymptotics of @xmath276 but directly from the definition of @xmath268 in the impact parameter representation . since the @xmath289 norm of the gluon wavefunction is the same in the momentum and in the position space , we have@xmath290 the only subtlety is that in the lhs we are not integrating over the whole @xmath221 plane , and thus the limits of the @xmath264 intergration have to be adjusted accordingly . a moment s thought shows that the correct limits should be put at the typical @xmath264 values contributing to @xmath268 at @xmath291 and @xmath292 : @xmath293 so , we recover the same logarithm as above , and this time @xmath288 enters explicitly . we have worked throughout in the toy model of scalar quarks . however , it should be easy to adapt our considerations to the realistic case of fermionic matter . one would have to compute the shock wave crossing vertex for the fermion field . this will require solving the dirac equation in the shock wave background . we expect that our results about factorization and suppression of radiation at large angles will remain true in the fermionic case as well . so far we were making the technical simplifying assumption that particle @xmath76 does not qcd - radiate . this is of course not true in @xmath110 collisions at the lhc , when both colliding partons are colored . we will now discuss how one could relax or remove this restriction . consider the following two key properties of qcd radiation : 1 . near - collinear emission dominates . 2 . its amplitude takes a factorized form . these properties are true for the standard hard perturbative processes . for the t - scattering with non - radiating @xmath76 , we have also shown them to be true , provided that a gluon emission factor is adjusted accordingly . we conjecture that these properties continue to hold when both @xmath76 and @xmath75 are allowed to radiate . in practice , this implies that the dominant part of the emitted radiation can be described using the independent emission approximation : first compute the radiation off @xmath75 ( taking @xmath76 classical ) , then off @xmath76 ( taking @xmath75 classical ) . intuitively , this can be justified as follows . the fact that the near - collinear emission dominates is due to the @xmath294 singularity in the gluon emission factor , combined with a phase space cutoff @xmath295 we have seen that shock wave crossing tends only to suppress radiation at large angles by distorting the gluon wavefunction , and we do not expect this tendency to reverse when @xmath76 is allowed to radiate . thus collinear radiation should dominate also for the t - scattering . once we know that collinear emission dominates , and thus the emitted radiation does not change the hard transverse momentum flow of the process , it seems reasonable that the amplitude should factorize into the product of the @xmath10 scattering with the hardest momentum exchange times the gluon emission factors . the independent emission approximation is probably adequate for most practical purposes . nevertheless , to try to go beyond it is an interesting theoretical challenge . we will now describe pictorially a generalization of our formalism which , we believe , can describe simultaneous emissions from @xmath76 and @xmath75 without any extra approximation ( except , of course , large cm energy and small scattering angle ) . the starting point is the emission amplitude in the impact parameter representation ( [ eq : miimp ] ) ( see appendix [ sec : multi ] for its generalizations to two and more gluons ) . the physical meaning of this equation in terms of the two - particle wavefunction and individual eikonal factors was explained above . suppose now that both particles split . the amplitude can be constructed according to the following three steps ( see fig . [ fig : ab ] ) . 1 . we evolve the partons from infinity to the transverse plane @xmath296 where the collision is assumed to happen . we introduce many - particle wavefunctions for the splitting products of both @xmath76 and @xmath75 . the total wavefunction in the transverse collision plane is the product of the two:@xmath297 here @xmath298 @xmath299 are the transverse coordinates of left- and right - movers . the @xmath300 can be computed via the flat - space light cone perturbation theory . for the one - gluon emission they are the same as in ( [ eq : miimp ] ) . when the splitting products cross the transverse collision plane , the wavefunction @xmath301 is multiplied with eikonal factors , one for each pair of opposite - movers . it is not difficult to guess that these factors are equal to @xmath302 where @xmath51 is the @xmath10 eikonal phase from ( [ eq : eikr ] ) , and @xmath303 , @xmath304 are the longitudinal momentum fractions carried by partons @xmath305 and @xmath0 . 3 . finally , to find s - matrix elements , we compute the overlap with the outgoing state wavefunctions . these are simple plane waves if the partons do not undergo any splittings after the shock wave crossings . if such splittings are present , like in part ( i ) of ( [ eq:1 g ] ) , these are more complicated functions of external momenta . however , since at this stage left- and right - movers no longer interact , the flat - space light cone perturbation theory can be used to find them . _ _ , in which both the right - moving _ _ @xmath76 _ and left moving _ @xmath75 _ split before colliding . _ , scaledwidth=50.0% ] we think that this generalized formalism , apart from providing an attractive mental picture , could find interesting future applications , especially in the problem of gravitational radiation emission . the main point of this paper is that including radiation in small - angle transplanckian scattering is , after all , a tractable problem . the gravitational interaction producing eikonal phase factors happens instantaneously , while the processes of particle splitting are spread in time . based on this observation , we developed a formalism which allows explicit computations of scattering amplitudes in presence of hard , quantum , radiation . in the impact parameter representation , the radiating particle splits into a multi - particle virtual state , whose wavefunction , computed via light - cone perturbation theory , is then multiplied by individual eikonal factors . we demonstrated the usefulness of our formalism on the concrete problem of initial state qcd radiation in transplanckian scattering . we will not repeat here the detailed discussion of the obtained results given in the introduction and in section [ sec : disc ] . we believe however that this example by no means exhausts the list of possible applications . we are particularly hopeful about a possibility to shed new light on the problem of gravitational radiation emission , which is always on our mind . we thank babis anastasiou , stefano frixione , paolo nason , carlo oleari , and especially zoltan kunszt and riccardo rattazzi for useful discussions and comments . this work is partially supported by the eu under rtn contract mrtn - ct-2004 - 503369 and by miur under the contract prin-2006022501 . we thank the galileo galilei institute for theoretical physics for the hospitality and the infn for partial support during the completion of this work . here we will discuss quantization of the free gluon field in the shock wave background , as well as the gluon emission vertices , the gauge invariance , and the absence of gluon emission terms localized on the shock wave . we start from the maxwell lagrangian in curved spacetime , which integrating by parts can be rewritten as @xmath306\,.\ ] ] notice that while the @xmath13-dimensional ricci tensor of the as metric is zero for @xmath307 as a consequence of einstein s equation , the 4-dimensional ricci tensor of the metric @xmath122 induced on the sm brane is nonzero . namely , it has a nonzero component@xmath308 ( compare with ( [ eq : lapl ] ) where the laplacian is with respect to all @xmath82 transverse directions ) . let us fix the curved space lorenz gauge @xmath309 in this gauge the eom take the form:@xmath310 we first discuss the gluon propagator across the shock wave . to find it we need to solve the eom with the initial conditions @xmath311 for @xmath87 . consider first the light - cone gauge case @xmath312 it is easy to see that the shock wave metric has @xmath313 , which implies @xmath314 . the other gauge field components are found to satisfy the equations:@xmath315 & = \frac{1}{4}\partial_{\mathbf{x}}^{2}a_{-}\,,\end{aligned}\ ] ] just as in the scalar field case , it is enough to find a matching condition , i.e. to relate solution of these equations for @xmath316 and @xmath317 one could use the method of section [ sec : thooft ] based on transforming to the @xmath91 coordinates . here we want to demonstrate a different , equivalent , approach . namely , we regularize the above equations by smearing the @xmath131-functions . one can show that the terms put in the rhs of the equations can be dropped in this analysis , since their effect goes to zero when the regulator is removed . all the other terms are however important . from the first equation , we find how the transverse components varies across the shock wave:@xmath318 subsituting this solution into the equation for @xmath319 we find:@xmath320\,e^{-i\frac{p^{-}}{2}x^{+}+i\mathbf{p}.\mathbf{x}}\exp(i\frac{p^{-}}{2}\int_{-\epsilon}^{x^{-}}\delta(x^{-})\phi(\mathbf{x}))\ , . \label{eq : a-}\ ] ] thus on the other side of the shock wave:@xmath321 these are the desired matching conditions . taking the fourier transform we recover the rule ( [ eq : gluoncross ] ) . a general solution of the eom ( [ eq : gauge ] ) is a linear combination of the just found solution in the gauge @xmath322 with a pure gauge solution@xmath323 the gauge parameter @xmath324 is given by eq . ( [ eq : modes ] ) as a general solution to the klein - gordon equation . let us now discuss the gluon emission term ( [ eq : gluonem ] ) in a general gauge . there are several quantities in ( [ eq : gluonem ] ) with @xmath325-function singularities on the shock wave . thus one may wonder if there is a contact emission term localized on the shock wave . in fact such a contribution is absent , so that one can always compute the gluon emission as a sum of two separate integrals for @xmath135 and @xmath87 . to see this , one can argue as follows . first of all , as already mentioned in section [ sec : gauge ] , localized terms are absent in the light - cone gauge @xmath322 . in this gauge @xmath326 does not contain @xmath131-function singularities as one can see from the explicit solution ( [ eq : ai]),([eq : a- ] ) . the @xmath131-function does appear in @xmath327 and in @xmath328 , but all contractions involving these terms necessarily contain @xmath329 and vanish . second , consider the pure gauge case ( [ eq : pure ] ) . in this case there are several @xmath131-function terms in ( [ eq : gluonem ] ) . however , one can show that they cancel among themselves . the reason for this cancellation is as follows . since the integrand in ( [ eq : gluonem ] ) is a lorentz invariant , we can compute it in the @xmath91 coordinates ( [ eq : xt ] ) . in these coordinates both @xmath330 and @xmath324 are continuous , and the integrand has at most @xmath331-function singularity on the shock wave . to demonstrate the absence of localized terms by a concrete example , let us show that the one - gluon emission amplitude is gauge invariant . we thus have to show that the amplitude to emit a longitudinally polarized gluon is zero , without inclusion of any extra terms localized on the shock wave . the one - gluon emission amplitude is given by the coordinate - space integral:@xmath332^{\ast}\overleftrightarrow{\partial}_{\mu}\phi _ { p}^{\text{in}}(x)\right\ } a_{\nu}^{\text{out}}(l,\varepsilon;x)\,.\ ] ] here @xmath333 is the outgoing gluon wavefunction . in the considered longitudinal case @xmath334 we have:@xmath335 the integral splits into two parts : @xmath135 , @xmath87 . each of these can be integrated by parts and , using the current conservation , reduces to a boundary term localized on the shock wave . these boundary terms are not quite identical:@xmath336-\mathbf{p}.\mathbf{x}\right ) } \right\ } e^{i\left ( \frac{1}{2}l^{-}x^{+}-\mathbf{l}.\mathbf{x}\right ) } \,,\\ \mathcal{m}_{(x^{-}<0 ) } & = \int dx^{+}d^{2}\mathbf{x}\,\left\ { e^{i\left ( \frac{1}{2}p^{\prime-}[x^{+}+\phi(\mathbf{x})]-\mathbf{p}^{\prime}.\mathbf{x}\right ) } \overleftrightarrow{\partial}_{+}e^{-i\left ( \frac{1}{2}p^{-}x^{+}-\mathbf{p}.\mathbf{x}\right ) } \right\ } e^{i\left ( \frac{1}{2}l^{-}[x^{+}+\phi(\mathbf{x})]-\mathbf{l}.\mathbf{x}\right ) } \,.\end{aligned}\ ] ] however , after integrating in @xmath95 and taking into account the resulting @xmath124-conserving @xmath131-function , they are seen to cancel . the partonic cross section with @xmath11 gluons emitted @xmath337 is given by the phase space integral @xmath338 we assume that @xmath76 and @xmath75 collide head on along the @xmath78 direction . we use the light - cone phase space adapted to the direction of motion of each particle:@xmath339 \delta^{(4)}(p_{i}-p_{f})=2\delta(p_{i}^{+}-p_{f}^{+})\delta(p_{i}^{-}-p_{f}^{-})\delta^{(2)}(\mathbf{p}_{i}-\mathbf{p}_{f})\,.\end{gathered}\ ] ] the momentum conserving @xmath131-function is saturated by integrating in @xmath340 , which gives@xmath341 the differential cross section in the momentum transfer @xmath23 and the bjorken @xmath22 is thus given by:@xmath342 where @xmath343 @xmath344 under the integral sign . let us look at the leading logarithmic corrections to the cross section which come from the radiation of many gluons . we want to verify that they have the correct form in order to be reabsorbed into the pdfs normalized at the scale @xmath25 . to begin with , consider the emission of two gluons . in the lla , we are looking for @xmath345 corrections to the cross section . one can show that , because of the form of the denominators in our feynman rules , a gluon which does not cross the shock wave will not give rise to a large logarithm . thus the relevant diagrams are those with both gluons emitted at @xmath87 , shown in fig . [ figure2gluons ] . let us consider the first of these diagrams , and define : @xmath346{l}p^{\prime-}=z_{1}z_{2}p^{-}\\ l_{2}^{-}=(1-z_{2})p^{-}\\ l_{1}^{-}=z_{2}(1-z_{1})p^{-}\ , . \end{array } \right.\ ] ] computing this amplitude using the feynman rules and going into the impact parameter representation , we find @xmath347 , with : @xmath348 where @xmath349 , @xmath350 the integrand has the expected form ( three - particle wavefunction in the transverse plane)@xmath351(individual eikonal factors)@xmath352(outgoing states ) . let us estimate this amplitude for @xmath353 . in this limit we will find the double logarithm associated with @xmath354 , while in the other regions there are those associated with splittings into gluons . now , the integral in @xmath94 is dominated by values much smaller than those dominating the integrals in @xmath355 and @xmath356 . neglecting @xmath94 with respect to @xmath355 and @xmath356 , we obtain : @xmath357 a double logarithm can be obtained only if the amplitude behaves like @xmath358 . in turn , this means that we must look for the situation in which the integrand behaves like @xmath359 , which is true only if the @xmath355 integral is dominated by much smaller values than those dominating the @xmath356 integral . this will happen if and only if @xmath360 . we conclude that the gluon emitted closer to the shock wave must have a larger transverse momentum . we will come back to this later , when we generalize to an arbitrary number of gluons . thus for @xmath360 , we can neglect @xmath355 with respect to @xmath356 in the integrand , and the last integral factorizes giving : @xmath361 where @xmath268 is the gluon emission factor introduced in eq . ( [ eq : f ] ) . after squaring and integrating in @xmath362 and @xmath363 , this gives a double logarithm of @xmath25 . for completeness let us verify explicitly that the contribution from the region @xmath364 is subdominant . one can show that the amplitude depends on @xmath362 and @xmath363 as follows : @xmath365{lr}\frac{\mathbf{l_{2}}_{j}\mathbf{l_{2}}_{i}}{|\mathbf{l_{2}}|^{4 } } & \mbox { if } \,|\mathbf{l_{1}}|\ll|\mathbf{l_{2}}|\ll b_{c}^{-1}\\ b_{c}^{\frac{n}{n+1}}\left ( \frac{1}{|\mathbf{l_{2}}|}\right ) ^{1+\frac { 1}{n+1}}\,\log\left ( \frac{|\mathbf{l_{2}}|^{\frac{1}{n+1}}}{|\mathbf{l_{1}}|\,b_{c}^{\frac{n}{n+1}}}\right ) & \mbox { if } \,|\mathbf{l_{1}}|\ll b_{c}^{-1}\ll|\mathbf{l_{2}}|\\ \frac{\mathbf{l_{1}}_{i}\mathbf{l_{1}}_{j}}{|\mathbf{l_{1}}|^{4}}\,\left ( \frac{|\mathbf{l_{1}}|}{|\mathbf{l_{2}}|}\right ) ^{\frac{1}{n+1 } } & \mbox { if } \,b_{c}^{-1}\ll|\mathbf{l_{1}}|\ll|\mathbf{l_{2}}| \end{array } \quad.\right.\ ] ] it is immediate to see that from each of the three regions we only get single logarithms . the second diagram in fig . [ figure2gluons ] is the same with @xmath370 . since the leading contributions come from integration over different regions of transverse momenta , in the lla there is no interference between the two diagrams . putting all together and including also the double logarithms arising from the regions @xmath371 and @xmath372 , which can be computed in a similar way , we finally obtain : @xmath373 ^{2}.\end{aligned}\ ] ] which shows that the optimal factorization scale is @xmath25 . generalization to an arbitrary number @xmath374 of emitted gluons is straightforward . consider the typical relevant diagram shown in fig . [ figuremgluons ] , and let us look at the transverse momenta involved in the quark - gluon vertices . in the first one from below only @xmath375 appears , thus the contribution to the amplitude will be @xmath376 , like in the case of one gluon emission . in the next vertex both @xmath375 and @xmath377 are involved , but it is obvious that its contribution should reduce to @xmath378 when @xmath379 . this is true for all the @xmath374 vertices : if the transverse momentum @xmath380 of a gluon is much larger than those of the gluons which were emitted previously , then its contribution to the amplitude will be @xmath381 . thus in general we can write , for the diagram in fig . [ figuremgluons ] : @xmath382 where : @xmath383 fourier - transforming this expression and considering the limit @xmath384 , we would obtain an expression analogous to ( [ 2gluonsimpactparspace ] ) with @xmath374 integrals instead of two . from the structure of the amplitude in @xmath380 space , it is clear that it will be : @xmath385 where the multi - particle wavefunction @xmath386 : @xmath387 power of a large logarithm comes from the region @xmath388 . when computing the total cross section with @xmath374 identical gluons in the final state , we can always reorder the gluons so that @xmath389 . then in the lla only the shown diagram contributes , with a @xmath390 factor from @xmath391 putting all together , we get @xmath392 ^{m},\ ] ] where : @xmath393 all these large logarithms are absorbed into the pdf normalized at the scale @xmath287 . g. veneziano and j. wosiek , jhep * 0809 * , 023 ( 2008 ) [ http://arxiv.org/abs/0804.3321[arxiv:0804.3321 ] [ hep - th ] ] . jhep * 0809 * , 024 ( 2008 ) [ http://arxiv.org/abs/0805.2973[arxiv:0805.2973 ] [ hep - th ] ] . s. b. giddings , d. j. gross and a. maharana , phys . rev . d * 77 * , 046001 ( 2008 ) [ http://arxiv.org/abs/0705.1816[arxiv:0705.1816 ] [ hep - th ] ] ; s. b. giddings and m. srednicki , phys . d * 77 * , 085025 ( 2008 ) [ http://arxiv.org/abs/0711.5012[arxiv:0711.5012 ] [ hep - th ] ] ; s. b. giddings and r. a. porto , http://arxiv.org/abs/0908.0004[arxiv:0908.0004 ] [ hep - th ] . n. arkani - hamed , s. dimopoulos and g. r. dvali , phys . b * 429 * , 263 ( 1998 ) [ http://arxiv.org/abs/hep-ph/9803315[arxiv:hep-ph/9803315 ] ] ; i. antoniadis , n. arkani - hamed , s. dimopoulos and g. r. dvali , _ ibid . _ * 436 * , 257 ( 1998 ) [ http://arxiv.org/abs/hep-ph/9804398[arxiv:hep-ph/9804398 ] ] ; s. b. giddings and s. thomas , phys . rev . d * 65 * , 056010 ( 2002 ) [ http://arxiv.org/abs/hep-ph/0106219[arxiv:hep-ph/0106219 ] ] ; s. dimopoulos and g. landsberg , phys . lett . * 87 * , 161602 ( 2001 ) [ http://arxiv.org/abs/hep-ph/0106295[arxiv:hep-ph/0106295 ] ] . j. l. feng and a. d. shapere , phys . rev . * 88 * , 021303 ( 2002 ) [ http://arxiv.org/abs/hep-ph/0109106[arxiv:hep-ph/0109106 ] ] . l. anchordoqui and h. goldberg , phys . d * 65 * , 047502 ( 2002 ) [ http://arxiv.org/abs/hep-ph/0109242[arxiv:hep-ph/0109242 ] ] . y. v. kovchegov and k. tuchin , phys . d * 74 * , 054014 ( 2006 ) [ http://arxiv.org/abs/hep-ph/0603055[arxiv:hep-ph/0603055 ] ] . j. c. collins , d. e. soper and g. sterman , nucl . b * 261 * , 104 ( 1985 ) .

we investigate hard radiation emission in small - angle transplanckian scattering . we show how to reduce this problem to a quantum field theory computation in a classical background ( gravitational shock wave ) . in momentum space , the formalism is similar to the flat - space light cone perturbation theory , with shock wave crossing vertices added . in the impact parameter representation , the radiating particle splits into a multi - particle virtual state , whose wavefunction is then multiplied by individual eikonal factors . as a phenomenological application , we study qcd radiation in transplanckian collisions of tev - scale gravity models . we derive the distribution of initial state radiation gluons , and find a suppression at large transverse momenta with respect to the standard qcd result . this is due to rescattering events , in which the quark and the emitted gluon scatter coherently . interestingly , the suppression factor depends on the number of extra dimensions and provides a new experimental handle to measure this number . we evaluate the leading - log corrections to partonic cross - sections due to the initial state radiation , and prove that they can be absorbed into the hadronic pdf . the factorization scale should then be chosen in agreement with an earlier proposal of emparan , masip , and rattazzi . in the future , our methods can be applied to the gravitational radiation in transplanckian scattering , where they can go beyond the existing approaches limited to the soft radiation case . 1.0 cm * radiation problem in transplanckian scattering * 1.0 cm paolo lodone and slava rychkov + _ scuola normale superiore and infn , pisa , italy _ 2.0 cm 1.5 cm september 2009