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despite major advances
in analytical spectroscopy , structural elucidation
of both natural and synthetic compounds continues to be a major challenge ,
as is illustrated by the recent revision of the structure of aquatolide
( 1a/1b ) , a natural product isolated from asteriscus aquaticus . initially reported as containing a
bicyclo[2.2.0]hexane core substructure , 1a ( figure 1 ) , upon subsequent re - examination of the spectroscopic data ,
indicated the structure to be more consistent with bicyclo[2.1.1]hexane 1b .
this structural revision was
supported by a detailed nmr analysis spurred on by quantum chemical
calculations and confirmed through x - ray crystallography .
the
problem of misassigned spectra ultimately leading to incorrect
structural assignments is becoming a more prevalent feature in the
contemporary chemical literature with no apparent signs of abating .
in fact , there have been in excess of 160 articles describing structural
revisions of organic molecules , predominately as a result of spectral
misassignment , in the decade since nicolaou and snyder published their
comprehensive review in 2005 on misassigned
structures as revealed by chemical synthesis . to curb the growing
trend of reported misassigned structures , we
propose an approach that better utilizes the vast structural information
contained in the ubiquitously acquired 1d h nmr data sets
with the purpose of achieving
structural correctness
while at the same time enhancing the reproducibility of downstream
research performed with the structurally correct compound in question .
the present study demonstrates that practically everything the chemist
needs to know for a correct structural elucidation process is contained
in the proton nmr fids .
our proposed protocol involves analysis of
1d h spectra including both quantum - mechanical prediction
of chemical shifts ( ) and scalar coupling constants ( j ) as well as extraction of compound - specific h nmr spectral parameters from the experimental data .
although even
classical manual analysis of the spectra is capable of providing sufficient
information to verify ( or revise ) a structure , we demonstrate here
that an iterative fitting process utilizing quantum mechanical spin
information ( hifsa ) is indispensable for
achieving rigorous structural elucidation and dereplication with a
high degree of reproducibility . to preserve the authenticity
of reported spectral information ,
originally acquired free
the approach
described here is applied to aquatolide by analysis of the published
data together with a reprocessing and hifsa fitting of the h fid that was archived in 2012 and provided by the authors of the
revision article .
a thorough analysis
of the data revealed the dangers and pitfalls of a superficial treatment
of 1d nmr spectroscopic data and will hopefully serve as a future
guide for avoiding similar spectral misinterpretations , including
deduction of newly discovered structures that were not there initially .
the key to both the suitability
of a proposed structure , or guidance for its revision , may be found
in the 1d h and c nmr spectra . in the case
of aquatolide ,
the suspect structure 1a was recently
evaluated by comparing the experimental data with that of the c and h chemical shifts predicted with quantum
chemical calculations .
significant deviations ( c ) of up to 24.33 ppm in the c domain indicated
a potential problem with the originally assigned structure . over 60
alternative scaffolds , along with their diastereomers , were generated
by both rational and arbitrary changes to the original structure .
jones ) , yielded a much better predictive fit than the original
structure with the largest c of 4.28 ppm .
the prediction of the h nmr chemical shifts of aquatolide
demonstrated much the same trend as the c study .
the
revised structure , 1b , exhibited a better fit ( largest
h = 0.27 ppm ) than the original structure
with the largest h = 1.31 ppm .
although deviations
of such magnitude are widely accepted as representing a reasonable
gap between theoretical or empirical predictions and experimental
observations , it is also well - known that nearly
identical yet different molecules can exhibit very minute chemical
shift differences in the range of up to a few hundred ppb in c and only a few tenths to sub ppb level in h
nmr spectra .
this obvious contradiction provides
a rationale for the need to perform comprehensive mining of 1d nmr
data in general structure analysis . originally proposed ( 1a )
and
the evaluation of h coupling constants
and multiplicities faced the challenge of a lack of comparison due
to the meager information content in the original reference article .
the quantity of coupling information obscured
by multiplets in the original article can be demonstrated by compiling
the reported couplings into a j - correlation map : figure 2a graphs all possible
scalar coupling combinations present in the molecule in the lower
left half , whereas the corresponding number
of bonds between coupled nuclei are given in the upper right half .
the map demonstrates the inherent risk associated with the reporting
of multiplets . for example , only three couplings were
reported mutually for the pair of coupled nuclei ( jh-1,h-2 , jh-1,h-10 , jh-2,h-10 ) and only one of the two couplings
( jh-4a , h-4b , jh-4a , h-5b ) , as
indicated by the divided cells in figure 2a . ignoring characteristic long - range couplings
( j ) ,
only six out of a total
of 22 values that reflect the pairwise relationship of all possible j and j couplings
were reported .
the unreported j and j couplings were obscured by multiplets
or simply not observed .
a j coupling
of 1.9 hz was proposed for nuclei h-1 and h-10 , but neither the observed
nor the conspicuously unobserved couplings were actually discussed
in the original article .
the apparent
lack of attentiveness to coupling patterns and coupling constants
exposes a general attitude that 1d proton nmr data is both uninterpretable ,
at least in great parts , and inferior to that of many 2d experiments .
unfortunately , this lack of attention to h nmr spectra
( the mother of all nmr experiments ) is very common
in both the natural product structural elucidation literature and
reports on the structural characterization of synthetic compounds .
in the case of aquatolide
, the original authors were likely led astray
by resorting to the all - too - common practice of moving on to the 2d
data without thoroughly understanding the 1d data
. moreover , lodewyk
et al . deemed the existing 2d data incapable of definitively verifying
the revised structure .
thus , the compound
was reisolated from asteriscus aquaticus , and an
nmr analysis was performed at 800 mhz .
it is reasonable to assume
that the two isolates yielded the same compound despite the lack of
reference material from the original work because the h and c data sets appear to be very similar .
the progress
achieved with the revision is illustrated
in the j - coupling correlation map in figure 2b , showing the reported experimental
values for the revised aquatolide structure . in this case , five out
of 18 j couplings and one out of four j couplings were observed .
interestingly ,
five j and two j long - range couplings were observed due to the rigid ring structure
and presence of an , unsaturated ketone .
although
the nmr results in the 2012 study represented a substantial qualitative
improvement over the data reported in the original article , a different overall focus and approach did not
lead to an exhaustive description of the chemical shifts ( )
and scalar coupling constants ( j ) present in this
molecule by resolving highly complex h nmr signal patterns .
in fact , a thorough treatment of all relevant 1d and 2d nmr data is
generally discouraged by current journal practices , relegating in
the best case such critical nmr information to the supporting information .
these practices only serve to reinforce the myth that h nmr data is both ambiguous and inferior to 2d nmr data . in
the revision ,
the use of quantum
chemical prediction tools for evaluating the observed scalar coupling
network led to a complete , yet theoretical , j - correlation
map ( supporting information , figure s1 ) . the
predictive exercise proposed 14 coupling constants above 1.0 hz , of
which
notably , the prediction
confirmed several instances of unusual coupling behavior , including
the unobservable to jh-2,h-9 and jh-9 , h-10 couplings
with near zero values .
however , several challenges remained
for a comprehensive representation
of the coupling network : ( i ) the magnitude of the coupling constants
obscured by multiplets can not be confirmed or unconfirmed ; ( ii ) four
of the observed coupling constants exhibit deviations of 0.50.8
hz from the predicted values ; ( iii ) the relative positions of protons
4a , 4b , 5a , and 5b could not be determined with certainty due to the
ambiguity of matching all of their exact chemical shifts ; ( iv ) two j coupling constants are nearly undetectable
( < 1.0 hz ) , whereas five j and j long - range coupling constants are > 1.0
hz , the origin of which requires a closer examination .
j - correlation
map of the homonuclear proton nmr
assignments reported for the original ( erroneous ) a and
revised b structures of aquatolide ( in ppm , m
= reported multiplicity ) .
cells in the upper right are the number
of bonds separating the two hydrogens . in the lower left
are j coupling
constants that are less than 1.0 hz due to 90 deg dihedral
relationships .
the addition of a in the bond numbers
4a and 5a indicate ( homo)allylic coupling relationships .
split cells
in the lower left represent coupling constants that are unequally
reported for the two nuclei , likely referring to observed line distances
rather than coupling constants .
yellow boxes in b indicate
changes in bond number compared with the original structure .
data
produced by modern ft - based nmr experiments are time domain data ,
free induction decays ( fids ) or series thereof , which are stored ,
processed , and handled digitally .
fids are relatively small files ,
machine and vendor specific , but in relatively transparent file formats ,
and importantly are easy to archive .
commercial as well as free software
tools are available for ( re)processing fids ( see , e.g. , http://nmr-software.blogspot.com/ for a listing and links ) .
moreover , the resolution of multiplets
may be achieved , in many cases , by optimizing post - acquisition data
processing parameters .
the present study became possible because
the h fid of the newly isolated aquatolide ( 1b ) was archived and accessible via the authors .
thus , the 800 mhz h fid could be reprocessed
with resolution enhancement ( e.g. , lorentzian
gaussian apodization )
to resolve even very small coupling constants ( 1.0 hz ) as
line splittings in all signals .
manual spectral interpretation of
an optimized spectrum led to a more complete j - correlation
map ( figure 3a ) , showing
that multiplets may be tentatively resolved through
optimized processing of fids and no additional experiments .
visual
interpretation of the resulting highly resolved multiplets may be
facilitated by software tools , such as schimanski s jvisualizer
( http://jvisualizer.sourceforge.net/ ) , to help simulate
the line patterns of manifold - coupled resonances using first order
assumptions . in most cases , the manually extracted j - couplings matched up well ( within 1 hz , often much better ) with
the predicted values ( figure 3 ) .
it is noteworthy to mention that strong apodization for
very strongly enhanced resolution can affect both the exact line distances
as well as the relative intensities of individual lines within resonances
and of resonances relative to each other .
accordingly , hifsa processing
typically uses spectra that are not or only weakly apodized .
( a ) results
of reprocessing the fid from the 800 mhz 1d h nmr spectrum
of aquatolide displayed on a j correlation
map .
the number of bonds separating two coupled nuclei are color - coded :
violet = j , blue = j , yellow = j , green = j , and pink = j. the gaps in the colored fields of the lower left indicate the limitation
of achievable coverage with manual spin analysis .
whereas all couplings
of 1 hz or more could be readily extracted , determination
of the long - range j - couplings typically requires
a computational approach .
( b ) final j - correlation
map , termed quantum interaction and linkage table ( quilt ; see main
text ) , achieved by hifsa fitting of the archived 800 mhz 1d h nmr data of aquatolide .
rather than being reported as blank
cells , which would indicate them being unknown or undetermined .
introduction of color coding to
the j - correlation
map in figure 3a visually
connects the two near symmetric halves of the j - correlation
map , i.e. , connecting bonds and coupling constant(s ) .
this facilitates
two important elements of 1d h nmr interpretation : ( a )
verification of all coupling constants that should be present due
to geminal ( j ) and vicinal ( j ) relationships with the notable exception of couplings
that are ( near ) zero due to ( near ) perpendicular dihedral bond angles ;
and ( b ) detection of long - range couplings ( j ) that are characteristic for the given structure , such
as aromatic , allylic , homoallylic , and w - type couplings .
although
these couplings are often small ( up to 3 hz ) , they can reach
values of > 10 hz under certain circumstances , such as the 2-fold
w - type
coupling pathway that is present in compound 1b showing
a 7.2 hz jh-2,h-10 .
accordingly , it is important to keep in mind that , in the same
molecule , geminal and vicinal j values can be smaller
than long - range j values and potentially generate
confusion in the early interpretation process .
again , 1b is a perfect example of such a situation as two j couplings are near zero , whereas five long - range couplings
lead to signal splittings in the 1.57.2 hz range . the aforementioned
data processing and prediction methodologies
will likely still exhibit gaps between observed and predicted values .
naturally , these must be investigated and resolved to fully confirm
the structure and utilize the information contained in the data .
the
hifsa technique iteratively fits , within the limits allowed by the
conformation and quantum mechanical parameters , the predicted values
into the observed spectrum to create a
high resolution data set that completely defines the j - coupling network ( see ref ( 16 ) for a discussion of and j precision ) .
this enables completion of the j - correlation map ,
creating a quantum interaction and linkage table ( quilt ) .
this comprehensive
approach allows the researcher to analyze a definitive homonuclear
data set to base structural assignments on the most definite information
that can be derived from the data . even in the case
of nearly matching theoretical and observable data ,
the final values
need to be correlated with known nmr results and the structural features
of the molecule .
this is a process that can not be completely automated
and requires the intervention of a knowledgeable spectroscopist . whereas
every shift and coupling constant computed with quantum mechanical
calculations ( for a review , see ref ( 11 ) )
is associated with a specific structural feature ,
a frequent issue is merely whether these values are predicted with
high enough accuracy to assign experimental values that are very close
to each other unambiguously . in the case of aquatolide , a j constant greater than 7 hz is certainly
worthy of closer inspection ,
as are two j values of nearly zero , all occurring in the same molecule of only
15 carbons . ideally , all observed and potentially observable j - couplings should be verified by considering the impact
of geometries , such as the phenomena associated with strained rings
and allylic and homoallylic relationships . another role for
the hifsa process , which involves
the prediction
of spin parameters from energy - minimized structures as starting values
for the iteration , is the use of the chemical
shift and j - coupling predictions to distinguish between
the two structures . as shown in figure 4a
, significant differences exist between both proposed
structures and the actual ( fitted ) values , especially in the bicyclic
ring structure involving protons h-1 , h-2 , h-9 , and h-10 .
the average
difference of chemical shifts ( ) in the final hifsa
profile favors the revised structure , 0.3060 ppm compared to 0.3990
ppm for the original structure .
however , this comparison alone is
not conclusive as the chemical shift prediction algorithms are not
yet mature enough to distinguish between the near - identical molecules , 1a/1b . in contrast ,
comparison of the coupling
constants in figure 4b shows that the revised structure
exhibits a better fit , especially in the bicyclic ring structure .
although the average difference ( j ) across
all 28 coupling constants of 1.643 hz already favors the revised structure
compared to 2.063 hz for the original structure ( j = 0.420 hz ) , figure 4b shows that four individual coupling constants exhibit
major differences with a total j of 14.551
hz ( average of 3.638 hz ) .
( i ) the magnitude of the jh-1,h-2 for a dihedral relationship
of 0 in 1a would be more in line with
a value of 9 hz , contrasting the 2.502 hz measured .
( ii ) in
cyclobutane relationships , the coupling between h-2 and h-9 can not
be neglected , especially not a jtrans as present in 1a , which
are known to give rise to coupling constants of up to 3 hz ; the revised interpretation as a j of 0.513 hz in 1b demonstrates how
potentially misleading the ( apparent ) lack of coupling can be .
( iii )
representing the cyclobutane form of a 2-fold w or
jcis coupling , known to reach up to 18 hz , the jh-1,h-10 relationship
would be expected to be much larger in the original structure , 1a .
( iv ) the jh-2,h-10 relationship would be expected to be 2 hz larger than was
measured .
considering that couplings are related to structure , geometry ,
and bonding , it is important to keep in mind that both the absolute
differences and the signs of the coupling constants are diagnostic
and indicative of the correct structure .
difference of chemical
shifts ( in ppm , a ) and coupling
constants ( in hz , b ) between the hifsa fitted structure
and the original vs revised structures .
the following analysis provides a model treatment of h homonuclear nmr data , which should be reported for even apparently
straightforward structural assignments .
confirmation employing 2d
data sets is appropriate after the 1d spectrum has been thoroughly
examined and can focus on issues that are otherwise not fully resolved .
h-1 is the only proton
on the two - carbon bridge of the bicyclo[2.1.1]hexane core of 1b .
the chemical shift of this signal is at 4.4797
ppm because it is deshielded by the adjacent lactonic alkyl oxygen .
the signal was reported as a dd in the original article and as a triplet
in the revision article .
the j coupling
with h-2 ( 2.502 hz ) at the closest bicyclo[2.1.1]hexane bridgehead
is clearly observed but rather small due the 50 dihedral angle .
a j ( by two pathways ) coupling of 1.839
hz is observed with h-10 , the remote bicyclo[2.1.1]hexane bridgehead
proton .
the occurrence of j couplings
in strained rigid ring systems has been previously described and exemplifies the significance of long - range couplings in general .
the original aquatolide structure also placed
h-1 at a position where it was three bonds away from h-2 and four
bonds away from h-10 .
however , in the original structure , the dihedral
angle between h-1 and h-2 approaches 0. proton h-2 occupies
a bridgehead position of the bicyclo[2.1.1]hexane core of 1b .
the chemical shift of its dd signal is at 3.2598 ppm , making
it the third most downfield proton in this molecule .
interestingly ,
the j coupling with h-9 on the cyclobutane
ring is not observed .
the quantum chemical calculations put the coupling
constant at less than 0.5 hz ( predicted at 0.119 hz ) , which
is due to a nearly 90 dihedral angle . the jh-2,h-10 coupling ( by two routes )
on the two bridgehead carbons is a remarkable 7.219 hz .
however ,
this value may be predicted ( hifsa processing predicted 6.299 hz ,
the quantum mechanical calculations yielded 6.767 hz ) and has been
observed in other cyclobutanes as well
as in bicyclo[2.1.1]hexane derivatives .
the magnitude of this coupling may be attributed to the rigid w
conformation present in the molecule and the fact that there are two
parallel j coupling pathways .
notably ,
the h-2 coupling pattern and j values are very likely
the explanation as to why , in the original aquatolide structure , protons
h-2 and h-9 were placed into a j relationship ,
whereas protons h-2 and h-10 were placed into a j relationship . a 7.2 hz j coupling
and an unobservable j coupling may have
seemed more reasonable by the authors of the original assignment but
are fully explained by the revised structure .
proton h-9 is
located at one of the one - carbon bridges of the bicyclo[2.1.1]hexane
core of 1b .
the chemical shift of its signal around
2.9230 ppm is at the higher end of what is expected for a methine
hydrogen on a carbon adjacent to a ketone .
curiously , this signal
appears to be a singlet even though it has j relationships with h-2 and h-10 , both of which are also on the cyclobutane
ring .
the unobservable ( calculated at 0.074 hz ) jh-9,h-10 coupling constant must
be attributed again to a nearly 90 dihedral angle . in the original
aquatolide structure ,
proton h-9 was also placed at a three bond distance
from h-10 , but no explanation was offered for the existence of the
small coupling constant .
h-10 is on the opposite bridgehead
carbon from h-2 of the bicyclo[2.1.1]hexane
core .
it is reported as a dd resonance at 2.6411 ppm in both
the original publication and the revision article .
the resonances
of the four hydrogens of the two contiguous methylene
groups are crowded into the 1.842.54 ppm interval .
their complex splitting as well as the possible dynamic nature of
the ring at these positions tends to obscure the multiplicities and
determination of coupling constants .
the present study assigns the
relative positions of 4a , 4b , 5a , and 5b based on karplus relationships
and unambiguously assigned chemical shift values and reconfirms the
assignments through the previously reported noes .
h-4a exhibits
the most downfield chemical shift of the four methylene hydrogens
and has previously been designated as a dd .
h-4a has a reported
6.7 hz coupling constant with its j h-5b
neighbor . on the other hand ,
the jh-4a , h-5a coupling is small and not easily observable ;
optimized processing revealed the underlying complexity of the signal
and allowed determination of jh-4a , h-5a as 2.794 hz .
chemical shifts and coupling patterns are consistent
with the position of h-4a pointing into the eight - membered ring in
close proximity to the ketone oxygen and h-10 . at this position ,
the
dihedral angle between h-4a and h-5a is nearly 90 , and the dihedral
angle between h-4a and h-5b approaches 135 with jh-4a , h-5b being observed
as 6.766 hz . the position of h-4a is confirmed with noesy , which shows
correlations to both h-10 and h-4b . the resonance is a broad ddd due
to an underlying 0.298 hz jh-4a , h-6 coupling .
the signal for h-4b has the most upfield chemical
shift of the
four methylene hydrogens and is centered at 1.9657 ppm .
in addition to the jh-4a , h-4b coupling
of 16.172 hz , h-4b shows j couplings
with h-5a and h-5b , which are easily obscured in this complex signal .
the small 1.578 hz coupling may be attributed to jh-4b , h-5a , whereas the large jh-4b , h-5b coupling
was determined as 11.763 hz .
proton h-5a signal resonates between
h-4a and h-5b and has also
previously been designated as a multiplet . upon closer examination
,
however , this signal appears as a very complex but clearly defined
ddddq , as seen in figure 5 .
there is a possible total of 64 individual peaks , but overlap
considerations bring it down to 36 discernible lines .
the reason that
this signal exhibits sharper lines than h-5b , h-4a , and h-4b may be
related to the fact that the c-5 to h-5a bond is aligned with
the neighboring sp orbitals at c-6 .
the sp hybridized orbitals of h-5a and the c-5 bond are aligned or nearly
aligned with the orbitals of the c-6 to c-7 double bond , imparting
the orientation of the c h bond .
possible dynamic movement
of the c-5c-6c-7 carbon array , which produces four
major conformations ( see pages s36 ff . of ref
( 2 ) ) , lead to a specific ( t , bo , c ) and characteristic time - averaged spin coupling pattern ,
especially for the protons at c-5 .
this portion of the aquatolide
molecule is the only substructural fragment that is likely to give
rise to dynamic movement , the rest of the molecule being fairly rigid .
however , because of the allylic orientational effect , a slight barrier
may exist , thus favoring only one of the conformations with aquatolide
then being rendered semirigid .
a study involving a structural arrangement
similar to the present case ( 6- vs 8-membered ring in aquatolide )
was observed for 3-aryl-5r - aryl-6t - carbethoxycyclohex-2-enones .
the largest coupling constant is attributed
to a geminal jh-5a , h-5b coupling
( 20.006 hz ) , which separates the signal into two almost baseline
separated subpatterns .
the jh-5a , h-4a and jh-5a , h-4b couplings have already been described . protons h-4b , 5a , and 6 appear
to orient themselves toward the outside of the 8-membered ring ( figure 6 ) .
a 3.208 hz jh-5a , h-6 coupling
is also observed , and the observed quartet may be attributed to a
2.142 hz homoallylic jh-5a , h-13 coupling .
homoallylic couplings have been described by jackman and
sternhell for a number of cases .
an example
that resembles aquatolide exhibits a 1.8 hz homoallylic coupling reported
in a 6-methyl-3,4-dihydro-2h - pyran . upon closer examination ,
the h-5b multiplet located
between the h-5a and h-4b signals is identified as a ddddq .
the homoallylic jh-5b , h-13 coupling exhibits a similar j coupling value ( 2.245 hz ) to that of jh-5a , h-13 .
the signal for the olefinic
proton at h-6 has a chemical shift of 5.8507 ppm .
it was reported
as a multiplet in the original publication and as a ddt in the revision
article .
the jh-5a , h-6 and jh-5b , h-6 couplings described above are in agreement with previous work on
allylic couplings .
therefore , the multiplicity
of the signal should be accurately represented as a ddq ( figure 5 ) .
there are a total
of 16 peaks in this signal : ten are readily discernible and six require
stronger lorentzian gaussian resolution enhancement to be discernible .
optimizing
processing parameters reveal coupling constants and
line counts present in the signals for h-5a and h-6 of 1b .
gaussian apodization function
of lb = 1.4 hz and gf = 0.17 ( 17% aq ) .
gaussian apodization function of
lb = 2.5 hz and gf = 0.25 ( 25% aq ) and demonstrate that all
theoretical lines of these complex multiplets can
indeed be deciphered by manual analysis facilitated by tools such
as jvisualizer ( http://jvisualizer.sourceforge.net/ ) .
actually ,
proton h-5a resonates as a ddddq , and h-6 gives rise to a ddq signal .
three - dimensional representation of 1b showing the
spatial relationships in the 8-membered ring computed with density
functional theory .
the olefinic methyl group , h-13 , with a signal centered at
1.8698
ppm , was reported as a multiplet in the original publication and as
a quartet in the revision article . as the h-13 protons
are coupled
to h-5a , h-5b , and h-6 , with j couplings of 2.142 ,
2.245 , and 1.546 hz , respectively , it should be described as a ddd . both methyl groups on the gem dimethyl moiety
the methyl
group that is closest to the lactone ( figure 6 ) is designated as c-14 , whose hydrogens
have a h chemical shift of 1.0544 ppm .
the methyl
group that is closest to h-9 is designated as c-15 with hydrogens
at 1.1941 ppm .
this orientation is revealed in the noesy spectrum ,
which shows the protons at 1.1941 ppm correlated strongly
with h-9 and more moderately with h-1 , h-10 , and h-14 .
the quilt concept ,
introduced above for 1d hnmr , can be employed
to represent the entirety of a complex 2d nmr cross - peak map into
a more straightforward graphical format . in the case of aquatolide ,
as shown in the corresponding correlation map
( original noesy quilt , figure 7a ) , plotting internuclear distances on the upper diagonal
relative to cross peaks on the lower diagonal , the noesy approach
may be a hit - or - miss situation .
expected noesy correlations may or
may not be observed with a given set of acquisition and processing
parameters .
of particular concern with the structure determination
of aquatolide in the original article is the apparent lack of correlations
for the crucial h-1 , h-2 , h-9 , and h-10 protons , such as h-2 to h-10
( figure 7a ) . without
these correlations , it is difficult to confirm the original structure .
the revision article described a much more complete family of noesy
correlations ( revised noesy quilt , figure 7b ) , especially between the four key protons
of the bicyclo[2.1.1]hexane core , such a h-2 to h-9 .
an apparent cross peak
between h-2 and h-10 seems to favor the original structure over the
revised structure .
this is likely due to the presence of an antiphase
cross peak , or cosy cross peak , resulting from a coherence transfer
between j - coupled spins .
noesy
correlation maps ( noesy quilts ) of the original ( a ) and the
revised ( b ) structures ( precision as reported ) .
the upper
right halves contain the distances between nuclei taken from the revision
article and a 3d model ( in parentheses ) .
the bottom
left
halves are actual noesy cross peaks observed as either strong ( xx )
or weak ( x ) correlations .
distances without parentheses were taken
from the revision article , and those in parentheses were determined
with avogadro molecule editor and visualizer .
a detailed analysis of the revised noesy quilt ( figure 7b ) shows that h-1
correlates
with h-2 , h-9 , h-14 , and h-15 .
h-2 correlates strongly with both h-1
and h-9 while being more moderately correlated with h-5b , h-6 , h-10 ,
h-14 , and h-15 .
the noesy spectrum of h-9 shows a strong correlation
to the h-2 and h-15 methyl protons and weaker correlations to h-1 ,
h-13 , and h-10 .
h-10 shows correlations to h-2 , h-4a , h-4b , h-9 , h-14 ,
and h-15 .
the position of h-4a relative to h-4b is also supported
by the noesy spectrum as h-4a correlates to h-4b , h-5a , h-5b , and
h-10 . in turn
the position of h-5b relative
to h-5a is supported by noesy correlations to h-2 , h-4a , h-5a , and
h-6 .
the latter shows a correlation with the h-13 methyl protons ,
which in turn exhibit a correlation with h-6 and h-9 .
as previously
described , the relative orientation of the c-14 and c-15 methyl groups
relies on the noesy data .
the
hmbc experiment is a powerful method to confirm or predict structural
connectivity features via long - range heteronuclear coupling ( jc , h ) .
heteronuclear correlations
play an important role in the overall structural determination , but
there are some important limitations .
a survey of marine natural product
revisions suggested that a significant number of misassigned structures
are associated with interpretation of the hmbc data .
this was primarily due to the incomplete nature of the
experimentally observed hmbc correlations .
this situation can be clearly
seen , in the case of aquatolide , with the hmbc quilt shown in figure 8 , which by nature
is asymmetric . in the original publication , 9 of 24 jc , h and 19 of 42 jc ,
h possible correlations were observed . in the revision
publication , 13 of 24 jc , h and 37 of 45 jc , h possible
correlations were observed . from these examples , it may be proposed
that , at best , hmbc data may be used to favor one set of possible
structures rather than actually proving one structure .
similar
to all nmr techniques , both the acquisition and processing parameters
play a substantial role in what correlations may be observed or not
observed .
for example , the absence of key j hmbc correlations , which will exhibit variation according to the
3-bond karplus relationship between the h and c , may be a result of the experimentally acquired data falling outside
of the coupling constant range in the standard hmbc experiment , which
is typically optimized for jc , h = 7.08.5 hz for h , c dihedral angles
of 180. it is frequently necessary to perform two or three hmbc
experiments optimized for smaller j - couplings ( jc , h = 4.06.0 hz ) and/or
extend the number of increments of the evolution time to reveal the
smaller couplings that occur later in the evolution time .
to reveal
the maximum number of correlations , other experiments may be used
for extracting couplings over 35 bonds , e.g. , lr - hsqmbc .
heteronuclear correlation experiments do not
typically reveal if an observed cross peak represents a 2- , 3- , or
even 4-bond coupling .
fully and correctly assigning all protons and ,
thus , all protonated carbons would serve to reduce this ambiguity
considerably .
long - range heteronuclear quilts summarize both the observed
direct
( jc , h ) and jc , h correlations in the original ( a ; hetcor and long - range hetcor , respectively ) vs revised
( b ; hsqc and hmbc , respectively ) aquatolide structures .
the numbers inside the and atom number grid reflect the number ,
n , of connecting bonds ( j ) .
color coding of boxes : black = one
bond , violet = two bonds , blue = three bonds ; white = four and more
bonds . color coding of numbers : black and white = jc , h correlation ; gray jc , h correlations .
the heteronuclear quilts from the original aquatolide publication
data ( figure 8a ) shows
that all of the observable cross peaks in the long - range hetcor experiment
may be attributed to jc , h and jc , h correlations .
although this
was congruent with the original structure , the incompleteness of the
correlation map ( a well - known downside of the long - range variant of
the hetcor experiment ) was consistent
with other possible structures as well .
an hmbc 2d experiment in the
revision article identified several key relationships ( hmbc quilt , figure 8b ) , but this set
alone could not definitively favor the revised structure over the
original one and required additional evidence .
notably , there are
seven instances where a jc , h coupling
is jc , h for the revised structure
and would be jc , h for the
original .
the five correlations that are identifiable as cross peaks
in hmbc are c-1 to h-9 , c-4 to h-10 , c-8 to h-2 , c-10 to h-4a , and
c-10 to h-4b . however , two jc , h couplings are not evident : c-9 to h-1 and c-12 to h-10 .
conversely ,
there are five instances where observed jc , h couplings are jc , h for the
revised structure that would be jc , h for the original structure .
accordingly , in line with the
revision , four of them are not seen as hmbc cross peaks ( c-4 to h-9 ,
c-5 to h-13 , c-9 to h-4a , and c-9 to h-4b ) , whereas one is indeed
observed : c-12 to h-9 .
although these provide a strong argument for
the revised structure over the original , these results are not overwhelmingly
conclusive . in particular , the only jc , h coupling observed for the revised structure must be
addressed .
the geometry of the correlating moiety has a characteristic
w arrangement that would allow the back lobes of sp orbitals on c-3 and c-9 to overlap , thus providing a mechanism
for the transmission of the observed spin coupling effects .
while this manuscript was under preparation , the group of hh published
the total synthesis of aquatolide .
sharing
of the 400 mhz h nmr spectrum fid of this publication
and a 1.1 mg sample of the compound , which was used to acquire a 900
mhz data set , permitted both a rapid verification of the result of
this work and the mutual congruence of the structural assignments .
for this purpose , the hifsa profiles of the 400 and 900 mhz data of
the synthetic sample were generated and compared with the profile
obtained from the 800 mhz of the natural material .
the results ( table 1 ) reveal the expected
high consistency of all three profiles and also confirm the reported
scaling capability of hifsa .
furthermore ,
in line with the interpretation of the dynamic effects that broaden
the signals of h-4a , h-4b , and h-5a of the 8-membered ring ( see above ) ,
the small but significant differences observed for the couplings of
these protons reflect the impact of the magnetic field strength on
the peak separation , leading to greater line broadening due to incomplete
averaging as well as the slight experimental differences of the two
measurements ( temperature and concentration ) .
accordingly , the minor
deviations in the j - patterns actually confirm the
inferences regarding the peak broadening effects .
overall , we
learn from this comparison that dynamic effects play enough of a role
in hifsa profiles such that they have subtle but characteristic effects
on the determined coupling constants in complex signals .
when interpreting
these subtle effects , one has to keep in mind that the observed coupling
constants represent weighted averages of the coupling constants of
all conformers .
therefore , dynamic effects influence coupling constants
as determined by hifsa and include temperature , field strength , and
sample concentration . furthermore , line distances in h
nmr spectra are not coupling constants , unless the spin system is
pure first order , which is rarely truly the case and is certainly
not the case in aquatolide .
representing an iterative method , hifsa
determines the experimental coupling constants , but
the underlying nmr experiment , detects conformationally averaged coupling
on the ( slow ) nmr time scale . as a result , unless all populations
and their abundance are known , the true underlying j values can not be determined .
the small but diagnostic differences
in the j values and increased signal widths of h-4a ,
h-4b , and h-5b reflect the field - dependent dynamic of the 8-membered
ring system ( see main text ) .
the following points summarize key lessons
to be learned , or reminded of , from the aquatolide case .
the proper acquisition
and accurate interpretation of 1d h data ( the mother
of all nmr spectra ) is a crucial
first step in structure elucidation . especially for the purpose of
obtaining preliminary structural information , h spectra
will usually be the first 1d spectra acquired , and this choice is
largely driven by sensitivity , due to the limited levels of material
frequently encountered early in an isolation protocol .
subsequent
1d and 2d experiments will expand on and/or confirm the 1d h data .
although the 1d c data is particularly important
to elucidate proton - deficient molecules , nmr spectra of both nuclei
are important for subsequent structural dereplication .
the importance
of 1d h data should be respected , beginning with acquisition
of the data , and followed through with the appropriate post - acquisition
processing . in particular ,
lorentzian gaussian or other resolution
enhancement post - acquisition processing , including zero - filling , can
be used to observe the greater details of coupling patterns present
in complex signals .
however , it must be conceded that even meticulous
processing may not reveal all of the signal information and , therefore ,
coupling information due to signal overlap , exceedingly small coupling
values , and signal - to - noise issues , may still make extraction of all
of the spectral information problematic . in this context , it
should be noted that standard h nmr spectra acquired under
quantitative conditions are entirely fit for the purpose of qhnmr
quantitation , allowing for the assessment of the purity of the investigated
compounds .
as qhnmr spectra need to be acquired with good signal - to - noise
( s / n ) , they elegantly serve the dual purpose of enabling recognition of splitting / coupling patterns through resolution - enhanced
post - acquisition processing and lc - independent purity assessment as
required by journals
. computational
evaluation of structures using both h
and c data , together with the calculation of
values , is the first tier in the evaluation of a proposed structure .
prediction of coupling constants based on the optimized geometry of
the proposed structure is the second tier of h spectra
evaluation .
finally , the observed coupling information may be further
enhanced with iterative fitting processes utilizing the quantum mechanical
spin information inherent in the structural geometry in a third tier
of evaluation .
although hifsa may ultimately reveal inconsistencies
in a proposed structure , a careful analysis of the hifsa parameters
must still be undertaken even in the case of a good fit .
primarily ,
the evaluated j coupling constants should
be consistent with the dihedral angles present in the proposed 3d
molecular structure .
of particular concern are instances of unobservable j coupling constants due to dihedral angles
near 90 : the lack of measurable coupling differs significantly
from missing j values in reported tables or quilts .
therefore , it is a necessary requirement to verify both what is observed
and what is not observed .
it is difficult to know from the literature
how often unobservable j couplings occur
in structural elucidation : as unobservables , they
can not be observed and thus are not reported , but so are many other
obvious couplings . whereas the computation of average and maximum c chemical
shift deviations is an accepted means of assessing the plausibility
of ( revised ) structures , the accuracy
of available h chemical shift prediction tools is not
yet sufficient to establish analogue measures for h - based
computer - aided structure elucidation ( case ; http://www.acdlabs.com/comm/elucidation/2013_10.php ) . however ,
precise and accurate reporting of h nmr data
( see ref ( 16 ) and below )
is an important and powerful instrument of both dereplication and
structure elucidation .
the simplicity of the 1d h nmr experiment has a tendency
to hide the information richness of the spectra . in fact , with the
exception of proton - deficient compounds , the assortment of multibond
couplings ( j ) that encodes the
network of proton resonances of a given molecule provides plentiful
structural information , and all of them have to be compatible with
the proposed structure .
a generally useful approach is to challenge
multiplets as particularly information - rich signals .
one efficient means of mining this information is to perform full
spin analysis ( hifsa ) , which captures the h spin network
assignments in a qm - proof manner .
spin simulation software , required
for this purpose , has been available since the 1960s ( laocoon ) , and
modern tools are more powerful than ever .
it is important to note
that the assignment of all chemical shifts and couplings requires
spectral simulation to account for non - first - order effects , which
are frequently observed even with
part of the realization
of the information richness is the consideration of long - range couplings
as both a subtlety to be explored and a great resource for structural
information .
the occurrence of long - range couplings indicates particular
and sometimes unique structural characteristics .
for example , in the
aquatolide case , allylic j , homoallylic j , and strained ring j twofold w couplings were observed .
although
long - range couplings might be viewed as minor and esoteric ,
they can impart important and valuable constraints as to the plausibility
of a particular structure .
because of the general accessibility of 2d data , 1d
nmr experiments
have taken a
backseat in the structure elucidation
toolbox . however , it is important to realize that one can not rely
solely on the workhorse 2d nmr spectra ( cosy , hsqc , hmbc ) .
the evidence
contained in 1d data sets , particularly in the h domain
involving abundant j coupling , simply can not be ignored
when making conclusions about the structure ; all of the data , including
the 1d h information , has to match .
collectively , 2d nmr
experiments can serve to confirm structural assignments , including
those made from 1d 1h analyses , but not replace or even override
them as evidence .
another important reflection resulting from the
aquatolide case : although the lack of an hmbc ( or any other 2d ) cross - peak
can be diagnostic , it is predominantly a lack of information .
it can
be due to either structural constraints or be an artifact of the acquisition
parameters .
the observation of an unexpected strong hmbc cross - peak
is a clear warning sign of a wrong structure .
in fact , peak intensities
and jc , h coupling values play an important
role in the correct interpretation of hmbc and other 2d nmr experiments
that involve j coupling mechanisms . proper preservation and dissemination
of experimental fids in electronic format is an important aspect of
any structural elucidation process .
adequate information
must be supplied in order that research results may be reproduced .
the availability of fids permits a comparison of the nmr data for
published structures with nmr data for newly acquired compounds either
by isolation or by synthesis for facilitating dereplication and identifying
novel structures .
dereplication based solely on typically published h chemical shift and multiplicity tables is insufficient .
even if high resolution spectra ( images )
are included in the supporting
information of a publication , the opportunity for accurate dereplication
can not be achieved .
therefore , the original fids in electronic format
should be supplied as part of the dissemination of published work .
the compilation and maintenance
of databases , such as the crystallography open database , is a worthwhile contribution to the field of
structure elucidation .
fledgling nmr fid databases have emerged , but a concerted effort by both journal editors and publication authors
to participate is overdue .
most desirable for scientific
purposes are free archives which , similar to free software , are not
just freely accessed , but also associated with distribution rights
that establish the freedom to use the data portion of an ongoing evolutionary
process and methodology improvement with reference to the original
authors .
the consistency of structure elucidation
reports and their efficient dissemination has broad implications not
only for accurate publication of chemical structures but also for
exploitation of these structures for their biological , pharmaceutical ,
and environmental applications . in the current situation ,
as described
in the introduction , much research has been
expended for the synthesis of molecules exhibiting interesting biological
activities , only to find that the structures originally reported were
incorrect .
the reproducibility of new structures and
related discoveries rests on the ability of future researchers to
dereplicate the structure and possibly reassess the sample , or at
least its h nmr spectrum .
the hifsa - based dereplication
of synthetic relative to isolated aquatolide presented in the section
hifsa of synthetic aquatolide
exemplifies the efficiency of the approach .
near - identical ( but
not really identical ! ) chemical properties are the breeding ground
for wrong assignments , misidentification , synthetic chemistry misdirection ,
and wasted time and resources , leading to long - lasting confusion in
upstream and downstream research . concerning h nmr , subtleties
drive dereplication .
in fact , attention to detail can turn standard
1d h nmr into a powerful dereplication tool .
this applies
particularly to natural products , as their combinatorial , biosynthetic
origin makes the existence of very close or near - identical congeners
with partial stereochemical variations very likely . at the same time
,
1d c nmr represents a complementary approach to dereplication
that is readily automated due to the simplistic pure shift nature
of h broad - band decoupled c spectra .
there are numerous cases of natural products that represent near - identical
molecules , which are highly likely to produce near - identical nmr spectra
( e.g. , the [ iso-]silybins ) , but are also
likely associated with distinct biological properties and/or taxonomic
sources , and sometimes new chemical structures ( e.g. , leubethanol
from the plant leucophyllum frutescens vs elisabethanol
from the gorgonian octacoral pseudopterogorgia elisabethae ) . even when congeneric molecules are
not near - identical themselves , but only with regard to their ( highly
similar ) h nmr spectra , the comprehensive h nmr analysis is well - suited to produce compelling structural evidence
as well as highly specific data for structural dereplication and reproducibility
( see below ) .
one example of a new chemical structure investigated
using this approach is the new antituberculosis drug lead ecumicin . finally , it is important to point out that chemical
shifts exhibit solvent dependence ; therefore , this is another significant
consideration in nmr - based dereplication . from a conceptual
perspective
hifsa profiles can be considered as one unideterminant
data set for a given structure and provides a potential substitute
for the mixed melting point determination representing the gold standard
for chemical identity , especially if the second can not be determined
due to practical / sample limitations .
consequently , the following tenets
are simple ways to enhance reproducibility by means of best practices
in nmr - based structural analysis : ( i ) assign all protons ( and carbons )
and all couplings ; ( ii ) report chemical shifts ( ) precisely
to three or even better four decimal places ( 1 ppb ) ; ( iii )
report coupling constants ( j ) precisely to one or
even better two decimals ( 100 mhz ) ; ( iv ) perform full spin
analysis ( e.g. , hifsa ) and report complete sets of h spin
parameters , e.g. , as supporting text or vendor - specific but open formats ,
such as perch pms files ; and ( v ) make raw nmr data ( fids ) publically
accessible and part of publications .
certainly , there are additional
best practices related to the acquisition of h nmr spectra ,
which will in turn enhance the reliability and reproducibility of
interpretation .
these best practices include ( i ) the habit of depleting
dissolved oxygen in the sample ( freeze pump thaw or
he degassing ) and ( ii ) being cognizant of how solvents affect the
acquisition and characteristics of h nmr spectra . for
example , the chloroform deuterium signal may be difficult to lock
at high fields ; thus , solvent effects
on line shape ( viscosity ) and shimming ( split fields ) should also
be considered .
the quilt format is more intuitive for
human use than the ubiquitous tabular or graphical formats used in
the laboratory and in publications today .
in particular , quilts simplify
the assessment of the completeness of the nmr structural information ,
as empty boxes are spotted readily and represent the only allowed
gaps , indicating a lack of correlation that is in line with the proposed
structure .
moreover , quilts are flexible in accommodating the
most common nmr experiments : 1d 1h ( h j - quilt in figure 3 ) , homonuclear ( e.g. , noesy quilt in figure 7 ; can be expanded to , e.g. , tocsy ) , and heteronuclear
( e.g. , hmbc quilt in figure 8 ; can be expanded to hsqc as diagonal ) spectra can all be
transposed in the quilt format . finally , the quilt format can
be readily standardized and provide
nmr data in a machine readable , unified format , making it an ideal
reporting format for computational processing .
potential downstream
applications of data published in quilt format include , but are not
limited to , spectroscopic databases , dereplication , and computer - assisted
structure elucidation tools .
collectively ,
all above points reflect on the generally well - known but sometimes
forgotten fact that spectroscopic structure elucidation is based on
indirect rather than direct evidence and is the product of deductive
reasoning rather than a picture of the molecule . as
a result , spectroscopic evidence is intrinsically limited , and respecting
this limitation is key to sound structure elucidation .
the imperative
of always considering alternative structures is one valuable means
of addressing this challenge .
another is to distinguish the difference
between the terms proof and consistent with
in structure elucidation documents .
the case of aquatolide exemplifies
some of the pitfalls , but also new insights , that can be gained from
adhering to these principles as closely as possible .
the nmr measurements were described
previously for the natural aquatolide ( 800 mhz ) and the synthetic material ( 400 mhz ) .
a sample of unnatural ( )-aquatolide ( 1.1 mg in
0.7 ml cdcl3 ) was also subject to 900 mhz nmr analysis .
for reprocessing of the h fid ,
the chemical shift of the
residual solvent signals , chcl3 , at h 7.2600 was used as the chemical shift reference .
the 800 mhz data
for figure 3a and figure 5a were processed
using lorentzian
gaussian apodization functions with lb values
of 1.0 to 3.0 hz and gaussian factors of 0.100.30 ,
centering the gaussian function at 1030% of the acquisition
time . for hifsa ,
gaussian
window function ( line broadening = 0.3 , gaussian factor =
0.05 ) prior to two zero fills to 256 k and fourier transformation . the h iterative
full spin analysis ( hifsa )
the optimized spectral parameters were saved as perch parameter
text files ( * .pms ) .
four and two decimal places for h and j values , respectively , were considered significant .
the measurements of interatomic distances were performed with the
free software avogadro ( http://avogadro.openmolecules.net ) v1.1.1 using the mol files exported
by perch . | the revision of the structure of
the sesquiterpene aquatolide from
a bicyclo[2.2.0]hexane to a bicyclo[2.1.1]hexane structure using compelling
nmr data , x - ray crystallography , and the recent confirmation via full
synthesis exemplify that the achievement of structural correctness
depends on the completeness of the experimental evidence .
archived
fids and newly acquired aquatolide spectra demonstrate that archiving
and rigorous interpretation of 1d 1h nmr data may enhance
the reproducibility of ( bio)chemical research and curb the growing
trend of structural misassignments . despite being the most accessible
nmr experiment ,
1d 1h spectra encode a wealth of information
about bonds and molecular geometry that may be fully mined by 1h iterative full spin analysis ( hifsa ) .
fully characterized
1d 1h spectra are unideterminant for a given structure .
the corresponding fids may be readily submitted with publications
and collected in databases .
proton nmr spectra are indispensable for
structural characterization even in conjunction with 2d data .
quantum
interaction and linkage tables ( quilts ) are introduced for a more
intuitive visualization of 1d j - coupling relationships ,
noesy correlations , and heteronuclear experiments .
overall , this study
represents a significant contribution to best practices in nmr - based
structural analysis and dereplication . |
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truly two - dimensional materials became a subject of intense research with the experimental isolation of graphene about one decade ago @xcite . in the wake of the many developments driven initially by research in this graphite monolayer , other two - dimensional crystals such as transition metal dichalcogenides , hexagonal boron nitride ( hbn ) , phosphorene , and others , have gained prominence due to rich and outstanding electronic , magnetic , structural , and optical properties @xcite .
the prospect of stacking individual monolayer materials with different properties holds the promise of a new paradigm in solid state physics as this modular concept of layered van der waals heterostructures might enable the tailoring of physical properties to levels much beyond the bandgap engineering that is mainstream in semiconductor heterostructures @xcite . a key role in such heterostructures would likely fall to hbn . while many two - dimensional building blocks are praised for their superior intrinsic electronic properties ,
these are detrimentally sensitive to interactions with substrates , other layers , and to contamination @xcite . with a large bandgap and a lattice mismatch of less than 2% w.r.t .
graphene , hbn has the potential to preserve graphene s celebrated properties within such heterostructures and is currently the insulating substrate of choice for clean , atomically flat deposition or interfacing of two - dimensional crystals @xcite .
beyond such a passive role , the properties of hbn also allow for an active role .
the monolayer of hbn has a honeycomb lattice structure similar to that of graphene , yet one of its two sublattices is occupied by boron ( b ) , and the other by nitrogen ( n ) atoms , see fig .
[ picbw1 ] .
this results in a strong ionic bond and a bandgap of @xmath0ev @xcite .
since inversion symmetry is naturally absent in this crystal , a piezoelectric response is possible @xcite , i.e. , a change in the bulk electric polarization @xmath1 when subjected to external stress . )
leads to a vanishing pseudomagnetic vector potential @xmath2 and does not induce a polarization @xmath1 .
( b , c ) realizations of the strain tensor @xmath3 that lift the trigonal symmetry and generate a change in the polarization . the induced polarization and the vector potential are always orthogonal , @xmath4 . , scaledwidth=48.0% ] the ability to control bulk polarization mechanically and , conversely , to convert electric fields into mechanical displacements is of enormous interest in the realm of energy harvesting , particularly so at the micro- and nanoscale , where a vision of self - powered miniaturized electronic devices is being strongly pursued in materials science @xcite . on another front
, a strong piezoelectric coupling has been shown to be an important tool in cooling nanoelectromechanical systems ( nems ) to their mechanical quantum ground state @xcite .
such applications demand a strong piezoelectric material from the outset and that , in turn , requires a good insulator with a robust interplay between the underlying electronic and mechanic / lattice degrees of freedom .
density functional theory ( dft ) calculations have established that an hbn monolayer has among the highest specific piezoelectric coefficients ( @xmath5pc / n ) known @xcite .
combined with the lowest surface mass density of all known piezoelectric crystals , this might allow for nems with as yet unknown force sensitivity @xcite .
moreover , hbn could provide the piezoelectric coupling in a layered graphene / hbn heterostructure and thus allow for the electromechanical manipulation of graphene with an electric field .
its strong piezoelectric characteristics , high mechanical stability , and easy handling make hbn a prime material for such technological applications .
the lattice of ( isotropically deformed ) hbn does not belong to one of the 10 polar classes and hence , hbn exhibits no spontaneous polarization .
however , it does sustain one when subjected to _
anisotropic _ deformation . in this paper
, we use the modern theory of polarization and the geometric phase approach @xcite to calculate the electronic contribution to the piezoelectric tensor of hbn in an entirely analytical way . an ionic contribution is not considered , here @xcite . a dft calculation in the context of hbn nanotubes
established that the dominant electronic contribution ( @xmath6 ) to the polarization arises from the @xmath7 valence band , and that it has the same sign as the remaining contribution from the @xmath8 valence bands @xcite .
therefore , a minimal yet promising ansatz for the analytical description of piezoelectricity in hbn consists in focusing entirely on the @xmath7 bands . as we demonstrate ,
the low energy bandstructure of the @xmath7 bands is already sufficient to derive results in qualitative and good quantitative agreement with dft calculations .
due to the underlying honeycomb lattice , low energy electrons in hbn effectively behave as ( massive ) dirac fermions .
this is similar to the situation in graphene , except for the mass term associated with the different orbital energies at the b and n atoms .
the difference in electronegativity between the two species causes electron transfer from b to n within the @xmath8 bonds @xcite and results in a bond with an ionic character , in contrast to the purely covalent bond of graphene @xcite .
the broken sublattice symmetry gives rise to the bandgap @xcite .
such a model has already been used to describe the chirality - dependent piezoelectric response of hbn nanotubes @xcite . in the vicinity of the @xmath9 points in the hexagonal reciprocal lattice ,
the effective hamiltonian is then @xmath10 where @xmath11 , with @xmath12 as the magnitude of the nearest neighbor tight - binding hopping amplitude and @xmath13 as the interatomic distance . in the absence of strain , @xmath14 . in our notation , @xmath15 , where @xmath16 are the cartesian components of the electron s crystal momentum measured relative to the high - symmetry points @xmath9 ( @xmath17 ) and @xmath18 ( @xmath19 ) .
the vector @xmath20 is defined in terms of the three pauli matrices that address the sublattice degree of freedom ( pseudospin ) in this problem .
since the real electron spin does not play a role in the following , it is not made explicit in our expressions .
the sublattice potential @xmath21 arises due to the different on - site energies at the boron ( @xmath22 ) and nitrogen ( @xmath23 ) atoms , and gives rise to a bandgap of @xmath24 in hbn . when @xmath14 , the energy dispersion associated with eq . is the hyperbola @xmath25 centered at each @xmath9 point .
the vector @xmath26 encodes the electron - lattice coupling for anisotropic strains and provides the essential mechanism through which the system can sustain a strain - induced polarization .
it is well known that the effect of such lattice deformations can be accounted for via the pseudomagnetic vector potential @xmath2 in the hamiltonian @xmath27 .
the form of eq . aptly reflects the minimal - type substitution @xmath28 , where the pseudomagnetic vector potential is given by @xcite @xmath29 this definition is given in terms of the strain tensor @xmath30 , where @xmath31 is the local displacement field , in general a function of position , although here we shall focus on strictly uniform and planar strain configurations .
the parameter @xmath32 describes the variation of the hopping amplitude @xmath33 w.r.t .
bond length in linear order and @xmath34 @xcite . in sec .
[ coupling ] , we discuss the complete prefactor / coupling strength in detail . the electron - phonon coupling encoded in @xmath2 has the qualitative effect of displacing the center of the fermi circles from @xmath35 to @xmath36 @xcite .
this affects the berry curvature in the parameter space @xmath37 , where @xmath38 $ ] parametrizes the sublattice potential . in a microscopic description of strain - induced electrical polarization ,
one formally and conventionally identifies two additive contributions @xcite .
the first one , so called ionic contribution , arises from the breakdown of the cauchy - born rule and the need to explicitly consider relative ionic displacements within the crystal s unit cell that are not accounted for by the macroscopic strain field @xmath3 .
this ionic contribution can be characterized analytically if an accurate empirical force constant model to describe the lattice degrees of freedom is known @xcite . in the case of hbn
, such calculations were performed by michel and verberck @xcite .
the second , electronic contribution arises from the induced electronic density and is the specific focus of this paper , computed within the quantum phase approach @xcite . from an _ ab - initio _ standpoint , a common strategy to identify these two contributions
consists in ( i ) computing the _ electronic _ polarization as a function of strain while keeping the ions clamped and ( ii ) performing the same computation with fully relaxed ions , which yields the _ total _ ( electronic and ionic ) polarization .
note that the ionic and electronic contributions have opposite sign for hbn @xcite . to determine the electronic contribution to the piezoelectric constant of an hbn monolayer
, we conceive a gedankenexperiment in which the gap parameter in eq .
varies adiabatically from @xmath39 ( graphene ) to @xmath40 ( hbn ) .
such adiabatic change is accompanied by the development of a bulk polarization induced dipole moment per unit area whose magnitude is obtained from @xcite @xmath41 here , @xmath42 is the @xmath43-th cartesian component of the induced polarization vector , @xmath44 is the unit charge , and the factor of 2 accounts for the spin degeneracy .
the integral over half the brillouin zone ( bz ) around each valley combined with the summation over @xmath45 recovers the full bz integral required .
the berry curvature is given by @xmath46 where @xmath47 is a valence eigenstate of eq .
with @xmath48 .
from eq . , one straightforwardly resolves the berry curvatures @xmath49 where @xmath50 . to be specific
, we consider now the calculation of @xmath51 according to eq . .
integration over the adiabatic parameter leads to @xmath52 this is followed by the momentum integration over a square centered at each of the two high symmetry points @xmath9 and @xmath18 of the undistorted bz . to conserve the total number of states , the area of each square is exactly half of the first bz zone , i.e. @xmath53 . after restoring the prefactor
, this bz integration leads to an entirely analytical expression for @xmath51 ( and likewise for @xmath54 ) . for piezoelectricity , the linear response of @xmath1 w.r.t .
strain is relevant . as eq .
shows that @xmath2 is linear in strain , it is appropriate to focus on the leading order of the induced polarization in the pseudomagnetic vector potential : @xmath55 \;{\boldsymbol{a}}\times\hat{\textbf{z } } + \mathcal{o}(a^3 ) .
\label{pvsa}\ ] ] this is the main result of our analytic calculation . on one hand , it manifests a new and useful qualitative result : the pseudomagnetic vector potential and the induced polarization are orthogonal , @xmath4 , irrespective of the state of strain . on the other hand , the exact and simple analytical expression in eq .
allows us to extract definite quantitative predictions regarding the magnitude of the piezoelectric coefficient in hbn .
the components of the direct and converse piezoelectric tensors are , respectively , given by @xmath56 where @xmath57 is the stress tensor .
the crystal of hbn belongs to the point group @xmath58 ( @xmath59 ) which , for the lattice orientation introduced in fig .
[ picbw1 ] containing a mirror plane perpendicular to the @xmath60-axis , imposes the symmetry constraints @xmath61 while all other components vanish identically @xcite .
the piezoelectric response is thus characterized by only one number , and we call @xmath62 and @xmath63 the direct and converse piezoelectric constants , respectively .
the direct and converse effects are related through the elastic tensor , @xmath64 , which , since we have only one independent component in each , reduces to the simple relation @xmath65 . to confirm consistency of our model with symmetry constraints , note that eq . implies @xmath66 . together with eq .
, this leads to , e.g. , @xmath67 analogously , we can verify that all the relations in eq .
are indeed satisfied by the model .
the piezoelectric constant is explicitly given by @xmath68 .
\label{e222}\ ] ]
the electromechanical coupling strength @xmath69 in eq . arises from a low energy approximation of a tight - binding hamiltonian that describes electronic hopping among the @xmath70 orbitals of neighboring atoms in the honeycomb lattice of hbn @xcite . under strain ,
the interatomic distances are changed and the hopping amplitude @xmath33 is modified accordingly .
this couples the electronic system to the lattice degrees of freedom to an extent that is controlled by the parameter @xmath32 which reflects the sensitivity of the hopping amplitude to changes in the bond length .
since , as in graphene , the @xmath7 band comes about due to electron hopping between the @xmath70-orbitals of nearest - neighboring atoms , @xmath71 corresponds to the slater - koster parameter @xmath72 , and it is natural to expect an exponential decay of @xmath71 with increasing interatomic distance @xcite . in analogy with a parametrization that is fairly accurate in graphene @xcite , we consider @xmath73 where @xmath74 denotes the hopping amplitude at the equilibrium bond length @xmath75 .
we can estimate @xmath76 from existing data for the slater - koster parameters @xmath72 in hbn with first- , second- , and third - nearest neighbors that are fit to accurately reproduce the bandstructure obtained from dft calculations @xcite . both
the first- and the third - nearest neighbor hopping occur between b and n atoms . with @xmath77 and @xmath78 for the first and third neighbor hopping amplitudes , respectively , we find @xmath79 , which is a value very similar to that for graphene @xcite .
this similarity is not surprising as the atomic orbitals involved are the same in the two systems , and the relaxed interatomic distance is nearly the same , too . for consistency of @xmath80 and @xmath81 ,
we have used the values from ref .
@xcite in our estimate for @xmath76
. however , literature values for the nearest neighbor hopping amplitude cumulate rather around @xmath82 and we thus infer @xmath83ev @xcite .
the dimensionless parameter @xmath84 depends on microscopic details of the lattice dynamics . in lowest order of a valence - force - field model @xcite
, it is given by .
this results in an electromechanical coupling strength of @xmath85ev in eq . .
putting this together with all the other relevant parameters listed in table [ decaytable ] , we evaluate eq . and finally estimate the contribution of the @xmath7 electrons to the total piezoelectric constants to be @xmath86 duerloo _
_ obtained the values @xmath87c / m in a fully relaxed - ion dft calculation and @xmath88c / m under clamped - ion conditions ( note that our coordinate convention is different from the one used by these authors ) @xcite . as described
earlier , the latter corresponds to the electronic contribution and is the one appropriate for direct comparison with the figures quoted in eq . since our model accounts only for the electronic part .
we further recall that our calculation hinges entirely on the electronic effects associated with @xmath7-band electrons , justified by the fact that , according to first principles calculations , these account for 80% of the electronic piezoelectric response @xcite .
this factor of @xmath89 can be incorporated in our results allowing us to refine the numbers in eq . to @xmath90c
/ m and @xmath91pc / n as the prediction for the electronic contribution to the piezoelectric constants . given the uncertainty inherent to our estimate of the electromechanical coupling strength @xmath69 above
, we consider this result to be in good quantitative agreement with the first principles value of @xmath92c / m . beyond the scope of the current work
, it would be interesting to obtain _ ab - initio _ a more precise value of the logarithmic derivative of the hopping , @xmath76 , so the quantitative accuracy of our model can be fully assessed .
we reiterate the impressive magnitude of the piezoelectric response in hbn already pointed out by duerloo _
et al . _ as well as michel and verberck @xcite . for comparison ,
the piezoelectric tensor components of quartz vary in the range @xmath93pc / n @xcite . the numbers in eq .
show that a single , atomically thin layer of hbn is essentially as good a piezoelectric as a crystal of quartz . .
the parameter @xmath76 is discussed around eq . and
@xmath84 follows from a lowest order valence - force - field model @xcite .
the value for @xmath13 stems from refs .
@xcite and is also used for @xmath94 . with @xmath95ev @xcite and @xmath96 , @xmath97 corresponds to a bandgap of @xmath98ev @xcite . for @xmath99
, we use the elastic constants @xmath100n / m and @xmath101n / m , as reported in ref .
@xcite ( voigt notation ; different lattice orientation ) .
[ cols="<,<,<,<",options="header " , ]
we have obtained exact analytical results for the induced polarization and piezoelectric constant of monolayer hbn within the quantum geometric phase approach . in our minimal model , which is proven to satisfy the symmetry constraints expected for the point group @xmath58 ( @xmath59 ) , the interaction between deformations and the electronic degrees of freedom is captured in the effective two - band hamiltonian via a pseudomagnetic vector potential .
ionic degrees of freedom are not considered . using existing literature estimates for the relevant bandstructure parameters and elastic constants in this system , we find that the converse and direct piezoelectric constants for this model are as high as @xmath102c / m and @xmath103pc / n , respectively .
the strain - induced polarization @xmath1 is exactly perpendicular to the pseudomagnetic vector potential @xmath2 .
we also provide an estimate for the so far unknown coupling strength of the strain - induced pseudomagnetic vector potential in hbn , namely , @xmath104ev . that the magnitude of the piezoelectric coefficient obtained here agrees well with the value extracted from independent dft calculations attests to the validity and pertinence of the minimal model , especially since it provides a simple analytical result for its dependence on the basic material parameters .
another advantage of our calculation is that , through eqs . and , one can interpret the piezoelectric effect in this material as a consequence of the displacement of the dirac point under strain from its default position at @xmath9 in the bz : a measurement of the electric polarization is thus an indirect measure of how much and along which direction the dirac point drifts from @xmath9 under strain .
our findings for atomically flat hbn might be ultimately put to test in hopefully upcoming experiments which , to our knowledge , have not been reported yet .
we thus provide an analytical and concise description of piezoelectricity in hbn that is of relevance for the understanding of nanoscale devices containing hbn as a piezoelectric component , including heterostructured nems based on two - dimensional materials .
md and gb thank the european science foundation and the deutsche forschungsgemeinschaft ( dfg ) for support within the eurographene project congran and the dfg for funding within sfb 767 and for 912 .
vmp was supported by the national research foundation ( singapore ) under its medium sized centre programme and crp grant `` novel 2d materials with tailored properties : beyond graphene '' ( grant no .
nrf - crp6 - 2010 - 05 ) .
l. britnell , r. v. gorbachev , r. jalil , b. d. belle , f. schedin , a. mishchenko , t. georgiou , m. i. katsnelson , l. eaves , s. v. morozov , n. m. r. peres , j. leist , a. k. geim , k. s. novoselov , and l. a. ponomarenko , science * 335 * , 947 ( 2012 ) .
a. d. oconnell , m. hofheinz , m. ansmann , radoslaw c. bialczak , m. lenander , erik lucero , m. neeley , d. sank , h. wang , m. weides , j. wenner , john m. martinis , and a. n. cleland , nature ( london ) * 464 * , 697 ( 2010 ) .
the transfer of negative charge from b to n within the @xmath8 bond is overcompensated by the charge transfer within the @xmath7 bond which gives the boron atom an effective negative charge in equilibrium @xcite . | due to their low surface mass density , two - dimensional materials with a strong piezoelectric response are interesting for nanoelectromechanical systems with high force sensitivity . unlike graphene , the two sublattices in a monolayer of hexagonal boron nitride ( hbn ) are occupied by different elements , which breaks inversion symmetry and allows for piezoelectricity .
this has been confirmed with density functional theory calculations of the piezoelectric constant of hbn .
here , we formulate an entirely analytical derivation of the electronic contribution to the piezoelectric response in this system based on the concepts of strain - induced pseudomagnetic vector potential and the modern theory of polarization that relates the polar moment to the berry curvature .
our findings agree with the symmetry restrictions expected for the hbn lattice and reproduce well the magnitude of the piezoelectric effect previously obtained _ ab - initio_. = 1 |
The short break in the 2012 Republican primary calendar has come and gone; Wisconsin, Maryland and the District of Columbia hold their primaries on Tuesday.
98 delegates are at-stake in the three contests, which fall at a pivotal moment in the campaign, as Romney gathers up establishment support and begins to look more and more like the inevitable nominee. A clean sweep on Tuesday night would further solidify this perception. A Santorum upset on the other hand, would give a jolt to Santorum's campaign and perhaps make Romney's "inevitable nominee" status look, well, not quite so inevitable.
Here are five important things to note about the three contests.
1.) The delegate math will strongly favor the winner.
A total of 98 delegates are at stake on Tuesday: 42 in Wisconsin, 19 in D.C., and 37 in Maryland. The District of Columbia's primary is winner-take-all, meaning that whoever receives the highest percentage of the vote gets all of the delegates.
Maryland and Wisconsin are both winner-take-all by congressional district. The allotment scheme in Maryland and Wisconsin allows the second-place finisher potentially to score a couple of delegates here or there if he is able to carry any congressional districts, but for the most part the winner of the state will get a big majority of the state's delegates.
2.) Wisconsin is the big prize.
Although Wisconsin does not have a lot more delegates than Maryland, it's the primary Tuesday that matters the most as far as perception is concerned. Just look at the candidates' schedules over the past 10 days since the Illinois primary, and this becomes very clear. Candidates have spent far more time in Wisconsin than in Maryland or D.C.
Why?
Maryland and D.C. are both blue states. In the general election they will be virtually ignored because they are easily assumed to be Obama wins. Their victories bring no trump cards. Wisconsin is viewed as a swing state. Obama carried it in 2008, but the state has one Republican Senator, a Republican Governor and a mixed Congressional delegation.
3.) Money, Money, Money.
Candidates and their allies have poured serious change into the Wisconsin airwaves. Romney and his allies have spent upwards of $3.1 million on TV ad buys, according to a source tracking GOP ad buys. For comparison, Santorum and his allies have spent roughly $717,000 on TV ad buys, a margin of about 4:1.
Romney and Santorum aren't alone on the airwaves. The Super PAC supporting Newt Gingrich- Winning Our Future- made a small ad buy in the Badger state- $120,381, according to their FEC filings.
Though it's much smaller than the amount spent in Wisconsin, the pro-Romney Restore Our Future Super PAC has also spent money in Maryland. The group has spent $436,204 on ad buys in the state, according to their FEC filings.
4) All signs point to Romney.
Polling indicates that Romney is ripe to sweep Wisconsin and Maryland. There has been no polling in Washington, D.C., though the assumption is that he'll carry the district as well. After all, he seems to be the establishment favorite. What's more establishment than D.C.? Plus, Santorum failed to qualify for the ballot in the District of Columbia, so his name will not appear as an option for voters.
5) But don't look for the rest of the field to bow out Wednesday.
Rick Santorum has pledged to fight on until his home state of Pennsylvania holds its primary on April 24th. Newt Gingrich appears to be committed to staying in the race until Romney reaches 1,144 delegates - the number needed to secure the nomination. And then there's Ron Paul, who shows no signs of slowing down.
If the current polling holds and Romney is able to sweep all three primaries, he would increase his already strong delegate lead, making it almost impossible, mathematically speaking, for the other candidates to catch up to him. However, just as likely, he'll continue to share the field for the foreseeable future. ||||| It’s either the beginning of the end, or more of the same, depending on which candidate is talking.
But tonight’s trifecta of primaries in which 98 delegates are at stake — in Wisconsin, Maryland and Washington, D.C. — come at a crucial point in the 2012 Republican primary race.
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They will almost certainly push Mitt Romney past the 600-delegate mark, according to most press counts. As for Rick Santorum, Wisconsin represents his last chance for a crucial Midwestern victory and a loss there could hobble his campaign headed into his home state of Pennsylvania on April 24.
Below are POLITICO’s five things to watch on primary night.
1) The margin of victory
It’s not a novel idea, but it’s an important one. If Santorum ekes out a win over Romney, it will be a surprise, come-from-behind victory in the last Midwestern state where the Pennsylvanian has a shot. It’s a coup that would be very unlikely to change the outcome of the GOP race, but which would certainly make it hard for the front-runner to declare game over.
If Romney wins, as he’s expected to do, the question will be his margin.
“Is he going to get double digits?” said Charlie Sykes, a well-known and highly-influential conservative radio host in Wisconsin.
With support from Rep. Paul Ryan and Sen. Ron Johnson, Romney has, he noted, “the entire conservative infrastructure of the state…that ought to be very influential with the primary voters.”
Romney also enjoys as “favorable a climate among conservatives as he could have had there,” Sykes said, given what he described as the “pragmatic, principled conservative electorate” within the base — as well as a lack of any real “Stop Romney” movement on state talk radio.
Throughout the GOP primary contest, Romney has struggled with “very conservative” voters, as well as evangelicals. Faring well with that group of the base would help to ease lingering concerns about him, especially after getting behind him in recent days the state’s best-known tea party leaders.
And a large margin of victory would deal a potentially dangerous blow to Santorum ahead of the April 24 primary in his home state. The infection could spread to Santorum’s poll numbers there, something that Romney’s camp is hoping for, and would help the front-runner start finally trying to bring down the curtain on the primary battle Wednesday.
2) The fight for the Milwaukee suburbs
Waukesha County in the Milwaukee suburbs remains one of the bellwethers that almost every Republican and reporter cites as a must-watch on election night. Simply put, it’s the county that’s the likeliest indicator of whether Romney or Santorum will emerge as the victor.
To that end, Craig Gilbert, of the Milwaukee Journal Sentinel, wrote over the weekend about the key role that Milwaukee, Green Bay and the Milwaukee suburbs will play in the primary race.
In addition to Waukesha, there are also Washington and Ozaukee counties. The three are major Republican suburbs of Milwaukee.
If Santorum is down by more than 10 points in those suburbs, it will be hard for him to make it up in the less-populous rural areas of the state, according to one Wisconsin GOP insider. As for Milwaukee and Green Bay, they make up about two-thirds of the Republican electorate statewide and are the two major media markets in which Romney and his super PAC have been investing heavily.
Another reason the suburbs are worth watching? As Gilbert wrote, “If Romney wins those base counties by significant margins, it would be a telling accomplishment, because these counties are less moderate, less affluent and more socially conservative than the white-collar suburbs Romney won so easily in Illinois two weeks ago.”
Demographics have been the best predictor of performance for both Romney and Santorum throughout the primary cycle, but the front-runner has been making inroads with some of the GOP subgroups that have been traditionally less friendly to his candidacy. Santorum, however, has not. | – You've probably heard this before, but today's Republican primaries in Wisconsin, Maryland, and DC are pretty important. They'll surely push Mitt Romney past the 600 delegate mark (does that make it "halftime"?), and they represent Rick Santorum's last chance to win a Midwestern state, Politico reports. Here's what you need to know: Wisconsin is what matters: It doesn't award very many more delegates than Maryland, but Maryland is guaranteed to go blue in November, whereas Wisconsin is a swing state, ABC News points out. Romney's the favorite… Polls show he could sweep both states; indeed, Wisconsin conservative radio host Charlie Sykes is asking if Romney can win by double digits. ...and a conservative darling? In Wisconsin Romney has support from "the entire conservative infrastructure of the state," Sykes says, including Paul Ryan and Ron Johnson. This could be a chance for him to finally score well with self-proclaimed "very conservative" voters. Bought and paid for: Of course, Romney has spent handsomely to secure his lead; he and his allies have poured $3.1 million into Wisconsin TV ads, about four times what Santorum and co. have spent. Scott Walker is watching to see how strong turnout is. Turnout is expected to be the key to his June 5 recall election, so today's primary represents a sort of early test for the GOP machine. No one bothered polling DC but everyone pretty much assumes Romney will win. Both because he's the establishment favorite, and because, well, Santorum didn't get his name on the ballot. Newt Gingrich is still here: Though you'd be forgiven if you didn't notice—his campaign is "near-suspended," traveling and spending very selectively, according to Politico. He's focused mainly on Maryland, and needs to post a respectable percentage to justify continued press attention. |
President Trump Donald John TrumpWhite House counsel called Trump 'King Kong' behind his back: report Trump stays out of Arizona's ugly and costly GOP fight Trump claims he instructed White House counsel to cooperate with Mueller MORE on Saturday reacted to the indictment of 12 Russian military officers “for conspiring to interfere with the 2016 presidential election” by blaming former President Obama and the “deep state.”
“The stories you heard about the 12 Russians yesterday took place during the Obama Administration, not the Trump Administration,” he tweeted from Scotland. “Why didn’t they do something about it, especially when it was reported that President Obama was informed by the FBI in September, before the Election?”
The stories you heard about the 12 Russians yesterday took place during the Obama Administration, not the Trump Administration. Why didn’t they do something about it, especially when it was reported that President Obama was informed by the FBI in September, before the Election? — Donald J. Trump (@realDonaldTrump) July 14, 2018
Obama issued sanctions against Russia for the meddling in the election in December 2016.
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He also expelled 35 Russian diplomats from the U.S. and ordered two Russian compounds to be closed.
Special counsel Robert Mueller Robert Swan MuellerSasse: US should applaud choice of Mueller to lead Russia probe MORE is now leading the investigation into Russian interference in the election, as well as possible collusion within the Trump campaign. His probe led to the 12 indictments announced on Friday by the Justice Department. They are charged with hacking Democratic National Committee (DNC) officials and dispersing the stolen documents online.
The Trump administration has emphasized that the indictments do not indicate any level of collusion by a member of the Trump campaign. Trump has repeatedly said there was no collusion.
Trump went on to question “Where is the DNC Server, and why didn’t the FBI take possession of it?”
He proposed that the server could have been kept hidden by the “Deep State.”
....Where is the DNC Server, and why didn’t the FBI take possession of it? Deep State? — Donald J. Trump (@realDonaldTrump) July 14, 2018
The deep state is a conspiracy theory that claims high-level officials run a shadow government working against Trump.
Trump has suggested in the past a conspiracy around the computer servers at the DNC that Russians hacked during the election.
The FBI reportedly has not directly assessed the hacked server during the agency investigation, instead relying on information from a private security firm.
-Updated 10:32 a.m. ||||| Roger Stone: I'm 'probably' unnamed person mentioned in Robert Mueller indictment
CLOSE The indictments were announced Friday by Deputy Attorney General Rod Rosenstein as part of the ongoing special counsel probe into potential coordination between the Trump campaign and Russia. (July 13) AP
Former Trump campaign adviser Roger Stone acknowledged late Friday that he's "probably" the unnamed person mentioned in special counsel Robert Mueller's indictment against 12 Russian military intelligence officers who allegedly sought to influence the 2016 presidential election.
Mueller's indictment, unveiled days before President Donald Trump is set to meet Russian President Vladimir Putin, asserts that the Russian suspects engaged in a far-reaching hacking scheme that targeted the Democratic National Committee and the Hillary Clinton presidential campaign.
The indictment also referenced a U.S. person who "was in regular contact with senior members of the presidential campaign of Donald J. Trump" and exchanging messages with the conspirators, who were posing as Guccifer 2.0.
In an interview with CNN's Chris Cuomo, Stone said that he's "probably" the person named in the filing.
Roger Stone: I probably am the person in the indictment https://t.co/zOWDTXBFFy — Christopher C. Cuomo (@ChrisCuomo) July 14, 2018
Stone's admission is a reversal of sorts. Earlier Friday, the longtime Republican strategist told The Hill that his messages with Guccifer 2.0, which Stone admitted to having exchanged in the past, were "benign based on its content context and timing." But he denied he was the person named in Friday's indictment "because I wasn't in regular contact with members of the Trump campaign," The Hill reported.
Stone maintained that the exchange was benign in his interview with CNN, and acknowledged he was in contact with Trump campaign officials.
He told CNN he hadn't read the "extensive document" and "misunderstood" the reference to the messages when he denied being the unnamed person. The messages were included in the indictment, raising speculation that Stone was the unnamed person.
More: 12 Russian intelligence officers indicted for hacking into DNC, Clinton campaign
Related: Read the Russian election meddling indictment of 12 Russian nationals
Contributing: Kevin Johnson, Erin Kelly and Jessica Estepa
Read or Share this story: https://usat.ly/2umyMK9 ||||| Special counsel Robert Mueller Robert Swan MuellerSasse: US should applaud choice of Mueller to lead Russia probe MORE’s indictment of Russian military officers in the 2016 hacking of the Democratic National Committee (DNC) appears to make reference to former informal Trump campaign adviser Roger Stone Roger Jason StoneRoger Stone challenges Dems to produce WikiLeaks evidence Google chief defends company during Capitol Hill grilling Alex Jones heckles Google CEO heading into House hearing MORE.
The longtime GOP strategist acknowledged to CNN that messages included in the latest indictments match ones that he previously released relating to the hacker Guccifer 2.0, but he denied that he is the person referred to in the indictment “because I wasn't in regular contact with members of the Trump campaign.”
Stone told The Hill in a text that his “24 word exchange with someone on Twitter claiming to be Guccifer 2.0 is benign based on its content context and timing,” adding that he said the same during his testimony before the House Intelligence Committee last year.
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“This exchange is entirely public and provides no evidence of collaboration or collusion with Guccifer 2.0 or anyone else in the alleged hacking of the DNC emails, as well as taking place many weeks after the events described in today’s indictment,” he continued.
The indictment released Friday refers to “a person who was in regular contact with senior members of the presidential campaign of Donald J. Trump” who was contacted by the Russian officers under the guise of the hacker Guccifer 2.0.
The document cites messages where Guccifer 2.0 wrote to the individual “please tell me if i can help u anyhow ... it would be a great pleasure to me” and “what do u think of the info on the turnout model for the democrats entire presidential campaign.”
The individual replied to the last message, “Pretty standard.”
Those messages match up with Twitter direct messages exchanged between Stone and Guccifer 2.0. Stone posted screenshots of the messages last year.
Stone has emerged as a person of interest in Mueller’s probe into Russian efforts to meddle in the 2016 presidential election, and some of Stone's associates have recently been subpoenaed in the probe.
The former Trump campaign adviser said during an interview last month with Hill.TV’s “Rising” program that it’s possible that he’ll be indicted in Mueller’s probe.
Mueller on Friday indicted 12 Russian intelligence officers in the hacking of the DNC in 2016.
Stone noted to CNN on Friday that Deputy Attorney General Rod Rosenstein Rod Jay RosensteinMueller’s real challenge Graham vows to push Trump’s AG pick through Judiciary Committee House GOP set to grill Comey MORE had said "that they knew of no crime by US citizens" when he announced the indictments.
"They included my exchange with Guccifer, which is now public, in the indictment. And it's benign. So I don't know that it refers to me," Stone told the network.
"There is no allegation in the indictment that any American was a knowing participant in the alleged unlawful activity or knew they were communicating with Russian intelligence officers," Rosenstein said Friday while announcing the charges.
— Niall Stanage contributed to this report. | – With 12 Russians indicted Friday for allegedly hacking the 2016 US election, President Trump is blaming an unexpected figure: President Obama, the Hill reports. "The stories you heard about the 12 Russians yesterday took place during the Obama Administration, not the Trump Administration," Trump tweeted Saturday. "Why didn't they do something about it, especially when it was reported that President Obama was informed by the FBI in September, before the Election?" However, Obama did punish Russia with sanctions and the expulsion of 35 diplomats. Trump's administration, meanwhile, insists the indictments show no evidence of Russia collusion—although the hacks did begin hours after then-candidate Trump called on Russia to hack Hillary Clinton's emails. For more on the hack and indictments: Key excerpts: "The conspirators covertly monitored the computers of dozens of DCCC and DNC employees, implanted hundreds of files containing malicious computer code ('malware'), and stole emails and other documents from the DCCC and DNC 5," per one of several indictment excerpts in the New York Times. The hackers are also accused of releasing stolen documents through a website dubbed "Organization 1" (apparently Wikileaks) and using "a network of computers located across the world, including the United States." Roger Stone: The Trump confidant said Friday that he's "probably" the one mentioned in the indictments who messaged with the conspirators and was regularly in contact with top Trump campaign officials, USA Today reports. It's partly a reversal, since Stone told the Hill earlier that his Twitter messages with hackers were "benign" and he denied being the one named in the indictments "because I wasn't in regular contact with members of the Trump campaign." |
the knowledge gained from the sequencing and extensive annotation of the saccharomyces cerevisiae genome over the past decade has enabled researchers to take a genome - wide view of yeast genes and proteins . because it is now possible to present information about the s.cerevisiae genome in its entirety ,
basic questions about protein function and cellular processes can be studied on a larger scale by searching for and studying every gene involved , rather than just one or a few genes .
moreover , researchers new to studies in s.cerevisiae can begin their inquiry at the genome level and be led to individual genes , rather than the more classical approach of starting with a phenotype and determining the genes involved . to provide a composite overview of the genes and proteins of s.cerevisiae , the saccharomyces genome database ( sgd ; )
has created the genome snapshot ( ) . the genome snapshot presents a graphical summary of this genomic information , which is also available through sgd 's ftp site ( ) and advanced search form ( ) . the current status of the entire s.cerevisiae genome is displayed on a single page and organized into two categories : ( i ) an inventory of the different types of chromosomal features found in s.cerevisiae and ( ii ) a summary of the distribution of gene product annotations among gene ontology ( go ) terms , which reflect the molecular function , biological role and cellular localization of the gene products ( 1 ) .
the genome snapshot includes information on genomic features as well as summaries of go annotations .
the total number of biologically significant open reading frames ( orfs ) in s.cerevisiae has been the subject of debate since the genome sequence was finished , and estimates continue to change as new experimental evidence becomes available ( 25 ) . in august 2003 ,
uncharacterized and dubious , according to the degree of certainty that they actually encode proteins .
the assignment to one of these categories is based on manual review of experimental evidence and sequence conservation .
dubious orfs are not conserved in closely related saccharomyces species , and no experimental evidence currently exists that a gene product is produced .
uncharacterized orfs have orthologs in at least one other species , suggesting that they are bona fide protein - coding genes , but to date there is no experimental evidence to support this .
verified orfs are those for which experimental evidence demonstrates that a gene product is produced in s.cerevisiae .
it is important to note that these classifications are meant to provide a current best estimate of the coding capacity of the genome .
the classifications are fluid and are updated continually as new experimental results become available , during the normal process of literature curation ; it is typical for a designation to change from uncharacterized to verified as more information is published . the color - coded pie chart at the top of the genome snapshot summarizes the current classification status of all the orfs in the yeast genome ( figure 1a ) . over the period from august 2003 through june 2005 , the number of verified orfs increased by 238 , from 4065 to 4303 .
the number of dubious orfs stayed relatively constant over this time period , decreasing from 820 to 818 .
the genome inventory is in tabular form and displays several types of information for each chromosome and for the genome as a whole ( figure 1b ) .
although the complete sequence for s.cerevisiae was first published in 1996 ( 6 ) , annotation of the genome remains an ongoing process ( 24,7 ) . in the past 5 years
, the yeast genome catalog has expanded to include 426 new protein - coding genes and 255 other non - protein - coding features ( centromeres , ars sequences , trna genes , rrna genes , etc . ) .
the genome inventory lists all types of chromosomal features currently annotated in sgd and provides a count for each type .
clicking on any feature type initiates a search that uses sgd 's advanced search tool ( ) to find all the features in sgd of that type .
information for all chromosomal features is available in the sgd_features.tab file at sgd 's ftp site ( ) .
a tabular overview summarizes the status of go annotation at sgd ( figure 2a ) .
the first column total number of annotations shows the total number of s.cerevisiae gene products ( protein and rna gene products ) currently annotated to each of the three go ontologies : biological process , molecular function and cellular component ( 1,8 ) ( see for detailed information about the go project ) .
the total number of annotations column does not include annotations to the three terms that represent lack of knowledge at this time , molecular function unknown , biological process unknown or cellular component unknown ; these numbers are reported in the number of gene products annotated as unknown column .
unknown annotation indicates that there are no published data available for that gene product , in that category .
not included in these counts , for either column , are go annotations made for orfs classified as
not physically mapped. go annotations for s.cerevisiae gene products are included in the gene_association.sgd file available at sgd 's ftp site ( ) .
this last section of the genome snapshot displays distributions , presented as bar graphs , of gene products annotated to go terms other than unknown ( figure 2b ; cellular component graph not shown ) .
instead of providing the distribution based on the specific term to which the gene product was annotated , which would make the graphs quite large and difficult to interpret , gene products are more broadly grouped using yeast go slim terms .
the yeast go slim is a subset of go terms that apply to broad categories of cell processes , functions or components ( and as such are placed at a high level in their respective ontologies ) .
yeast go slim terms allow grouping of genes into categories , some of which are very general ( e.g. dna metabolism and nucleus ) and others that are tailored to yeast biology ( e.g. sporulation and bud ) . for example
, dna replication is a high - level term in the biological process ontology that has a number of more granular child terms .
genes annotated to these child terms are all involved in the process of dna replication and thus are grouped into the go slim category of that name .
the go slim terms for each of the gos ( molecular function , biological process or cellular component ) are listed on separate graphs , along with the percentage of s.cerevisiae gene products ( proteins and rnas ) annotated to a specific term that maps up the ontology to that go slim term . since some gene products are annotated to go terms that map to more than one go slim term , there is some redundancy in these distributions .
lists of orfs annotated to these go terms may be accessed using the go slim mapper ( ) or the advanced search tool ( ) .
an alternative processing of the same data , with some redundancies removed , is available from the go_slim_mapping.tab file on the sgd ftp site ( ) .
the genome snapshot includes information on genomic features as well as summaries of go annotations .
the total number of biologically significant open reading frames ( orfs ) in s.cerevisiae has been the subject of debate since the genome sequence was finished , and estimates continue to change as new experimental evidence becomes available ( 25 ) . in august 2003 ,
uncharacterized and dubious , according to the degree of certainty that they actually encode proteins .
the assignment to one of these categories is based on manual review of experimental evidence and sequence conservation .
dubious orfs are not conserved in closely related saccharomyces species , and no experimental evidence currently exists that a gene product is produced .
uncharacterized orfs have orthologs in at least one other species , suggesting that they are bona fide protein - coding genes , but to date there is no experimental evidence to support this .
verified orfs are those for which experimental evidence demonstrates that a gene product is produced in s.cerevisiae .
it is important to note that these classifications are meant to provide a current best estimate of the coding capacity of the genome .
the classifications are fluid and are updated continually as new experimental results become available , during the normal process of literature curation ; it is typical for a designation to change from uncharacterized to verified as more information is published .
the color - coded pie chart at the top of the genome snapshot summarizes the current classification status of all the orfs in the yeast genome ( figure 1a ) . over the period from august 2003 through june 2005 ,
the number of dubious orfs stayed relatively constant over this time period , decreasing from 820 to 818 .
the genome inventory is in tabular form and displays several types of information for each chromosome and for the genome as a whole ( figure 1b ) . although the complete sequence for s.cerevisiae was first published in 1996 ( 6 ) ,
annotation of the genome remains an ongoing process ( 24,7 ) . in the past 5 years
, the yeast genome catalog has expanded to include 426 new protein - coding genes and 255 other non - protein - coding features ( centromeres , ars sequences , trna genes , rrna genes , etc . ) .
the genome inventory lists all types of chromosomal features currently annotated in sgd and provides a count for each type .
clicking on any feature type initiates a search that uses sgd 's advanced search tool ( ) to find all the features in sgd of that type .
information for all chromosomal features is available in the sgd_features.tab file at sgd 's ftp site ( ) .
a tabular overview summarizes the status of go annotation at sgd ( figure 2a ) .
the first column total number of annotations shows the total number of s.cerevisiae gene products ( protein and rna gene products ) currently annotated to each of the three go ontologies : biological process , molecular function and cellular component ( 1,8 ) ( see for detailed information about the go project ) .
the total number of annotations column does not include annotations to the three terms that represent lack of knowledge at this time , molecular function unknown , biological process unknown or cellular component unknown ; these numbers are reported in the number of gene products annotated as unknown column .
unknown annotation indicates that there are no published data available for that gene product , in that category .
not included in these counts , for either column , are go annotations made for orfs classified as
not physically mapped. go annotations for s.cerevisiae gene products are included in the gene_association.sgd file available at sgd 's ftp site ( ) .
this last section of the genome snapshot displays distributions , presented as bar graphs , of gene products annotated to go terms other than unknown ( figure 2b ; cellular component graph not shown ) . instead of providing the distribution based on the specific term to which the gene product was annotated , which would make the graphs quite large and difficult to interpret ,
the yeast go slim is a subset of go terms that apply to broad categories of cell processes , functions or components ( and as such are placed at a high level in their respective ontologies ) .
yeast go slim terms allow grouping of genes into categories , some of which are very general ( e.g. dna metabolism and nucleus ) and others that are tailored to yeast biology ( e.g. sporulation and bud ) . for example , dna replication is a high - level term in the biological process ontology that has a number of more granular child terms .
genes annotated to these child terms are all involved in the process of dna replication and thus are grouped into the go slim category of that name .
the go slim terms for each of the gos ( molecular function , biological process or cellular component ) are listed on separate graphs , along with the percentage of s.cerevisiae gene products ( proteins and rnas ) annotated to a specific term that maps up the ontology to that go slim term . since some gene products are annotated to go terms that map to more than one go slim term , there is some redundancy in these distributions .
lists of orfs annotated to these go terms may be accessed using the go slim mapper ( ) or the advanced search tool ( ) .
an alternative processing of the same data , with some redundancies removed , is available from the go_slim_mapping.tab file on the sgd ftp site ( ) .
the wealth of information describing the genes and proteins of s.cerevisiae has both necessitated and made possible the creation of sgd 's new genome snapshot , a constantly updated overview of the genome .
this page answers a range of questions , from the most basic how many genes in s.cerevisiae encode proteins? to more complex questions regarding which and how many genes are involved in particular cellular processes . by making accessible lists of uncharacterized orfs , it points researchers to some of the many intriguing questions that remain to be answered about the yeast genome and biological processes .
finally , genome snapshot documents the characterization of the genome , both by tracking annotation of orfs to go terms and by tracking increases in the number of verified orfs .
sgd is committed to continually expanding its resources to increase the ease of access to information about s.cerevisiae and welcomes all comments from the research community toward this end .
please send any suggestions about the genome snapshot or any other tool at sgd to : [email protected] .
verified orfs are those for which experimental evidence demonstrates that a gene product is produced in s.cerevisiae .
uncharacterized orfs have orthologs in at least one other species and are likely to encode proteins although experimental proof has not yet been published .
dubious orfs are those unlikely to encode a protein because they are not conserved in closely related saccharomyces species , and because no data exist demonstrating that a protein is produced .
( b ) the genome inventory ( ) . a total count of each feature type in the genome as well as a count of each feature type on each chromosome is displayed in this table .
( note that data for chromosomes iv through xiv are not shown in the figure . )
definitions for each feature type can be found in sgd 's glossary . clicking on any feature type
initiates a search that uses sgd 's advanced search tool ( ) to find all the features in sgd of that type .
( a ) summary of go annotations ( ) . the column , total number of annotations , refers to the total number of s.cerevisiae gene products ( protein and rna gene products ) currently annotated to one or more terms ( other than unknown ) in each of the three go ontologies : biological process , molecular function and cellular component . the number of gene products annotated to
( b ) distribution of gene products by process , function and component ( ) . shown
are percentages of gene products annotated to a specific term that maps up the ontology to a yeast go slim term .
the yeast go slim is a high - level subset of go terms that allows grouping of genes into broad categories ( see text for details ) . | sequencing and annotation of the entire saccharomyces cerevisiae genome has made it possible to gain a genome - wide perspective on yeast genes and gene products . to make this information available on an ongoing basis ,
the saccharomyces genome database ( sgd ) ( ) has created the genome snapshot ( ) .
the genome snapshot summarizes the current state of knowledge about the genes and chromosomal features of s.cerevisiae .
the information is organized into two categories : ( i ) number of each type of chromosomal feature annotated in the genome and ( ii ) number and distribution of genes annotated to gene ontology terms .
detailed lists are accessible through sgd 's advanced search tool ( ) , and all the data presented on this page are available from the sgd ftp site ( ) . |
Here Are The 2017 MacArthur 'Genius' Grant Winners
Enlarge this image toggle caption John D. and Catherine T. MacArthur Foundation John D. and Catherine T. MacArthur Foundation
It's not often you'll find these 24 names in the same place. They are historians and musicians, computer scientists and social activists, writers and architects. But whatever it may read on their business cards (if they've even got business cards), they now all have a single title in common: 2017 MacArthur Fellow.
The John D. and Catherine T. MacArthur Foundation has announced the winners of this year's fellowship — often better known as the "genius" grant — and the list includes a characteristically wide array of disciplines: There's painter Njideka Akunyili Crosby, for instance, and mathematician Emmanuel Candès and immunologist Gabriel Victora, among many others.
(Note: The foundation is among NPR's financial supporters.)
Each of the recipients has been selected for having "shown extraordinary originality and dedication in their creative pursuits and a marked capacity for self-direction" — and each will receive a $625,000 award from the foundation "as an investment in their potential," paid out over five years with no strings attached.
Jason De León, an anthropologist who studies and preserves the objects left behind by people crossing the U.S.-Mexico border, tells NPR's Kelly McEvers he's got an idea of how he's planning to use that money: "Pay off my student loans," the 40-year-old scholar laughs.
"But you know, really, we see this grant as a way to facilitate the work that we're doing even more and to push it in new directions," De León continues. "It's really exciting to think about all these projects that me and many of my collaborators have been workshopping for years now. We're going to have resources to do these things."
You can find the full list of winners below — paired with the foundation's description of their work and, where possible, links to NPR's previous coverage to get to know them better.
Njideka Akunyili Crosby, 34, painter living in Los Angeles:
"Visualizing the complexities of globalization and transnational identity in works that layer paint, photographic imagery, prints, and collage elements."
Sunil Amrith, 38, historian living in Cambridge, Mass.:
"Illustrating the role of centuries of transnational migration in the present-day social and cultural dynamics of South and Southeast Asia."
Greg Asbed, 54, human rights strategist living in Immokalee, Fla.:
"Transforming conditions for low-wage workers with a visionary model of worker-driven social responsibility."
Annie Baker, 36, playwright living in New York City:
"Mining the minutiae of how we speak, act, and relate to one another and the absurdity and tragedy that result from the limitations of language."
Performing Arts 'The Flick' Tells The Story Of The Movies, Off The Screen 'The Flick' Tells The Story Of The Movies, Off The Screen Listen · 8:01 8:01
Regina Barzilay, 46, computer scientist living in Cambridge, Mass.:
"Developing machine learning methods that enable computers to process and analyze vast amounts of human language data."
Dawoud Bey, 63, photographer and educator living in Chicago:
"Using an expansive approach to photography that creates new spaces of engagement within cultural institutions, making them more meaningful to and representative of the communities in which they are situated."
Emmanuel Candès, 47, mathematician and statistician living in Stanford, Calif.:
"Exploring the limits of signal recovery and matrix completion from incomplete data sets with implications for high-impact applications in multiple fields."
Jason De León, 40, anthropologist living in Ann Arbor, Mich.:
"Combining ethnographic, forensic, and archaeological evidence to bring to light the human consequences of immigration policy at the U.S.–Mexico border."
U.S. 'Living, Breathing Archaeology' In The Arizona Desert 'Living, Breathing Archaeology' In The Arizona Desert Listen · 6:31 6:31 U.S. Understanding Migrants Through The Things They Carried Understanding Migrants Through The Things They Carried Listen · 8:03 8:03
Rhiannon Giddens, 40, singer, instrumentalist and songwriter living in Greensboro, N.C.:
"Reclaiming African American contributions to folk and country music and bringing to light new connections between music from the past and the present."
Nikole Hannah-Jones, 41, journalist living in New York City:
"Chronicling the persistence of racial segregation in American society, particularly in education, and reshaping national conversations around education reform."
Cristina Jiménez Moreta, 33, social justice organizer living in Washington, D.C.:
"Changing public perceptions of immigrant youth and playing a critical role in shaping the debate around immigration policy."
Taylor Mac, 44, theater artist living in New York City:
"Engaging audiences as active participants in works that dramatize the power of theater as a space for building community."
Rami Nashashibi, 45, community leader living in Chicago:
"Confronting the challenges of poverty and disinvestment in urban communities through a Muslim-led civic engagement effort that bridges race, class, and religion."
Viet Thanh Nguyen, 46, fiction writer and cultural critic living in Los Angeles:
"Challenging popular depictions of the Vietnam War and exploring the myriad ways that war lives on for those it has displaced."
Kate Orff, 45, landscape architect living in New York City:
"Designing adaptive and resilient urban habitats and encouraging residents to be active stewards of the ecological systems underlying our built environment."
Trevor Paglen, 43, artist and geographer living in Berlin:
"Documenting the hidden operations of covert government projects and examining the ways that human rights are threatened in an era of mass surveillance."
Visiting A CIA 'Black Site' Visiting A CIA 'Black Site' Listen
Betsy Levy Paluck, 39, psychologist living in Princeton, N.J.:
"Unraveling how social networks and norms influence our interactions with one another and identifying interventions that can change destructive behavior."
Derek Peterson, 46, historian living in Ann Arbor, Mich.:
"Reshaping our understanding of African colonialism and nationalism in studies that foreground East African intellectual production."
Damon Rich, 42, designer and urban planner living in Newark, N.J.:
"Creating vivid and witty strategies to design and build places that are more democratic and accountable to their residents."
Stefan Savage, 48, computer scientist living in La Jolla, Calif.:
"Identifying and addressing the technological, economic, and social vulnerabilities underlying internet security challenges and cybercrime."
Technology Study May Shed Light On How To Stop Spam Study May Shed Light On How To Stop Spam Listen · 4:03 4:03
Yuval Sharon, 37, opera director and producer living in Los Angeles:
"Expanding how opera is performed and experienced through immersive, multisensory, and mobile productions that are infusing a new vitality into the genre."
Tyshawn Sorey, 37, composer and musician living in Middletown, Conn.:
"Assimilating and transforming ideas from a broad spectrum of musical idioms and defying distinctions between genres, composition, and improvisation in a singular expression of contemporary music."
Gabriel Victora, 40, immunologist living in New York City:
"Investigating acquired, or adaptive, immunity and the mechanisms by which organisms' antibody-based responses to infection are fine-tuned."
Jesmyn Ward, 40, fiction writer living in DeLisle, Miss.:
"Exploring the enduring bonds of community and familial love among poor African Americans of the rural South against a landscape of circumscribed possibilities and lost potential." ||||| In this Sept. 21, 2017 photo provided by the John D. and Catherine T. MacArthur Foundation, Cristina Jimenez Moreta poses in New York City. Moreta, co-founder and executive director of United We Dream,... (Associated Press)
In this Sept. 21, 2017 photo provided by the John D. and Catherine T. MacArthur Foundation, Cristina Jimenez Moreta poses in New York City. Moreta, co-founder and executive director of United We Dream, a national network of groups led by immigrant youth was named Wednesday, Oct. 11, 2017, as one of... (Associated Press)
CHICAGO (AP) — A director who has taken opera from the concert hall to the streets of Los Angeles and an organizer who helped put a human face on the plight of young undocumented immigrants are among this year's MacArthur fellows and recipients of the so-called "genius" grants.
The Chicago-based John D. and Catherine T. MacArthur Foundation on Wednesday announced the 24 fellows, who each receive $625,000 over five years to spend any way they choose. The recipients work in a variety of fields, from computer science to theater, immunology and photography.
The foundation has awarded the fellowships annually since 1981 to people who show "exceptional creativity in their work and the prospect for still more in the future." Previous winners have included "Hamilton" playwright Lin-Manuel Miranda, and author-journalist Ta-Nehisi Coates. There is no application process. Instead, an anonymous pool of nominators brings potential fellows to the foundation's attention. Those selected learn they've been chosen shortly before the awards are announced.
For opera director and producer Yuval Sharon the news that he had been selected was "an enormous shock and honor." When the foundation called, he assumed they were seeking a referral for someone else who'd been nominated.
"I'm totally amazed," said Sharon, 37, the founder and artistic director of The Industry, a Los Angeles-based production company that produces operas in nontraditional spaces and formats. A 2015 production transported audience members and performers to various locations in Los Angeles via limousines, with singers and musicians performing along the way and at each stop.
His next work, an adaptation of the radio program "War of the Worlds" will utilize decommissioned World War II sirens to broadcast the performance occurring inside the theater onto the streets. The sounds of performers stationed outdoors — and likely the traffic and other street noise — will then be transmitted back into the concert hall.
Sharon said he comes across many people who don't think opera is for them, but he hopes hearing about these kinds of "audacious experiments" will peak their interest.
Another fellow, Cristina Jiménez Moreta, is co-founder and executive director of United We Dream, a national network of groups led by immigrant youth.
Moreta, 33, and her parents came to the U.S. illegally from Ecuador when she was a child. At 19, she revealed her undocumented status publicly. It was a move that put her and her family at risk of deportation, but also placed her at the forefront of a movement to change the way immigrants are perceived.
She was instrumental in pressing for the 2012 adoption of Deferred Action for Childhood Arrivals, the now-endangered executive order that allowed thousands of undocumented young people to live without fear of deportation.
Moreta said the fellowship is recognition of the resilience shown by her parents and other immigrants who "had the courage to stand up and say 'we are here, this is our home and we are fighting.'"
The first people she told were her parents, who were fearful when she started organizing but now join her in marches and to pass petitions.
"They're very proud," she said.
Also selected was Deyoud Bey, a photographer and educator from Chicago whose portraits often feature people from marginalized communities. For "The Birmingham Project," he commemorated the 1963 bombing at a church in Birmingham, Alabama, that killed six children, with a series of portraits of Birmingham residents who were the age of each of the children killed and the age they would be if they had lived.
Others announced Wednesday were writer and cultural critic Viet Thanh Nguyen — whose novel, "The Sympathizer," about a communist double agent, won the 2016 Pulitzer Prize for fiction — and Derek Peterson, a historian of East Africa and professor at the University of Michigan.
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Online: www.macfound.org
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This story has been corrected to show 24 recipients of MacArthur grants, not 23. | – A director who has taken opera from the concert hall to the streets of Los Angeles and an organizer who helped put a human face on the plight of young undocumented immigrants are among this year's MacArthur fellows and recipients of the so-called "genius" grants. The Chicago-based John D. and Catherine T. MacArthur Foundation on Wednesday announced the 24 fellows, people who show "exceptional creativity in their work and the prospect for still more in the future." They each receive $625,000 over five years to spend any way they choose. The recipients work in a variety of fields, from computer science to theater, immunology, and photography (see the full list here). The AP reports previous winners have included Hamilton playwright Lin-Manuel Miranda, and author-journalist Ta-Nehisi Coates. There is no application process. Instead, an anonymous pool of nominators brings potential fellows to the foundation's attention. For opera director and producer Yuval Sharon the news that he had been selected was "an enormous shock and honor." When the foundation called, the 37-year-old assumed they were seeking a referral for someone else who'd been nominated. His next work, an adaptation of the radio program "War of the Worlds" will utilize decommissioned World War II sirens to broadcast the performance occurring inside the theater onto the streets. The sounds of performers stationed outdoors—and likely the traffic and other street noise—will then be transmitted back into the concert hall. As for what anthropologist Jason De León will do with the money, he quips to NPR, "Pay off my student loans." |
galactic nuclei with massive black holes ( mbhs ) are stellar systems with relaxation times that are often shorter than the age of the universe . in that case
the distribution function ( df ) of the system may approach a steady state .
this steady state is determined by the boundary conditions ( an inner sink , such as the tidal radius of the mbh , and an outer source at the interface with the host galaxy ) and by the mutual interactions between the stars themselves .
the nature of the `` microscopic '' interactions between the stars determines the rate at which the system relaxes to its steady state . with the notable exception of @xmath1-body simulations ( e.g. baumgardt , makino & ebisuzaki @xcite , @xcite ;
preto , merritt & spurzem @xcite ; merritt & szell @xcite ) , analyses of the evolution of the df near a mbh have almost exclusively relied on the assumption that the mechanism through which stars exchange angular momentum and energy is dominated by _ uncorrelated two - body interactions _ ( chandrasekhar @xcite ; see binney & tremaine @xcite for a more recent discussion ) .
this assumption is made in fokker - planck models ( e.g. bahcall & wolf @xcite [ hereafter bw76 ] ; bahcall & wolf @xcite [ hereafter bw77 ] ; cohn & kulsrud @xcite ; murphy , cohn & durisen @xcite ) , where the microscopic interactions are expressed by the diffusion coefficients , and in monte carlo simulations ( e.g. shapiro & marchant @xcite ; marchant & shapiro @xcite , @xcite ; freitag & benz @xcite , @xcite ) .
stars around mbhs are described as moving in the smooth average potential of the mbh and the stars , and the scattering by the fluctuating part of the potential is modeled as a hyperbolic keplerian interaction between a passing star and a test star .
the scattering effects accumulate non - coherently in a random - walk fashion .
the ( non - resonant ) relaxation time @xmath2 can be defined as the time @xmath3 it takes for the negative specific energy @xmath4 of a typical star ( hereafter `` energy '' ) to change by order unity .
this is also the time @xmath5 it takes for its specific angular momentum @xmath6 ( hereafter `` angular momentum '' ) to change by an amount of order @xmath7 , the maximal ( circular orbit ) angular momentum for that energythroughout this paper , `` angular momentum relaxation time '' means the time it takes until @xmath6 is changed by order @xmath8 , rather than by order @xmath6 .
the time - scale for changes by order @xmath9 is shorter than the angular momentum relaxation time by a factor @xmath10 . ] . in a spherical potential @xmath11/\sqrt{2{\mathcal{e}}}$ ] , where @xmath12 is the mbh mass , @xmath13 is the stellar mass and @xmath14 is the number of stars with orbital energies above @xmath15 ( more bound than @xmath15 ) .
on keplerian orbits @xmath16 , where @xmath17 is the semi - major axis .
when relaxation is dominated by uncorrelated two - body interactions , the `` non - resonant '' relaxation time @xmath18 of stars of mass @xmath13 can be written in the keplerian regime as @xmath19 where @xmath20 is the orbital period and @xmath21 is a dimensionless constant which includes the coulomb logarithm .
we assume throughout a single mass stellar population ; for numerical estimates we assume @xmath22 .
the assumption of uncorrelated two - body interactions is well - justified in many systems , such as globular clusters . however , rauch & tremaine ( @xcite , hereafter rt96 ) showed that this does not hold for motion in potentials with certain symmetries , in particular for keplerian motion in the potential of a point mass where the orbits do not precess because of the @xmath23 resonance between the radial and azimuthal frequencies .
this is to a good approximation the case for stars orbiting close , but not too close to a mbh , since wider orbits precess due to the potential of the enclosed stellar mass , while tighter orbits precess due to general relativity ( gr ) .
as long as the precession timescale @xmath24 ( the time to change the argument of the periapse @xmath25 by @xmath26 ) is much longer than the orbital period , the orbits effectively remain fixed in space over times @xmath27 and the interactions are correlated .
the orbiting stars can then be represented by one - dimensional elliptical `` wires '' whose mass density varies along the wire in proportion to the time spent there ( rt96 ) . in this picture the interaction between two stars can be described as the torque between two wires .
this results in mutual changes in _ both _ the direction and the magnitude of the angular momenta .
following rt96 , we denote such rr , which also changes the magnitude of @xmath28 _ _ , scalar rr__. the change grows coherently ( @xmath29 ) on timescales @xmath30 and non - coherently ( @xmath31 ) on longer timescales @xmath32 , where @xmath33 is the `` resonant relaxation '' ( rr ) timescale for the angular momentum ( eq .
[ e : trr ] ) . generally , @xmath34 when @xmath35 ( see eq .
[ e : trrm ] ) .
since the potential of the wires is stationary on time - scales @xmath36 , they do not exchange energy , and the energy relaxation timescale remains long , @xmath37 , even in the resonant regime .
the mechanism of rr is reminiscent of the kozai mechanism in triple stars ( kozai @xcite ) .
a more restricted type of rr occurs in any spherical potential , where the vector @xmath28 is conserved , but @xmath25 precesses . in that case
the orbital rosette can be represented by a mass disk extending between the orbital periapse and apo - apse .
the mutual torques exerted by such azimuthally symmetric disks change _ only _ the direction of @xmath28 , but not its magnitude .
this type of rr persists even in the presence of gr precession .
following rt96 , we denote such rr , which changes only the direction of @xmath28 , _
vector rr_. the significance of the distinction between scalar and vector rr is that scalar rr can deflect stars into `` loss - cone '' orbits ( @xmath38 ) where they fall into the mbh , either directly ( `` infall '' ) or gradually ( `` inspiral '' ) , whereas vector rr can only randomize the orbital orientation , but can not affect the loss rate . in this paper
we explore the consequences of rr on the stellar df and on the infall and inspiral rates .
the mechanism of rr is briefly reviewed in
[ s : rr ] . the galactic center ( gc ) model is defined and the assumptions and approximations are discussed in [ s : model ] . in [ s : dens ] we solve the fokker - planck equation in energy and analyze the effects of rr on the df ( [ ss : df ] ) and on the stellar current ( [ ss : flow ] ) . in [ s : implications ] we discuss the observational consequences of rr , such as the event rates of tidal disruption ( [ sss : tiddisr ] ) and gravitational wave ( gw ) emission ( [ sss : gw ] ) .
we discuss our results in the context of the young , non - relaxed stars in the gc ( [ ss : gc ] ) .
we discuss and summarize our results in
[ s : summary ] .
the resonant relaxation time @xmath39 is estimated by evaluating @xmath40 , the coherent change in the magnitude of the specific angular momentum up to a time @xmath24 .
the change @xmath40 is then the step size ( `` mean free path '' ) for the non - coherent growth of the angular momentum over times @xmath41 . two nearby stars with semi - major axes @xmath17
exert a mutual specific torque @xmath42 . within a distance @xmath17 from the mbh the net torque on
a test star fluctuates away from zero as @xmath43 and @xmath44 for @xmath41 the torques on a particular star - wire become random , and the change in angular momentum grows in a random walk fashion with a timescale @xmath45 , defined here as @xmath46 where @xmath47 , @xmath48 is a numerical factor of order unity , to be determined by simulations , and the last approximate equality holds in the keplerian regime .
the @xmath1-body simulations of rt96 indicate that @xmath49 for scalar rr ( [ ss : trrs ] ) and @xmath50 for vector rr ( [ ss : trrv ] ) ( see their eqs .
8 , 15 and table 4 for @xmath51 and @xmath52 ; @xmath53 ) .
we adopt these values here .
we verified these result , to within an order of unity , by carrying a few full small scale @xmath1-body simulations .
our simulations exhibited a substantial scatter in the value of @xmath48 , as already noted by rt96 .
this introduces an uncertainty in quantitative estimates of the efficiency of rr .
further detailed analysis and simulations , outside the scope of this study , are needed to refine these numerical estimates . over most of the relevant phase space ,
the precession is due to the deviations from pure keplerian motion caused by the potential of the extended stellar cluster ( `` mass precession '' ) .
this occurs on a timescale @xmath54 , which assuming @xmath55 and after averaging on @xmath6 , can be expressed as @xmath56 and where @xmath57 is a dimensionless constant . for simplicity
we adopt here @xmath58 , the value for circular orbits .
the @xmath6-averaged rr timescale can then be written as @xmath59 since @xmath60 for small @xmath17 where @xmath55 , the rr rate of angular momentum relaxation is much higher than the rate of energy relaxation in the resonant regime .
this qualitative analysis has been verified by detailed numerical @xmath1-body simulations by rt96 and by rauch & ingalls ( @xcite , hereafter ri98 ) . for most of @xmath6-space ,
orbital precession is dominated by the mass of the stellar cluster and the rr relaxation timescale is well approximated by @xmath61 , which is a function of energy only .
however , when the orbital periapse is very close to the mbh , precession is dominated by gr effects ( `` gr precession '' ) .
this is important for our analysis of the inspiral rate of gw sources ( [ sss : gw ] ) . in this case
the timescale for precession is given by @xmath62 , which is a strong function of @xmath6 , @xmath63 where @xmath64 is the angular momentum of the last stable orbit ( lso ) for an orbit of specific kinetic energy @xmath65 .
generally , both precession mechanisms operate , and the scalar rr timescale @xmath66 is given by substituting @xmath67 in eq .
( [ e : trr ] ) , where the opposite signs reflect the fact that mass precession is retrograde whereas gr precession is prograde .
thus , the scalar rr timescale is@xmath68 when @xmath69 and gr precession dominates , the rr timescale is ( eq . [ e : trrm ] ) @xmath70 the fact that scalar rr becomes much less efficient due to gr precession is crucial for the viability of gw emission from inspiraling stellar objects ( `` extreme mass - ratio inspiral sources '' , emris ) , since it allows compact remnants to be very rapidly deflected to strongly relativistic orbits , but then stall `` on the brink '' and instead of falling directly into the mbh , inspiral into it gradually by the emission of gw .
we return to this issue in [ sss : gw ] .
we analyze below the dynamics of scalar rr and its effects on the stellar df , both numerically ( [ s : dens ] ) and by monte - carlo simulations ( [ s : implications ] ) .
these two approaches require different formulations of the rr timescale .
the numerical analysis is carried out in the 1d @xmath15-space , where the @xmath6-dependences are absorbed in the @xmath6-averaged terms .
for this purpose we use the relation @xmath71 ( eqs . [
e : trrs ] ) to define the @xmath6-averaged time it takes a star to random - walk from @xmath72 to the loss - cone @xmath73 as @xmath74 since at low energies @xmath75 , it initially decreases with @xmath15 toward the mbh .
however , at very large energies near the mbh , where gr precession becomes important ( @xmath76 ) , @xmath77 increases again ( fig .
[ f : gc ] ) .
the monte carlo simulations are carried out in 2d ( @xmath15,@xmath6)-space .
for this purpose we define a general expression for the scalar angular momentum relaxation time , @xmath78 , which applies in any regime ( eqs .
[ e : tr ] , [ e : trr ] , [ e : trrs ] ; see also footnote [ ft : tj ] ) .
@xmath79^{-1}\,.\label{e : tj}\ ] ] vector rr grows coherently ( @xmath80 ) on timescales @xmath81 , where @xmath82 is the timescale for a change of order unity in the total gravitational potential @xmath83 caused by the changes in the stellar potential @xmath84 due to the realignment of the stars as they rotate by @xmath26 on their orbits,@xmath85 where @xmath86 is a dimensionless constant of order unity , and where the last approximate equality holds for @xmath87 . for simplicity
we adopt here @xmath88 . in analogy to scalar rr ( eq .
[ e : jw ] ) , the maximal coherent change in @xmath28 is @xmath89 that is , @xmath28 rotates by an angle @xmath90 already during the coherent phase .
on timescales @xmath91 , @xmath92 can not grow larger , as it already reached its maximal possible value , but the orbital inclination angle is continuously randomized non - coherently ( @xmath93 ) on the vector rr timescale ( eq . [ e : trr ] ) , @xmath94 where the last approximate equality holds for @xmath87 . note
that while the torques driving scalar and vector rr are the same , vector rr is much more efficient than scalar rr , @xmath95 , due to the much longer coherence time @xmath96 . furthermore , vector rr proceeds irrespective of any precession mechanisms that limit the efficiency of scalar rr .
in this section we state our assumptions , approximations and definitions , many of which are commonly used in the analysis of stellar systems with mbhs .
since the gc is the best studied case of a stellar cluster with a mbh , and since it is representative of typical _ lisa _ targets , we scale the parameters to values appropriate for this system .
our goal is to find the stellar df in presence of rr . a full solution in ( @xmath97)-space is complex and is not attempted here . for simplicity , the analysis carried out here is in @xmath15-space only and it assumes an underlying spherical symmetry .
the @xmath6-dependent loss - cone terms are approximated by their @xmath6-averaged effective terms , which are functions of @xmath15 only .
recent observations show that a tight empirical relation exists between the mass of mbhs , @xmath12 , and the velocity dispersion @xmath98 of their host bulge or galaxy ( ferrarese & merritt @xcite ; gebhardt et al .
@xcite ) , @xmath99 where @xmath98 is measured at the galaxy s effective radius ( tremaine et al .
@xcite ) . both the exponent and the pre - factor have small uncertainties , which we ignore here .
the galaxy obeys the @xmath12-@xmath98 relation , with @xmath100 , and @xmath101 ( tremaine et al .
@xcite ) . the mbh dominates the dynamics of stars within its `` bondi radius '' , or radius of influence , @xmath102 where in the last step we used the @xmath12-@xmath98 relation . within @xmath103
the system is approximately keplerian , and deviations from keplerian motion become important only for times @xmath104 , where @xmath105 is the orbital period and the energy is @xmath106 .
we assume a single mass population with an underlying spherically symmetric df , so that @xmath107 ( stars per phase space volume @xmath108 ) .
following bw76 we assume that for @xmath109 the df is maxwellian , @xmath110 where @xmath111 is the number density at @xmath103 in the gc assuming a mean mass of @xmath112 ( genzel et al .
@xcite ) and where @xmath113 is the 1d velocity dispersion at @xmath103 . for keplerian orbits ,
the density @xmath114 ( stars per @xmath115 ) is @xmath116 the density @xmath117 ( stars per @xmath118 ) is @xmath119 and the density @xmath120 ( stars per @xmath121 ) is @xmath122 two stellar components contribute to the local stellar density at radius @xmath123 .
one is the tightly bound stars with energy @xmath124 , or @xmath125 .
the other is the unbound , or marginally bound stars with energy @xmath126 ( or @xmath127 ) and high eccentricities , which spend only a small fraction of their orbit inside @xmath123 .
when unbound stars dominate the local population , for example because rr or stellar collisions have destroyed most of the tightly bound stars there , the density profile is given by @xmath128 we express the local relaxation time , which generally depends on the nature of the relaxation process and on radius , in terms of a reference time @xmath129 , which we define as the nr relaxation time at @xmath103 , @xmath130 where the last equality assumed the @xmath12-@xmath98 relation and the stellar density in the gc .
the coulomb factor is @xmath131 ( bw76 ) , where @xmath132 is the maximal impact parameter for perturbations by stars interior to @xmath123 , and @xmath133 is the minimal impact parameter for small deflections , @xmath134 .
the local nr relaxation time may be quite different from @xmath129 when the density distribution of the system strongly deviates from the steady state configuration @xmath135 ( [ ss : df ] ) . at high enough energy
the df vanishes , @xmath136 , because stellar objects can not survive close to the mbh .
the value of @xmath137 depends on the process that destroys the stars .
if they are compact objects , they fall directly into the mbh or inspiral into it by gw emission . if they are main sequence stars , they are destroyed by disruptive stellar collisions in the high density cusp around the mbh , or are tidally captured and heated until disruption , or are tidally disrupted when their orbital periapse @xmath138 falls below the tidal disruption radius , @xmath139 .
stars are destroyed by the mbh either by scattering or decaying in @xmath15-space to the point where @xmath140 , or by scattering in @xmath6-space to the point where @xmath141 ( or @xmath142 ) . scattering in @xmath6-space
is by far more efficient ( frank & rees @xcite ; lightman and shapiro @xcite ; see footnote [ ft : tj ] ) , and the tidal disruption rate is dominated by stars on low-@xmath15 and low-@xmath6 orbits .
stars enter the loss - cone , defined by @xmath143 , in two regimes of phase - space , depending on their orbital energy , which determines the ratio between the angular momentum change per orbit , @xmath144 , and @xmath145 . for small energies ( long periods ) ,
@xmath146 . in this `` full loss - cone ''
( or `` kick '' ) regime , the df remains essentially unmodified by the existence of a loss - cone . for high energies ( short periods ) near the mbh , @xmath147 .
in this `` empty loss - cone '' ( or `` diffusive '' ) regime stars slowly diffuse into the loss - cone and are then promptly destroyed on a dynamical time , and the df is modified by the existence of the loss - cone .
the stellar density vanishes inside the loss - cone , @xmath148 , and gradually falls to zero toward it , @xmath149 for @xmath150 ( lightman & shapiro @xcite ) .
this also modifies somewhat the df in @xmath15-space .
note that scalar rr is typically efficient only deep in the empty loss - cone regime , where mass precession is negligible .
there is a critical energy where @xmath151 , that demarcates the transition between the empty and full loss - cone regimes .
the size of the loss - cone , and therefore the critical energy , depends on the nature of the loss - process .
the critical energy for prompt stellar disruption @xmath152 , corresponds to a distance scale of @xmath153 where @xmath154 ( eq . [ e : rh ] ) .
most of the contribution to the stellar destruction rate is from stars with @xmath155 .
similarly , there is a critical energy for stellar destruction by gw inspiral , @xmath156 .
gw inspiral takes much longer than direct disruption .
unless the star starts out on a short - period ( high-@xmath15 ) orbit , it will be scattered again directly into the mbh , or to a high-@xmath6 orbit where gw dissipation is negligible .
thus , @xmath157 ( alexander & hopman @xcite ) . we adopt below for numerical calculations the values of the critical energies in the gc , where for consistency with our assumed single mass population , we consider only prompt disruption and gw inspiral at the last stable orbit , @xmath158 . in the gc ,
the semi - major axes corresponding to these critical energies are @xmath159 and @xmath160 ( see fig .
[ f : sa ] ) .
thus , our model describes a population of compact objects , and our predicted prompt disruption rates will be slightly lower than the actual tidal disruption rates , which occur at the somewhat larger @xmath161 and thus have a lower critical energy , closer to @xmath162 .
a complete treatment of the loss - cone problem involves the solution of the fokker - planck equation in @xmath163-space ( cohn & kulsrud @xcite ) .
however , an approximate solution can be obtained by solving the fokker - planck equation in @xmath15-space only , while accounting for the loss - cone by adding sink terms to the equation ( bw77 ) .
this is the approach we adopt here
. the tidal disruption rate due to nr relaxation has been discussed extensively in the literature ( see e.g. lightman and shapiro @xcite ; frank & rees @xcite ; cohn & kulsrud @xcite ; syer & ulmer @xcite ; magorrian & tremaine @xcite ; alexander & hopman @xcite ; merritt & poon @xcite ; wang & merritt @xcite ; hopman & alexander @xcite ; baumgardt et al .
@xcite ) . the differential nr loss - cone diffusion rate ( stars per @xmath164 ) is estimated to be of the order @xmath165 neglecting here the weak logarithmic @xmath6-dependence that expresses the depletion of phase space near the loss - cone .
when rr is the dominant relaxation process , then for timescales @xmath166 the differential loss - cone refilling rate is ) differs from the corresponding term in rt96 , which applies only for timescales @xmath36 , and an isotropic df .
the rate predicted by eq .
( [ e : rrlc ] ) is in good agreement with the values obtained by the @xmath1-body simulations of ri98 . ]
@xmath167 note that vector rr does not enter into the fokker planck equation and does not play a role in the diffusion in @xmath15-space since the system is assumed to be spherically symmetric , and vector rr does not change @xmath6 .
following bw76 , we define the dimensionless quantities @xmath168 and write the fokker - planck equation ) is written in the form of a particle conservation relation , which , as shown by bw76 , is equivalent to the usual fokker - planck form @xmath169 , where @xmath170 and @xmath171 are the diffusion coefficients . ] as @xmath172 where the current @xmath173 , defined to be the net rate at which stars flow to energies @xmath174 , is given by ( bw76)@xmath175\times\nonumber \\ & \times & \left\ { \max(x , y)\right\ } ^{-3/2}.\end{aligned}\ ] ] the sink terms @xmath176 and @xmath177 represent the @xmath6-averaged differential loss rate of stars per energy interval , by nr and rr respectively , due the existence of a loss - cone in @xmath6-space .
this is an approximate substitute for the full @xmath178 treatment .
the nr sink term @xmath179 is expressed by the form ( eq . [ e : nrbw ] in appendix b ) proposed by bw77 , which smoothly interpolates between the empty and the full loss - cone regimes and approximates the logarithmic depletion of phase space near the loss - cone boundary ( [ ss : losscone ] ) . in the empty loss - cone regime , which is of interest here , @xmath180 this quadratic behavior arises since a fraction @xmath181 of the stars is accreted per local relaxation time , which is itself proportional to @xmath182 .
the rr sink term @xmath177 is expressed by ( eqs .
[ e : trrm ] , [ e : rrlc ] ) @xmath183 where @xmath184 is the dimensionless @xmath6-averaged rr time , defined in eq .
( [ e : tave ] ) .
the rr efficiency factor @xmath185 in eq .
( [ e : dgdt ] ) parametrizes the uncertainties in the efficiency of rr and in the approximations involved in eq .
( [ e : rrr ] ) , for example the effect of the partial depletion of phase - space outside the loss - cone ( note that the depletion is small , see ri98 fig .
[ 2a ] ) . for simplicity , we assume that @xmath185 is a constant .
we expect @xmath186 , and show below that the choice @xmath187 yields results that are consistent with those of rt96 and ri98 , but we also explore rr for a range of @xmath185 values to determine the robustness of our results .
the rr sink term becomes negligible compared to the nr sink term for lower energies , were @xmath188 ( fig .
[ f : gc ] ) .
we follow bw76 by assuming as boundary conditions @xmath189 the first boundary condition for @xmath190 expresses the assumption of a thermal reservoir at the radius where the stars are no longer bound to the mbh ( eq . [ e : mb ] ) . in reality , they are bound to the total enclosed mass of the mbh and stars , however the bw76 treatment neglects the stellar mass and assumes keplerian motion around the mbh .
the second expresses the existence of a mass - sink at energy @xmath191 . because of the large dynamical range in the problem , it is more convenient for numerical purposes to express eqs .
( [ e : dgdt]-[e : bc ] ) in logarithmic energy ( see appendix [ s : loge ] ) . here
we explore the effect of rr on the steady state df .
we begin by checking the numerical convergence of eq .
( [ e : dgdt ] ) to the bw76 solution , @xmath192 with @xmath193 for @xmath194 , which is obtained under the assumption that the @xmath15-dependent @xmath6-averaged sink terms can be neglected , @xmath195 , and that the disruption of stars by the mbh can be expressed by the boundary condition @xmath136 . figure ( [ f : bw76 ] ) confirms that the df indeed converges to this solution on a relaxation timescale , and we also verified that this holds irrespective of the initial df assumed .
rapid conversion was also confirmed by the @xmath1-body simulations of merritt & szell ( @xcite ) .
the bw76 df corresponds to a power - law density profile @xmath196 with @xmath197 ( equation [ e : nr ] ) . since @xmath198 , and @xmath199 ,
the implied _ local _ nr time is @xmath200 we now add back the nr and rr sink terms and solve the full problem . figure ( [ f : bwrr ] ) shows the results of the steady state solution of equation ( [ e : dgdt ] ) for several values of @xmath185 . the @xmath201 case ( nr only ) reproduces the solution studied by bw77 , who showed that the presence of the nr sink term does not change the power - law behavior and index of the df .
we find , as expected , that for low energies where rr is negligible , neither does the presence of the rr sink term . at higher energies , the response of the df depends on the efficiency of rr . for @xmath202
, rr is so efficient that it exponentially depletes the high energy end of the df .
however , for the likely efficiency factor @xmath187 , gr precession at high energies limits the efficiency of rr ( cf fig .
[ f : gc ] ) , and the df is not completely depleted , but continues to rise toward @xmath203 after a moderate initial drop . the solution of the fokker - planck equation determines the stellar current @xmath173 into the mbh .
this in turn determines the rates and modes of stellar capture by the mbh . since most of the contribution to prompt infall events comes from orbits with energy @xmath204 , and to gw inspiral from @xmath205 ( [ ss : losscone ] , [ s : implications ] ) , the current at these critical energies determines the prompt infall and gravitational inspiral event rates . in the gc , @xmath206 and @xmath207 ( [ ss : losscone ] ) .
the rate at which stars flow toward the mbh is given by @xmath208 where the dimensional current scale is set by @xmath209 for non - equilibrium dfs , @xmath210 , and there is a large current @xmath211 .
the `` sink - less '' bw76 solution ( [ ss : df ] ) has a steady state `` zero - current '' ( @xmath212 ) solution that is @xmath15-independent and is strongly suppressed by the bottle - neck at @xmath213 .
the presence of the loss - cone , as expressed by the nr and rr sink terms , modifies the df at high energies and shifts the effective high - energy boundary to lower energies . as a result
, @xmath214 increases well above the zero - current solution and becomes @xmath15-dependent .
figure ( [ f : flow ] ) shows the current @xmath173 for several values of the rr efficiency factor @xmath185 . the accelerated relaxation due to rr increases the current above the values induced by nr only . for @xmath187 the largest enhancement
is attained at about the critical energy for gw . when @xmath202 , rr is so efficient that the current depletes the df already at energies @xmath215 . as a consequence ,
the current drops to zero at @xmath216 , and therefore so does the gw inspiral event rate ( which is @xmath217 , see eq . [
[ e : gwj ] ] ) . figure ( [ f : rates ] ) shows separately the contributions of the nr and rr sink terms in eq .
( [ e : dgdt ] ) to the total capture rate , and demonstrates that far from the mbh ( low-@xmath15 ) , where most tidally disrupted stars originate , nr dominates the capture rate , whereas at closer distances ( high-@xmath15 ) , where gw inspiral stars originate , rr dominates the capture rate ( see also fig .
[ f : gc ] below ) .
most previous estimates of the loss rates did not take into account rr . here
we show that rr can strongly influence the gw inspiral rate , and may play an important role in determining the dynamical structures observed in the inner gc .
figure ( [ f : chi ] ) shows the change in the estimated rates of prompt infall and inspiral due to the inclusion of rr , as function of the rr efficiency parameter @xmath185 .
rr does not significantly increases the rate of prompt infall events .
this result has already been demonstrated by the @xmath1-body simulations of rt96 and ri98 , and is explained by the fact that most tidally disrupted stars originate from low-@xmath15 orbits with @xmath218 ( lightman & shapiro @xcite ; baumgardt et al .
@xcite ) , where mass precession suppresses scalar rr .
our analysis is complementary to that of rt96 and ri98 in that they took into account relaxation in @xmath6-space , but not in @xmath15-space , whereas ours explicitly solves self - consistently the df and star current in @xmath15-space , but does not deal with the flow in @xmath6-space .
our results confirm the conclusion that for the likely value of the rr efficiency factor @xmath187 , the tidal disruption rate is enhanced by rr by only a factor of @xmath219 ( figs [ f : flow ] , [ f : chi ] ) .
we note , however , that for higher values of @xmath185 , the tidal disruption rate may increase significantly .
the detection of gw emission from compact remnants inspiraling into mbhs ( emris ) , is one of the major goals of the planned space - borne _ lisa _ gw detector .
the predicted event rate per galaxy is very uncertain , as estimates vary in the range @xmath220 per galaxy ( e.g. hils & bender @xcite ; sigurdsson & rees @xcite ; ivanov @xcite ; freitag @xcite , @xcite ; hopman & alexander @xcite ) . only stars originating from tightly bound orbits with energies
@xmath221 can complete their inspiral and reach a high - frequency orbit observable by _ lisa _ , without being scattered prematurely into the mbh or to a wider orbit .
an approximate upper - limit for the semi - major axis from which inspiral is possible can be obtained by equating the inspiral time @xmath222 with @xmath223 , the nr timescale for scattering by @xmath224 , ( hopman & alexander @xcite ) , @xmath225 ( the corresponding critical energy is @xmath226 ) . there are three phases in the orbital evolution of a star that ends up as a gw source .
the first is a scattering - dominated phase in @xmath6-space , where energy losses are negligible .
this is followed by a transition phase , when @xmath227 , gw dissipation becomes significant , and the inspiral time is comparable to the scattering time .
finally , the star spirals in by gw emission so rapidly that it effectively decouples from the gravitational perturbations of the background stars .
the value of @xmath228 is determined in the second , transition phase by the interplay between angular momentum relaxation and gw dissipation .
the @xmath6-values typical of the transition phase are also those where gr - precession quenches rr , at @xmath229 ( eq .
[ e : tgr ] ) . as a result , @xmath228 is still determined by nr through eq .
( [ e : dgw ] ) _ even when rr dominates the dynamics at _ @xmath230 . to verify that rr does not significantly affect the transition phase of inspiral and the value of the critical energy , we followed the approach used by hils & bender ( @xcite ) and hopman & alexander ( @xcite ) , who performed monte carlo ( mc ) simulations of the scattering of stars in @xmath6-space .
we compare the case where @xmath231 ( as was assumed in hils & bender @xcite ; hopman & alexander @xcite ) to the case where @xmath78 includes rr ( eq . [ e : tj ] ) .
figure ( [ f : sa ] ) shows our results in terms of the inspiral fraction @xmath232 , the fraction of mc experiments that end with the star spiraling in , relative to the total , which also includes the experiments that end with the star plunging directly into the mbh without emitting a detectable gw signal ( the third possibility of diffusion to lower energies is not relevant here since only @xmath6-scattering is considered ) .
the critical semi - major axis corresponds to @xmath233 .
figure ( [ f : sa ] ) shows that rr has little effect on the value of @xmath234 , which is completely determined by nr .
furthermore , the outcome is not sensitive to the exact value of @xmath235 where rr is quenched , as is demonstrated by the fact that @xmath234 is only slightly decreased when the strength of gr precession is artificially lowered by a factor of 10 ( by increasing @xmath185 to 10 ) , which is equivalent to assuming a smaller value of @xmath235 . because @xmath232 is well approximated by a step function at @xmath234 ( or equivalently ,
@xmath236 is a step function at @xmath237 ) , the inspiral event rate per galaxy _ without rr _ can be estimated by ( hopman & alexander @xcite ) @xmath238 where @xmath239 is the population fraction of the specific gw sources under consideration ( e.g. white dwarfs ) .
figure ( [ f : chi ] ) shows that the gw inspiral event rate reaches its maximal enhancement , of about an order of magnitude , for @xmath240 and is enhanced over a wide range of values . only when @xmath202 is the rr depletion of high energy gw inspiral candidates with @xmath205 so strong ( fig .
[ f : bwrr ] ) that the gw inspiral rate falls below that predicted for nr only .
this depletion can be expressed by introducing an effective high - energy cutoff @xmath241 , such that @xmath242 for @xmath243 .
two very different situations can occur , depending on whether the critical energy @xmath156 is larger or smaller than the cutoff energy @xmath244 . if @xmath245 , the df vanishes for all energies where stars could complete their inspiral . in this case
the gw event rate is vanishingly small .
fortunately for the prospects of emri detection , it appears likely that this is _ not _ the case ( see figs . [
f : flow ] , [ f : rates ] , [ f : chi ] ) .
when @xmath246 , the gw event rate is given by @xmath247 where the last equality follows from eq .
( [ e : dgdt ] ) in steady state .
the galactic mbh is the prototypical _ lisa _ target ( the orbital frequencies around more massive mbhs are below the _ lisa _ sensitivity band ) . applying our result to the gc , we estimate that rr increases the predicted _ lisa _ event rate per galaxy by up to a factor ( fig .
[ f : flow ] ) @xmath248 over previous predictions that assumed nr only .
one caveat is that our analysis neglects the effects of mass segregation in a multi - mass population .
for example , low - mass remnants will be driven by mass segregation to a flatter density distribution , which will decrease their contribution to the inspiral event rate ( hopman & alexander @xcite , @xcite ) , and the opposite will happen for high mass objects . here
we do not consider a multi - mass population .
at a distance of @xmath249 kpc ( reid & bruthaler @xcite ) , the galactic mbh is the closest and most accessible mbh .
astrometric and radial velocity measurements of stars closely orbiting the mbh indicate that its mass is @xmath250 ( schdel et al .
@xcite ; ghez et al .
@xcite ; eisenhauer et al .
@xcite ; for a review see alexander @xcite ) .
observations of the gc provide the most detailed information available about stars close to a mbh , where the orbits are keplerian .
the galactic mbh offers , in principle , the best chances of confronting rr with observations .
we consider here the implications of rr for several observed and predicted features of the gc : the young coherent star disks , the central randomized cluster and the relaxed old giants ; the orbital parameters of the innermost stars ; the stellar density distribution ; and the hypothesized dense stellar cluster of stellar black holes ( sbhs ) .
figure ( [ f : gc ] ) compares the distance scales and the ages or lifespans of the various dynamical structures and components in the inner pc of the gc with the relaxation timescales .
the nr timescale in the gc , which is roughly independent of radius , is @xmath251 ( eq . [ e : tr ] ) .
the scalar rr relaxation time @xmath252 is shown for @xmath253 , or , equivalently , for @xmath254 with @xmath187 . at large radii
the rr time decreases towards the center , but for small radii , where gr precession becomes significant , it increases again ( see [ s : rr ] )
. the vector rr timescale @xmath255 , in contrast , decreases unquenched with decreasing radius .
structures whose estimated age exceeds these relaxation timescales must be relaxed .
structures whose lifespan exceeds the relaxation timescales may be affected , unless we are observing them at an atypical time soon after they were created . as is further discussed below , rr
can naturally explain some of the systematic differences between the various dynamical components in the gc .
the observed deviations from spherical symmetry of the potential in the gc do not affect rr .
as an example , one may consider a ring of mass @xmath256 and radius @xmath123 .
such a perturbation to the potential would change orbits with semi - major axis @xmath17 on the kozai time ( kozai @xcite ) @xmath257 , which is larger than @xmath258 by a factor of order @xmath259 .
this implies that only if the mass of the ring is comparable to the enclosed mass , such a perturbation to sphericity will be important .
this is not the case in the gc .
for example , the heaviest young stellar disk has a mass @xmath260 ( nayakshin et al .
@xcite ) , giving @xmath261 for @xmath262 .
two distinct young stellar populations in the gc may be of particular relevance for testing rr . at distances of @xmath263@xmath264 pc from the mbh
there are about @xmath265 young massive ob stars ( @xmath266 , lifespan of @xmath267 myr ) , which are distributed in two nearly perpendicular , tangentially rotating disks ( levin & belobodorov @xcite ; genzel et al .
@xcite ; paumard et al .
it appears that these stars were formed by the fragmentation of gas disks ( levin & belobodorov @xcite ; levin @xcite ; nayakshin & cuadra @xcite ; nayakshin & sunyaev @xcite ; nayakshin @xcite ) .
this young population co - exists with a relaxed population of long - lived evolved giants ( @xmath268 , @xmath269 ; genzel , hollenbach & townes @xcite ) . inside the inner @xmath270 the population changes .
there is no evidence for old stars , and the young stars there ( the `` s - stars '' ) are main - sequence b - stars ( @xmath271 , lifespans of @xmath272 yr ; ghez et al .
@xcite ; eisenhauer et al .
@xcite ) on randomly oriented orbits with a random ( thermal ) @xmath6-distribution .
the orbital solutions obtained for a few of the s - stars indicate that they are tightly bound to the mbh ( ghez et al .
@xcite ; eisenhauer et al .
@xcite ) . there is to date no satisfactory explanation for the presence of the s - stars so close to the mbh ( see alexander @xcite for a review ) .
one possibility is that they originated far from the mbh and were captured near it by dynamical exchange interactions ( gould & quillen @xcite ; alexander & livio @xcite ) . in that case
only their lifespan can be confidently determined , but not their actual age .
another possibility is that they also originated in the star disks . in that case
their age is the same as that of the disks and is much shorter than their lifespan .
the existence of coherent dynamical structures in the gc constrains the relaxation processes on these distance scales , since the relaxation timescales must be longer than the structure age @xmath273 to avoid randomizing it .
figure ( [ f : gc ] ) shows that the observed systematic trends in the spatial distribution , age and state of relaxation of the different stellar components of the gc are consistent , and perhaps even caused by rr .
the star disks are young enough to retain their structure up to their inner edge at @xmath270 , where @xmath274 and vector rr can randomize the disk .
it is tempting to explain the s - stars as originally being the inner part of the disk .
however , rr alone can not explain why the s - stars are systematically less massive than the disk stars .
regardless of their origin , their random orbits are consistent with the effect of rr .
vector rr can also explain why the evolved red giants beyond @xmath275 , in particular the more massive ones with @xmath276 are relaxed , since @xmath277 out to @xmath278 pc .
note that scalar rr is in itself not efficient enough to drain the s - stars , but it can play a role in their non - zero eccentricities ( see also levin @xcite ) .
rapid rr changes the orbital eccentricities . on the timescales
relevant for observations ( @xmath279 eq . [ e : tprec ] ) , the change grows linearly and could be detected , in principle , by precision astrometry .
however , the effect is small . in the linear regime
the shortest time - scale for changes in @xmath6 is determined by scalar rr .
the fractional change per orbit is @xmath280 ( eq . [ e : jw ] ) , which corresponds to a change in eccentricity of @xmath281 . for the best measured orbit ( the star s2 with @xmath282 .
eisenhauer et al .
@xcite ) the predicted change per orbit is @xmath283 ( assuming @xmath284 , @xmath285 and @xmath286 ) .
this is beyond the current astrometric precision .
figure ( [ f : ngc ] ) shows the density distribution @xmath117 ( eqs . [ e : nr ] , [ e : nru ] ) and the distribution of semi - major axis @xmath287 ( eq .
[ e : na ] ) for a model of the gc with different values of @xmath185 .
the central depletion in the distribution of the semi - major axis ( or equivalently , energy ) does not appear in the space density profile , because unbound and weakly bound stars on eccentric orbits spend a fraction of their orbit in the center .
the effect of rr on the density distribution only appears as a gradual flattening of the cusp slope to @xmath288 ( eq .
[ e : nru ] ) .
the effect on the observed projected surface density distribution will be even less noticeable .
rr is predicted to flatten the density distribution only at @xmath289 , for @xmath187 .
farther out the distribution is virtually identical with the nr solution . since there are no observational data on the density distribution for distances @xmath290 ( schdel et al .
@xcite ) , it is presently not possible to test this aspect of rr in the gc .
however , if @xmath291 , the space density will flatten farther out , on a length - scale that may be observationally accessible . it should be emphasized that any detailed comparisons between the observed stellar distribution and models will likely be difficult ( alexander @xcite , @xcite ) .
the observed density profile in the inner @xmath292 pc falls as @xmath293 ( genzel et al .
@xcite ) , less steeply than predicted by the single mass bw76 solution .
it is highly likely that additional dynamical processes beyond the simple picture considered here are at work , such as mass segregation ( bw77 ) .
furthermore , a large fraction of this observed distribution is comprised of massive stars with lifespans shorter than either the nr or rr relaxation times ( fig .
[ f : gc ] ) ; these stars probably do not trace the relaxed population .
we note that if the power - law profile were to continue to very small radii , the smallest radius @xmath294 where a star is still statistically expected to be found , @xmath295 ( for @xmath296 ) , would be well inside radius where rr depletes the cusp . if such a yet undetected population of tightly bound stars exists , it should exhibit an exponential central suppression at @xmath297 .
it is likely that the galactic mbh is surrounded by a dynamically significant distribution of dark mass in the form of compact remnants , in particular sbhs that have sunk to the center by mass - segregation over the lifetime of the galaxy ( morris @xcite ; miralda - escud & gould @xcite ; hopman & alexander @xcite ; freitag , amaro - seoane & kalogera @xcite ) .
the existence of dark matter can be constrained by detecting orbital deviations from purely keplerian motions ( mouawad et al .
@xcite ; alexander @xcite ) .
the co - existence of a dense cluster of sbhs with the dense stellar cusp may have interesting dynamical implications ( e.g. alexander & livio @xcite ) .
efficient rr could deplete this dark mass component by rapidly draining the compact remnants into the mbh . for our assumed rr efficiency factor
@xmath187 the depletion will be significant only on scales @xmath298 ( fig .
[ f : ngc ] ) with negligible dynamical implications for the observed stars . however , if @xmath299 , the inner @xmath300 will be depleted .
future high resolution observations of stellar orbits may therefore further constrain rr .
rr may also affect the emission of gamma rays by annihilation of hypothetical dark matter ( dm ) particles near mbhs .
it was shown that gravitational scattering between dm and stars leads to a dm density profile @xmath301 ( gnedin & primack @xcite ; merritt @xcite ) .
this profile implies an annihilation rate which is proportional to @xmath302 . in presence of rr ,
the inner cut - off of the cusp @xmath303 will be large as compared to the situation discussed in the literature where rr is absent , thus somewhat decreasing the annihilation rate .
rr is a coherent relaxation process that operates when symmetries in the gravitational potential restrict the evolution of the orbits ( r96 ; ri98 ; tremaine @xcite ) . as a result
, the orbits maintain their orientation over many orbital periods , and over that time the stars exert coherent mutual torques .
these efficiently change the orbital angular momentum @xmath28 ( energy relaxation continues on the slow nr timescale ) .
rr operates only under specific conditions .
however , when these are met , it can be orders of magnitude more efficient than nr . here
we consider _ scalar rr _ , which affects both the direction and magnitude of @xmath6 , in the regime around a mbh where the orbits are keplerian ( where both mass and gr precession are negligible ) , and _ vector rr _ , which affects the direction but not the magnitude of @xmath6 , in the regime around a mbh where the potential is spherical .
scalar rr can deflect stars into the mbh , whereas vector rr can only change their orbital orientation .
in this paper we studied the effect rr has on the energy df of stars near a mbh .
we explored the consequences for the disruption and capture of stars by the mbh , in particular through inspiral by gw emission , and used our results to interpret the properties of the observed dynamical components in the gc .
the complex full 2 + 1 @xmath304 problem was reduced to an approximate 1 + 1 @xmath305 fokker - planck equation , which we solved numerically .
we also carried out monte carlo experiments to test some of our assumptions .
our results are as follows .
( 1 ) rr leads to the depletion of the high - energy end of the df ( stars tightly bound to the mbh ) , accompanied by an enhanced current of stars to high energies .
the exact extent of the depletion and the effective high - energy cutoff depend on the poorly determined efficiency of rr .
the currently available estimates of the rr efficiency factor indicate that @xmath306 .
( 2 ) we confirm the result of rt96 that for @xmath187 , the direct tidal disruption rate is only modestly enhanced by rr .
this is because scalar rr is most efficient close to the mbh where the orbits are keplerian , whereas most of the tidally disrupted stars originate farther away from the mbh . a higher rr efficiency than assumed here could substantially _ increase _ the tidal disruption rate .
( 3 ) we show , in contrast , that the gw inspiral rate is dominated by rr dynamics , and is likely increased by almost an order of magnitude relative to the rate predicted assuming nr only .
this is because stars undergoing gw inspiral originate very close to the mbh . a higher rr efficiency than assumed here could substantially _ decrease _ the gw inspiral rate by completely depleting the tightly bound stars . ( 4 )
we apply our results to the gc and show that vector rr can naturally explain the inner cutoff of the ordered star disks at @xmath263 pc and the transition to the randomized inner s - star cluster , as well as the randomized state of the old red giants in the inner @xmath278 pc .
we also show that scalar rr is consistent with the presence of the disks , as it is too slow to disrupt them .
if the s - stars were born in the disk on circular orbits , then scalar rr may explain may explain their present non - zero eccentricities .
we note that there are additional processes that could be affected by rr , which we did not study here .
stars that undergo tidal capture and subsequent tidal heating ( `` squeezars '' , alexander & morris @xcite ) also originate close to the mbh , where rr dominates the dynamics .
squeezars could be directly observed in the gc if rr substantially enhances their rates .
a similar process is the tidal capture of a binary companion by an intermediate mass black hole in a young cluster and the subsequent roche - lobe feeding that could power an ultra - luminous x - ray source ( hopman , portegies zwart & alexander @xcite ; hopman & portegies zwart @xcite ; baumgardt et al .
the role of rr in tidal capture is still unclear , as there is no rr quenching by gr precession at the tidal capture radius that can stop the star from being rapidly destroyed .
there are several limitations and uncertainties in our results that will have to be addressed by future studies .
our treatment of the problem in @xmath15-space incorporates the rr sink terms in approximate form only .
the efficiency of rr is poorly determined as it has been calibrated based on a restricted set of @xmath1-body simulations and its dependence on the parameters of the stellar system has not been investigated in full .
this uncertainty is significant , as it could potentially reverse the sign of the effect of rr on the gw inspiral rate . while the rate is increased by an order of magnitude if @xmath187 , it is completely suppressed if @xmath202 ( fig . [ f : chi ] ) .
an important omission in our treatment is the assumption of a single mass stellar population .
a multi - mass population will induce mass segregation .
this will modify the df directly ( bw77 ) , and likely also change the rr efficiency .
the stellar df also depends on processes that destroy one type of star while not affecting others , such as stellar collisions ( e.g. freitag & benz @xcite ; @xcite ) .
progress on these issues will likely require large scale numerical simulations .
the effects of rr on the df of stellar systems with mbhs have not yet been studied by @xmath1-body simulations .
the recent fully self - consistent @xmath1-body simulations of baumgardt et al .
( @xcite , @xcite ) , preto et al .
( @xcite ) and merritt & szell ( @xcite ) , indicate that such studies are almost within reach of current hardware .
such simulations are particularly important for predicting gw inspiral rates , as these depend on a combination of complex mechanisms , including mass - segregation and rr , which are hard to assess with ( semi- ) analytical methods ( e.g. baumgardt et al .
our analysis shows that it may be of considerable importance to use a relativistic potential in such simulations ( see e.g. rauch @xcite ) , since otherwise it is unclear whether rr is quenched , and a large number of stars may fall directly into the mbh without emitting an observable gw signal .
yet larger - scale modeling will require abandoning the exact @xmath1-body approach in favor of approximate methods such as monte carlo simulations with rr ( freitag & benz @xcite , @xcite ) or numerical 2 + 1 fokker - planck models .
we note that throughout we assumed a spherically symmetric df
. deviations from spherical symmetry may affect both rr and the loss - cone structure in phase - space ( see e.g. magorrian & tremaine [ @xcite ] , who discuss the possibility of a loss wedge in case of a triaxial df ) .
typically this enhances the event rates .
finally , we note that the observed dynamics of the gc provide a promising empirical basis for calibrating and cross - checking theoretical and numerical studies of rr .
because of the large ratio of the tidal radius and the radius of influence , the natural way to integrate the fokker - planck equation is to divide the energy range into equal logarithmic intervals . for convenience
we give here the equations in terms of the logarithmic distance variable @xmath307 .
the fokker - planck equation ( [ e : dgdt ] ) without sink terms is then written as @xmath308 where @xmath309 with@xmath310 the logarithmic expressions for the sink terms can be included directly from eq .
( [ e : dgdt ] ) by replacing @xmath311 . written this way , the numerical integration is simple and can be easily done over many orders of magnitude in energy .
for convenience we reproduce here eq . (
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shapiro , s.l . , &
marchant , a.b . , 1979 ,
apj , 225 , 603 sigurdsson , s. , and rees , m. j. , 1997 , 284 , 318 syer , d. , ulmer , a. , 1999 , mnras , 306 , 35 tremaine , s. , et al . , 2002 , , 574 , 740 tremaine , s. , apj , 625 , 143 wang , j. , merritt , d. , 2004 , apj , 600 , 149 | resonant relaxation ( rr ) of orbital angular momenta occurs near massive black holes ( mbhs ) where the potential is spherical and stellar orbits are nearly keplerian and so do not precess significantly .
the resulting _ coherent _ torques efficiently change the magnitude of the angular momenta and rotate the orbital inclination in all directions . as a result ,
many of the tightly bound stars very near the mbh are rapidly destroyed by falling into the mbh on low - angular momentum orbits , while the orbits of the remaining stars are efficiently randomized .
we solve numerically the fokker - planck equation in energy for the steady state distribution of a single mass population with a rr sink term .
we find that the steady state current of stars , which sustains the accelerated drainage close to the mbh , can be @xmath0 larger than that due to _ non - coherent _
2-body relaxation alone .
rr mostly affects tightly bound stars , and so it increases only moderately the total tidal disruption rate , which is dominated by stars originating from less bound orbits farther away . we show that the event rate of gravitational wave ( gw ) emission from inspiraling stars , originating much closer to the mbh , is dominated by rr dynamics .
the gw event rate depends on the uncertain efficiency of rr .
the efficiency indicated by the few available simulations implies rates @xmath0 times higher than those predicted by 2-body relaxation , which would improve the prospects of detecting such events by future gw detectors , such as _ lisa .
_ however , a higher , but still plausible rr efficiency can lead to the drainage of all tightly bound stars and strong suppression of gw events from inspiraling stars .
we apply our results to the galactic mbh , and show that the observed dynamical properties of stars there are consistent with rr . |
non - hodgkin lymphoma ( nhl ) consists of a heterogeneous group of malignancies with varied clinical presentation and biological behaviors .
the estimated number of new cases in 2014 is 70 000 , which represents 4% of all cancers diagnosed and 3% of cancer deaths in the united states .
the histological subtypes of nhl are typically classified as indolent and aggressive histologies . although nhl is predominantly managed with chemotherapy , radiation therapy is used as definitive treatment among patients with early - stage indolent lymphoma and natural killer ( nk ) t - cell lymphoma .
radiation therapy is also used as consolidative treatment in patients with early - stage and bulky aggressive histologies following chemotherapy . despite growing evidence of the benefit of radiation therapy for patients with nhl ,
concerns regarding radiation - associated late toxicities persist and , consequently , radiation therapy is omitted in the management strategy of many patients for whom it may be of benefit . in an effort to reduce radiation - related toxicity ,
these include reducing the dose of radiation in both definitive and consolidative radiotherapy , smaller field sizes and using modern radiotherapy techniques , such as intensity - modulated radiation therapy .
there are several studies examining the dosimetric benefits of proton therapy in patients with hodgkin lymphoma ( hl ) [ 68 ] ; however , there are limited published data reporting outcomes of patients with nhl treated with proton therapy .
the present study evaluated the disease control , toxicities and radiation dose delivered to various organs at risk ( oars ) using proton therapy either definitively or in combination with chemotherapy among a cohort of consecutively treated patients with nhl .
between january 2008 and january 2014 , 11 patients with nhl were treated with definitive ( n = 6 ) or consolidative radiation therapy ( n = 5 ) .
all patients were treated on an institutional review board - approved outcomes tracking protocol with proton therapy . prospectively collected data in the charts
were extracted , including patient and disease characteristics prior to treatment , chemotherapy , proton treatment plan and acute and late side effects and disease control .
this cohort included four patients with indolent orbital lymphoma , three patients with primary mediastinal lymphoma , two patients with plasmablastic lymphoma and two patients with nk t - cell lymphoma .
malt , mucosa - associated lymphoid tissue ; dlbcl , diffuse large b - cell lymphoma ; cvad , cyclophosphamide , vincristine , doxorubicin and dexamethasone ; nk , natural killer ; r - chop , rituximab , cyclophosphamide , doxorubicin ( hydroxydaunomycin ) , vincristine and prednisolone ; c , cycles ; cr , complete response ; r - ice , rituximab , carboplatin and etoposide ; r - eshap , rituximab , etoposide , methylprednisolone , cytarabine and cisplatin ; hyper - cvad , hyperfractionated cyclophosphamide , vincristine , doxorubicin and dexamethasone ; smile , dexamethasone , methotrexate , ifosfamide , l - asparaginase and etoposide ; rbe , relative biological effectiveness ; fx , fractions ; bid , twice daily ; ned , no evidence of disease ; awd , alive with disease .
patients were simulated supine with custom immobilization devices including vaclok bags ( civco medical solutions , orange city , ia ) and aquaplast facemasks ( qfix , avondale , pa ) for those patients with disease involving the head and neck region .
all patients underwent a three - dimensional ( 3d ) computed tomography ( ct ) scan with intravenous contrast .
patients with mediastinal disease or abdominal disease underwent a 4d ct simulation to account for respiratory motion during planning .
scans were transferred to mimvista ( mim software , cleveland , oh ) , and fusions with diagnostic scans were generated .
both the pre- and post - chemotherapy staging scans were fused for patients treated with chemotherapy .
a modified involved - field treatment plan was developed for all patients , similar to the involved - site radiation therapy guidelines . in patients with indolent orbital lymphoma ,
partial orbital radiation was given , where the gross tumor volume ( gtv ) included gross disease seen on ct simulation , the clinical target volume ( ctv ) included the pre - biopsy volume as defined on the pre - biopsy ct or magnetic resonance imaging ( mri ) scan fused to the ct simulation , and the planned target volume ( ptv ) was the ctv with a 5 mm margin to account for set - up uncertainty . in patients with nk t - cell lymphoma ,
the gtv included the sites of involved disease seen on the pretreatment positron emission tomography ( pet)/ct scan fused to the ct simulation , while the ctv included a 5 mm margin within the soft tissue in addition to the entire lymph node station in which enlarged lymph nodes were found .
a ptv margin of 5 mm on the ctv was used . in patients with primary mediastinal b cell lymphoma and lymphoblastic lymphoma ,
the gtv was the residual disease seen at the time of ct simulation , while the ctv included all mediastinal , hilar and cervical lymph node stations that were involved at the time of diagnosis with expansion to account for 4d motion of the mediastinum of up to 5 mm , and the ptv was a 58 mm margin on the ctv .
target and oar volumes were transferred into eclipse ( varian medical systems , salt lake city , ut ) and 3d conformal proton plans were generated .
a smearing factor was included in the proton range compensator design to account for any intrafraction or interfraction motion perpendicular to the beam .
distal and proximal margins were calculated for each proton beam ( ctv depth mm 1.025 + 1.5 mm ) to account for ct - number - to - proton - stopping - power conversion uncertainties ( 2.5% ) . a 1.5 mm water - equivalent margin
was added to the range to account for proton beam reproducibility ( 1 mm ) , water measurement uncertainty during commissioning ( 0.3 mm ) and range compensator fabrication error ( 0.2 mm ) .
field apertures were calculated from the ptv with a block margin to account for the proton beam penumbra at the target depth , and range compensators were calculated using an 810 mm smearing margin .
the minimum target coverage parameter was ptv dose to 95% volume ( d95% ) greater than 95% .
thoracic oar dose constraints were lung volume receiving 20 gy ( v20 ) < 30% , mean lung dose < 14 gy and mean heart dose < 20 gy .
the median follow - up for all patients was 38 months , and seven of the nine living patients have more than 2 years of follow - up .
one patient with nk t - cell lymphoma had progressive disease immediately after completing radiation therapy and died .
another patient with plasmablastic lymphoma was diagnosed with a gastro- esophageal junction tumor outside the radiation field during follow - up and died 6 years following treatment .
the 3-year overall survival rate for the cohort was 91% and the 3-year local control rate was 91% .
table ii summarizes acute and late radiation - associated toxicities for the entire cohort of 11 patients .
four patients were treated with definitive proton therapy for indolent orbital lymphoma in an effort to reduce the dose to the brain .
two of these patients had mucosa - associated lymphoid tissue ( malt ) lymphoma and received 30.6 gy ( relative biological effectiveness , rbe ) in 1.8 gy fractions .
the other two patients had low - grade follicular lymphoma and received 24 gy ( rbe ) in 1.5 gy fractions .
all four patients tolerated proton therapy well , with grade 12 dermatitis ( n = 4 ) , grade 12 headache ( n = 2 ) and/or grade 1 fatigue ( n = 2 ) .
three patients later developed grade 3 cataracts in the treated eye . in these patients ,
the lens had been either entirely in the ptv ( n = 2 ) or partially in the ptv ( n = 1 ) .
one patient developed late grade 1 anhidrosis and another patient developed late grade 1 epiphoria .
three patients were treated with consolidative proton therapy for primary mediastinal b - cell lymphoma to reduce the radiation dose to the heart , lungs , esophagus and breasts .
two of these patients had a complete response to six cycles of r - chop ( rituximab , cyclophosphamide , doxorubicin , vincristine and prednisolone ) chemotherapy and one patient required second - line chemotherapy with continued pet - positive residual disease before high - dose chemotherapy with autologous stem cell transplant .
the dose of proton therapy delivered ranged from 30.6 to 41.4 gy in 1.51.8 gy fractions .
acute toxicities included grade 1 to 2 dermatitis ( n = 3 ) , grade 1 fatigue ( n = 3 ) and other grade 1 gastrointestinal ( n = 2 ) and pulmonary toxicities ( n = 2 ) . at the time of last follow - up there were no grade 2 or greater late toxicities .
this included one located in the head and neck and the other in the stomach and left adrenal gland .
the patient with the head and neck site developed a ge junction cancer out - of - field a few years following treatment and died approximately 6 years following proton therapy .
acute toxicities were grade 1 nausea ( n = 1 ) , grade 1 mucositis ( n = 1 ) and grade 2 dermatitis ( n = 1 ) . there were no grade 2 or greater late toxicities . finally , two patients received definitive proton therapy for treatment of nk t - cell lymphoma of the head and neck region in an effort to reduce the dose to the parotid glands , oral cavity and brain .
one patient had progressive disease and died 5 months later , while the other patient is a 4-year - old boy with involvement extending from the nasopharynx to hypopharynx , who is free of disease at 9 months after completing treatment .
acute toxicities were grade 12 dermatitis ( n = 2 ) , grade 2 mucositis , grade 2 laryngeal edema requiring steroids , grade 3 dysphagia ( n = 1 ) and grade 2 anorexia ( n = 1 ) .
this study is the first to report on a cohort of patients with nhl treated with proton therapy .
proton therapy led to local control rates similar to what is expected with photon radiation , but was delivered with the objective of reducing the long - term side effects of radiation .
several published studies have evaluated the use of proton therapy in hl , but there are few data regarding outcomes of patients treated with proton therapy for nhl .
three studies have evaluated the dosimetric impact of using proton therapy in nhl , including studies from massachusetts general hospital ( mgh ; boston , ma ) , m. d. anderson cancer center ( mdacc ; houston , tx ) and university of florida ( uf ; jacksonville , fl ) and there is a case report from loma linda university medical center ( llumc ; loma linda , ca ) . the study from mgh included four patients with diffuse large b - cell nhl involving the mediastinum treated with proton therapy , and showed reduced cardiac , lung , spinal cord and integral doses with excellent disease control and minimal acute toxicities .
the study from mdacc discussing proton therapy in mediastinal lymphoma included two patients with nhl and showed similar results .
the uf study evaluating the dosimetric benefit of proton therapy compared with 3d conformal radiotherapy in two patients with primary mediastinal b - cell lymphoma demonstrated a clinically meaningful reduction in dose to the heart , lungs and esophagus . finally , a case report from llumc demonstrated that proton therapy can minimize the volume of normal brain tissue receiving low- to moderate - dose radiation in a patient with primary b - cell lymphoma .
these dosimetric studies provide a rationale for the use of proton therapy in the treatment of nhl to potentially reduce the risk of late radiation toxicities .
, who demonstrated a 50% reduction in secondary cancer development among patients treated at mgh with proton therapy compared with matched patients from the surveillance , epidemiology , and end results ( seer ) program registry .
all three patients with primary mediastinal b - cell lymphoma had an excellent response to consolidative proton therapy and no evidence of disease during follow - up .
patients with primary mediastinal b - cell lymphoma generally present at a young age , similar to those with hl involving the mediastinum , and would likely derive the same benefits with proton therapy as patients with hl . in a prospective study , hoppe et al
. demonstrated significant and clinically meaningful dose reduction with proton therapy when compared with 3d and intensity - modulated radiation therapy .
these patients with nhl represent an important cohort who should be considered for consolidative treatment with proton therapy .
furthermore , many of these patients are being treated with dose - dense chemotherapy regimens in an effort to avoid radiation therapy and its associated toxicities .
therefore , in the few patients receiving radiation therapy as part of their treatment , proton therapy should be strongly considered . in patients with orbital lymphoma ,
local disease control outcomes were favorable and consistent with outcomes described in the literature [ 1921 ] . given that the majority of patients with indolent orbital lymphoma achieve long - term survival , it is important to minimize the potential for late treatment - associated toxicities .
the patients in this cohort had similar rates of subacute toxicities ( i.e. cataracts , anhidrosis ) to patients treated with photon therapy .
proton therapy has the advantage of sparing the dose to the pituitary , ipsilateral temporal lobe and ipsilateral hippocampal head , all of which receive low - dose radiation with similarly fractionated conventional photon therapy .
other effective strategies for treating orbital lymphoma have been investigated . in 2011 , lowry et al . published their results of 361 sites of indolent nhl randomized to 4045 gy in 2023 fractions or 24 gy in 12 fractions and 640 sites of aggressive nhl randomized to 4045 gy in 2023 fractions or 30 gy in 15 fractions .
there was no difference in overall response rate , progression - free survival or overall survival between the standard- and low - dose arms in either group .
analyzed a cohort of 20 patients with nhl with ocular adnexal involvement treated with low - dose radiation consisting of two fractions of 2 gy . at a median follow - up of 26 months ,
the treatment was well tolerated , with mild acute side effects in 30% and no late toxicities .
furthermore , patients treated with this low - dose regimen have the option of re - irradiation in the case of local - regional relapse . with conjuctival malt lymphoma ( provided
there is no disease behind the equator of the globe on high - quality orbital mri ) , patients can be treated effectively with an anterior orthovoltage field ( 250300 kv ) .
considering that very low doses for orbital lymphoma are emerging as an effective alternative , the true value of its use in patients with indolent histologies still remains to be seen .
however , more aggressive histologies of the orbit require higher doses , which would benefit from proton therapy . although this study demonstrates that proton therapy can be safely and effectively delivered to patients with nhl involving other anatomical areas , including the abdomen and head and neck region , nhl includes a broad range of anatomic disease locations and histologic subtypes , making it difficult to generalize the benefits of a particular radiation modality among all cases of nhl .
while low - grade indolent lymphoma ( predominantly malt and follicular lymphoma ) and nk t - cell lymphoma can be effectively treated with radiation therapy alone , aggressive histologies ( diffuse large b - cell lymphoma , plasmablastic and burkitt lymphoma ) require individualized chemotherapy regimens in combination with radiation therapy .
current national comprehensive cancer network ( nccn ) guidelines include photons , electrons or protons as appropriate treatment modalities for nhl , depending on clinical judgement .
although ideal , a randomized controlled trial comparing proton and photon therapy based on a primary endpoint of late toxicity is unlikely because of the numerous potential sites of disease , the long time interval between treatment delivery and manifestation of late side effects , and the shrinking role of radiation owing to persistent concerns of radiation - associated toxicities by medical oncologists .
in addition to offering lower radiation doses and involved site radiation therapy , proton therapy may allow more patients to receive the most effective and safe treatment .
the major limitations of the present study are its small sample size and the diversity of primary disease sites and histologies among patients with nhl . despite nccn endorsement for
the use of proton therapy in cases where the dose to the oars can be reduced significantly compared with photon radiation , many patients evaluated at our center for proton therapy for whom the proton plans were superior to the photon plans could not obtain insurance coverage for the treatment of their nhl with protons .
these experiences illustrate the challenges that researchers face when investigating the role of proton therapy for different diseases .
the present study did not examine all possible clinical scenarios in which proton therapy may benefit patients with nhl ; the patients included in this study represent a typical cross - section of disease presentations encountered by radiation oncologists .
more long - term follow - up of all surviving patients included in this study is essential for continued monitoring of disease status and late toxicities .
longer follow - up and additional patients are needed to confirm our findings . given the variable disease locations , histologies and biologic behaviors of nhl , prospective studies evaluating proton therapy in the treatment of this disease will be complex , and likely require pooled data from multiple institutions to demonstrate adequate local control and lower rates of late toxicities .
disclosure forms provided by the authors are available with the full text of this article at www.informahealthcare.com/lal . | proton therapy ( pt ) is a highly conformal type of radiation therapy that can target the tumor while sparing dose to surrounding normal tissues .
this study reviews a single institution 's experience managing patients with non - hodgkin lymphoma ( nhl ) treated with pt .
eleven patients with nhl were treated with pt from january 2008 to january 2014 on an institutional review board - approved outcomes tracking protocol , and included patients with indolent orbital lymphoma ( n = 4 ) , primary mediastinal b - cell lymphoma ( n = 3 ) , plasmablastic lymphoma ( n = 2 ) and natural killer ( nk ) t - cell lymphoma ( n = 2 ) .
the median follow - up was 38 months .
the 2-year rate of local control was 91% , with one patient with nk t - cell lymphoma having recurrence in - field .
toxicities were limited to grade 2 at highest , during follow - up .
pt is a feasible and effective treatment for nhl .
early outcomes are favorable .
longer follow - up and more patients are needed to confirm our findings . |
Washington, DC-- Well-understood physical and chemical processes can easily explain the alleged evidence of a secret, large-scale atmospheric spraying program, commonly referred to as "chemtrails" or "covert geoengineering," concludes a new study from Carnegie Science, University of California Irvine, and the nonprofit organization Near Zero.
Some groups and individuals erroneously believe that the long-lasting condensation trails, or contrails, left behind aircraft are evidence of a secret large-scale spraying program. They call these imagined features "chemtrails." Adherents of this conspiracy theory sometimes attribute this alleged spraying to the government and sometimes to industry.
The authors of this study, including Carnegie's Ken Caldeira, conducted a survey of the world's leading atmospheric scientists, who categorically rejected the existence of a secret spraying program. The team's findings, published by Environmental Research Letters, are based on a survey of two groups of experts: atmospheric chemists who specialize in condensation trails and geochemists working on atmospheric deposition of dust and pollution.
The survey results show that 76 of the 77 participating scientists said they had not encountered evidence of a secret spraying program, and agree that the alleged evidence cited by the individuals who believe that atmospheric spraying is occurring could be explained through other factors, such as typical airplane contrail formation and poor data sampling.
The research team undertook their study in response to the large number of people who claim to believe in a secret spraying program. In a 2011 international survey, nearly 17 percent of respondents said they believed the existence of a secret large-scale atmospheric spraying program to be true or partly true. And in recent years a number of websites have arisen claiming to show evidence of widespread secret chemical spraying, which they say is linked to negative impacts on human health and the environment.
"We wanted to establish a scientific record on the topic of secret atmospheric spraying programs for the benefit of those in the public who haven't made up their minds," said Davis. "The experts we surveyed resoundingly rejected contrail photographs and test results as evidence of a large-scale atmospheric conspiracy."
The research team says they do not hope to sway those already convinced that there is a secret spraying program--as these individuals usually only reject counter-evidence as further proof of their theories--but rather to establish a source of objective science that can inform public discourse.
"Despite the persistence of erroneous theories about atmospheric chemical spraying programs, until now there were no peer-reviewed academic studies showing that what some people think are 'chemtrails' are just ordinary contrails, which are becoming more abundant as air travel expands. Also, it is possible that climate change is causing contrails to persist for longer periods than they used to." Caldeira said. "I felt it was important to definitively show what real experts in contrails and aerosols think. We might not convince die-hard believers that their beloved secret spraying program is just a paranoid fantasy, but hopefully their friends will accept the facts."
###
The Carnegie Institution for Science (carnegiescience.edu) is a private, nonprofit organization headquartered in Washington, D.C., with six research departments throughout the U.S. Since its founding in 1902, the Carnegie Institution has been a pioneering force in basic scientific research. Carnegie scientists are leaders in plant biology, developmental biology, astronomy, materials science, global ecology, and Earth and planetary science. ||||| In a first of its kind effort, a large group of top atmospheric chemists has weighed in on one of the most persistent conspiracy theories on the internet: that the U.S. government is involved in a campaign to deliberately spray chemicals from planes at high altitudes.
This "chemtrails" conspiracy theory is bunk, the experts conclude in a new study published this week in the journal Environmental Research Letters.
SEE ALSO: Lip plumper Kylie Jenner is also a chemtrails conspiracy theorist
Chemtrails is a conspiracy theory that pops up frequently in Reddit comment threads, on Twitter, dedicated chemtrails websites and Instagram photos of aircraft.
Many pilots who use Instagram have gone along with the idea, mockingly, by placing chemtrails stickers on their suitcases, and falsely labeling levers in the flight deck as chemtrail on/off switches.
Contrails from jet aircraft fill the sky over Florence, Italy. Image: Robert Alexander/Getty Images
The study, from the University of California at Irvine, the Carnegie Institution for Science and the nonprofit organization Near Zero surveyed 77 atmospheric chemists and geochemists to see if they have come across any evidence of a large-scale chemtrail spraying program.
A total of 76 out of the 77 experts said that they have not come across any such evidence that supports chemtrail theories.
These experts were also asked to examine the most common pieces of evidence cited by chemtrail proponents, such as the unusual persistence of aircraft contrails and supposedly high levels of particular chemicals found in soil samples.
The study found that such chemical analyses were flawed, and that the mainstream view on aircraft contrails is the most likely explanation for why some persist longer than others.
The mainstream scientific view on contrails is that heat and water vapor from aircraft engines produces condensation in the cold, dry upper atmosphere. Such trails, known as contrails, can be seen from the ground.
It is these trails that conspiracy theorists have focused on. To chemtrails believers, the chemicals being sprayed could be used to control the food supply, promote population control, or manipulate weather patterns. Some even think it is a scheme to either fight, or possibly create, climate change.
"A small but vocal segment of the population firmly believes that these are composed not merely of condensed water vapor but of chemicals and elements such as strontium, barium and aluminum that powerful, high-level entities have been intentionally and covertly releasing into the atmosphere for decades," a press release associated with the study states.
"They find the increased number and lingering presence of these aerial streaks suspicious and claim to have identified toxic substances in soil and water samples."
Unlikely to convince die-hard conspiracy theorists
The study's authors note that, despite the thorough debunking, they face an uphill battle when it comes to changing minds with this research.
#itsnotatheory #chemtrails #chemtrailawareness #chemtrailspraying #chemtrail A photo posted by _Anon_404_ (@_anon_44_) on Jul 3, 2016 at 2:25pm PDT
"Our goal is not to sway those already convinced that there is a secret, large-scale spraying program — who often reject counter-evidence as further proof of their theories — but rather to establish a source of objective science that can inform public discourse," the study states.
Study co-author Steven Davis, an associate professor of Earth system science at UC Irvine, said the chemtrails conspiracy theory is tied to the growth of the internet. The study also cites evidence that it is linked to growing distrust of elites and social institutions.
“The chemtrails conspiracy theory maps pretty closely to the origin and growth of the internet, where you can still find a number of websites that promote this particular brand of pseudoscience,” he said in a press release.
“Our survey found little agreement in the scientific community with claims that the government, the military, airlines and others are colluding in a widespread, nefarious program to poison the planet from the skies.”
Ken Caldeira, a co-author of the study who is a well-known climate change researcher, said this was the first peer-reviewed study "showing that what some people think are chemtrails are just ordinary contrails."
A contrail seen over Sydney, Australia. Image: Corbis via Getty Images
The growth of the conspiracy theory also parallels the expansion of the aviation sector worldwide, he said in a statement.
“Contrails are becoming more abundant as air travel expands. Also, it is possible that climate change is causing contrails to persist for longer than they used to,” Caldeira said.
Davis, of U.C. Irvine, said that despite the nearly unanimous results, the study won't be the last word on this issue.
“We don’t imagine that we’re going to sway the beliefs of hardcore adherents to the chemtrails conspiracy theory with this study," he said in a statement. "But we thought it was important to go on the record with fundamental scientific facts to refute claims that the government is deliberately spreading harmful chemicals from aircraft.” | – The government is definitely not secretly spraying chemicals from planes for nefarious purposes, according to a study whose authors admit that they are unlikely to persuade conspiracy theorists that "chemtrails" do not exist. Researchers from Carnegie Science, University of California Irvine, and the nonprofit organization Near Zero spoke to dozens of top atmospheric scientists and found that 76 out of 77 had seen no evidence whatsoever of any secret chemical spraying, Mashable reports. A 77th reported encountering high levels of atmospheric barium in a remote area with standard 'low' soil barium. according to the study, which was published in Environmental Research Letters. The researchers say the trails left by aircraft are ordinary condensation trails—contrails—though those trails may be lasting longer than they used to because of climate change, and there are more of them than there used to be because of the growth of air travel. They say they carried out the study to have something on the record to refute the "chemtrails" theories that one survey found were believed by more than 15% of Americans. "I felt it was important to definitively show what real experts in contrails and aerosols think," researcher Ken Calderia from Carnegie Science says in a press release. "We might not convince die-hard believers that their beloved secret spraying program is just a paranoid fantasy, but hopefully their friends will accept the facts." |
excess body weight , from overweight to overt obesity , is associated with adverse health outcomes . in view of the time - trends of the obesity epidemic and the related cost burden ,
the search for effective strategies for weight reduction and long - term maintenance of weight loss ( wl ) is at the top of the agenda of public health systems .
the current first - line strategy includes several treatment options and dietary interventions to be implemented together with an exercise program .
it is not infrequent to observe people following one diet after another and experiencing multiple failures which , in turn , lead to higher body weight and adverse consequences on body composition and fat distribution .
the higher the number of attempts , the more difficult the adherence to further interventions . the use of antiobesity drugs could be considered , but many of them have recently been banned . in the presence of severe ( body mass index > 40 kg / m ) or complicated obesity , bariatric surgery could be proposed .
this therapeutic option is effective but is not devoid of complications and may be irreversible .
obesity - related complications , such as diabetes , hypertension , or sleep apnea , are likely to occur more frequently with increasing body mass index ( bmi ) and rapid and considerable wl is mandatory to curtail such risks . in this scenario ,
about 40 years ago , after the introduction of protein - sparing modified fast ( psmf ) achieved through the use of oral high - protein foods or liquid formula diets by blackburn and bistrian , several studies evaluated its effectiveness and safety [ 9 , 10 ] .
they showed that responsible and supervised very low - calorie diets ( vlcds ) could be considered safe and appropriate therapy for obesity .
the purpose of the present study was to investigate the potential role of a 2-week course of enteral treatment with a very low - calorie protein - based formula in the management of severe obesity .
the rationale of this treatment option rests on the following considerations : ( 1 ) vlcds appear to be able to reduce cardiovascular risk rapidly and effectively [ 9 , 10 , 12 ] ; ( 2 ) vlcds induce considerable short- and long - term wl ; ( 3 ) optimal compliance with the intervention , as active participation of the patient , is not required ; ( 4 ) continuous administration of the intervention formula by enteral route enables the maintenance of the body amino acid pool . before being proposed for clinical use ,
accordingly , in the present study , attention was focused not only on efficacy in terms of improving the cardiometabolic risk profile but also on the feasibility and safety of the procedure .
this is an open - label interventional study in severely obese , adult out - patients .
all subjects consecutively ( from april 2010 to february 2013 ) attending the clinical nutrition unit of our institution for a wl program were screened for inclusion into the study .
patients had to fulfill the following criteria to be eligible : age 18 years , severe obesity ( body mass index ( bmi ) 40 kg / m ) , and history of multiple failures in wl programs .
exclusion criteria were age 70 years , type-2 diabetes mellitus on insulin , a psychiatric disorder , previous ( < 1 year since last chemo- or radiotherapy ) or current neoplastic disease , established vascular disease , recent history of diet - induced or unintentional wl ( within the previous 6 months ) , moderate - to - severe heart failure , arrhythmia , renal failure ( creatinine > 1.5 mg / dl ) , current hepatitis , liver cirrhosis , any type of gastrointestinal disease , moderate - severe hypoalbuminemia ( < 3.0 g / dl ) , altered serum electrolytes , established gouty and any other contraindication to enteral nutrition , and refusal to give written informed consent .
patients were prescribed a homemade very low - calorie ( ~6 kcal / kg of ideal body weight / day ) protein - based formula ( 2000 ml per day ) by enteral route for 14 days .
a polyurethane 8-french nasogastric tube was inserted on day 1 and removed at the end ( day 15 ) of the cycle .
the nutritional formula was administered continuously ( 24 hours a day ) by means of a small , light , and rechargeable peristaltic feeding pump ( flocare infinity , nutricia , italy ) equipped with phthalates and latex - free infusion line .
the enteral nutrition bag and the pump were supplied in a backpack , thus enabling patients to continue to lead a normal life , pursuing their activities of daily living as usual .
the intervention formula was made up of a fixed amount of amino acids ( arginine , ornithine - alpha - ketoglutarate , taurine , cysteine , tryptophan , hydroxyproline , and citrulline ) and a variable quantity of high - quality ( milk whey ) proteins ( nepisond ; gefaldiet service srl , italy ) in order to reach a total protein content of 1.2 g per kilogram of ideal body weight calculated by lorentz 's equations : height 100 ( height 150)/4 , for men ; height 100 ( height 150)/2.5 , for women .
other components of the formula were prolipolytic substances ( coenzyme q10 and l - carnitine ) , linseed oil ( 10 grams per day ) , policosanol , fructooligosaccharides , potassium , sodium , and magnesium chloride .
the enteral nutritional treatment was also complemented by the daily oral administration of a complete ( 100% of recommended dietary allowances ) multivitamin - multimineral supplement , alkalizing substances ( calcium carbonate , 1500 mg daily ; magnesium carbonate , 850 mg daily ; potassium bicarbonate , 500 mg daily ; sodium bicarbonate , 1500 mg daily ; potassium citrate , 500 mg daily ) , and herbal remedies commonly marketed for their diuretic , antioxidant , antidiabetic , anti - inflammatory , hepatoprotective , and detoxifying properties ( equisetum , nettle , hawthorn , silymarin , orthosiphon , and fucoxanthin ) [ 1520 ] .
all patients were also prescribed treatment with a proton pump inhibitor and ursodeoxycholic acid : 900 mg daily and 450 mg daily for those with and without documented ( by ultrasonography ) cholestatic liver disease , respectively .
patients were allowed to drink water or unsweetened drinks freely ( not tea or coffee ) during the day . a minimum intake of 2 liters daily was recommended . in patients with a history of kidney stones ,
before the course , all treatments with hypoglycemic agents and diuretics were discontinued to avoid unintended hypoglycaemia and electrolyte imbalance .
other treatments with anti - hypertensive medications and uric acid and lipid - lowering drugs were left unchanged .
finally , a bowel preparation protocol was adopted for dinner two days before the start of intervention : on day 1 , 500 ml of probiotic fermented skimmed milk + vegetable side dish seasoned with olive oil + herbal laxative syrup ; on day 2 , 500 ml of probiotic fermented skimmed milk + vegetable side dish seasoned with olive oil . during the intervention
, no use of laxatives was allowed in order to avoid potassium and bicarbonate loss .
all the subjects had height ( to the nearest 0.5 cm ) and body weight ( to the nearest 0.1 kg ) measured by the same calibrated flat scales equipped with a telescopic , vertical steel stadiometer according to standard procedures .
the bmi was derived accordingly ( weight [ kg ] and height [ m ] squared ; kg / m ) .
waist and hip circumferences ( wc and hc , resp . ) were assessed ( to the nearest 0.5 cm ) using a plastic flexible tape . placing the tape perpendicular to the long axis of the body and parallel to the floor , wc and hc
were measured at the midpoint between the lowest rib and the iliac crest and around the largest portion of the buttocks , respectively .
venous blood samples were drawn after 8 to 12 hours of fasting and the following parameters were assessed on the same day by our institutional laboratory using conventional automated analyzers and commercial kits : hemoglobin , total lymphocyte count , blood urea nitrogen ( bun ) , creatinine , uric acid , glucose , insulin , c - peptide , glycated hemoglobin , growth hormone ( gh ) , insulin - like growth factor 1 ( igf-1 ) , total cholesterol , high - density and low - density lipoprotein cholesterol ( hdl and ldl , resp . ) , triglycerides , apolipoproteins a - i and b ( apoa - i and apob , resp . ) , albumin , serum enzymes ( cholinesterase , aspartate aminotransferase ( ast ) , alanine aminotransferase ( alt ) , gamma glutamyl transferase ( -gt ) , creatine phosphokinase ( cpk ) , and lactate dehydrogenase ( ldh ) ) , and electrolytes ( sodium , potassium , magnesium , calcium , and phosphorus ) .
insulin resistance was estimated by the homeostasis model assessment of insulin resistance ( homa - ir ) .
the triglyceride / hdl cholesterol ratio and apob / apoa - i ratio were also considered [ 22 , 23 ] .
systolic and diastolic blood pressure ( sbp and dbp , resp . ) were measured by appropriately sized standard sphygmomanometers after having the patient seated for at least 5 minutes in a chair , with feet on the floor and arm supported at heart level .
the average of three measurements , obtained at 2-minute intervals , was used for the analysis .
patients were also screened for the presence of cholestatic liver disease ( overt cholelithiasis or biliary sludge ) .
data on these parameters were collected at baseline ( day 0 ; tube placement ) and at the end ( day 15 ; tube removal ) of the intervention , before any pharmacological treatment was reintroduced .
patients were also asked to check their ketosis status daily by means of urine sample spot checks .
patients were asked to report the onset of any of the following side effects daily , using a self - administered questionnaire : asthenia , headache , dizziness , fainting , orthostatic hypotension , heartburn , nausea , vomiting , palpitations , muscle cramps , hunger , and constipation .
safety was also assessed by the evaluation of changes in the following hematological and biochemical parameters and , for those presenting with normal values , by the excursion outside of the reference ranges of our laboratory ( new cases ) : hemoglobin , total lymphocyte count , bun , creatinine , uric acid , albumin , serum enzymes ( cholinesterase , ast , alt , -gt , cpk , and ldh ) , and electrolytes ( sodium , potassium , magnesium , calcium , and phosphorus ) .
it was defined by the changes ( increase ( hdl , apoa - i , and gh ) or more frequently the reduction ( all the others ) ) in the following study parameters : body weight , bmi , wc , hc , whr , uric acid , glucose , insulin , homa - ir , c - peptide , glycated hemoglobin , igf-1 , total cholesterol , hdl , ldl , triglycerides , triglyceride / hdl ratio , apob , apob / apoa - i ratio , ast , alt , and -gt .
all statistical analyses were performed using the software medcalc for windows , version 11.3.0.0 ( medcalc software , mariakerke , belgium ) .
the level of significance was set at the two - tailed p value < 0.05 .
safety parameters were analyzed in and reported for the per - protocol ( pp ) population .
however , the analysis of efficacy parameters was conducted according to the intention - to - treat ( itt ) principle .
accordingly , all patients who had been assessed at baseline were included in the itt population .
data were presented as mean and standard deviation ( sd ) or counts and percentage , as appropriate .
group comparisons were performed using fisher 's exact test ( categorical variables ) and student 's t - test or wilcoxon 's test ( continuous variables ) .
changes in study parameters were investigated by student 's t - test or wilcoxon 's test for paired data , while proportions were compared with fisher 's exact test . a set of secondary analyses
was also performed by building generalized linear regression models , including changes ( difference = final baseline ) in study parameters as alternative dependent variables and age , gender , and diabetes as independent variables .
finally , logistic regression analysis of baseline features was considered to investigate the alterations ( values below or above the lower and the upper limit of laboratory range , resp . ) in safety parameters occurring in at least 10% of patients .
in total , 364 patients ( 59% females ; bmi ( mean sd ) , 46.6 7.2
based on ideal body weight ( mean sd , 61.2 7.1 kg ) the mean ( sd ) daily protein and calorie intake were 73.4 8.6 g / day and 383 34 kcal / day , respectively .
twenty - six patients ( 7% ; 13 men and 13 women ) had to discontinue the intervention within 48 hours .
discontinuation was only due to nasogastric tube intolerance ( physical discomfort or social reasons ) .
the features of dropouts were similar to those of completers ( supplementary table 1 , available online at http://dx.doi.org/10.1155/2015/723735 ) .
finally , compliance was optimal in completers , as confirmed by the evaluation of urinary ketosis .
constipation was the most frequently reported side effect ( 8.6% and 10.9% during the first and the second week , resp . ) .
other frequent ( > 10% ) side effects reported during the first week were headache and hunger .
the same applied to other symptoms , with the exception of muscle cramps . nonetheless , prevalence was almost below 5% .
the frequency of self - reported side effects throughout the study is reported in detail in table 2 .
overall , no side effects during the first and the second week was reported by 220 ( 65% ) and 270 ( 80% ) patients , respectively . in respect to hematological and biochemical variables ( table 3 ) , looking at mean values in the whole population , all safety parameters were affected by the intervention . an increase in the following values
was observed : hemoglobin , creatinine , uric acid , albumin , ast , alt , cpk , ldh , potassium , calcium , and phosphorus .
however , also a reduction in the following was detected : total lymphocyte count , bun , cholinesterase , -gt , sodium , and magnesium .
the greatest changes were observed for uric acid ( + 45% ) , ast ( + 48% ) , and alt ( + 47% ) levels , although only a limited number of patients reported values slightly higher than two times the upper limit of normality ( uric acid , n = 3 ; ast , n = 13 ; alt , n = 34 ) . in the other cases the change was almost negligible , as most patients retained values within the normal ranges for our laboratory ( as suggested also by 95% confidence intervals of the mean difference ) .
interestingly , according to regression analysis , the most frequent ( frequency > 10% ) alterations ( increase above the upper limit of laboratory range ) in biochemical parameters ( uric acid , alt , ast , and cpk ) occurred in male subjects ( p < 0.01 for all ) .
changes in uric acid were also more likely to occur in younger patients ( p < 0.01 ) . finally ,
the increase in alt was higher in those who had normal values at baseline ( for alt : + 75% versus + 37% , p < 0.001 ) . despite similar age ( women ,
40.1 [ sd , 10.8 ] versus men , 41.1 [ sd , 10.3 ] ; p = 0.422 ) and degree of obesity , as expected , male patients were characterized by more evident abdominal adiposity and abnormalities in cardiometabolic risk profile ( blood pressure and both glucose and lipid metabolism parameters ; supplementary table 2 ) . however , the prevalence of diabetes was almost comparable between genders ( p = 0.072 ) : 18.6% and 26.8% , in women and men , respectively .
the intervention resulted in significant wl ( itt population , 5.7% [ sd , 2.3 ] ; pp population , 6.1% [ sd , 1.8 ] ; table 4 ) .
this applied to both genders ( itt population : men , 5.9% [ sd , 2.5 ] versus women , 5.5% [ sd , 2.2 ] ; p = 0.118 ; supplementary table 2 ) .
wl resulted in significant improvement in blood pressure , in all anthropometric variables and most hematological and biochemical parameters .
as expected , uric acid and apob / apoa - i ratio showed an increase , while hdl , apoa - i , and igf-1 were significantly decreased ( table 4 ) .
these findings were substantially confirmed by gender - specific analyses ( supplementary table 2 ) . in secondary efficacy analyses ( multivariable linear regression ;
table 5 ) , it was observed that the improvement in glucose control - related variables ( glucose , insulin , homa - ir , c - peptide , glycated hemoglobin , triglycerides , and triglyceride / hdl ratio ) and blood pressure ( both systolic and diastolic ) was even greater in diabetic patients . in respect to the improvement of cardiometabolic profile , we report also that the diuretic therapy was no longer deemed necessary while oral hypoglycemic agents were reintroduced at half of the initial dose .
the present study has shown that a 2-week course of psmf , achieved through the administration of a very low - calorie protein - based formula by enteral route , is a feasible , safe , and effective procedure to be taken into due consideration for a composite weight loss program for the management of severe obesity .
the effectiveness of vlcd has been reported to rest on its appetite - suppressing ketogenic nature , which mimics the anorexia of starvation , and the satiating effect associated with its high - protein content [ 9 , 10 ] .
however , compared to previous studies in which the dietary regimen was achieved by pulsatile administration of low - calorie , low - carbohydrate , high - protein foods or liquid formula , the use of the enteral nutrition technique enabled around - the - clock administration .
the main advantage of this approach is the possibility of keeping the patient in steady - state conditions , reducing the difficulties in complying with a formula - based therapeutic regimen mainly due to hunger or palatability / acceptability as much as possible . in a state of complete absence of carbohydrates , which can be achieved only with the use of a specifically designed liquid formula , ketogenesis and enteral stimulation
it could not be excluded that compliance with and acceptability of the intervention were also to be ascribed to the fact that a feeding tube is perceived as real medical therapy . moreover
, the presence of the tube may emphasize the social disruptiveness previously reported for vlcds .
however , this approach can reasonably be proposed as a short - term intervention ( 24 weeks ) . compared to the other vlc interventions that commonly provide about 1000 kcal / day for up to 12 weeks
, a psmf approach provides about 400 kcal / day . nonetheless , protein and micronutrients malnutrition
this is a relevant issue , as most prolonged low - calorie dietary interventions shift to intake associated with risk of micronutrients inadequacy . in our study ,
discontinuation of therapy was unrelated to adverse effects and was driven only by intolerance to the tube , either for physical or social reasons .
self - reported side effects were few and mainly limited to the first days of the intervention .
previous studies have reported the occurrence or intensification of emotional disturbances , such as depression and anxiety during intensive wl [ 27 , 28 ] .
patients with psychiatric disorders were excluded during the baseline assessments and these symptoms were not observed in our experience . as , in order to minimize adverse effects , it is not recommended to prescribe dietary regimens with calorie content lower than basal metabolic rate , we also investigated the safety of this experimental intervention .
with exception of serum uric acid and aminotransferases , most changes in biochemical safety parameters still fell within the normal ranges .
this appears to generally occur during the first 6 weeks , with normalization during maintenance of a lower weight .
no attack of acute gouty arthritis was observed , but an incidence of up to 1 percent of this disorder has been reported during longer vlcd programs . the increase in aminotransferases is also consistent with the intense lipolytic activity and the intense flow of fatty acids to the liver .
however , contrary to previous evidence , wl was associated with a reduction in circulating igf-1 , which is consistent with short - term starvation and the similar effect on the immune system [ 30 , 31 ] , as reflected by the subclinical reduction in lymphocyte count .
it is reasonable to argue that most of these changes are transient , without relevant clinical implications , and can be normalized by returning to a balanced oral diet .
moreover , they were of limited entity and the consequence of an intervention of limited duration .
the intervention investigated herein has also proved to be effective in reducing body weight and improving the cardiometabolic risk profile .
this was particularly evident in diabetic patients , thus supporting the efficacy of vlcds in rapidly modifying cardiovascular risk [ 9 , 12 ] .
however , it also appeared to induce a detrimental reduction in hdl and apoa - i levels and an increase in apob / apoa - i ratio , despite the significant decrease also in apob , which is secondary to the restriction of saturated fat and cholesterol .
current guidelines recommend , as initial goal , a wl of 10% from baseline , to be achieved approximately over 6 months . in the present experience of two - week psmf by enteral route we observed a mean wl of ~6% .
we could hypothesize that the repetition of 2 or 3 courses of this therapy could bring consistent benefits to the patient .
however , despite optimal compliance and acceptability during enteral nutrition , the intervention lasts only 14 days and the patient still requires constant monitoring and follow - up evaluations . the present treatment procedure , alternated with periods of closely monitored oral diet , was designed to be included in a composite dietary rehabilitation program , with the gradual introduction of a balanced mediterranean - like diet . in respect to this , an apparent advantage may be the transient postdiet hypophagia observed after switching from a ketogenic diet to ad libitum food . nonetheless , thinking about the overall management pathway of severe obesity , a potential preoperative application to reduce anesthetic risk
psmf and more extensively prolonged vlcds have raised concerns and criticisms because of the risk of complications , which may occur not only during the intervention but also during the refeeding phase and are mainly related to electrolyte disturbances .
these include some major problems , such as nephrolithiasis or arrhythmias , and other minor issues ( headache , nausea , occasional vomiting , bad breath , fatigue , muscle cramps , and constipation ) .
however , our study shows that most complications can be easily prevented with the use of high - quality proteins and relevant electrolyte , vitamin , and mineral supplements [ 10 , 34 ] .
indeed , responsible use of this therapeutic regimen for short - term periods and careful selection of the candidates are mandatory . in the first instance , our treatment protocol was investigated in severely obese patients with a history of multiple failures .
accordingly , it is not proposed as first - line therapy , but as an alternative therapy before more advanced approaches , such as surgery , in high - risk patients with serious difficulties in complying with further dietary regimens .
finally , another concern with vlcds is weight regain . on the one hand , initial wl appears to predict lower body weight at follow - up . on the other
indeed , the therapy does not engage the patient in life style and food choice changes necessary to be successful in long - term weight reduction .
the long - term effects of the present treatment protocol , after inclusion into a composite weight management program , clearly need to be investigated and data collection is ongoing .
studies are also needed to measure changes in nutritional status , body composition , and energy expenditure , although evidence supports the beneficial effect of low - carbohydrate , high - protein diets and the use of milk whey proteins [ 35 , 36 ] .
the strengths of our study are the large study population , the rigorous selection of the patients , and the standardized and responsible approach . however ,
first , this was an observational study and randomized trials including control groups treated either with standard hypocaloric diet or oral vlcd should be performed to achieve a more rigorous evaluation among the plethora of available wl interventions .
second , the present report focused only on data addressing a single enteral course of treatment ; the impact of this intervention should be clearly evaluated within the broader context of a long - term composite weight management program .
particularly , in order to further support its use in clinical practice , postintervention normalization of safety parameters needs to be addressed . finally , the evaluation of self - perceived outcome measures ( e.g. , hunger or wellbeing ) by means of visual analogue scales would have been also informative . in conclusion
, a 14-day course of enteral treatment with a very low - calorie protein - based formula appears to be a feasible , likely safe , and efficacious therapeutic option to be taken into consideration for a composite weight loss program for the management of severe obesity . | background .
multiple weight loss failures among obese patients suggest the design of new therapeutic strategies .
we investigated the role of 2-week course of enteral treatment with a very low - calorie protein - based formula in the management of severe obesity .
methods .
we evaluated the feasibility , safety , and efficacy of 2-week continuous administration of a protein - based formula ( 1.2 g / kg of ideal body weight / day ) by nasogastric tube in severely obese adults ( body mass index ( bmi ) 40 kg / m2 ) .
results . in total , 364 patients ( 59% women ; bmi = 46.6 7.2 kg / m2 ) were recruited .
the intervention was discontinued within 48 hours in 26 patients , due to nasogastric tube intolerance .
no serious adverse events occurred . during the first and the second week ,
65% and 80% patients , respectively , reported no side effects .
all biochemical safety parameters were affected by the intervention , particularly uric acid ( + 45% ) and aminotransferases ( + 48% ) . in the other cases the change was negligible .
we observed significant weight loss ( 5.7 2.3% ) and improvement in blood pressure and glucose and lipid metabolism parameters ( p < 0.001 ) . conclusions .
a 2-week course of enteral treatment with a very low - calorie protein - based formula appeared a feasible , likely safe , and efficacious therapeutic option to be considered for inclusion into a composite weight loss program for the management of severe obesity .
this trial is registered with clinicaltrials.gov identifier : nct01965990 . |
the rare - earth nickel borocarbide compounds @xmath1ni@xmath0b@xmath0c exhibit superconductivity even when the rare - earth element @xmath1 is a magnetic ion @xcite . due to the possibility of studying the interplay between superconductivity and magnetism ,
these materials have remained at the forefront of condensed matter physics research for over a decade following their discovery @xcite .
for the non - magnetic ions @xmath2y and @xmath2lu , the superconducting critical temperatures are @xmath3k and @xmath4k respectively @xcite .
for the magnetic ions @xmath2ho , tm or er , nel states enter at temperatures below @xmath5 , whereas for @xmath2dy superconductivity is stable only within the antiferromagnetic region @xcite .
all the rare - earth nickel borocarbides share a nominally tetragonal crystal structure , though orthorhombic distortions can appear due to magnetoelastic effects @xcite .
the unit cell is formed of alternating @xmath1c and ni@xmath0b@xmath0 layers , with superconductivity understood to originate in the latter @xcite . in honi@xmath0b@xmath0c
, the superconductivity appears at @xmath6k .
subsequently , a cascade of different magnetic structures within a narrow range of temperatures 6.0k to 5.2k results in a near - reentrant behaviour of the superconducting phase@xcite .
the interplay between magnetism and superconductivity in honi@xmath7b@xmath7c has been succinctly probed by bitter decoration measurements by vinnikov et al.@xcite , where it was demonstrated that magnetic domain boundaries strongly pin superconducting vortices , at least in the commensurate magnetic phase at low temperatures ( @xmath8k ) .
similar pinning to magnetic domain boundaries was also observed in erni@xmath7b@xmath7c@xcite .
intriguingly , the antiferromagnetic state for @xmath9k in erni@xmath7b@xmath7c develops a ferromagnetic component below 2.3k @xcite raising the possibility of a subsequent spontaneous formation of superconducting vortices @xcite
. it would be intriguing to see if similar effects should occur at the metamagnetic transitions in honi@xmath7b@xmath7c .
this article is the first report of a small - angle neutron scattering ( sans ) study on this material . at zero and low applied fields we find sharply increasing sans as the samples are cooled through @xmath10k .
we associate this signal to scattering from magnetic surfaces ( i.e. domain walls ) in the low temperature collinear magnetic phases .
this article is continued as follows : in the following section ( sec . [ experimental ] ) we outline the materials and methods ; in the results section ( sec . [ results ] ) we report the results of our resistivity ( sec . [ resistivity ] ) , magnetization ( sec .
[ magnetizationsection ] ) and sans ( sec . [ sanssection ] ) measurements .
a short summary and discussion is provided in the concluding section ( sec .
[ conclusion ] ) .
single crystals of honi@xmath0b@xmath0c were grown using a slow - cooling flux method with isotropic enrichment of @xmath11b in order to reduce the neutron absorption in our sans experiments .
the details can be found elsewhere @xcite .
magnetization and transport measurements were performed in the physics laboratories at mcmaster university using a quantum design magnetic properties measurement system and a quantum design physical properties measurement system respectively .
resistance was measured by the standard four - point probe technique .
the sans experiments were carried out at the nist center for neutron research using the ng3-sans and ng7-sans instruments @xcite . in a typical setup ,
@xmath12 wavelength neutrons were used and the small - angle scattering detected with a 2d area detector placed @xmath13 m away from the sample .
two honi@xmath0b@xmath0c single crystals ( 8x5x1 and 5x4x1mm@xmath14 ) were co - aligned on an al sample holder by x - ray laue diffraction .
the holder was mounted into a superconducting cryomagnet so that the samples * c*-axes , applied field ( * h * ) and neutron beam directions were all initially coincident , with the @xmath15 $ ] and @xmath16 $ ] crystallographic axes were aligned horizontal and vertical respectively .
the field direction * h * of the cryomagnet was initially aligned relative to the neutron beam using the vortex lattice in a nb single crystal .
the honi@xmath7b@xmath7c scattering measurements detailed herein were carried out with * c * turned away by @xmath17 , so that * h * and the neutron beam direction were @xmath17 to * c * in the ( 110 ) plane .
datasets as a function of temperature were collected by applying the desired field at high temperatures @xmath18 , cooling to base temperature ( @xmath19k ) and then measuring at selected temperatures on warming .
figure [ resistance](a ) shows a plot of electrical resistivity @xmath20 as a function of temperature at zero field .
the current created by the four probe measurement lies in the ( ab ) plane of the crystal .
as can be seen in this figure , the onset of superconductivity appears at @xmath6k .
overall metallic behaviour can also be seen for t@xmath21t@xmath22 in the limited temperature range probed . in fig .
[ resistance](b ) , @xmath20 at low temperatures is shown as a function of applied field * h * in the two directions , @xmath23 and @xmath17 from the crystallographic * c*-axis , for direct comparison with the sans measurements . at @xmath24k and * h * @xmath25 * c * , the upper critical field is found at @xmath26k@xmath27 t , in agreement with previous works @xcite .
the coherence length at @xmath24k from this value is @xmath28 .
a kink at lower fields @xmath29 t can also be observed in this figure .
we note that the slope of @xmath30 steepens with increasing field through the kink , implying that the superconductivity abruptly weakens .
this can be associated with increased fluctuations arising from the lower @xmath31 of the reentrant region .
resistivity @xmath20 measurements as functions of temperature @xmath32 and of magnetic field @xmath33 .
( a ) shows @xmath34 at zero field ; ( b ) shows @xmath30 at @xmath24k and @xmath35k , with fields * h * applied parallel to * c * and also at 45@xmath36 to * c * in the ( 110 ) plane .
the arrow shows the point for h@xmath37(t=2k ) of the previous study @xcite . in ( a )
the yellow background shading highlights the superconducting region . ]
similar kinks are observed at @xmath38 t in the @xmath35k datasets . for * h * @xmath25 * c *
, we see that @xmath39k@xmath40 t in agreement with the expected form of @xmath41 @xcite . a slight decrease in @xmath42
is anticipated on rotation of * h * from * c * towards the tetragonal basal plane @xcite , and indeed a small leftwards shift of @xmath30 in the upper critical field region may be discerned going from * h * @xmath25 * c * to * h * applied @xmath43 from * c*. in the latter , the @xmath30 further rises into a broad maximum at fields above @xmath42 .
this may be a consequence of the metamagnetic transitions to be discussed in sec .
[ sanssection ] ; similar features in the resistivity have previously been reported for fields applied in the basal plane @xcite .
figure [ magnetization ] illustrates our magnetometry data . in fig .
[ magnetization](a ) , the zero field cooled ( zfc ) and field cooled ( fc ) magnetic responses in a small applied field of 1mt are plotted as a function of temperature .
the reentrant superconductivity manifests itself as a reduced superconducting response in the region @xmath44k to 6k . in fig .
2(b ) we show the magnetization at 2k as a function of increasing field applied parallel to * c * after cooling in zero field .
the overall signal is dominated by the linear paramagnetic response of a component of the ( @xmath45 ) ho@xmath46 moments , but one can estimate the value of the upper critical field from the point of departure from the linear normal state behaviour illustrated by the dashed line ; one then obtains @xmath47 t in agreement with our resistivity measurements [ fig .
[ resistance](b ) ] and previous hall probe results @xcite .
the @xmath48 data in fig .
[ magnetization](b ) can also be used to estimate the lower critical field value as @xmath49mt at @xmath24k , though this estimate does not take into account sample demagnetization or ho@xmath46 moment alignment effects .
magnetometry @xmath50 as functions of temperature @xmath32 and of magnetic field @xmath33 .
( a ) the temperature dependence of @xmath51 , measured after cooling in zero field ( zfc ) and field - cooling ( fc ) using a small applied field of 1mt .
( b ) @xmath48 at @xmath24k .
the dashed line indicates the linear paramagnetic response of a component of the ho@xmath46 moments at high fields .
the inset in each panel shows a magnified region of the main figure . in these measurements ,
the magnetic field is applied parallel to the * c * axis . for clarity
, yellow background shading has been added to highlight the superconducting region . ] in fig .
2(b ) we measure a linear paramagnetic response of 1750emumol@xmath52t@xmath52 , or 0.31@xmath53t@xmath52 per ho@xmath46 ion .
it is interesting to compare this with previously published values .
@xcite reports 0.3@xmath53t@xmath54ion in agreement with our measurement .
in contrast , a smaller value of 0.1@xmath53t@xmath54ion is reported in ref .
it should be noted that all works report comparable @xmath50 values at the metamagnetic transitions present for * h * @xmath55 * c * ; this is expected for an intensive quantity like magnetization .
the possible non - intensive nature of @xmath50 for * h * @xmath25 * c * suggests that its origin may not be an intrinsic property of the bulk of samples . in the next section ,
we moot the possibility that this magnetization arises from more easily polarisable ho@xmath46 moments at crystallographic grain boundaries and dislocations .
we now turn to the main results of this manuscript .
figures [ sans ] and [ ivsq ] summaries the dependences of the small - angle neutron scattering ( sans ) on temperature , applied field and scattering vector @xmath56 . as a function of applied field ,
honi@xmath7b@xmath7c exhibits a series of metamagnetic transitions with magnetic structures depending on the field direction @xcite . at low temperatures @xmath57k with *
h * applied along the @xmath16 $ ] easy axis , the magnetic structures are constructed from ferromagnetic sheets , with each sheet being a basal plane , within which all ho@xmath46 moments co - align along one of the four @xmath58 directions @xcite .
the zero - field structure consists of antiferromagnetically coupled basal plane sheets , denoted by @xmath59 . at the first metamagnetic transition at 0.41 t at 2k ,
a jump in the magnetization signals that two thirds of the basal plane sheets align along * h * @xmath60 $ ] and only one along @xmath61 $ ] ; this is denoted @xmath62 .
subsequently this becomes the high - field @xmath63 phase with another magnetization jump at the second metamagnetic transition at 1.07 t at 2k .
fields applied away from @xmath16 $ ] in the basal plane yield a second intermediate field phase @xmath64 .
the @xmath65 indicates that the magnetic structure is non - collinear ; it has a wave vector @xmath66(@xmath67 0 0 ) r.l.u .
a recent torque magnetometry study @xcite confirms that this phase does not appear for * h * applied within @xmath68 of [ 110 ] , in support of the results of mean - field theory accounting for the crystalline electric field and ruderman - kittel - kasuya - yosida exchange interaction @xcite . for fields applied along the hard * c * axis ,
there are no metamagnetic transitions over this field regime .
therefore , for our orientation of field direction @xmath69 from * c * in the ( 110 ) plane , we anticipate two clear metamagnetic transitions ; the first from @xmath59 to @xmath62 at @xmath70 t and the second to @xmath63 at 1.51 t .
integrated detector counts , summed over the range of ( @xmath71)x10@xmath72@xmath52 as a function of temperature at various magnetic fields applied 45@xmath36 from * c * in the ( 110 ) plane .
the zero field data collected in a separate experimental setup have their own intensity scale ( right ) .
, width=307 ] fig .
[ sans ] shows the sans intensity integrated over the 2d detector ( this corresponds to a @xmath56-range of @xmath73@xmath52 ) .
we see there are indeed three different field regimes that correspond to the expected metamagnetic transitions .
first , at low fields @xmath74 t and including zero field , the sans temperature dependences share a common form , with intensity at low temperatures entering abruptly , rather like an order parameter with a transition temperature of @xmath75k .
then , at an intermediate applied field of 1.5 t , the magnitude of this order - parameter - like response appears somewhat increased compared to the low field regime . finally at high fields
@xmath76 t the sans intensity rises smoothly with falling temperature , and also increases with increasing field . to understand the origin of the sans intensity appearing at low temperatures , we first consider the possibility that the sans signal at fields @xmath77 arises from superconducting vortices in the sample . to check for sharp bragg reflections from a well - defined superconducting vortex lattice , at selected low applied fields we also collected data as the samples were rocked through the expected bragg angles
the field direction of the cryomagnet was initially aligned relative to the neutron beam using the vortex lattice in a nb single crystal .
no angular dependence was observed in the rocking scans on our honi@xmath7b@xmath7c samples , precluding a well - defined vortex lattice . at zero field , a sans signal
is observed even when no superconducting vortices are present ( no spontaneously forming vortices are anticipated because the magnetic ground state is antiferromagnetic ) .
hence superconducting vortices , even in a disordered ensemble , can not account for the observed sans response .
next we turn to the possibility that temperature - induced sans is generated by multiple bragg scattering between slightly misoriented crystallites in the samples .
this possibility would be completely excluded by working at neutron wavelengths @xmath78 above the bragg cutoff @xmath79 where @xmath80 is the maximum @xmath81-spacing of the bragg diffraction planes . for honi@xmath7b@xmath7c , @xmath82 , corresponding to the @xmath83 magnetic bragg reflection that appears at @xmath8k in the commensurate nel state . unfortunately working at @xmath84
is infeasible due to the lack of flux at these wavelengths at even the best of today s neutron facilities .
instead we used @xmath85 .
nonetheless we may defenestrate multiple bragg scattering since this usually manifests itself as isolated spots on the small - angle detector that typically change rapidly with rotations of the sample or with neutron wavelengths . here , in contrast , we observe a smooth sans profile ( c.f .
[ ivsq ] ) that is insensitive to small changes in angle or wavelength .
intensity @xmath86 as a function of scattering vector @xmath56 at low temperatures and @xmath87 t .
a high temperature background has been subtracted .
the red line shows the power - law behaviour of @xmath88 with the fitted @xmath89.,width=307 ] fig .
[ ivsq ] shows the typical scattering vector @xmath90**q**@xmath91 dependence of the sans intensity @xmath86 induced at low temperatures . in this figure
we plot the behaviour at 0.08 t ( high temperature @xmath92k backgrounds have been subtracted ) but a similar behaviour for the induced sans intensity @xmath86 is observed at all fields .
the data fit well to a porod law @xmath93 with the fitted exponent @xmath94 at all fields . at 0.08 t , for example
, we find @xmath95 .
the atomic form factor @xmath96 of the ho@xmath46 moments is essentially constant at low @xmath56 , and the sans profile probes directly how these moments arrange .
the porod behaviour implies a network of interfaces or surfaces , with the @xmath94 signifying that these interfaces are smooth .
our experiments do not probe sufficiently small scattering vectors to access the guinier regime of the @xmath97 profile and we therefore deduce a lower bound @xmath98 for the characteristic size @xmath99 of the network . in the high field region , we find that the anisotropy of the temperature - induced sans is very similar to that of the crystallographic background , as characterized by the angular dependence of * q * measured over the 2d sans detector .
the same can be said for the low field region , although here there are fewer counts with which to make this evaluation . like
the temperature - induced foreground sans intensity , the crystallographic background exhibits a porod law @xmath100 , indicative of grain boundaries and dislocation surfaces .
it is likely that the temperature - induced sans also originates at these crystal grain boundaries and dislocations . in the antiferromagnetic @xmath59 region at zero and low fields , we conjecture that the grain boundaries and dislocations serve as pinning sites for antiferromagnetic domain walls that carry a net magnetic moment . due to the crystal electric field , at high fields the ho@xmath46 moments
align to the [ 110 ] direction that is nearest to the applied field * h * ; we postulate that additional small - angle scattering appears at decreasing temperatures from interfacial moments at the grain boundaries and dislocations that are susceptible to align directly along * h * instead of along @xmath16 $ ] . as mooted in sec .
[ magnetizationsection ] , these free moments at extrinsic interfaces may also account for the discrepancies between the reported values of the paramagnetic magnetization for * h * @xmath25 * c*.
to summarize , we have performed magnetometry , transport and small - angle neutron scattering ( sans ) measurements on honi@xmath7b@xmath7c single crystals .
additional sans intensity @xmath86 appearing at low temperatures is observed at all fields . in a low field region
@xmath101 t that includes zero field , the temperature dependence of the signal is order - parameter - like with a transition at @xmath75k . at high fields @xmath102 t ,
the sans increases continuously on cooling across the temperature range probed ( from @xmath19k to @xmath103k ) . at low but finite fields , superconducting vortices will exist in the sample with an arrangement that is known to be rather disordered from previous local hall probe @xcite and bitter decoration work @xcite .
sans @xmath97 profiles similar to those observed here were previously reported on polycrystalline sr@xmath104la@xmath105cuo@xmath0 and interpreted as scattering from disordered vortices @xcite .
such an interpretation can not account for our honi@xmath7b@xmath7c scattering data since we also observe a sans signal at zero field .
the agreement between the observed field regimes and the expected metamagnetic transitions , plus the porod - law behaviour exhibited in @xmath97 , lead us to conclude that the low - temperature sans stems from uncompensated moments at crystallographic grain boundaries and dislocations . at low fields ,
these uncompensated moments are associated with domain walls in the antiferromagnetic @xmath59 phase , while at high fields they are suggested to stem from paramagnetic moments at the interfaces that align along the field direction rather than along the nearest [ 110 ] easy axis in the bulk ferromagnetic structure .
we emphasize that these magnetic structures form a network of large length scales @xmath98 .
magnetic contrast over similar scales has already been observed in bitter decoration of non - superconducting tbni@xmath7b@xmath7c and of the normal state of erni@xmath7b@xmath7c @xcite . in these high - resolution decoration studies ,
the lamellar magnetic flux structures observed were thought to be linked to crystallographic twin boundaries by magnetoelastic stresses . in honi@xmath7b@xmath7c
magnetoelastic effects lead to an orthorhombic distortion such that the unit cell length along the [ 110 ] ( tetragonal ) direction closest to * h * shrinks by @xmath106% compared to @xmath107 $ ] @xcite .
these large magnetoelastic strains would likely favour the location of magnetic domain walls at crystallographic grain boundaries and dislocations @xcite .
it would be extremely interesting to explore , in future work , the physics of antiferromagnetic magnetoelastic domain wall boundaries using high - resolution microscopy techniques in honi@xmath7b@xmath7c and in other materials .
we acknowledge the support of the national institute of standards and technology , u.s .
department of commerce , in providing the neutron research facilities used in this work .
acknowledges support from danscatt .
this work utilized facilities supported in part by the national science foundation under agreement no .
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series * 150 * , 052279 ( 2009 ) . | the superconducting and magnetic properties of honi@xmath0b@xmath0c single crystals are investigated through transport , magnetometry and small - angle neutron scattering measurements . in the magnetic phases that enter below the superconducting critical temperature , the small - angle neutron scattering data uncover networks of magnetic surfaces .
these likely originate from uncompensated moments e.g. at domain walls pinned to crystallographic grain boundaries .
the field and temperature dependent behaviour appears consistent with the metamagnetic transitions reported in earlier works . |
auricular defects may be congenitally or occur secondary to trauma or surgical removal of a neoplasm .
although plastic surgery is capable of restoring missing tissues it may not be the ideal choice of treatment because of the complex shape and structure .
for restoration of complex organs such as ears , prosthetic restorations may be option to surgical restorations due to the aesthetical success of them.1,2 there are various methods for manufacturing an auricular prosthesis .
these are ( a ) hand sculpturing method , ( b ) impression of a similar ear , and wax modeling with this impression and ( c ) rapid prototyping techniques.3,4 conventional prosthetic treatment is done by taking the impression with irreversible hydrocolloid or silicone and afterwards forming the model ( cast ) by using hard dental stone .
wax model is prepared on this cast and final prosthesis is processed with silicone material .
this method may discomfort the patient and underlying tissues may distort and cause difference between the cast and the patient s tissues . besides , the conventional method needs more experience and more time for laboratory work.5,6 achievements in computer technology in 1980 s made it possible to produce 3 dimensional ( 3d ) models in computer medium by using the images obtained by using computerized tomography , magnetic resonance imaging or laser surface scanners .
computer aided manufacturing ( cam ) is production of this 3 dimensional ( 3d ) model by rapid prototyping technology.7 rp consists of two stages .
these stages are virtual stage ( modelling and simulating ) and physical stage ( fabrication ) .
this process allows the production of geometrically complex shaped models that would be impossible to produce .
most important disadvantages of this system are requirement of equipments and high cost.8,9 recently , six rapid prototyping technologies can be used to produce anatomic models : ( 1 ) stereolithography which is a layer by layer 3-d model production system in which the model can be produced from various ultra - violet photo - polymerizing resins by laser - fusing , ( 2 ) laminated object manufacturing , which creates 3-d models by laminating adhesive coated sheets of paper in which the adhesive is heat - activated by a focused laser beam , ( 3 ) selective laser sintering , which selectively fuses thin layers of heat fusible powders such as polycarbonate or glass - filled composite nylon and enables the direct fabrication of wax prototypes for development of facial prostheses that can be sterilized by epoxyethane and recycled , ( 4 ) solid ground curing which laser - polymerizes successive layers of resin through a stencil , ( 5 ) 3-d ink - jet printing , which selectively deposits binding material through a print head to fuse a thin layer of metallic or ceramic powder to a previously fused layer and then fired in a furnace for sinterizing , and ( 6 ) fused deposition modeling , which builds models by depositing layers of molten thermoplastic materials.7,10,11 advantages of cad / cam technique are ; ( 1 ) elimination of disturbance due to the impression material because there is no need to take impression , ( 2 ) possibility to form the model by avoiding deformation of the tissue due to the use of techniques that do not require contact such as ct or laser surface scanner ( 3 ) possibility to obtain more realistic looking prosthesis because the model is formed from natural tissues , ( 4 ) ability to store the models in hard disks , thus requirement of less space for storage .
prosthesis made from silicone lose characteristic properties and color by time , thus they only may be used maximum for two years .
because of this storage of models are very important.7,1215 when compared to all these advantages , only disadvantage of cad / cam technique is high cost . although most of the procedure is performed by the computer , expertise of clinician for application and coloring affects the success of the prosthesis.14,15
these stages are virtual stage ( modelling and simulating ) and physical stage ( fabrication ) .
this process allows the production of geometrically complex shaped models that would be impossible to produce .
most important disadvantages of this system are requirement of equipments and high cost.8,9 recently , six rapid prototyping technologies can be used to produce anatomic models : ( 1 ) stereolithography which is a layer by layer 3-d model production system in which the model can be produced from various ultra - violet photo - polymerizing resins by laser - fusing , ( 2 ) laminated object manufacturing , which creates 3-d models by laminating adhesive coated sheets of paper in which the adhesive is heat - activated by a focused laser beam , ( 3 ) selective laser sintering , which selectively fuses thin layers of heat fusible powders such as polycarbonate or glass - filled composite nylon and enables the direct fabrication of wax prototypes for development of facial prostheses that can be sterilized by epoxyethane and recycled , ( 4 ) solid ground curing which laser - polymerizes successive layers of resin through a stencil , ( 5 ) 3-d ink - jet printing , which selectively deposits binding material through a print head to fuse a thin layer of metallic or ceramic powder to a previously fused layer and then fired in a furnace for sinterizing , and ( 6 ) fused deposition modeling , which builds models by depositing layers of molten thermoplastic materials.7,10,11 advantages of cad / cam technique are ; ( 1 ) elimination of disturbance due to the impression material because there is no need to take impression , ( 2 ) possibility to form the model by avoiding deformation of the tissue due to the use of techniques that do not require contact such as ct or laser surface scanner ( 3 ) possibility to obtain more realistic looking prosthesis because the model is formed from natural tissues , ( 4 ) ability to store the models in hard disks , thus requirement of less space for storage .
prosthesis made from silicone lose characteristic properties and color by time , thus they only may be used maximum for two years .
because of this storage of models are very important.7,1215 when compared to all these advantages , only disadvantage of cad / cam technique is high cost .
although most of the procedure is performed by the computer , expertise of clinician for application and coloring affects the success of the prosthesis.14,15
at the first case , computerized tomography of the skull of a patient who has 2 implants at auricular region was obtained in order to have the model to produce the prosthesis ( figure 1 ) .
adhesion was maximized by soldering bars to the implants used for retention of prosthesis ( figure 2 ) . for this patient iti ( straumann inc . )
afterwards , 3d model was obtained from the data of computerized tomography by the help of a software ( mimics , materialise inc . ) . by the same software reciprocal model of the ear at intact side
following the saving of model in stl format , output of 3d model was taken by 3d ink - jet printer ( z printer ; z corp . inc . ) .
this acrylic model was transformed into wax model by conventional methods , and tried on the patient ( figure 4 ) .
no problems observed for the edge fitting for the model and then it is produced from silicone by conventional methods ( figure 5 ) .
at the second case , also computerized tomography of the skull of a patient who has 2 implants at auricular region was obtained as the first case ( figure 6 ) .
gold bars and matrixes in this patient ( figure 7 ) . as the first case
reciprocal image of the intact ear was used to form defected ear , it was saved in stl format and three dimensional output is obtained by stereolithography ( perfactory standard sxga+ , envisiontec inc . ) ( figure 8) . following the transformation of this acrylic model into wax model and tried on
, silicone prosthesis is finished by conventional methods ( figures 9 , 10 and 11 ) .
design and fabrication of auricular prosthesis by cad / cam techniques are advantageous because a highly skilled technician is not necessary to sculpt the ear .
procedure that allows impression without contact eliminates the errors likely to occur at impression taken by conventional methods . while impression materials used for taking the impression of face , dimensions may cause deformation of the underlying tissue due to their weight
the prosthesis produced by cad / cam techniques will be more realistic and will maintain good facial harmony . despite computerized technique
seems to be more complicated , finishing of prosthesis takes less time when compared to the conventional methods . also the digital images and molds can be preserved .
this feature is quite important when the need for renewal of the prosthesis for every two years due to the deformation and hardening of the silicone is considered .
the only disadvantage of this method is its requirement of expensive equipments and experienced computer software operator.4,5,14,16,17 although there are various rapid prototyping techniques , expensiveness of each promotes the investigators to find cheaper and that has wider field of usage.12,14 besides all , this technology is insufficient for the production of maxillofacial prosthesis . because taking the output of prosthesis directly from the silicone material is not yet possible and coloring is still a problem for clinicians . | maxillofacial prostheses are usually fabricated on the models obtained following the impression procedures .
disadvantages of conventional impression techniques used in production of facial prosthesis are deformation of soft tissues caused by impression material and disturbance of the patient due to .
additionally production of prosthesis by conventional methods takes longer time . recently
, rapid prototyping techniques have been developed for extraoral prosthesis in order to reduce these disadvantages of conventional methods .
rapid prototyping technique has the potential to simplify the procedure and decrease the laboratory work required .
it eliminates the need for measurement impression procedures and preparation of wax model to be performed by prosthodontists themselves in the near future this technology will become a standard for fabricating maxillofacial prostheses . |
in our current paradigm for the structure of galaxies , the stars we observe in an early type galaxy should be embedded in a dark matter halo . the stars and
any associated cold gas can comprise up to 16% of the halo mass ( e.g. spergel et al .
@xcite ) , although the actual mass fraction could be lower if star formation processes either eject gas from the halo or maintain it at the virial temperature of the halo .
the halo structure should be similar to an nfw model ( navarro et al .
@xcite ) , although the central density of the dark matter may be increased by adiabatic compression ( blumenthal et al .
unfortunately , for early - type galaxies , there is no simple conserved quantity that can be used to estimate a scale length for the stellar component in the way that angular momentum conservation can be used to estimate it for a disk galaxy .
[ fig : halo ] shows the expected surface density for a typical lens in terms of the dimensionless convergence @xmath4 relevant to gravitational lensing .
the effective radius @xmath2 of an early - type galaxy provides a characteristic scale for the luminous parts of the galaxy . on small scales ( @xmath5 )
the galaxy is dominated by the baryonic mass , with the dark matter contributing only @xmath6 of the projected density .
this is borne out by dynamical studies of the central regions of nearby galaxies in which there is no need for dark matter on these scales . on large scales ( @xmath7 )
there is no doubt that dark matter dominates , primarily based either on x - ray observations of nearby early - type galaxies ( e.g. fabbiano @xcite , lowenstein & white @xcite ) or weak lensing surveys ( e.g. sheldon et al .
@xcite ) . on intermediate scales ( @xmath8@xmath9 )
, there is considerable evidence that early - type galaxies show roughly the same conspiracy as late - type galaxies between the decline in the baryonic contribution and the rise of the dark matter contribution so as to have mass distributions that come close to producing a flat rotation curve ( e.g. rusin et al .
@xcite ) . however , there are recent data from the halo dynamics of nearby galaxies ( romanowsky et al .
@xcite ) , time delay measurements in gravitational lenses ( kochanek @xcite ) , and stellar dynamics in gravitational lenses ( treu & koopmans @xcite ) suggesting that this standard picture is either wrong and early - type galaxies have little dark matter in this region or that the density structure of early - type galaxies is very heterogeneous .
the latter possibility is difficult to reconcile with the tightness of either the familiar dynamical fundamental plane ( e.g. djorgovski & davis @xcite ) or the equally tight fundamental plane of gravitational lenses ( kochanek et al .
@xcite ) .
here we are going to focus on the ability of gravitational lenses to clarify these problems . in interpreting lens data
we must start with the dreaded `` lens model . '' for whatever reasons , these two words induce a mysterious level of anxiety in the populace at large , when the reality is that lens models are no more ( or less ) bizarre beasts than the `` dynamical models '' whose complexities , structures and degeneracies seem to be accepted with reasonable equanimity . for lens models ,
however , there is a strange belief that somehow data @xmath10 model yields random noise .
much of this arises because we tend to fit the models without providing a clear explanation of how lens models work , which quantities are constrained and how any degeneracies arise .
one objective of this review is to clearly explain how strong lens data constrain mass distributions . in
[ sec : lens ] we review how the most familiar type of lens data , image positions , constrain the mass distribution . then in
36 we explore how the statistics of the lens sample , stellar dynamics of lenses , time delay measurements and monitoring for microlensing variability can be used to avoid the limitations of constraints based only on image positions . model with no dark matter is shown by the heavy solid line , and the light solid lines show profiles where the baryons ( stars ) represent 25% , 15% or 5% of the total halo mass .
the dashed lines ( right hand scale ) show the fraction of the surface density in dark matter , @xmath11 , as a function of radius .
we expect a baryon fraction of @xmath12 if all baryons in the halo cool and form stars .
the logarithmic radial scale greatly exaggerates the apparent decline of the rotation curves .
, title="fig:",width=240 ] model with no dark matter is shown by the heavy solid line , and the light solid lines show profiles where the baryons ( stars ) represent 25% , 15% or 5% of the total halo mass .
the dashed lines ( right hand scale ) show the fraction of the surface density in dark matter , @xmath11 , as a function of radius .
we expect a baryon fraction of @xmath12 if all baryons in the halo cool and form stars .
the logarithmic radial scale greatly exaggerates the apparent decline of the rotation curves .
, title="fig:",width=240 ]
the fundamental frustration of gravitational lenses is that they always measure something very accurately , but that something is usually a degenerate combination of two interesting quantities . in this section
we review how lens galaxies constrain the mass distribution . in our discussion
we will focus only on the radial mass distribution ( the monopole ) . in actual lens models ,
the angular structure is always important , but for the determination of the monopole it is simply a source of `` noise . ''
the role of angular structure is discussed in detail in kochanek ( @xcite ) , but it has no particular effect on the discussion which follows .
all lens modeling , parametric or non - parametric , obeys the rules we are about to describe .
unfortunately , the gravitational lens community seems to be more interested in obfuscating than explaining what it is that lens data constrain ( mostly to our own detriment ) . for cuspy models of b1933 + 503 as a function of the inner density exponent @xmath13 ( @xmath14 ) and the profile break radius @xmath15 .
models with cusps significantly shallower or steeper than isothermal are ruled out , and acceptable models near isothermal must have break radii outside the region with the lensed images .
( left ) the monopole deflections of the b1933 + 503 models for the range of permitted cusp exponents @xmath13 .
the points show the radii of the lensed images , and the models only constrain the shape of the monopole in this region .
the monopole deflection is closely related to the square of the rotation curve .
, title="fig:",width=240 ] for cuspy models of b1933 + 503 as a function of the inner density exponent @xmath13 ( @xmath14 ) and the profile break radius @xmath15 .
models with cusps significantly shallower or steeper than isothermal are ruled out , and acceptable models near isothermal must have break radii outside the region with the lensed images .
( left ) the monopole deflections of the b1933 + 503 models for the range of permitted cusp exponents @xmath13 .
the points show the radii of the lensed images , and the models only constrain the shape of the monopole in this region .
the monopole deflection is closely related to the square of the rotation curve .
, title="fig:",width=240 ] ( @xmath16 ) and the break radius @xmath17 for three different asymptotic density slopes @xmath18 .
a hernquist model has @xmath19 and @xmath20 , an nfw model has @xmath19 and @xmath21 , and a pseudo - jaffe model has @xmath22 and @xmath20 .
unless the break radius is place interior to the b image , it is restricted to be close to isothermal ( @xmath22 ) .
, title="fig:",width=240 ] ( @xmath16 ) and the break radius @xmath17 for three different asymptotic density slopes @xmath18 .
a hernquist model has @xmath19 and @xmath20 , an nfw model has @xmath19 and @xmath21 , and a pseudo - jaffe model has @xmath22 and @xmath20 .
unless the break radius is place interior to the b image , it is restricted to be close to isothermal ( @xmath22 ) .
, title="fig:",width=240 ] fig .
[ fig : geometry ] illustrates a simple gravitational lens with two images located at radii @xmath23 from the center of the lens galaxy .
usually we assume a mass distribution @xmath24 which produces a ray deflection @xmath25 consisting of an unknown normalization @xmath26 multiplied by a deflection profile determined by the mass distribution @xmath27 .
because both images must correspond to a common source , the lens equation sets the constraint that @xmath28 which is easily solved to find a normalization of @xmath29 since the enclosed mass at any radius scales as @xmath30 , you get an accurate estimate for the enclosed mass independent of the profile . in particular , if you use the mass inside the mean image radius , @xmath31 , then the enclosed mass is independent of the slope ( @xmath32 ) of the deflection profile and has a fractional dependence on the profile of @xmath33 { \dr^2 \over \rbar^2 } \ ] ] that is second order in the asymmetry @xmath34 of the image positions .
as the lens becomes symmetric , @xmath35 , the images are approaching the einstein radius and the mass uncertainties diminish rapidly because for any circular lens the mean surface density of the material interior to the einstein radius @xmath36 is exactly @xmath37 where @xmath38 is the critical surface density for lensing . the mass normalization ( eqn .
[ eqn : norm ] ) is not very illuminating if our objective is to understand the property of the density distribution constrained by the lensed images . to understand the constraint we start by introducing the mean surface density in an annulus , @xmath39 where the mean surface density is related to the mass by @xmath40
the ray deflections at the two images are simply @xmath41.\ ] ] substituting these into the constraint equation ( eqn . [ eqn : constraint ] ) we find that @xmath42 the positions of the two images measure a combination of the mean surface density interior to the inner image and the mean surface density between the two images to the accuracy of the astrometric measurements
. this will still hold if we add angular structure to the lens model if we think of the angular deflections as an added source of noise in the constraint .
the surface densities are constrained to the range @xmath43 with a linear trade off @xmath44 between the surface densities in which the mass interior to b decreases as we add mass to the annulus between a and b. the particular combination of surface densities on the left side of eqn .
[ eqn : onezone ] arises because of the mass sheet degeneracy ( falco et al .
@xcite ) given a surface density @xmath45 , the image positions and flux ratios are unchanged if we transform the surface density to by @xmath46 .
it is called the mass sheet degeneracy because it corresponds to adding a sheet of surface density @xmath47 while reducing the mass scale of the original profile by the factor @xmath48 .
since the right side of eqn .
[ eqn : onezone ] is a measured quantity , the left side must be invariant under this transformation .
if the lens has additional images in the interior of the annulus , then we can measure more properties of the surface density .
the simplest example is to suppose that in addition to the images at @xmath49 and @xmath50 we also see an einstein ring image in the annulus at @xmath51 .
as discussed earlier , this is the unique point where the enclosed mass is determined uniquely , with @xmath52 in a spherical lens .
the added constraint allows us to determine the ratio @xmath53 which relates the surface density of the annulus inside the einstein ring to that outside the einstein ring . once again
, the constrained quantity combines two mean surface densities in a form which is invariant under the transformation associated with the mass sheet degeneracy .
this brings us to the gauss laws for ( spherical ) lens models given a lens with images bounded by the annulus @xmath54 : * only the total mass interior to @xmath50 and not its distribution is relevant , * the distribution of mass in the annulus @xmath54 is relevant only if there are additional lensed images in the annulus , and * the amount and distribution of mass exterior to @xmath49 is irrelevant .
parametric models must have enough degrees of freedom to vary these quantities , but the constraints on the profile shape apply only in the annulus and only to the extent there are additional constraints .
any extra degrees of freedom in a model beyond the mean annular densities are irrelevant .
if we have a lens like b1933 + 503 ( sykes et al .
@xcite ) with 10 lensed images produced by three source components ( see fig .
[ fig : b1933merlin ] ) , then the density structure in the annulus can be tightly constrained .
[ fig : mod1933a ] shows the constraints obtained by muoz et al .
( @xcite , also see cohn et al .
@xcite ) on density distributions of the form @xmath55 .
the acceptable models have parameters ( @xmath56 and @xmath57 ) that lead to nearly flat rotation curves over the annulus bounding the lensed images .
other recent examples are analyses of b0218 + 357 by wucknitz et al .
( @xcite ) and of 00472808 by dye & warren ( @xcite ) . ) and the projected fraction of the mass @xmath58 inside @xmath59 composed of dark matter .
the results are shown for three ratios @xmath60 between the break radius @xmath61 of the dark matter profile and the effective radius @xmath2 of the luminous galaxy .
the solid ( dashed ) contours show the 68% and 95% confidence levels for two ( one ) parameter .
note that the estimates of @xmath62 and @xmath58 depend little on the location of the break radius relative to the effective radius .
the bottom row shows all the mass profiles lying within the ( two parameter ) 68% confidence region normalized to a fixed projected mass inside @xmath59 . for comparison
we show the mass enclosed by a de vaucouleurs model ( dotted line ) and an sis ( offset dashed line ) .
while the allowed models exhibit a wide range of dark matter abundances , slopes and break radii , they all have roughly isothermal total mass profiles over the radial range spanned by the lensed images .
, width=480 ] another example of an additional constraint is if we can detect a central or odd image at radius @xmath63 . while there are few examples of central images as yet , their detection will become routine as the sensitivity of radio observations increase . carrying out the same analysis in terms of mean surface densities that lead to eqn .
[ eqn : onezone ] , we find the constraint @xmath64 between the mean density @xmath65 interior to image c and the mean density @xmath66 between images b and c. if we have a very asymmetric triple in which @xmath67 and @xmath68 , then the central density is larger by the factor @xmath69 .
the constraint in eqn .
[ eqn : onezone ] also holds , and it is easy to derive the constraints on other combinations of the mean surface densities to find that they all have the standard form with ratios of @xmath70 equal to an astrometric constraint .
the cleanest present example of a lens with a third image is the radio lens pmnj16320033 ( winn et al .
@xcite , winn , rusin & kochanek @xcite ) shown in fig .
[ fig : pmnj1632 ] . like b1933 + 503 ,
the mass distribution is constrained the mass profile is required to be close to isothermal with @xmath71 ( see fig .
[ fig : mod1632 ] ) .
routine detection of these central images also offers a new probe for black holes at the centers of the lens galaxy ( mao et al .
@xcite ) in the case of pmnj16320033 most models with a black hole as massive as expected from local scalings will produce a fourth image ( d ) close to image c but about 10 times fainter .
unfortunately , lenses with additional constraints are relatively rare , so we must find alternate means of breaking the degeneracy .
einstein ring images of the host galaxy can be found relatively easily , but they are better suited for constraining the angular structure of the lens than the radial structure . for lenses without additional constraints
this can be done statistically provided the lenses have relatively homogeneous mass distributions . for individual lenses without additional constraints we must either measure the mass @xmath72 in the interior or measure the surface density of the annulus @xmath73 .
the lens constraint eqn .
[ eqn : onezone ] then supplies the other surface density and we have an absolute measurement of the profile for @xmath74 . a very different approach is to break the degeneracy by using microlensing variability to determine the ratio @xmath75 between the surface density in stars and the total surface density in the annulus .
analyzing ensembles of lenses to estimate the mean mass distribution has two advantages over analyzing individual lenses .
first , it provides constraints over a broad range of radii ( relative to @xmath2 ) , and second , it breaks the mass sheet degeneracy .
the disadvantage of the method is that we must assume the density distributions of lenses are self - similar or at least heterogeneous in a manner that can be included as part of the model .
the mass sheet degeneracy is broken because all lenses must agree on the same ( scaled ) physical density distribution but have source and lens redshifts corresponding to different critical densities . thus , adding a constant physical density sheet corresponds to adding a different critical density sheet to each lens which can not be reconciled with the constraints .
this approach has been used by rusin et al .
( @xcite , @xcite ) to estimate both the average mass distribution and the evolution of stellar populations .
rusin et al . ( @xcite )
model the lens galaxy as the sum of a hernquist model normalized by the observed effective radius of the lens galaxy embedded in a dark matter halo of the form @xmath76^{(3-n)/2 } } \ ] ] were @xmath17 is the break radius and @xmath62 is the logarithmic slope of the central density cusp .
here we are interested in the dark matter slope @xmath62 and the fraction of the projected mass inside @xmath59 which is dark matter , although the full calculation includes variables for the scaling of galaxy mass - to - light ratios with redshift and mass .
[ fig : selfsim ] shows the resulting constraints on the cdm mass fraction projected inside @xmath59 and the logarithmic slope of the central density cusp of the dark matter .
while there is a degeneracy in the exact trade - off between the dark matter fraction and the slope , the total mass distribution is well - constrained and close to isothermal ( flat rotation curve ) .
the residuals about this mean mass profile can be entirely explained by a realistic spread in the mean stellar ages of the lens galaxies . .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ] .
the dotted contours show the 68% and 95% confidence limits from the self - similar models for @xmath77 .
the shaded regions show the models allowed ( 68% confidence ) by the formal velocity dispersion measurement errors , and the heavy solid lines show contours of the velocity dispersion in km / s .
we used the low gebhardt et al .
( @xcite ) velocity dispersion for hst14176 + 5226 because it has the smallest formal error .
these models assumed isotropic orbits , thereby underestimating the full uncertainties in the stellar dynamical models .
, title="fig:",width=144 ]
if we can use another technique to measure either @xmath78 or @xmath79 , then we can immediately use the basic lens constraint ( eqn .
[ eqn : onezone ] ) to determine the other mean surface density and obtain a tight constraint on the density distribution . for example , measuring the stellar velocity dispersion of the lens galaxy will constrain the mass well inside the einstein radius where it is dominated by stars , roughly corresponding to measuring @xmath79 .
another way to think about a dynamical measurement is to imagine that the galaxy has a mass profile @xmath80 where we know the mass @xmath81 inside the einstein radius @xmath36 accurately from the astrometry of the lensed images but can not constrain the density exponent @xmath62 .
a velocity dispersion measurement corresponds to measuring a virial mass @xmath82 on the scale @xmath83 of the aperture with a dimensionless constant @xmath84 compensating for projection effects , asphericity and orbital anisotropies . solving for the exponent
we find that @xmath85 \left [ \ln(r_v / r_e ) \right]^{-1 } \label{eqn : vscale}\ ] ] and we should be able to determine @xmath62 to an accuracy of @xmath86 since the ratio of the radii is @xmath87 .
this has been done for 10 systems as illustrated in fig .
[ fig : vdisp ] using the same parameter space as used for the self - similar models in fig .
[ fig : selfsim ] . with the exception of q2237
+ 0305 , where we see the images in the bulge of a nearby spiral galaxy , the parameter space and degeneracies of the individual velocity dispersion measurements are very similar to the results from the statistical analysis or the models of individual lenses with extra constraints .
there are a few lenses which may require more centrally concentrated mass distributions and a falling rotation curve ( e.g. pg1115 + 080 ) , and a few lenses which may require a less centrally concentrated mass distribution and a rising rotation curve ( e.g. hst14176 + 5226 ) .
treu & koopmans ( @xcite ) summarize their individual estimates of the mean logarithmic slope of the density finding results scattered about slightly rising rotation curve @xmath88 with an appreciable rms scatter of @xmath89 .
the error estimates for the effective slope @xmath62 seem to be 24 times smaller than expected from our simple scaling argument in eqn .
[ eqn : vscale ] .
the finding that the typical lens has a rising rotation curve is surprising given the expected halo structure shown in fig .
[ fig : halo ] , where we would expect to see a slowly falling rotation curve for @xmath90 independent of the baryon fraction . from fig .
[ fig : vdisp ] we might naively conclude that the stellar dynamical approach is superior to the statistical approach .
however , in producing this comparison , rusin et al .
( @xcite ) assumed a simple isotropic dynamical model and the formal uncertainties , which leads to two problems .
the first problem is that dynamical measurement uncertainties tend to be underestimated for example , the three velocity dispersion measurements for hst14176 + 5226 can be mutually consistent only if their error bars are expanded by 30% .
the second problem is that several systematic uncertainties have yet to be included in the comparison .
these arise because the distribution of stellar velocities is not gaussian and because galaxies are not spheres , leading to systematic problems when we use the spherical jeans equations to analyze the data .
the systematics are different from local stellar dynamical estimates because the profile slope ( e.g. eqn .
[ eqn : vscale ] ) compares a dynamical mass to a lensing mass rather than comparing two dynamical masses .
this makes estimates for the mass distribution using the stellar dynamics of lenses sensitive to simple calibration errors @xmath91 with @xmath92 between the measurement @xmath93 and the rms velocity @xmath94 in the jeans equations .
such errors cancel ( to lowest order ) in a purely stellar dynamical estimate of the mass distribution .
two simple examples are the effects of non - gaussian line - of - sight velocity distributions ( losvds ) and deviations from spherical symmetry .
while the jeans equations depend on @xmath94 , the measurement is usually the dispersion of the best - fit gaussian , and these two quantities differ by @xmath95 where @xmath96 is the dimensionless coefficient of an expansion of the losvd in gauss - hermite polynomials ( e.g. van der marel & franx @xcite ) .
the resulting corrections , @xmath97 , can be comparable to the formal measurement errors .
for example , romanowsky & kochanek ( @xcite ) were able to find models of pg1115 + 080 consistent with a flat rotation curve where treu & koopmans ( @xcite ) , who used only the jeans equations , could not .
arguably the distribution functions required to produce the agreement were unusual , but unusual is a very different statement from impossible .
similarly , galaxies are not spheres . from the virial theorem it is easy to show that an oblate ellipsoid of axis ratio @xmath98 has a ratio between the major and minor axis velocity dispersions that corresponds to a correction of order @xmath99 for @xmath100 .
making hst14176 + 5226 a @xmath100 galaxy viewed pole on leads to corrections large enough to make this system consistent with a nearly flat rather than a rising rotation curve , thereby eliminating the apparent disagreement between this lens and the results of the statistical analysis .
future analyses of lens dispersions need to treat these systematic uncertainties more carefully since for many purposes they are already larger than the formal measurement errors .
the party line these days is that the hubble constant is a known quantity based either on local estimates ( @xmath101 km / s / mpc , freedman et al .
@xcite ) or models of cmb fluctuations assuming a flat universe with a cosmological constant ( @xmath102 km / s / mpc , spergel et al .
@xcite ) . for
the purposes of this review , let us assume that the party is correct and consider its implications .
gravitational lens time delays measure a combination of the hubble constant and the surface density @xmath78 in the annulus between the images for which the delay was measured , so if we know @xmath103 then time delays provide a very simple means of breaking the degeneracy in eqn .
[ eqn : onezone ] . as in
[ sec : lens ] , we will discuss only the effects of the radial density distribution .
the effects of the angular distribution are well understood and are reviewed in kochanek ( @xcite ) .
the key to understanding time delays comes from gorenstein et al .
( @xcite , kochanek @xcite , see also saha @xcite ) who showed that the time delay in a circular lens depends only on the image positions and _ the surface density @xmath104 in the annulus between the images _ ( fig .
[ fig : geometry ] ) .
a useful approximation is to assume that the surface density in the annulus can be _ locally _ approximated by a power law , @xmath105 for @xmath106 , with a mean surface density in the annulus of @xmath78 .
the time delay between the images is then ( kochanek @xcite ) @xmath107 \label{eqn : delay1}\ ] ] where @xmath108 is the time delay for a singular isothermal sphere with comoving angular diameter distances @xmath109 , @xmath110 and @xmath111 between the observer , lens and source .
you must keep track of when using angular diameter distances has vanished .
almost all lensing calculations simplify if comoving angular diameter distances are used rather than `` normal '' angular diameter distances , because it is no longer necessary to keep track of the @xmath112 factors in many standard expressions . ]
the key point is that the time delay is largely determined by the average surface density @xmath78 in the annulus with only modest corrections from the local shape of the surface density distribution even when @xmath113 .
the second order expansion is exact for a singular isothermal lens ( @xmath114 , @xmath115 ) , and it reproduces the time delay of a point mass lens ( @xmath116 ) to better than 1% even when @xmath117 . estimates for pg1115 + 080 .
the lens galaxy is modeled as an ellipsoidal pseudo - jaffe model , @xmath118 , and the nearby group is modeled as an sis . as the break radius @xmath119 the pseudo - jaffe model becomes an sis model , and as the break radius @xmath120 it becomes a point mass .
the heavy solid curve ( @xmath121 ) shows the dependence of @xmath103 on the break radius for the exact , nonlinear fits of the model to the pg1115 + 080 data .
the heavy dashed curve ( @xmath122 ) is the value found using our simple theory of time delays based on the surface density .
the agreement of the exact and scaling solutions is typical .
the light solid line shows the average surface density @xmath123 in the annulus between the images , and the light dashed line shows the _ inverse _ of the logarithmic slope @xmath124 in the annulus ( @xmath125 ) . for an sis model
we would have @xmath126 and @xmath127 , as shown by the horizontal line .
when the break radius is large compared to the einstein radius ( indicated by the vertical line ) , the surface density is slightly higher and the slope is slightly shallower than for the sis model because of the added surface density from the group . as we make the lens galaxy more compact by reducing the break radius , the surface density decreases and the slope becomes steeper , leading to a rise in @xmath103 . as the galaxy becomes very compact ,
the surface density near the einstein ring is dominated by the group rather than the galaxy , so the surface density approaches a constant and the logarithmic slope approaches the value corresponding to a constant density sheet ( @xmath128 ) .
[ fig : pg1115],width=384 ] this relationship between annular surface density and time delays is the fundamental relationship to remember .
a popular parametric example is the scaling of the time delay for global power law models with @xmath129 . in these models the mass density scales as @xmath130 and circular velocities or ray deflections scale as @xmath131 where @xmath115 is the singular isothermal ( sis ) profile producing a flat rotation curve or a constant deflection . in these models
the time delay is @xmath132 to lowest order in @xmath34 ( witt et al .
although the logarithmic slope @xmath62 is a global parameter of the model , it enters the time delay only through the general requirements of eqn .
[ eqn : onezone ] and the surface density of the model near the einstein ring the surface density near the einstein ring is @xmath133 , so @xmath134 explains the scaling of the time delay .
[ fig : pg1115 ] shows a more complicated example where we compare estimates of @xmath103 from a complex parametric model for pg1115 + 080 consisting of an ellipsoidal lens plus its parent group to the value we would get simply calculating the surface density of the model and using the generalization of eqn .
[ eqn : delay1 ] for the angular structure of the lens ( kochanek @xcite ) .
as we would expect from our simple theory , the surface density of the lens and its local slope are all the information needed to predict the scaling of the hubble constant with the model parameters .
there are presently twelve lenses with published time delay measurements of varying accuracy : b0218 + 357 ( biggs et al .
@xcite ) , rxj0911 + 0551 ( hjorth et al .
@xcite ) , fbq0951 + 2635 ( jakobsson et al .
@xcite ) , q0957 + 561 ( kundi et al .
@xcite ) , he11041805 ( ofek & maoz @xcite ) , pg1115 + 080 ( schechter et al .
@xcite ) , b1422 + 231 ( patnaik & narasimha @xcite ) , sbs1520 + 530 ( burud et al .
@xcite ) , b1600 + 434 ( burud et al .
@xcite , koopmans et al .
@xcite ) , b1608 + 656 ( fassnacht et al .
@xcite ) , pks1830211 ( lovell et al
. @xcite ) and he21492745 ( burud et al
. @xcite ) .
the interpretation of these delays is controversial ( e.g. williams & saha @xcite , kochanek @xcite , koopmans et al .
@xcite and references therein ) , but the problem lies mainly with the limitations of the existing data .
the first problem is that several of the lenses are poorly suited to analysis because their photometric structure makes it difficult to perform the accurate astrometry of the images relative to the lens galaxy needed to interpret the delays for any mass distribution .
for example , the quasar images are too bright in b0218 + 357 , the lens is too faint in pks1830211 , and the position estimates depend on accurate corrections for extinction in b1600 + 434 and b1608 + 656 .
the second problem is that many of the delays are not known with sufficient accuracy because the monitoring programs were terminated after the initial delay estimate .
we need time delay measurement accuracies of 5% or better in order to have uncertainties in the surface density @xmath78 that are small compared to the regime of interest ( @xmath135 , see fig . 1 ) .
half of the lenses ( fbq0951 + 2635 , he11041805 , pg1115 + 080 , b1422 + 231 , pks1830211 and he21492745 ) have unacceptably high delay uncertainties .
the third problem is that we have too few systems to adequately understand environmental effects . while keeton & zabludoff ( @xcite ) somewhat exaggerate the importance of environmental effects on the interpretation of time delays ( much of the spread in their distributions is due to the uncertainties in the time delay measurement rather than the effects of the group ) , it is certainly true that environments affect the interpretation because the parent group or cluster of the lens galaxy contributes to @xmath78 .
for example , b1608 + 656 has two interacting lens galaxies inside the einstein radius and the lens galaxies of rxj0911 + 0551 and q0957 + 561 are members of relatively massive clusters where the cluster potential is important to interpreting the time delays .
in fact , if we assume the two time delay lenses in clusters ( q0957 + 561 and rxj0911 + 0551 ) have similar halo structures to the other lenses , then in order to obtain the same value of @xmath103 as that of the isolated lenses , the clusters must be contributing significantly to the average surface density ( @xmath136@xmath137 ) .
thus , by the time the sample is narrowed to isolated , early - type lenses with good astrometry , good photometry and accurate time delays , almost nothing is left . as a result
, i find much of the recent debate in lensing circles about time delay lenses to be sterile .
that one person s `` golden lens '' can match the party s value of @xmath103 with a flat rotation curve is largely meaningless when someone else s `` golden lens '' requires a constant mass - to - light ratio to do so unless you can also provide a coherent explanation of why the mass distributions of the two lenses should be different .
hence the philosophy we adopt here the party says @xmath103 is known and should not be challenged unless you want to count trees in siberia , so we should focus on why we can not produce a coherent story about the structure of lens galaxies at the party s value of @xmath103 before deciding to attempt a revolution .
one possibility , that many delay measurements are less accurate than believed , is easily solved by monitoring the lenses longer .
the other possibility , that the halo structures of early - type galaxies are heterogeneous rather than homogeneous , can be addressed independent of the actual value of @xmath103 .
we can make some initial observations about the homogeneity of halos .
if we take the four relatively isolated bulge - dominated time delay lenses ( pg1115 + 080 , sbs1520 + 530 , b1600 + 434 and he21492745 ) , then we can show that for the same value of @xmath138 , the lenses must have similar mass distributions . for @xmath139 they can have flat rotation curves , while for @xmath140their mass distributions must be nearly constant @xmath141 ( kochanek @xcite ) . while we can not ( without knowing @xmath103 ) use the time delays to determine which mass distribution is correct , we know that their mass distributions are homogeneous . if we use our surface density formalism , they have mean surface densities of @xmath142 with an upper limit of @xmath143 on the intrinsic scatter in @xmath78 between the halos .
the uncertainties are dominated by the time delay measurement uncertainties for the lenses ( kochanek @xcite ) .
this result is somewhat puzzling when we compare it to the stellar dynamical results .
treu & koopmans ( @xcite ) argue that pg1115 + 080 must have a falling rotation curve while the typical lens they have studied has a slightly rising rotation curve ( treu & koopmans @xcite ) .
but the homogeneity of the surface density estimates based on the time delays indicates that if pg1115 + 080 has a falling rotation curve then sbs1520 + 530 , b1600 + 434 and he21492745 must as well .
it is odd that the typical time delay lens would have a falling rotation curve while the typical stellar dynamical lens would have a rising rotation curve
the most likely solution is a systematic bias in one of the methods .
this will be easily addressed once we have a larger overlapping sample of galaxies with time delay and velocity dispersion measurements . and second @xmath144 derivatives of the delay - corrected differential light curves for the lensed images in our monitoring sample with adequate data in mid-2004 .
the point - type changes depending on whether the derivative measurements are consistent with zero .
the solid line shows the relation expected for a point source crossing a fold caustic , and the dashed line shows the lower limit on @xmath144 for a point mass lens .
the second derivatives are not very reliable at present because many of the light curves used for the estimates were quite short ( months ) we do not see multi - magnitude variations in any of our light curves .
, title="fig:",width=240 ] and second @xmath144 derivatives of the delay - corrected differential light curves for the lensed images in our monitoring sample with adequate data in mid-2004 .
the point - type changes depending on whether the derivative measurements are consistent with zero .
the solid line shows the relation expected for a point source crossing a fold caustic , and the dashed line shows the lower limit on @xmath144 for a point mass lens .
the second derivatives are not very reliable at present because many of the light curves used for the estimates were quite short ( months ) we do not see multi - magnitude variations in any of our light curves .
, title="fig:",width=240 ] at this point i believe the only good solution is to simply measure many more delays with significantly higher accuracies . with 25 accurate ( @xmath145 ) time delays in systems with good ancillary data ( photometry , astrometry )
, it will be relatively simple to determine the heterogeneity or homogeneity of early - type galaxy halos .
the delay sample will also better overlap systems with extra constraints or stellar dynamical measurements .
for a fixed value of @xmath103 , time delay measurements are a significantly better probe of the halo structure than either statistical studies or stellar velocity dispersion measurements because they are both more accurate and directly measure the quantity of greatest interest , the surface density in the transition region from luminous to dark matter , @xmath78 .
we have started such a program using the smarts 1.3 m telescope in the south and an array of telescopes in the north ( mdm , flwo , apo @xmath146 ) to monitor roughly 25 lenses 1 - 2 times / week when they are visible . since starting in early 2004
we have measured two new time delays in he04351223 and sdss1004 + 4112 .
we also see an abundance of microlensing variability , whose utility we discuss in [ sec : micro ] .
[ fig : lcurves ] shows the light curves for he04351223 and sdss0924 + 0129 from the first season of monitoring .
[ fig : dm0435 ] shows the results of fitting a model consisting of the luminous lens galaxy and an nfw dark matter halo to he04351223 constrained by the time delay measurement with the hubble constant fixed to @xmath147 .
if we start from a constant @xmath141 model and then reduce the mass of the luminous galaxy while adding the nfw halo , we see the goodness of fit improves with a minimum where the luminous galaxy has only @xmath148 of its mass in the constant @xmath141 model . as we improve the delay from its current 10% accuracy , these uncertainties will shrink more or less proportionately . the other obvious result from our first season
is that microlensing of lensed quasars is ubiquitous . in fig .
[ fig : lcurves ] you can see that the light curves of images a and d in he04351223 are nearly identical while those for b and c look different .
images a and d have the longest delay and are the pair for which we have a time delay measurement . in the first season images b and c were both fading by @xmath149 mag / year relative to a and d due to microlensing .
other light curves , like the ones for sdss0924 + 0129 shown in fig .
[ fig : lcurves ] , show only brightness variations due to microlensing .
collecting and analyzing the microlensing variability is important because it provides our final probe of halo structure using lenses .
microlensing variability depends on both the surface density in stars @xmath150 and the total surface density @xmath151 .
the regime for a standard halo model is that the total surface density is still relatively high ( @xmath152 ) but the stars make up a small fraction of the total ( @xmath153 , see fig .
[ fig : halo ] ) . in this regime , microlensing ( or substructure for that matter ) has a distinctive statistical pattern that strongly distinguishes between images that are saddle points and minima ( schechter & wambsganss @xcite ) .
in particular , there is considerable phase space for significantly demagnifying saddle point images .
the most dramatic example of this is the ( saddle point ) image d of sdss0924 + 0219 , which is almost ten times fainter than expected ( see fig . [
fig : sdss0924 ] ) .
we can already see in the sdss0924 + 0219 light curves of fig .
[ fig : lcurves ] that the images are being microlensed , but if the suppression of image d is due to microlensing we should eventually see it brighten dramatically , overshooting the flux of image a. because the statistical properties of the microlensing patterns depend on @xmath151 and @xmath75 we can constrain them by analyzing the light curves . in kochanek ( @xcite )
we developed a method for analyzing microlensing light curves and applied it to the only ( hitherto ) well - monitored lens q2237 + 0305 , focusing on the ogle light curves of wozniak et al .
( @xcite ) . in this system
we see four images of a quasar buried in the bulge of a low redshift spiral galaxy so we would expect to find that @xmath154 , and this is borne out when we analyze the microlensing variability as shown in fig .
[ fig : kstar ] . even after including all the other uncertainties ( sources sizes , relative velocities @xmath146 ) we find that @xmath155 if we include no prior assumption on the mean stellar masses , and @xmath156 if we force the mean stellar mass to be in the range of @xmath157-@xmath158 .
we do not yet have long enough light curves to make a similar analysis of any other lens , but we are beginning to get there .
[ fig : micro ] shows a crude view of the amount of microlensing , where we estimate the first and second derivatives of the light curves due to microlensing from the data available in mid-2004 .
most images have measurable first and second derivatives that can not be attributed to intrinsic variability .
since we want accurate time delays rather than simply quitting once the delay is measured to 10% , we will be monitoring systems like he04351223 for many more years .
the same longer time baselines are needed to obtain useful constraints on the statistical properties of the magnification pattern produced by the stars .
the microlensing variability can also be used to probe the structure of quasar accretion disks .
for example , even the limited data for sdss0924 + 0219 is sufficient to show that it must have an accretion disk that is significantly smaller than that in q2237 + 0305 , as we might expect from the lower luminosity of sdss0924 + 0219 .
the overall summary of this review is that the future is bright , but the present is painful . on the positive side , we understand the physics of constraining mass distributions with lenses very well . in general , analyses based on image constraints , statistics , velocity dispersions , time delays and microlensing are all generally consistent and indicate that early - type galaxies have appreciable dark matter on intermediate scales ( @xmath159 ) leading to a net mass distribution that is close to isothermal for the typical lens . on the negative side ,
we have not communicated our understanding of how gravitational lenses constrain mass distributions very well .
arguments about methods ( parametric versus non - parametric , statistics versus time delays versus dispersions and so on ) tend to obscure rather than illuminate the underlying unity of the results .
the fundamental question at this point is the degree to which early - type galaxy halos are heterogeneous in their structures on these scales .
most of this is driven by a fairly familiar astronomical problem .
first , there is a preferred , average , naive , straw man , or whatever mass model in which early - type galaxies follow the conspiracy of late - type galaxies and have nearly flat rotation curves with the contribution from the dark matter kicking in just as the contribution from the luminous matter fades .
theoretical halos with the expected baryonic mass fraction would be expected to lie close to this model , usually with a slowly falling rather than a truly flat rotation curve .
second , when we apply the available methods to the lens sample , we find that this is just about right , but there are signs that there is appreciable scatter about the mean . because of small sample sizes , measurement errors and systematic errors we can not yet be sure whether this scatter is real and the halo structure is genuinely heterogeneous or if we have simply underestimated our measurement uncertainties .
this puts the field in a confused state where everyone argues for their object or method but can not produce a synthesis of all the available results to produce a convincing final answer . until we can achieve this synthesis
we will continue to have a problem .
fortunately the way out is straightforward more data .
no one has found a fundamental flaw in any of the methods .
the problem is simply that the samples are too small and insufficiently overlapping to produce a clear result .
my own feeling is that the method with the least systematic problems for addressing the homogeneity or heterogeneity of early - type galaxy halos is monitoring lenses to measure accurate time delays and comparing the structure of lens galaxies at a fixed value of @xmath103 . for fixed @xmath103 ,
time delays measure the surface density of the galaxy near the lensed images essentially to the accuracy of the time delay measurement , and the surface density near the lensed images is exactly the quantity needed to understand the halo structure .
moreover , the long term monitoring needed to measure accurate time delays also provides microlensing variability light curves that can be used to constrain the fraction of the surface density in the form of stars .
there is a very convenient coincidence that the part of parameter space that should be occupied by the lens galaxies in a standard cdm model also has unique microlensing characteristics .
kochanek , c.s . ,
2004 , the saas fee lectures on strong gravitational lensing , part 2 of gravitational lensing : strong , weak , and micro , proceedings of the 33rd saas - fee advanced course , g. meylan , p. jetzer & p. north , eds .
( springer - verlag : berlin ) [ astro - ph/0407232 ] sykes , c.m . ,
browne , i.w.a . ,
jackson , n.j . , marlow , d.r . , nair , s. , wilkinson , p.n .
, blandford , r.d . ,
cohen , j. , fassnacht , c.d . , hogg , d. , pearson , t.j . ,
readhead , a.c.s . ,
womble , d.s . ,
myers , s.t . ,
de bruyn , a.g . , bremer , m. , miley , g.k .
, & schilizzi , r.t . , 1998 , mnras , 301 , 310 | while there is convincing evidence that the central regions ( @xmath0 ) of early - type galaxies are dominated by stars and that the outer regions ( @xmath1 ) are dominated by dark matter , the structure of early - type galaxies in the transition region ( a few effective radii @xmath2 ) between the stars and the dark matter is unclear both locally and in gravitational lenses .
understanding the structure of galaxies in this transition region is a prerequisite for understanding dark matter halos and how they relate to the luminous galaxy .
potentially the best probe of this region is the sample of @xmath3 strong gravitational lenses .
i review the determination of mass distributions using gravitational lenses using image positions , statistics , stellar dynamics , time delays and microlensing .
while the present situation is confusing , there is little doubt that the existing problems can be resolved by further observations . |
Illustration by Jim Festante. Photos by Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Jewel Samad/Getty Images; Patrick Smith/Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Mandel Ngan/Getty Images; Spencer Platt/Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Saul Loeb/Getty Images; Chip Somodevilla/Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Joshua Roberts/Getty Images; Justin Sullivan/Getty Images.
Courtesy of Library of Congress.
Illustration by Jim Festante. Photos by Getty Images.
Courtesy of Library of Congress.
Though the gentlemen who vied for the Republican presidential nomination disagreed on many things, from tax policy to contraception to the feasibility of establishing a colony on the moon, there's one critical issue on which they were firmly in accord: facial hair. This was true of the eventual nominees in the last election, and the one before that, and in every other presidential contest going back to 1916. One hundred years ago, two of the four men running for president were proudly hirsute, as were two of the four vice-presidential candidates. Today, the sitting president can't grow whiskers and his challengers wouldn't dare try. When did the beard lose its political prestige?
In his delightful 1930 monograph Concerning Beards, Edwin Valentine Mitchell notes that "the fortunes of the beard have always fluctuated through the ages. It flourishes for a time in full splendor, then diminishes in size, and finally disappears altogether, only to burst forth once more in all its former glory." In much of the premodern era, a healthy beard connoted influence and high status; Mitchell says that "one ancient king actually made a terrible scene because the reigning head of another state sent a beardless youth upon a political errand to his court." The opposite is true, too: Men pressed into servitude were often shorn of their beards as a sign of subjugation.
By the time of the Revolutionary War, facial hair had gone out of style in America, explains Victoria Sherrow in her Encyclopedia of Hair: A Cultural History. And, indeed, the first 15 U.S. presidents were beardless, though John Quincy Adams did sport a rather nice pair of muttonchops. A sign of the times: In 1830, a man named Joseph Palmer was jailed for a year in Fitchburg, Mass., after fending off four men who attempted to forcibly rid him of his widely loathed beard. (Palmer's gravesite is marked with a monument that reads "Persecuted for Wearing the Beard.”)
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In the mid-1800s, whiskers made a comeback in American political life—or, as Reginald Reynolds put it in his odd 1950 volume, Beards, "a beard was becoming almost as necessary as a Bible to a rising demagogue." Abraham Lincoln began his presidency as a baby-faced rube from rural Illinois, governing a country on the brink of collapse. After growing a beard at the behest of a schoolgirl, he vanquished the South and passed into legend.
Every subsequent president up to William Howard Taft wore some sort of facial hair, except for Andrew Johnson, who was impeached, and William McKinley, who was assassinated. If you wanted the Republican Party's nomination, a beard was as necessary then as a Reagan fetish is now.
That changed in the early 1900s, likely due to the advent of the Gillette safety razor, which debuted in 1903 and eased the performance of what had long been a hated and bloody chore. Soon thereafter, the military banned beards, as they interfered with the seal on gas masks. By 1930, Edwin Valentine Mitchell would write that, "In this regimented age the simple possession of a beard is enough to mark as curious any young man who has the courage to grow one."
In politics, that's been the case ever since. No sitting president has worn facial hair since Taft. Charles Evans Hughes was the last bearded major-party presidential nominee; he lost to Woodrow Wilson in 1916. Today, it’s received wisdom that candidates should be clean-shaven. “Except for a brief window from Sept. 11 to 2003-2004, most of the last 15 years in politics have been about change, and a wizened graybeard doesn’t really convey change,” says Jeff Jacobs, creative director and founder of NextGen Persuasion, a campaign consultancy firm. “In 500 campaigns I’ve almost never had a conversation with a candidate about whether or not to have facial hair,” explains Democratic media consultant John Rowley. “It’s almost like conventional wisdom about facial hair has already hit candidates before they even run.”
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The beard’s absence from modern American politics can be partially blamed on the two scourges of the 20th century: Communists and hippies. For many years, wearing a full beard marked you as the sort of fellow who had Das Kapital stashed somewhere on his person. In the 1960s, the more-or-less concurrent rise of Fidel Castro in Cuba and student radicals at home reinforced the stereotype of beard-wearers as America-hating no-goodniks. The stigma persists to this day: No candidate wants to risk alienating elderly voters with a gratuitous resemblance to Wavy Gravy.
A few politicians have managed to win elective office in spite of their hairy visages. Moderate, beard-having Ohio Republican Steve LaTourette has been a House stalwart since 1995. Who liked Rep. David Obey's beard? The voters of Wisconsin's seventh district did: They elected its wearer to 21 consecutive terms before Obey retired in 2011. Sen. Tom Coburn sometimes wears a beard, and its occasional appearance is eagerly awaited by Hill types. Coburn's beard even has its own tribute Twitter account, which boots up whenever the senator's whiskers begin to sprout. (Sample tweet: "i've asked tom to spend a few minutes combing me before tonight's #SOTU, i must maintain my supple virility.")
Sometimes, a beard makes it seem like a politician is either emerging from or embarking on a three-day Smirnoff bender. “A lot of times people associate beards with what happens after you lose a campaign and you let yourself go,” says Jacobs. Indeed, one need only picture a dazed, broken Al Gore circa 2001, puffy and bearded like a white-collar woodsman gone to seed, to understand why politicos identify facial hair with failure and shame. There are other negative connotations, too. "One misperception is that somebody who has a beard is lazy and can't be bothered to shave, sort of on par with somebody who's too lazy to brush his teeth," says Phil Olsen, the founder and self-appointed captain of Beard Team USA, who would know. "Some people perceive beards as disrespectful."
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When I asked John Rowley if he could think of a circumstance when he might actually advise a candidate to grow facial hair, he paused for a few seconds. “Maybe when people have a lot of scars on their face from an accident,” he finally answered.
Barring a surge in the number of disfigured men running for office, voters shouldn’t expect the political beard to re-emerge anytime soon. Because the real reason most candidates don't have beards is because most men don't have beards, and there’s nothing to be gained by deviating from the mainstream. “Candidates get criticized mercilessly on what their appearance is, so they go to great lengths to get a political uniform down that isn't too distracting,” says Rowley. Which makes sense: The last thing a candidate wants is for his crazy beard to distract from his sober, rational message about living on the moon.
And yet, though beards might not be all that common, they’re actually well received among the general population. "I do a lot of work with visual communications, facial expressions, how people read faces," says Jeff Jacobs. "Facial hair poses no distraction or causes no aversions whatsoever." Academic research bears this out: In a 1990 paper for the journal Social Behavior and Personality, J. Ann Reed and Elizabeth M. Blunk reported "consistently more positive perceptions of social/physical attractiveness, personality, competency, and composure for men with facial hair." More recently, researchers Barnaby J, Dixson and Paul L. Vasey rejected the notion that "facial hair decreases a male's perceived social status because it is associated with traits such as vagrancy." In fact, participants in their study "rated bearded men as having higher social status than clean-shaven men."
Are there any politicians whose campaigns might have been helped if they had worn beards? “You put John Kerry in the room with a well-groomed beard, and it makes it a lot harder for that flip-flopper charge to stick,” says Jacobs. “He seems like a guy who changes his positions because they evolve, and because he thinks about things.” Former New Mexico governor Bill Richardson ran for the Democratic presidential nomination in 2008, only to drop out after getting no traction in Iowa and New Hampshire. Soon thereafter, he grew a beard; if he had had one during the primaries, voters might not have been scared off by his hideous double chin. And despite his name, Jon Huntsman struck this year's Republican primary voters as the sort of person who might faint in terror if invited pheasant-shooting. A beard might have lent his campaign a solidity that it so desperately lacked.
Beards won’t take hold in politics, it seems, until a bearded candidate wins a high-profile election. Politicians are unabashed copycats and generally won’t try a new campaign strategy until it’s been proven to work. Howard Dean’s successful use of online organizing in the 2004 presidential primaries paved the way for every digital campaign tactic in use today. Bill Clinton’s smooth jazz stylings in 1992 led directly to the “Saxophone Congress” of 1994. ||||| New ‘Beard PAC’ to raise unlimited funds to support bearded candidates
By Eric W. Dolan
Thursday, April 4, 2013 19:57 EDT
The United States has a serious lack of bearded politicians, according to a newly formed Super PAC that hopes to reverse the situation.
The group, called Bearded Entrepreneurs for the Advancement of a Responsible Democracy (BEARD), officially filed with the Federal Elections Committee on Wednesday. It plans to raise unlimited sums of money to support bearded candidates nationwide.
Jonathan Sessions, who founded Beard PAC along with Andy Shapero, told Raw Story the group plans to create a beard review committee to investigate the quality and longevity of beards on candidates. He explained that his Super PAC would not support candidates sporting only a mustache, but would consider a goatee “on the right candidate.”
“With the resurgence of beards in popular culture and among today’s younger generation, we believe the time is now to bring facial hair back into politics,” Sessions said in a statement announcing the new Super PAC.
“We haven’t had a bearded major party candidate run for President since Charles Evans Hughes ran and lost in 1916, and there has been a recent wave of retirements amongst bearded Congressmen, including David Obey and Steve LaTourette,” he added. “Our hope is that we can start to reverse this disturbing trend.”
Sessions acknowledged his Super PAC would likely only support male candidates, though he was willing to support a bearded woman if the situation should arise. He said it was a shame that less than 20 percent of the 113th Congress was made up of women. Sessions fully supports electing women to Congress, but his group if solely focused on the “niche” of bearded candidates, he explained.
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[Man with beard via Shutterstock] | – At last, a super PAC that can be described as hirsute—it's Bearded Entrepreneurs for the Advancement of a Responsible Democracy, aka BEARD, a political action committee dedicated to advancing bearded candidates. Founded by Jonathan Sessions and Andy Shapero, BEARD is as quirky as you might imagine: A planned committee will work to root out fly-by-night beards by investigating the quality and longevity of candidates' facial hair, reports the Raw Story. A mustache alone won't be enough to qualify, but goatees will be considered "on the right candidate," says Sessions. Sessions notes that the US had not had a "bearded major party candidate" make a bid for the White House since Charles Evans Hughes in 1916; further, bearded congressmen like David Obey and Steve LaTourette have retired in recent years. "With the resurgence of beards in popular culture and among today's younger generation, we believe the time is now to bring facial hair back into politics," says Sessions. He adds that BEARD is not opposed to funding female candidates, should a bearded one appear. (Slate took a lighthearted look at the long-running lack of political beards during the 2012 election.) |
indentation tests have been used for decades to identify mechanical properties of articular cartilage @xcite and to assess its viability @xcite .
there is a wide variety of indentations tests and their possible applications .
first of all , indentation tests can be classified with respect to the type of indenter used ( cylindrical flat - ended , spherical , etc . ) . in the simplest case of cylindrical indenter ,
the contact area is supposed to remain constant during the indentation process , and only two mechanical variables , namely , the contact force , @xmath0 , and the indenter displacement , @xmath1 , can be recorded as functions of time during the depthsensing indentation .
second , indentation tests can be viewed according to the main mechanical parameter determined ( e.g. , short - time bulk modulus @xcite , indentation stiffness @xcite , pulsatile dynamic stiffness @xcite ) that , of course , depends on the mathematical model employed .
for instance , the derivative @xmath2 is known as the indentation stiffness , and will be a variable quantity for time - dependent materials like articular cartilage .
third , indentation tests can be classified according to protocol types ( e.g. , multiple ramp - and - hold protocol for creep test @xcite ) .
this means that the time - history of loading is important . finally ,
depending on the primary variable parameter chosen , one can distinguish displacement - controlled or load - controlled indentation tests , when @xmath1 or @xmath0 is assumed to be controlled , respectively .
in particular , linear and non - linear monotonic displacement - controlled and force - controlled indentation loading paths were considered recently by @xcite . in their recent paper ,
@xcite employed a hybrid - type test consisting of two stages , one of which is displacement - controlled , while the other can be regarded as load - controlled . in the present note ,
we apply the viscoelastic layer model for evaluating the so - called rebound indentation test and clarifying its applicability for assessing viability of articular cartilage .
we consider a cylindrical , flat - ended indentation test , which is composed of two stages . in the first stage , called the indentation phase , the sample is subject to loading at a constant speed @xmath3 to achieve an indentation depth of @xmath4 .
that is the indenter displacement is assumed to be specified according to the law @xmath5 the maximum indenter displacement at the end of the first stage is given by @xmath6 hence , specifying the values of @xmath3 and @xmath4 , we obtain the duration of the first stage @xmath7 .
note that instead of an imposed maximum displacement , @xmath4 , @xcite operated with a prescribed value of maximum strain ( deformation ) @xmath8 , which depends on the layer sample thickness @xmath9 .
further , we assume that at the indentation depth @xmath4 the load is immediately removed and the second stage , called the recovery phase , lasts for a theoretically indefinite time . in the recovery phase
, we have @xmath10 we distinguish in the notation the displacements , @xmath11 and @xmath12 , and the contact loads , @xmath13 and @xmath14 , corresponding to aforementioned two test stages . in the first stage ,
the function @xmath11 is specified by eq .
( [ 1jt(2.1 ) ] ) , while @xmath13 is unknown . on the contrary ,
the displacement function @xmath12 is unknown , whereas the contact load @xmath14 is specified by eq .
( [ 1jt(2.3 ) ] ) , in the second stage .
let us assume that an articular cartilage sample may be modeled as a viscoelastic layer of thickness @xmath9 bonded to a rigid substrate . for the sake of simplicity , we neglect friction and assume that poisson s ratio , @xmath15 , of the layer material is time independent .
these are standard assumptions made in most of the mathematical models .
then , based on the solution to the elastic contact problem of frictionless indentation of an elastic layer @xcite and applying the elastic - viscoelastic correspondence principle @xcite , one can arrive at the following equation between the indenter displacement @xmath1 and the applied force @xmath0 : @xmath16 here , @xmath17 is the contact radius , @xmath18 is a dimensionless factor accounting the thickness effect through the ratio @xmath19 @xcite , @xmath20 is the relaxation modulus , @xmath21 is the time variable , @xmath22 is the time moment just preceding the initial moment of contact .
it has been tacitly assumed that @xmath23 for @xmath24 .
note that eq .
( [ 1jt(1.3 ) ] ) was previously used in a number of studies @xcite .
let @xmath25 be the relaxed elastic modulus , that is the limit of modulus @xmath20 at @xmath26 .
taking into account the relation @xmath27 , where @xmath28 is the relaxation function , we rewrite eq .
( [ 1jt(1.3 ) ] ) in the following form : @xmath29 considering eq .
( [ 1jt(1.6 ) ] ) as an integral equation with respect to @xmath1 , one arrives at the inverse relationship @xmath30 where @xmath31 is the creep function . with the appropriate relaxation function @xmath28 and creep function @xmath31 , eqs .
( [ 1jt(1.6 ) ] ) and ( [ 1jt(1.7 ) ] ) can be used in the general case of viscoelastic solid . in the indentation phase , according to eqs .
( [ 1jt(2.1 ) ] ) and ( [ 1jt(1.6 ) ] ) , we will have @xmath32 the maximum contact load @xmath33 is given by @xmath34 in the recovery phase , in accordance with eq .
( [ 1jt(1.7 ) ] ) , we can write @xmath35 in view of ( [ 1jt(2.3 ) ] ) , the last integral in ( [ 1jt(4.3 ) ] ) is equal to @xmath36 , where @xmath37 is defined by ( [ 1jt(4.1a ) ] ) .
the derivative @xmath38 entering the first integral in ( [ 1jt(4.3 ) ] ) can be computed by differentiating the both sides of eq .
( [ 1jt(4.1 ) ] ) .
thus , taking also into account eq .
( [ 1jt(4.1a ) ] ) , we can rewrite eq .
( [ 1jt(4.3 ) ] ) as follows : @xmath39 \psi(\tau)\,d\tau .
\label{1jt(4.4)}\ ] ] it is interesting and very important to observe that , in view of ( [ 1jt(4.4 ) ] ) , the rebound displacement @xmath12 does not depend on the layer material constants @xmath25 and @xmath15 as well as on the layer s thickness @xmath9 .
if the layer s material follows a linear standard three - parameter viscoelastic solid model , we will have @xmath40 where @xmath41 is the characteristic relaxation time of strain under applied step of stress , @xmath42 is the ratio of the relaxed elastic modulus @xmath25 ( the limit of modulus @xmath20 at @xmath26 ) to the unrelaxed elastic modulus @xmath43 ( modulus @xmath20 at @xmath44 ) , i.e. , @xmath45 . according to eq
( [ 1jt(1.4 ) ] ) , we have @xmath46 after the substitution of the expressions ( [ 1jt(1.5 ) ] ) , eq .
( [ 1jt(4.4 ) ] ) yields @xmath47 it is interesting and important to point out that in view of ( [ 1jt(4.5a ) ] ) the rebound displacement @xmath12 depends on the time variable @xmath21 only through the exponent factor @xmath48 .
following @xcite , we determine the rebound strain , @xmath49 , as the relative elastic reverse displacement that the viscoelastic layer recoves to from the moment of unloading . in other words
, we put @xmath50 now , taking into account eqs .
( [ 1jt(2.1 ) ] ) and ( [ 1jt(2.2 ) ] ) , we rewrite eq .
( [ 1jt(3.1 ) ] ) in the form @xmath51 where @xmath52 is the maximum strain at the end of the loading stage , and it is assumed that @xmath53 .
[ figurer2.pdf ] according to ( [ 1jt(3.2 ) ] ) and ( [ 1jt(4.5a ) ] ) , in the case of standard viscoelastic solid model , the rebound strain can be represented as @xmath54 where @xmath55 is a dimensionless constant , which is proportional to the factor @xmath8 and depends on the ratios @xmath42 and @xmath56 .
the experimental points depicted in fig .
[ figurer2.pdf ] were obtained by @xcite in the indentation tests with a relative large maximum indentation strain of 30 per cent .
based on ( [ 1jt(3.2z2 ) ] ) , we make use of the following formula @xmath57 with three fitting parameters @xmath55 , @xmath58 , and @xmath41 .
the results of the least - squares best fit of the analytical expression ( [ 1jt(3.2z3 ) ] ) to the experimental data are as follows : @xmath59 , @xmath60 s , @xmath61 ( normal cartilage ) and @xmath62 , @xmath63 s , @xmath64 ( artificially degraded cartilage ) .
it should be noted that in the both cases , the values of parameter @xmath58 are different from @xmath65 ( which is the experimentally imposed maximum strain @xmath66 ) . in other words ,
the cartilage samples do not show complete recovery .
further , the characteristic relaxation time @xmath41 is found to decrease with degradation .
such a tendency is in agreement with that obtained by @xcite in the shear creep test for human articular cartilage .
in the present study , the rebound indentation test has been evaluated in the framework of viscoelastic layer model . for the contact force @xmath13 in the displacement controlled stage and for the indentation displacement @xmath12 in the load - controlled stage , the closed - form analytical expressions ( [ 1jt(4.1 ) ] ) and ( [ 1jt(4.4 ) ] ) , respectively , have been derived for an arbitrary viscoelastic solid model . in the case of standard viscoelastic solid model ,
a simple exponential behavior was established for the rebound displacement @xmath12 ( see eq .
( [ 1jt(4.5a ) ] ) ) .
the theoretically predicted dependence of @xmath12 on the time variable @xmath21 only through the exponent @xmath48 was verified using the three - parameter fitting formula for the rebound strain ( [ 1jt(3.2z3 ) ] ) . from the view point of assessing viability of articular cartilage ,
the main finding of the present study is that the rebound displacement @xmath12 does not depend on the layer material constants @xmath25 and @xmath15 as well as on the layer s thickness @xmath9 . at the same time
, the rebound deformation mainly depends on the characteristic relaxation time @xmath41 , which is attributed to the articular cartilage permeability .
the authors would like to thank dr .
m. stoffel ( rwth aachen university ) for bringing their attention to the paper of @xcite .
one of the authors ( i.a . ) also gratefully acknowledges the support from the european union seventh framework programme under contract number piif - ga-2009 - 253055 .
preliminary findings of this study were presented at a research seminar of the laboratory for biomechanics and biocalometry ( university of basel ) .
the authors are thankful to professor a.u .
dan daniels and dr .
d. wirz for valuable discussion
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78b , 347357 . | the rebound indentation test consisting of the displacement - controlled and load - controlled stages is considered for a frictionless cylindrical flat - ended indenter .
the mechanical behavior of an articular cartilage layer sample is modeled in the framework of viscoelastic model with time - independent poisson s ratio .
closed - form analytical expressions for the contact force ( in the displacement controlled stage ) and for the indentation displacement ( in the load - controlled stage ) are presented for an arbitrary viscoelastic solid model .
the case of standard viscoelastic solid model is considered in detail .
it has been established that the rebound displacement ( that is the indentation displacement in the load - controlled stage ) does not depend on the relaxed elastic modulus and poisson s ratio as well as on the layer s thickness .
, rebound indentation test , cartilage layer , viscoelastic contact problem |
A poll suggests Pope Benedict XVI had big shoes to fill in Mexico, where he celebrates Mass today before heading to Cuba.
There is really no better place to measure the pulse of a country than in a beauty salon. And in Mexico City, in Vanessa Gonzalez's salon, the trip of Pope Benedict XVI to Mexico measures at, she pauses, approximately zero. “I have not heard one client talking about it,” she says.
But during the last papal visit to this country ten years ago – by the late Pope John Paul II – the swirling chairs and shampoo stalls were abuzz. “People adore Juan Pablo,” she says.
Pope Benedict XVI arrived in Mexico on Friday, and today celebrates an open mass in a park in Silao, Guanajuato, a deeply Catholic state in central Mexico, before heading on to Cuba tomorrow.
His trip has not been without controversy. He comes amid gruesome drug violence that has claimed 50,000 lives, and while most victims are rival traffickers, anyone can end up a target, including a public figure. He is bypassing Mexico City altogether, leaving some residents feeling snubbed and others speculating that he is avoiding the capital's embrace of gay marriage and abortion (the Vatican says the altitude is what's keeping him away). And Guanajuato state happens to be run by the ruling, Catholic-friendly National Action Party (PAN), which some see as a political message. They say it's no coincidence that the pope is visiting the country as it is about to kick off its presidential race.
But away from the political chatter, regular Mexicans are hardly paying attention. Mexico is devoutly Catholic, home to the second-largest Catholic population in the world behind Brazil. But the current pope has done little to move Mexican Catholics the way his predecessor did – John Paul II often brought the faithful to tears.
Ms. Gonzalez says even her father, a man not easily moved, broke down crying upon passing a caravan carrying John Paul II on his first-ever trip to the nation in 1979. He would visit Mexico five times in total.
Her mother, meanwhile, is devoutly Catholic and easily moved, praying a full hour each morning and another hour each night. But she hasn't even talked about Benedict XVI's visit – Gonzalez didn't even exactly know when he was scheduled to arrive. If it were John Paul II, she says, she'd probably know his entire itinerary.
In fact, mention the current pope and the first words out of everyone's mouth is “seco,” meaning dry. That's usually followed by “serio,” or serious. Some say he seems harsh, and most of all, he's not “charismatic.”
“He doesn't have charm,” says Julio Valdez, a parking valet outside a local Catholic parish.
“I don't know anything about this pope,” says Elizabeth, who makes tortillas outside the same church and says she's too shy to share her last name. “Everything that John Paul did and said was good, just good,” she says, her face lighting up. “You just say his name, and I am full of emotion.”
Their feelings are reflected in a survey by Demotecnia, which showed that 77 percent of Catholics surveyed said that if they are moved at all by the pope's visit, it doesn't compare to how they felt ahead of John Paul II's visits. Only 20 percent of Catholics polled said they were “very excited” about the trip.
A good portion of those must live in Guanajuato. The state hosting Benedict this weekend is among the most religious in Mexico, with 94 percent calling themselves Catholic, according to the Mexican census. It may be a coincidence but when the Monitor was recently in Guanajuato to write about the pope's visit, the first three people interviewed were named in order: Jesus, Magdalena, and Moises.
Moises Silva, leaving the main basilica of the state capital Guanajuato on Ash Wednesday, said he was planning on battling the mobs to capture a glimpse of the pope. “It is a blessing that he is going to visit,” said Mr. Silva.
Magdalena Vargas, a city accountant, said her feelings of joy were “infinite.” “One can hardly believe that the highest representative is coming here,” she said. “We are overjoyed.” ||||| Pope Benedict XVI addressed hundreds of thousands of Mexicans seeking a message of hope for their violence-plagued country at an open-air Mass on Sunday, saying renewing their hearts and faith would help them in troubled times.
Pope Benedict XVI waves from the popemobile wearing a Mexican sombrero as he arrives to give a Mass in Bicentennial Park near Silao, Mexico, Sunday, March 25, 2012. (AP Photo/Eduardo Verdugo) (Associated Press)
Pilgrims wait for the arrival of Pope Benedict XVI for Mass in Bicentennial Park near Silao, Mexico, Sunday March 25, 2012. (AP Photo/Eduardo Verdugo) (Associated Press)
Pilgrims cheer and sing as they wait at the site where Pope Benedict XVI will give a Mass in Bicentennial Park near Silao, Mexico, Sunday March 25, 2012. (AP Photo/Dario Lopez-Mills) (Associated Press)
Pilgrims cheer and sing as they wait at the site where Pope Benedict XVI will give a Mass in Bicentennial Park near Silao, Mexico, Sunday March 25, 2012. (AP Photo/Dario Lopez-Mills) (Associated Press)
A baby is handed to Pope Benedict XVI for his blessing as he makes his way to the Plaza de la Paz in his popemobile, in Guanajuato, Mexico, Saturday March 24, 2012. At the entrance to Guanajuato, Benedict... (Associated Press)
A man waves a Mexican flag as a woman holds a portrait of Pope Benedict XVI, prior his arrival at the symbolic key ceremony of the city of Guanajuato, Mexico, Saturday March 24, 2012. At the entrance... (Associated Press)
Pilgrims cheer and sing as they wait at the site where Pope Benedict XVI will give a Mass in Bicentennial Park near Silao, Mexico, Sunday March 25, 2012. (AP Photo/Dario Lopez-Mills) (Associated Press)
A pilgrim cheers at the site where Pope Benedict XVI will give a Mass in Bicentennial Park near Silao, Mexico, Sunday March 25, 2012. (AP Photo/Dario Lopez-Mills) (Associated Press)
Pope Benedict XVI looks at white doves freed by children on the balcony of the Casa del Conde Rul in Guanajuato, Mexico, Saturday, March 24, 2012. Benedict arrived in Mexico Friday afternoon, a decade... (Associated Press)
Pope Benedict XVI arrives aboard of his popemobile in Guanajuato, Mexico, Saturday, March 24, 2012. Benedict arrived in Mexico Friday afternoon, a decade after the late Pope John Paul II's last visit.... (Associated Press)
Pope Benedict XVI waves from the popemobile wearing a Mexican sombrero as he arrives to give a Mass in Bicentennial Park near Silao, Mexico, Sunday, March 25, 2012. (AP Photo/Eduardo Verdugo) (Associated Press)
A vendor sells flags with the image of Pope Benedict XVI on a road near the site where the pontiff will give Sunday Mass at the Bicentennial Park near Silao, Mexico, Saturday March 24, 2012. (AP Photo/Dario... (Associated Press)
Pope Benedict XVI waves from the popemobile after a symbolic key ceremony in Leon, Mexico, Saturday March 24, 2012. Benedict arrived in Mexico Friday afternoon, a decade after the late Pope John Paul... (Associated Press)
He urged Christians "to look deeply into the human heart, especially in times of sorrow as well as hope, as are the present times for the people of Mexico and of Latin America." He spoke in the shadow of the Christ the King monument, one of the most important symbols of Mexican Catholicism.
Benedict compared the need for a "pure, sincere, humble" heart in present times to the situation in Biblical Israel "as it became aware of the persistence in its midst of evil and sin as a power, practically implacable and impossible to overcome."
He opened the Mass by presenting the gift of a mosaic of Jesus Christ to be displayed at the monument.
The pope flew over the monument in a Mexican military Superpuma helicopter en route to the Mass at Bicentennial Park, where he rode in the popemobile through an enthusiastic crowd. One person handed the pope a broad-brimmed Mexican sombrero that he wore on his way to the altar at the sun-drenched park.
"We pray for him to help us, that there be no more violence in the country," said Lorena Diaz, 50, who owns a jeans factory in Leon. "We pray that he gives us peace."
Benedict wanted to come to Guanajuato state specifically to see and bless the statue, which Pope John Paul II always wanted to visit but never did, said the Vatican spokesman, the Rev. Federico Lombardi.
The 72-foot (22-meter) bronze monument of Christ with its outstretched arms serves as a potent reminder to Mexicans of the 1926-1929 Roman Catholic uprising against the government and its anti-clerical laws that prohibited public Masses such as the one Benedict will celebrate before an estimated 350,000 people.
The statue "expresses an identity of the Mexican people that contains a whole history in relation to the testimony of faith and those who fought for religious freedom at the time," said Monsignor Victor Rene Rodriguez, secretary general of the Mexican bishops conference.
After nightfall Sunday the pope will remotely inaugurate its new lighting system.
Guanajuato state was the site of some of the key battles of the Cristero War, so-called because its protagonists said they were fighting for Christ the King. Historians say about 90,000 people died before peace was restored. The region remains Mexico's most conservatively Catholic.
With roads closed, pilgrims walked for miles to the Mass with plastic lawn chairs, water and backpacks. Old women walked with canes. Some Mass-goers wrapped themselves in blankets or beach towel-sized Vatican flags, trekking past vendors selling sun hats, flags, potato chips and bottles of juice.
Hundreds of young priests in white and black cassocks, waiting to pass through the metal detectors, shouted "Christ Lives!" and "Long Live Christ the King!" _ the battle cry of the Cristeros.
Many Mexicans said they were surprised by the warmth of Benedict, whose image is more reserved and academic than his popular predecessor, John Paul II, who was dubbed "Mexico's pope."
By Sunday morning, that seemed to have changed completely.
"Some young people rejected the pope, saying he has an angry face. But now they see him like a grandfather," said Cristian Roberto Cerda Reynoso, 17, a seminarian from Leon. "I see the youth filled with excitement and enthusiasm."
The pope was expected to continue his theme of calling Mexicans back to their faith to deal with the troubles of the times, including corruption, violence and poverty that has divided many families as some migrate to the United States in search of work.
"People leave for the good of their families," said Jose Porfirio Garcia Martinez, 56, an indigenous farmworker who came to the mass with 35 others from Puebla. "For us it's difficult, not seeing them for 10 years, communicating by phone and by Internet."
On Saturday, the pope called on the young to be messengers of peace in a country traumatized by the deaths of more than 47,000 people in a drug war that has escalated during a government offensive against cartels.
Eight relatives of victims of violent crime were invited to meet the pope as he left Guanajuato's government palace, Calderon's office said. Lombardi noted it wasn't a sit-down meeting so much as a brief greeting.
While the pope drew a rapturous response from the faithful, his second day in Mexico was not without criticism, particularly concerning the church's treatment of children and sexual abuse.
Victims of Marcial Maciel, the founder of the Legionaries of Christ, launched a book Saturday containing documents from the Vatican archives showing that Holy See officials knew for decades that Maciel was a drug addict who sexually abused his seminarians.
The 84-year-old pope, who will be going to Cuba on Monday, did not directly address the scandal during his limited remarks Saturday. But Lombardi said his words about the need to protect children from violence referred also to the need to protect them from priestly sexual violence.
___
Associated Press writer Michael Weissenstein reported this story in Silao and Nicole Winfield reported in Leon. AP writers Adriana Gomez Licon in Guanajuato and E. Eduardo Castillo in Leon contributed to this report.
___
Follow AP reporters covering the pope: twitter.com/(hashtag)!/AP/pope-visit | – Under the shadow of the Christ the King monument in the Roman Catholic heart of Mexico, Pope Benedict XVI said Mass before hundreds of thousands today, urging the violence-plagued nation to "look deeply into the human heart, especially in times of trouble." The Mass was a second call for Mexicans to fall back on their faith in coping with the drug war that has killed more than 47,000 lives, notes the AP. "We pray for him to help us, that there be no more violence in the country," said one woman. "We pray that he gives us peace." The pope first flew over the 72-foot monument, one of the cornerstones of Catholicism in Mexico, before riding through an adoring Bicentennial Park crowd in the Popemobile sporting a sombrero that someone had handed him. Meanwhile, the Christian Science Monitor reports that while Mexico may have welcomed Benedict with open arms, he's no "Juan Pablo." Benedict heads tomorrow to Cuba; Hugo Chavez will reportedly be there, following chemotherapy treatments. |
every year , a large number of patients present in the emergency department with low back pain .
fractures of the sacrum appear with a low incidence in these patients , with sacrum stress fractures even rarer .
they are more commonly recognized in athletes , especially long - distance runners.1
2
3
4 many conjectures have been made regarding the pathology of these fractures , with the most relevant being weakened bone or unusual loads that the normal bone is able to withstand.5 the high loads applied after birth are responsible for those fractures that are more common in the postpartum period.6
7
8
9 plain radiographs can not be performed during the pregnancy ; therefore , magnetic resonance imaging ( mri ) is the gold standard for diagnosis .
most commonly , a vertical shear in the sacrum is recognized with osseous edema in the surrounding tissues . in the majority of the cases ,
the fracture is treated conservatively with immobilization , manual therapy , hydrotherapy , and analgesics , which are used with great caution due to the drug interactions with the fetus.10 pain control is extremely difficult in these patients ; therefore , epidural catheters are used in some cases .
the purpose of this study is to report an extremely rare case of prepartum sacral stress fracture ( only two prepartum sacral stress fractures are described in the literature),7
10 which was treated conservatively with great effort for adequate pain control and delivery of a healthy newborn .
a 30-year - old patient who was 36 weeks and 4 days pregnant was referred by the obstetrics for low back pain that started 1 week prior . she reported discomfort and pain during activities of daily living beginning 7 days before her scheduled examination by her obstetrician .
application of heat in the area , together with hydrotherapy , reduced the pain and the feeling of discomfort .
the patient reported exercising for 1 hour of swimming or 1 hour of dancing three times every week .
she reported only the use of paracetamol for the management of the pain in her back and that she had gained 5,500 g during her pregnancy .
the patient reported pain at the posterior iliac spine and had positive gaenslen and patrick tests .
pain was also reproduced with pressure over the iliosacral joint . due to the presence of the gestation ,
mri was performed and a vertical shear in the patient 's left sacrum was recognized .
1 ) .
1 ( a d ) magnetic resonance images reveal a vertical shear fracture in the patient 's left sacrum and osseous edema in the surrounding tissues .
taking into consideration the risks of the displacement of the fracture due to the increased tension in the pelvis during a normal vaginal delivery , we recommended the delivery of the fetus by cesarean section .
after the cesarean section , the patient started to mobilize with short walks under oral analgesics .
atraumatic fractures of the sacrum are an extremely rare medical entity , which is mostly diagnosed in runners.3 only nine cases of postpartum sacral stress fractures have been reported in the literature.11 in the majority of the cases , the patient 's bone density was within normal limits ; therefore , the etiology of the fractures remained obscure.11
12 nevertheless , only two cases of stress sacral fracture have been reported in the prepartum period.7
10
usually , affected patients report pain in the lower back , the sacroiliac region , the buttocks , or the groin that does not resolve with common analgesics . during the clinical examination ,
a normal bone density is found , a fact that is in accordance with the extremely low incidence of pregnancy - related osteoporosis ( 0.4 patients per 100,000 women ) that is noted in the third trimester of the pregnancy.13
plain radiographs are often normal with positive findings in only 2 of 27 cases and should not be used due to the fact that the unborn child is exposed to unnecessary radiation.2 mri is the gold standard in imaging of these fractures because the fetus is not exposed to radiation and the extent of the injury is reported with great detail .
the majority of the patients are found to have a vertical fracture of the sacrum with surrounding bone edema in the mri.1
2
5
for the evaluation of bone density of women with sacral fractures , postpartum bone density can be measured to assess for pregnancy - related osteoporosis.13 most often , osteoporosis is described in the third trimester of pregnancy . in most cases , bone density returns to normal limits 5 to 10 years after delivery.13 apart from fractures in the sacrum , fractures in the hip , the proximal femur , or the vertebral bodies have been described .
biomechanical changes have been documented during pregnancy , which lead to the closure of the sacroiliac joint ( sij ) .
several factors can be responsible for compromising the stability of the sij , such as altered posture and load - bearing capacity , changes in ligamentous and joint capsule tension , altered muscle length , reduced muscle strength , and poor muscular coordination , to name just a few.14 to compensate for the increased load , most mothers will adopt an exaggerated lumbar lordosis while standing.15 as the lumbar spine moves into greater extension , the sacrum moves into greater nutation,16 and as a result , the compression loads acting on the sij when in upright postures are increased .
drugs should be used with caution and only in cases of severe pain because of the effects on the fetus according to the stage of the pregnancy .
also , the risk of preeclampsia should be considered to achieve a successful birth delivery.10 the most common analgesic that can be safely used in all trimesters of pregnancy is oral paracetamol .
ibuprofen has been used by anesthesiologists for pain control but under a maximum daily dose of 1,600 mg.10 in cases of severe pain , epidural anesthesia is recommended because of the less effective systemic side effects.10
in most cases , patients return to their prior condition after 6 weeks with conservative treatment . in all cases , a high level of clinical suspicion
is required and adequate pain control must be achieved for the best results and the quick return to activities of daily living .
sacral stress fractures should be considered in the differential diagnosis of patients with low back pain during pregnancy
. a high degree of clinical suspicion is essential for a proper and early diagnosis , and adequate pain control should be administered for the delivery of a healthy newborn by cesarean section .
commentary on : atraumatic sacral fracture in late pregnancy : a case report
giannoulis and colleagues and the commentary by professor schildhauer touch upon two important aspects : diagnostic and therapeutic uncertainties continuing to surround sacral fractures clinicians ' unease regarding management of pregnant patients it remains a continued reality of medical systems around the world that sacral fractures continue to be missed or patients with sacral pain experience delays in diagnosis to the point of experiencing full - fledged cauda equina syndrome without intervention .
of course hindsight is always golden , but sharpening our clinician 's tools for risk assessment and teaching the principles of sacral fractures to medical trainees should not be unreasonable goals for a better future . for practitioners in charge of spine care , knowledge of sacral pathology should also be a foundational expectation .
we have all the necessary diagnostic tools with plain radiographs , computed tomography , mri , and radionuclide scans ; we just need to know when to ask for them and how to process their information provided and then to act on findings we receive .
better knowledge of sacral fracture classifications and their implications is also desirable.1 aospine international has assembled a group of experts to try to improve on the current state of sacral fracture classifications and will hopefully soon be able to provide us with a better - validated and easy - to - use system in the not too distant future .
when caring for pregnant patients with back problems , the state of spine practitioners around the world is probably still best described as
the general care approach is usually to wait and see until such time that delivery is completed and then next steps can be taken .
this case report underscores the difficulties pregnant women commonly experience regarding the diagnostic and therapeutic uncertainty of our medical community .
ebsj hopes that this article and the accompanying commentary will ignite the curiosity of our scientifically minded readership in investigating problems pregnant patients with serious back disorders sometimes face . | study design case report .
objective sacral fractures , traumatic or atraumatic , are a rather rare cause of low back pain .
the majority of the cases of pregnancy - related sacral fractures are reported as a postpartum complication , and only few cases of sacral atraumatic fractures have been reported in the last trimester of the pregnancy .
the aim of this study is to report a rare case of atraumatic sacral fracture in the third trimester of pregnancy .
methods we report the case of a 30-year - old caucasian european woman during her 37th week ( 36 weeks and 4 days ) of gestation , who complained during her scheduled obstetric examination of continuous low back pain with no associated history of trauma .
the patient performed activities of daily living with a normal level of fatigue and reported no running or walking long distances .
she was examined in our department , and a magnetic resonance imaging scan was performed that showed a vertical nondisplaced fracture in her left sacrum .
results the patient was treated conservatively , and analgesics were administrated according to the consensus of the orthopedic and the anesthesiology departments .
no further complications were recognized in the remaining period of her pregnancy , and a healthy child was born by caesarean section .
conclusions atraumatic fractures of the sacrum should be included in the differentiated diagnosis of pregnant patients with low back pain . |
small metal particles have long been known to exhibit resonant excitations known as `` particle '' or `` surface '' plasmons .
such particles , if they have dimensions small compared to the wavelength of light , can exhibit sharp optical absorption peaks , which are typically in the near - infrared or the visible .
these absorption peaks play an important role in the optical response of suspensions of metal particles in a dielectric host@xcite , and have been the subject of a large amount of study , both experimental and theoretical . because of recent advances in sample preparation ,
it has become possible to study _ ordered _ arrays of such particles@xcite . for chains of metallic particles ,
the coupling between the plasmons comes mainly from the electric field produced by the dipole moment of one nanoparticle , which induces dipole moments on the neighboring nanoparticles .
the dispersion relations for both transverse ( @xmath0 ) and longitudinal ( @xmath1 ) plasmonic waves can then be calculated in the so - called quasistatic approximation@xcite , in which the curl of the electric field is neglected .
this approximation is reasonable when the particles are separated by a distance small compared to the wavelength of radiation .
while this approximation neglects some significant coupling between the plasmonic waves and free photons@xcite , it gives satisfactory results over most of the brillouin zone . in this paper , we first review the dispersion relations of propagating plasmonic waves in a liquid crystalline host , as originally calculated by pike and stroud @xcite .
we also outline an extension of this approach to treat the dispersion relations in the presence of an external magnetic field . for the case of no magnetic field
, we briefly show how the dispersion relations for the @xmath0 and @xmath1 waves are modified when the metallic chain is immersed in a liquid crystal host .
we consider two types of such hosts : a nematic liquid crystal ( nlc ) and a cholesteric liquid crystal ( clc ) .
an nlc is characterized by a uniaxially anisotropic dielectric tensor .
a unit vector parallel to the symmetry axis of this tensor is known as the director .
a clc can be viewed as a nematic in which the director rotates about an axis perpendicular to the plane ( the `` twist axis '' ) with a characteristic pitch angle .
we note that much of the notation and derivations used in this paper follow those originally presented in pike and stroud @xcite . using a simple approximation outlined below ,
we show that for the nlc case , both the @xmath1 and @xmath0 waves are modified when the director of the liquid crystal is either parallel to or perpendicular to the metallic chain . for the perpendicular case ,
the two @xmath0 branches are split into two non - degenerate linearly polarized branches . for the clc
we show that , while the @xmath0 branches once again split into two non - degenerate branches , the resulting waves are elliptically polarized , and are described by dispersion relations dependent on the characteristic pitch angle . after this brief discussion
, we outline the extension of the calculations for the clc host to include the effects of an external magnetic field .
in particular , we suggest that such a field may lead to a method of creating a one - way waveguide composed of a linear chain of metallic particles .
proposals for one - way wave guides are extensive , including proposals for one - way waveguides at the interface between two materials @xcite and along chains of ellipsoidal particles arranged in a spiral configuration@xcite .
our proposal for a one - way waveguide differs from these both in the use of a chain of spherical metallic particles and in the possibility of tuning the dispersion relations via an applied magnetic field .
the remainder of this paper is organized as follows . in the next section ,
we recap the formalism which allows us to approximately calculate the dispersion relations for @xmath1 and @xmath0 waves in the presence of a liquid crystal host . in section iii , we modify the formalism to include an external magnetic field , in section iv we provide numerical examples , and we follow these by a brief concluding discussion in section v.
we consider a chain of identical metal nanoparticles , each a sphere of radius @xmath3 , arranged in a one - dimensional periodic lattice along the @xmath4 axis .
the @xmath5 particle is assumed centered at @xmath6 ( @xmath7 ) .
let us assume that the quasistatic approximation is valid , that is , the electric field is curl free ; this case is approximately applicable when both the radius of the particles and the distance between them are small compared the wavelength of light @xcite .
it is important to note that other corrections to this approximation exists , such as radiative corrections outlined by weber and ford@xcite .
we first consider how the plasmon dispersion relations are modified when the particle chain is immersed in an anisotropic dielectric , under the influence of an applied magnetic field .
we assume that the host medium has a dielectric tensor ( @xmath8 ) , with principal dielectric constants @xmath9 , @xmath9 , and @xmath10 . the medium inside the metallic particles is assumed to have a dielectric tensor @xmath11 with principal diagonal components given by @xmath12 and off diagonal elements given by @xmath13 .
we assume that @xmath12 has the drude form : @xmath14 and @xmath13 has the form @xmath15 here @xmath16 is the plasma frequency , @xmath17 is the cyclotron frequency , @xmath18 is the magnitude of the applied magnetic field , @xmath19 is the charge of an electron , @xmath20 is the mass of an electron , @xmath21 is the speed of light , and @xmath22 is a relaxation time , and the last form on the right - hand side of eqs .
( [ eq : epsw ] ) and ( [ eq : eps_off ] ) applies when @xmath23 .
the results below are easily extended to other forms for @xmath12 , as would be required in order to apply this work to nanoparticles composed of real metals such as au or ag . following the formalism of pike and stroud @xcite we can write down the electric field at @xmath24 due to a sphere with polarization @xmath25 as @xcite @xmath26 where repeated indices are summed over , any external magnetic field is set to zero , and @xmath27 and @xmath28 are defined in pike and stroud @xcite . to obtain a self - consistent equation for plasmonic waves along a chain immersed in an anisotropic host , we consider the polarization of the @xmath5 particle , which we write as @xmath29 , where @xmath30 is the electric field within the @xmath5 particle .
this field , in turn , is related to the external field acting on the @xmath5 particle and arising from the dipole moments of all the other particles .
we approximate this external field as uniform over the volume of the particle , and denote it @xmath31
. this approximation should be reasonable if we remain in the region of validity for the quasistatic approximation .
then @xmath32 and @xmath31 are related by @xcite @xmath33 here @xmath34 is a " depolarization matrix defined , for example , in stroud .
@xmath31 is the field acting on the @xmath5 particle due to the dipoles produced by all the other particles , as given by eq .
( [ eq : polfield ] ) .
hence , the dipole moment of the @xmath5 particle may be written @xmath35 where @xmath36 is a `` t - matrix '' describing the scattering properties of the metallic sphere embedded in the surrounding material .
finally , we make the assumption that the portion of @xmath31 which comes from particle @xmath37 is obtained from eq .
( [ eq : polfield ] ) as if the spherical particle @xmath37 were a point particle located at the center of the sphere within the quasi - static approximation . with this approximation , and combining eqs .
( [ eq : polfield ] ) , ( [ eq : pinn ] ) , and ( [ eq : tmatrix ] ) , we obtain the following self - consistent equation for coupled dipole moments : @xmath38 using eq .
( [ eq : selfconsist ] ) , we can determine the dispersion relations for the @xmath1 and @xmath0 waves for the case of no external magnetic field , provided the director axis of the liquid crystal coincides with the direction of the metallic chain .
in this case , the dispersion relations for the @xmath1 waves for nearest neighbor interactions between the metallic particles are found to be given by @xmath39 and for the @xmath0 waves as @xmath40 where the notation of pike and stroud @xcite has been used .
the calculated dispersion relations given by eqs .
( [ eq : lwave1 ] ) and ( [ eq : twave1 ] ) are shown in fig .
[ figure1 ] for the liquid crystal known as e7 , using the principal dielectric constants given by mller @xcite . for plasmon waves along a chain of metallic nanoparticles , in the presence of an nlc host .
we plot @xmath41 , where @xmath16 is the plasma frequency , as a function of @xmath42 , where @xmath43 is the distance between sphere centers .
green and blue ( x s and + s ) : @xmath1 and @xmath0 modes for a chain embedded in an nlc with director parallel to the chain .
the nlc is assumed to have principal dielectric tensor elements @xmath44 and @xmath45 parallel and perpendicular to the director , corresponding to the material known as e7 . in this and
subsequent plots @xmath46 , where @xmath3 is the metallic sphere radius . also shown are the corresponding @xmath1 and @xmath0 dispersion relations ( black and red solid lines , respectively ) when the host is isotropic with dielectric constant @xmath47 . ] as a second example , we also write down the dispersion relations for the case of no external magnetic field when the director of the liquid crystal is perpendicular to the metallic chain . in this case
we get two non - degenerate linearly polarized @xmath0 branches and a single @xmath1 branch . again considering the case of nearest neighbor interactions ,
we find @xmath48 where the notation of pike and stroud @xcite is used .
if we assume that the metallic particle has a drude dielectric function of the form @xmath49 , then the dispersion relation for @xmath1 and @xmath0 waves , given in eqs .
( [ eq : lwave1 ] ) , ( [ eq : twave1 ] ) , and those in eq .
( [ eq : disp_perp ] ) neglect damping of the waves due to dissipation within the metallic particles . to include the effect of damping
, one can simply solve eqns .
( [ eq : lwave1 ] ) , ( [ eq : twave1 ] ) or ( [ eq : disp_perp ] ) for @xmath50 , using the drude function with a finite @xmath22 .
the resulting @xmath50 will be complex in both cases ; @xmath51^{-1}$ ] gives the exponential decay length of the @xmath1 or @xmath0 wave along the chain .
modes ( asterisks , in green ) and @xmath0 modes ( + s and x s , shown in dark and light blue ) , divided by the plasma frequency @xmath16 , are plotted versus @xmath42 .
the nlc has the same dielectric tensor elements as in fig . 1 .
also shown are the corresponding @xmath1 ( solid black ) and @xmath0 ( solid red ) branches for an isotropic host with @xmath52 .
note that the @xmath0 branches which were degenerate in fig .
1 are split into two branches in this nlc geometry . ]
next , we consider the case where the host is a cholesteric liquid crystal , also known as a chiral nematic liquid crystal . in such a material , the director , instead of pointing everywhere in the same direction , rotates in space about an axis perpendicular to the director . to be definite , we assume that the director @xmath53 has the following dependence on position : @xmath54 that is
, the director rotates around the @xmath4 axis with pitch angle @xmath55 .
we still assume that the chain of nanoparticles lies along the @xmath4 axis .
thus , the director is always perpendicular to that chain . as a simple model
, we assume that the dielectric tensor of the cholesteric liquid crystal is locally the same as that of an nlc , again assuming the external magnetic field is zero , except that the symmetry axis of the tensor spirals around the @xmath4 axis with pitch angle @xmath55 .
the tensor can then be written @xmath56 where @xmath57 is the dielectric tensor of a nematic liquid crystal with nonzero components @xmath58 , @xmath59 , and @xmath60 is a matrix corresponding to a rotation about the @xmath4 axis by twist angle @xmath61 , with non - zero components @xmath62 this model is , in fact , a special case of a more general model given for a cholesteric liquid crystal in berreman et al .
@xcite .
next , we calculate the dispersion relations for plasmonic waves propagating along the chain of metallic nanoparticles in the presence of this host , using a simple approximation .
we again start with eq .
( [ eq : selfconsist ] ) . for simplicity
, we include only nearest - neighbor interactions .
then , for the case of a clc host , eq .
( [ eq : selfconsist ] ) becomes @xmath63 .
\label{eq : selfconsist_rotate}\end{aligned}\ ] ] here @xmath64 represents the dipolar field at the position of @xmath65 induced by the dipole @xmath66 . to a good approximation
, this field will be the same as that found in the case of an nlc host with director perpendicular to the chain , except that both the induced dipole @xmath66 , and the corresponding dipolar field , are rotated by an amount which increases linearly with position along the @xmath4 axis .
( this way of expressing the dipolar field is only approximately valid , because the sphere is embedded in a dielectric which is not only anisotropic but also inhomogeneous , varying with position along the @xmath4 axis . ) with this assumption , the product @xmath67 can be written as @xmath68 where @xmath60is given by eq .
( [ rotationmatrix ] ) . from these equations
, we can see that the @xmath1 and @xmath0 waves are still decoupled , as in the case of an nlc host with director perpendicular to the chain .
the @xmath1 modes are unchanged from the nlc case , but the @xmath0 modes are altered .
( [ eq : selfconsist_rotate ] ) can be rewritten as @xmath69 , \label{eq : selfcon_two}\end{aligned}\ ] ] where we use @xmath70 and @xmath71 which corresponds to a rotated dipole moment .
we now write out eq .
( [ eq : selfcon_two ] ) explicitly and obtain dispersion relations for the two transverse branches .
we consider only the @xmath72 and @xmath73 components of eq .
( [ eq : selfcon_two ] ) , since the @xmath1 branch is unchanged from the purely nlc case and does not couple to the @xmath0 branches .
we denote the non - zero diagonal elements of the product matrix @xmath74 by @xmath75 and @xmath76 . after a little algebra , and using the @xmath77 block of eq .
( [ rotationmatrix ] ) for @xmath78 , we obtain the following equation determining the two - component column matrix @xmath79 whose components are @xmath80 , @xmath81 : @xmath82 where @xmath83 is found to have components @xmath84 eq .
( [ eq : disperchiral ] ) has nontrivial solutions if @xmath85 = 0 .
\label{eq : disperchiral1}\ ] ] the left - hand side of eq .
( [ eq : disperchiral1 ] ) is quadratic in @xmath12 and thus has two solutions for @xmath12 as a function of @xmath86 .
we plot these two solutions in fig .
[ figure3 ] using values for the dielectric constants from mller@xcite and for various values of the twist angle @xmath87 . if @xmath88 , these lead to two solutions for @xmath2 as a function of @xmath86 , or equivalently , of @xmath89 ( since @xmath86 is monotonic in k in the range @xmath90 ) .
we use the convention that @xmath91 .
if we use the drude form for @xmath12 with a finite @xmath22 to include single - grain dissipation , we write @xmath92/2 $ ] .
then there are four solutions for @xmath93 and hence for @xmath89 , of which two have @xmath94 , as required physically .
thus , this procedure again gives two @xmath0 branches which include single - particle damping if @xmath12 has the drude form with a finite lifetime . for plasmon waves along a chain of metallic nanoparticles in the presence of a cholesteric liquid crystal host .
we assume that the director rotates about an axis parallel to the chain of metal nanoparticles with a pitch angle @xmath55 .
the red ( open square and filled square ) plots and blue ( crosses and triangles ) represent the two @xmath0 branches for @xmath95 and @xmath96 respectively , while the black ( full circles and asterisks ) correspond to @xmath97 ( nematic liquid crystal ) . in all cases
we assume @xmath98 and @xmath99 .
the green points ( full circles ) represent an isotropic host with @xmath100 . ]
we will now discuss how the dispersion relations are changed when there is a clc host and an external magnetic field is applied parallel to the chain axis , which is also the twist axis of the clc . in this case , the dielectric tensor of the metallic host , as given by eq .
( [ eq : eps_off ] ) , is no longer diagonal . even though the dielectric tensor of the metallic particle has off - diagonal terms , the calculation of the dispersion relations again starts from eq .
( [ eq : selfconsist_rotate ] ) and generally follows the derivation outlined in section [ chiral_der ] .
since the magnetic field is parallel to both the chain axis and the twist axis of the clc , the @xmath1 branch will again decouple from the two @xmath0 branches .
furthermore , the @xmath1 branch will not be modified by the external magnetic field , and behaves similarly to the @xmath1 branch in the clc case discussed earlier .
the two @xmath0 branches are expected to be the solutions of a @xmath101 matrix equation similar to eq .
( [ eq : comp_nofield ] ) , but including additional terms related to the external magnetic field . to obtain the dispersion relations in a magnetic field
, we need to know how the matrices @xmath102 , @xmath103 , @xmath104 , and @xmath105 are modified from their zero - field values .
because the off - diagonal elements of the dielectric tensor satisfy @xmath106 , in a magnetic field , it can be shown that @xmath107 and @xmath108 are both diagonal and unchanged from their zero - field forms .
we may write these diagonal elements @xmath109 and @xmath110
. however , @xmath102 and @xmath103 become non - diagonal in a magnetic field and are also independent of @xmath111 , @xmath112 , and @xmath113 .
we denote this matrix simply @xmath114 .
we denote the matrix elements of the @xmath77 projection of @xmath114 by @xmath115 , @xmath116 , @xmath117 , and @xmath118 . after some additional algebra , we find that the non - zero matrix elements of the corresponding @xmath119 matrix @xmath120 can be written out explicitly .
the matrix @xmath121 now includes the contribution from the scattering matrix @xmath114 , the green s function @xmath122 , and the elements of the @xmath77 rotation matrix defined in eq .
( [ rotationmatrix ] ) .
the matrix elements are given as @xmath123 \nonumber \\
m_{yy } = { \cal g}_{yy}[t_{yy}\cos(kd)\cos(\alpha d ) + it_{xy}\sin(kd)\sin(\alpha d ) ] \nonumber \\ m_{xy } = { \cal g}_{yy}[t_{xy}\cos(kd)\cos(\alpha d ) - it_{yy}\sin(kd)\sin(\alpha d ) ] \nonumber \\ m_{yx } = { \cal g}_{xx}[it_{xx}\sin(kd)\sin(\alpha d ) -t_{xy}\cos(kd)\cos(\alpha d ) ] .
\label{eq : magfield}\end{aligned}\ ] ] with the external magnetic field parallel to the director of the clc , one can now determine the dispersion relation for the two @xmath0 waves as nontrival solutions to eq .
( [ eq : disperchiral1 ] ) .
the dispersion relations corresponding to eqs .
( [ eq : magfield ] ) are again given implicitly by eq .
( [ eq : disperchiral1 ] ) .
we have not , as yet , evaluated these relations numerically , but some qualitative points can already be inferred from the form of the matrix elements . of most interest , the presence of a magnetic field will lead to dispersion relations which are _ non - reciprocal _ , i. e. , @xmath124 in general .
the magnetic field appears only in the off - diagonal elements @xmath125 and @xmath126 , which are linear in the field except for very large fields . from this result
, it is found that @xmath116 and @xmath127 have terms which are linear in field , while @xmath115 and @xmath118 are independent of field to that order .
the terms involving @xmath116 and @xmath127 in eq .
( [ eq : magfield ] ) are multiplied by @xmath128 and thus change sign when @xmath89 changes sign .
thus , the secular equation determining @xmath129 is not even in k , implying that the dispersion relations are non - reciprocal .
this non - reciprocality disappears when the host is an nlc because then @xmath130 and the terms involving @xmath128 vanish .
although the dispersion relations are non - reciprocal , we do not yet know whether there is a region of one - way propagation , i. e. , where for certain frequencies waves can only propagate in one direction . in future work
, we plan to solve these relations numerically to investigate this intriguing possibility .
as a first numerical example , we calculate the plasmon dispersion relations for a chain of spherical drude metal particles immersed in an nlc and @xmath131 .
we consider two cases : liquid crystal director parallel and perpendicular to the chain axis , which we take as the @xmath4 axis . for @xmath10 and @xmath9 , we take the values found in experiments described in mller@xcite , which were carried out on the nlc known as e7 . for comparison , we also show the corresponding dispersion relations for an isotropic host of dielectric constant which is arbitrarily taken as @xmath132 .
the results of these calculations are shown in figs . 1 and 2 in the absence of damping ( @xmath23 in the drude expression ) .
as can be seen , both the @xmath1 and @xmath0 dispersion relations are significantly altered when the host is a nematic liquid crystal rather than an isotropic dielectric ; in particular , the widths of the @xmath1 and @xmath0 bands are changed .
when the director is perpendicular to the chain axis , the two @xmath0 branches are split when the host is an nlc , whereas they are degenerate for an isotropic host , or an nlc host with director parallel to the chain .
next , we turn to the case of a chain of metal particles immersed in a cholesteric liquid cystal .
we assume that the nematic axis lies in the @xmath133 plane , the chain runs parallel to the @xmath4 axis , and the nematic axis rotates about the @xmath4 axis with a pitch angle @xmath55 .
the calculated dispersion relations for the two @xmath0 branches are shown in fig . 3 for two different choices of pitch angle @xmath55 , as well as for @xmath130 , corresponding to the purely nematic case .
for comparison , we also show the dispersion relation for the doubly degenerate @xmath0 branch when the host is an isotropic dielectric with dielectric constant @xmath100 .
we again assume that there is no dissipation . as is evident
, the dispersion relations do depend slightly on @xmath55 .
but while in the case of an nlc host the two @xmath0 branches are linearly polarized with polarization along the @xmath72 and @xmath73 axes , respectively , the two @xmath0 branches in the cholesteric case are no longer linearly polarized .
instead , each of these two branches has a polarization vector which rotates as a function of @xmath4 .
we have not attempted to plot this in the figure .
the present calculations and formalism leave out several effects which may be at least quantitatively important . first , in our numerical calculations , but not in the formalism
, we have omitted all dipolar couplings beyond the nearest neighbors .
inclusion of further neighbors will quantitatively alter the dispersion relations in all cases considered , but these effects should not be very large , as is already suggested by the early calculations in brongersma et al@xcite for an isotropic host .
another possible effect will appear when @xmath134 is significantly greater than @xmath135 , namely , the emergence of quadrupolar and higher quasistatic bands which will mix with the dipolar band and change its shape@xcite . even for @xmath136 the plasmon dispersion relations will still be altered by an nlc or clc host in the manner described here .
the present treatment also omits radiative damping which may be important at certain wave vectors and at long wavelengths@xcite .
we have not extended the present approach to include such radiative effects but do expect that they will provide only a quantitative change , and not qualitatively change the effects we have described . from the point of view of applications ,
the use of a liquid - crystalline host is appealing because liquid crystals are significantly affected by an applied electric field .
for example , the director of an nlc tends to align with the applied electric field .
thus , the dispersion relations of the propagating plasmonic waves could be , in principle , controlled by such an applied electric field .
this control could be quite useful , for example , in developing filters for propagating plasmonic waves .
the application of an external magnetic field along with an external electric field would allow one to tune the frequency range where only one wave direction is allowed to propagate , this has potential applications in optical relay systems , optical filters , and as a filter for backscattering waves . to summarize
, we have shown that the dispersion relations for plasmonic waves propagating along a chain of closely spaced nanoparticles of drude metal are strongly affected by external electric and magnetic fields .
when under the influence of only an electric field we find that for both materials , the dispersion relations are affected .
if the host is a uniaxially anisotropic dielectric ( such as an nlc ) , the dispersion relations of both @xmath1 and @xmath0 modes are significantly modified , compared to those of an isotropic host , and if the director axis of the nlc is perpendicular to the chain , the two degenerate transverse branches are split . if the host is a clc , with rotation axis parallel to the chain , we find that the @xmath0 modes are again split into nondegenerate bands , whose dispersion relations now depend on the pitch angle @xmath55 . however , in contrast to the nlc case , the two @xmath0 branches are no longer linearly polarized .
these effects suggest that the propagation of such plasmonic waves can be tuned , by subjecting the liquid crystal to a suitable electric field , so as to change the frequency band where wave propagation can occur , or the polarization of these waves .
this control may be valuable in developing devices using plasmonic waves in future optical circuit design . under the influence of an external magnetic field
, we find that for a clc host the @xmath0 waves are likely to be non - reciprocal , i. e. , to have a dispersion relation where @xmath124 .
possibly there may be a frequency range in which only one direction of wave propagation is allowed .
if this is confirmed by numerical calculation , this type of system would have a possible application as a filter for backscattered waves in an optical system .
this work was supported by the center for emerging materials at the ohio state university , an nsf mrsec ( grant no .
dmr0820414 ) .
maier , s. a. , kik , p. g. , atwater , h. a. , meltzer , s. , harel , e. , koel , b. e. , requicha , a. a. g. `` local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides , '' _ nature mater .
_ * 2 * , 229 ( 2003 ) .
yu , z. , veronis , g. , wang , z. , fan , s. `` one - way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal , '' _ phys .
lett . _ * 100 * 023902 ( 2008 ) .
j. mller , c. snnichsen , h. von poschinger , g. von plessen , t. a. klar , and j. feldmann , `` electrically controlled light scattering with single metal nanoparticles , '' _ appl .
_ * 81 * , 171 ( 2002 ) . | a chain of metallic particles , of sufficiently small diameter and spacing , allows linearly polarized plasmonic waves to propagate along the chain . in this paper , we describes how these waves are altered when the liquid crystal host is a nematic or a cholesteric liquid crystal ( nlc or clc ) with or without an applied magnetic field .
we find that , in general , the liquid crystal host , either nlc or clc , alters the dispersion relations of the transverse ( @xmath0 ) and longitudinal ( @xmath1 ) waves significantly from the dispersion relations for an isotropic host .
we show that by altering the director axis of the liquid crystal relative to the long axis of the metallic chain , that the @xmath0 branch can be split into two non - degenerate linearly polarized branches ( nlc host ) or two non - degenerate elliptically polarized branches ( clc host ) . when an external magnetic field is applied parallel to both the long axis of the metallic particles and the director of the clc host , we find that the dispersion relations are odd in an exchange in sign for @xmath2 for the non - degenerate elliptically polarized @xmath0 branches .
that is , the application of an external magnetic field leads to the realization of a one - way waveguide . |
primary enteroliths arise due to the stasis of the intestinal contents , and the underlying pathologies include diverticular disease , blind pouches , intestinal stenosis , and strictures .
secondary enteroliths can be caused by the migration of renal stones or gallstones into the gastrointestinal tract . according to previous studies ,
the terminal ileum is the most common location in the small intestine because of its alkaline ph and high calcium concentration .
there has been an increase in the incidence of enterolithiasis in recent times due to the advancement in radiological investigations .
we report a case of enterolithiasis presenting a diagnostic dilemma , which was solved only after exploratory laparotomy
a 57-year - old male patient presented with complaints of abdominal pain , distension of abdomen , non - passage of stool , and vomiting of 1 week s duration to the emergency department of jawaharlal nehru medical college , amu , aligarh .
the pain was colicky , and it progressed to dull ache and was moderate in intensity .
the patient reported similar episodes of pain 2 weeks earlier , which was subsided by conservative management .
the patient had never undergone surgery or gastrointestinal endoscopy in the past . on examination ,
in addition , visible peristalsis was present over the abdomen , and the bowel sounds were exaggerated .
there were no scars on the abdomen and pelvis , and nor was there any evidence of groin hernias .
erect chest x - ray showed multiple opacities in the bilateral lung field with emphysematous changes ( figure 1 ) .
there was a radio - opaque shadow in the right lower abdomen , the significance of which was unclear .
the ultrasonography was suggestive of the intussusception of the bowel loops in the right lower abdomen , causing features of intestinal obstruction .
the patient was advised laparotomy , but he refused any surgical intervention ; he was , therefore , managed conservatively .
repeat abdominal plain film showed improvement in the condition of the small bowel , with a change in the position of the radio - opaque shadow in the pelvis from the right side of the abdomen in the previous film to the left side .
the general condition of the patient improved , and he was discharged on personal request on the fifth day .
a ) x - ray of the abdomen shows multiple air fluid levels with a radio - opaque shadow onthe right side of the abdomen .
b ) x - ray of the abdomen demonstrates multiple air fluid levels with a radio - opaque shadow in the pelvis .
three days after discharge , the patient again reported with similar complaints and was readmitted .
plain film of the abdomen showed multiple air fluid levels with a radio - opaque shadow in the pelvis .
perioperatively , there was a band present constricting the small bowel at approximately 122 cm distal to the duodenojejunal junction .
two strictures were present in the small bowel : the first one at approximately 228 cm distal to the duodenojejunal junction and the second on eat almost 45 cm distal to the first one . a stone ( 22 cm in size , oval in shape , dark brown in color , and hard in consistency ) was present between the 2 strictures .
there was mesenteric creeping over the small bowel at multiple places ( figure 2 ) .
release of band with the resection of the stricture segment was performed , and end ileostomy and mucus fistula were created .
histopathological examination of the resected specimen showed transmural inflammation with caseating granuloma along with numerous epithelioid cells , confirming the diagnosis of tuberculosis .
the patient was discharged after an uneventful postoperative stay of 8 days on antitubercular drugs and care of ileostomy ( figure 3 ) .
the rare pathophysiology of post - tuberculosis enterolithiasis was explained to the patient , and informed consent was taken from him for the publication of his case in a medical journal .
he had a satisfactory recovery after ileostomy closure and was discharged in good general condition on antitubercular drug therapy .
a ) section of the lymph node shows normal follicles with granuloma formation , comprising areas of necrosis with langhans giant cells surrounded by an admixture of epithelioid cells and lymphocytes .
b ) section of the intestine demonstrateschronic inflammatory infiltrates with the presence oflanghansgiant cells along with areas of necrosis .
chomelin j. , a french physician , was the first to describe enterolithiasis in 1710 in his medical series of historie de lacademie royal as a case of stone formation in a duodenal diverticulum discovered during an autopsy .
in the early twentieth century , there were additional reports of distal small bowel obstruction secondary to enterolithiasis in the terminal ileum .
there has recently been an increase in the reported cases owing to the rapid development of gastrointestinal and imaging techniques .
williams in 1908 and edwards in1930 reported a few cases of enterolithiasis . the chemical composition of enteroliths was reported by sjoqvist in 1908 .
pfahler was the first to make the radiological diagnosis of enterolithiasis in 1915 . by the mid twentieth century , de witt et al .
reported their case series on enterolithiasis amongst a wide age population and shed further light by additional individual case reports .
it has become readily recognized that primary enteroliths result from stasis , leading to clumping and elimination .
diverticular disease of the small bowel is a leading etiology , followed by stricturing of the intestine from infectious ( tuberculosis ) or inflammatory ( crohn s disease ) processes .
primary enteroliths were further subcategorized by atwell and pollock in 1960 into true and false stones on the basis of chemical composition .
the colon , including the appendix , is the most common location of enterolithiasis . in the small intestine ,
the most common location is the terminal ileum , where alkaline ph favors calcium salt precipitation over food particles which act as a nidus .
the decreased motility or stasis of the bowel seems to be the crucial pathognomonic factor in the formation of enteroliths .
the anatomic alterations of the gastrointestinal tract ( e.g. , diverticula , duplication cysts , or pathological conditions such as strictures due to bowel diseases like crohn s disease or tuberculosis ) may be associated with the stasis of the intestinal contents .
the stasis of the contents in the intestine leads to crystallization and subsequent formation of stone .
bowel resection and anastomosis may also lead to blind loop formation and result in the continuous deposition of the intestinal contents .
the examination of the stone mainly shows fecal material similar to a true primary enterolith .
the presence of an enterolith , even in the absence of intestinal obstruction , should warn us of the possibility of an intestinal stricture .
stones in the intestine may remain asymptomatic , dissolve spontaneously , and pass slowly through the gastrointestinal tract .
interestingly , the patient in our case report complained of recurrent episodes of pain abdomen and signs of intestinal obstruction .
the differential diagnosis includes gallstones , urolithiasis , calcified lymph nodes , and pancreatic calcifications .
the most important radiological signs are typical dense rim with a pale core in oval , round , or rectangular shadows , coin - end - on appearance of the shadows , wide mobility of radio - opaque shadows in relation to the fixed structures in successive plain radiographs of the abdomen , and wide separation in one with closeting together in other radiographs .
these stones may change their location on radiographs due to the peristaltic movements of the bowel . in our patient
also , repeat abdominal plain films showed a change in the position of the radio - opaque shadow in the pelvis from the right side of the abdomen in the previous film to the left side .
intestinal tuberculosis causes strictures of the intestine and impairs the intestinal flow , creatingfavorable conditions for the development of stones in the intestine .
nevertheless , enteroliths are a very rare condition in tuberculosis since most patients never become symptomatic or because symptoms are not attributable to enteroliths . in summary
patients with intestinal obstruction require laparotomy with strictureplasty or segmental bowel resection . in the present case ,
the presence of a radio - opaque shadow that kept on changing its position posed a diagnostic dilemma , which was solved only after laparotomy .
enterolithiasis is a rare finding , but its incidence and prevalence has been on the rise in recent times .
stasis secondary to various underlying pathologies plays a significant role in the pathogenesis of this disease and provides an important clue in its etiologic recognition , chemical classification , and clinical presentation .
clinical diagnosis depends on the history and physical examination of the patient supported by radiological imaging . though rare
, the presence of a radio - opaque shadow in the setting of intestinal obstruction should raise the suspicion of enterolithiasis .
the use of a minimally invasive technique should be tried to treat this condition initially ; nevertheless , most cases will require exploratory laparotomy because of multiple strictured bowel segments .
the possible pathophysiology behind the enterolithiasis is the stasis of digestive juices and food particles between the strictures .
these food particles act as a nidus for stone formation , and crystallization occurs due to the inflammatory mechanism in the bowel because of chronic inflammation secondary to tuberculosis .
most of the previously reported cases related to enterolithiasis are of cholelithiasis , nephrolithiasis , and crohn s disease . | primary enterolithiasis is a rare surgical ailment .
the underlying cause is intestinal stasis . numerous anatomical and micro environmental factors such as enteritis , incarcerated hernia , malignancy , diverticula , blind loops , and enteroenterostomy
predispose to clinically significant concretions .
enterolithiasis in tuberculosis can be due to the presence of strictures , intestinal bands , or interbowel / parietal adhesions , leading to intestinal stasis .
secondary enterolithiasis is generally caused by gallstones or renal stones migrating to the gastrointestinal tract due to fistula formation . during stasis ,
food particles act as a nidus and calcium salts are deposited over the food particles , leading to stone formation . a 57-year - old male patient presented to the emergency department of jawaharlal nehru medical college , amu , aligarh , with features of intestinal obstruction .
the patient underwent emergency laparotomy , revealing 2 strictures in the distal ileum with 15.24 cm of the bowel between them containing a 22 cm enterolith .
the strictured segment was resected , and end ileostomy and mucus fistula were created .
the patient s postoperative recovery was fine , and he wasdischarged with ileostomy on antitubercular treatment ( after histopathologicalconfirmation ) .
ileostomy closure wasplanned after 6 weeks .
the incidence and prevalence of enterolithiasis has been on the rise recently because of advancement in radiological imaging studies .
endoscopic and surgical stone removal along with the treatment of the underlying pathology is recommended . |
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Three days after convicted kidnapper and rapist Ariel Castro hanged himself in his jail cell, NBC News has obtained police interrogation tapes that provide insight into how close he came to being caught — including a phone call he made to one of the victims' mothers — and personal letters in which he writes about long-held thoughts of suicide.
The 53-year-old former bus driver was sentenced to life plus 1,000 years after pleading guilty to 937 counts including rape, kidnap and aggravated murder following the decade-long incarceration of Amanda Berry, Gina DeJesus and Michelle Knight at his Cleveland home. NBC News has obtained four hours of videotape from a source familiar with the criminal investigation showing Castro being interrogated just hours after he was arrested in May.
Ariel Castro's family claims body, coroner says
In a TODAY exclusive that aired Friday, excerpts from the video show Castro revealing several close calls with law enforcement over the years before eventually being caught. He also recounts how he abducted and abused the three women. Out of respect for the victims, NBC News is not showing Castro speaking out about the details of his crimes and has reached out to the victims' lawyers to alert them about the report.
Within hours of Castro’s arrest, he began admitting his horrific crimes to interrogators. He appeared surprised by what he had gotten away with for so long, including the day he abducted DeJesus, then 14, in April of 2004. He said there were surveillance cameras at her middle school that should have captured him just 15 minutes before he kidnapped her.
When he first abducted Knight in August of 2002, Castro said he had a girlfriend who visited his house and noticed a television on in the room where Knight was being secretly held.
“She seen that I had a TV on in the upstairs room,’’ Castro said in the interrogation video. “And she says, ‘What is that? You have a TV on up there?’ And my heart started beating, and I was like, ‘OK, she's probably catching onto something.”
Castro said he even once used Berry’s cell phone to call her mother and tell her that Berry was alive after abducting her in April of 2003.
“I think I said something ... that I have her daughter and that she's OK and that she's my wife now — something like that, you know, probably not the exact words,’’ Castro said in the police tapes.
Castro said he hung up before having any conversation with Berry’s mother. Neither Castro nor any of his close relatives were ever interviewed by authorities at that time for Berry’s disappearance following the phone call, he said.
Today Convicted kidnapper Ariel Castro is interrogated just hours after his arrest in May.
“Nothing led us to talk to him,’’ FBI special agent Vicki Anderson told NBC News in May. “You know, there were no indications that we should go talk to him. We canvassed the neighborhood. We did all of those things. Nothing led us to Ariel Castro.”
Castro also talked about how his now-6-year-old daughter with Berry, who was born in his house, begged him to stop locking all the doors. On the day the three captive women escaped, he left a bedroom door open, which allowed Berry to make it to the front door and yell for help. Two neighbors came over, and a hole was kicked through the bottom of the door to allow Berry to crawl through with her daughter. Berry then called 9-1-1 and Castro was apprehended.
“I know I let my guard down,’’ Castro said in the interrogation video.
NBC News also obtained a pair of letters Castro wrote to his children around Father’s Day while he was in jail.
“I still can’t believe what I did to put me in the situation that I’m in now,’’ he wrote.
Related: Ariel Castro's death is 'last slap' to victims' faces, psychologist says
“Everything he has done is indicative of a narcissistic personality disorder,” forensic psychologist Dr. J. Buzz Von Ornsteiner told TODAY. “He's self-centered. He's self-absorbed. It's all about him.”
When investigators searched Castro’s home in May, they found a note from 2004 in which he contemplated suicide, writing, “I want to put an end to my life and let the devil deal with me.” Castro was initially on suicide watch when he was first put in jail, but had been downgraded before he hung himself with a bedsheet in an Ohio state prison on Tuesday, according to his attorney, Craig Weintraub. Prison officials are investigating how he was able to hang himself, as he was supposed to be checked by guards every half hour.
His thoughts of suicide were also apparent during the interrogation.
“I just want to crash through the window,’’ he said.
“These degenerate molesters are cowards,’’ Tim McGinty, the Cuyahoga County prosecutor who secured Castro’s conviction, said in a statement released Thursday. “They con and capture vulnerable children. This man couldn’t take, for even a month, a small portion of what he had dished out for more than a decade.
“Let this be a message to other child kidnappers: There will be a heavy price to pay when you are caught. You won’t enjoy the captive side of the bars.”
Editor's note: An earlier version of this report identified the police interrogation tapes as FBI tapes. ||||| Cleveland kidnapper Ariel Castro said he called the mother of one of his captives and told the woman her daughter was alive and had become his wife, according to interrogation tapes.
FILE - In this Aug. 1, 2013 file photo, Ariel Castro bows his head in the courtroom during his sentencing sentencing in Cleveland. Castro, 53, now serving a life sentence for the kidnapping and rape,... (Associated Press)
FILE - In this July 26, 2013 Ariel Castro sits in a Cleveland courtroom where he pleaded guilty to 937 counts of rape and kidnapping for holding three women captive in his home for a decade. Castro,... (Associated Press)
Castro also told investigators that authorities missed opportunities to catch him while he held the three women captive for more than a decade in a house with boarded up windows where they were repeatedly beaten and raped.
Castro says in the video _ obtained by NBC and first reported Friday on the "Today" show _ that he told Berry's mother that her daughter was OK. He says he made the call on Amanda Berry's cellphone.
"I think I said something ... that I have her daughter and that she's OK, and that she's my wife now _ something like that, you know, probably not the exact words," he told investigators.
When asked for the mother's response, Castro said: "I hung up so we didn't have a conversation."
Castro, 53, was a month into his life sentence when he committed suicide Tuesday night. His family collected his body from the Franklin County Coroner's office Friday.
Castro also told investigators that authorities missed opportunities for catching him while he held the kidnapped women, who were ages 14, 16 and 20 when captured.
Castro told investigators that cameras at the school of victim Gina DeJesus should have captured him there 15 minutes before she was abducted.
"You could have broke the case right then and there," he said.
Castro said a girlfriend noticed a TV on in a room occupied by victim Michelle Knight and got him worrying he might be caught.
"Was it a close call?" an investigator said.
"Yeah," he said.
A message was left with representatives of the victims Friday morning.
The "Today" show report also provides additional details about a 2004 note Castro wrote that investigators found when they searched the house. "I want to put an end to my life and let the devil deal with me," a section of the note read.
Two state reviews are underway, Ohio prisons spokeswoman JoEllen Smith said, one looking into the suicide itself, and the other is examining whether Castro received proper medical and mental health care leading up the suicide.
Castro was sentenced Aug. 1 to life in prison plus 1,000 years after pleading guilty to 937 counts, including kidnapping and rape, in a deal to avoid the death penalty. "I'm not a monster. I'm sick," he told the judge at sentencing.
Castro's captives _ Berry, DeJesus and Michelle Knight _ disappeared separately between 2002 and 2004. They were rescued from Castro's run-down house May 6 when Berry broke through a screen door.
Investigators said the women were bound, repeatedly raped and deprived of food and bathroom facilities.
___
Associated Press Writer Julie Carr Smyth contributed to this report.
___
Andrew Welsh-Huggins can be reached on Twitter at https://twitter.com/awhcolumbus. | – Just when you thought the worst details of the Cleveland kidnapping case had been aired, more facts emerge via police tapes of Ariel Castro's interrogation. In addition to Castro describing his thoughts of suicide, NBC News reports the tapes reveal a shocking confession: Castro once called Amanda Berry's mom—using Berry's cellphone—to tell her her daughter was safe and now his "wife." He hung up before she could respond, Castro said. Castro also explains on the tapes that it was his own young daughter (born to Berry) who pleaded with him to unlock his house's doors, ultimately leading to the three women's escape: "I let my guard down," he said, when he left a bedroom door open, allowing Berry to yell for help from the front door. NBC News notes that Castro seemed surprised he got away with his crimes for so long, telling police they missed a chance to catch him on surveillance cameras outside Gina DeJesus' school. "You could have broke the case right then and there," he said, per the AP. And though he wouldn't commit suicide for another nine years, a 2004 note shows Castro long battled suicidal thoughts. "I want to put an end to my life," he wrote, "and let the devil deal with me." During the interrogation, he told police, "I just want to crash through the window." |
the immune system is a highly evolved system that functions to provide organisms with the ability to resist pathogenic agents and is characterised by two pathways : innate and acquired .
the innate immune system can be exposed to a variety of physical and chemical stressors .
the interactions of xenobiotics with the immune system could finally induce immunosuppression with development of viral , bacterial or fungal diseases .
the innate immune defence consists of a large number of humoral and cellular factors , which play an important role as the first line of defence against a wide range of infective agents .
important responses involve changes in the hepatic , neuroendocrine , haematopoietic and immune systems to re - establish homeostasis in the organism .
the eurasian beavers are subject to partial protection and that is why in our country we have beaver overpopulation . because of such large quantities it colonizes new places .
it is also approaching human habitats where is exposed to a wider range of both chemical and stress factors .
this species has been the subject of many reintroduction and translocation programmes with varying success [ 3 , 4 ] .
the beaver is a wildlife animal which can be a good indicator of environment pollution and effect of this pollution on cells mediated and humoral mediated immunity .
actually it is a good mammalian model for analysing heavy metal accumulation in the wild life organisms .
populations , which have undergone bottlenecks or re - introduction may exhibit the poliethiological stress and in consequence reduced disease resistance .
there is no information in the literature about cellular and humoral defence mechanisms and protection against diseases of eurasian beavers . for the first time we tried to examine the basic parameters of innate immunity of this species for developing new methods of prevention against infectious diseases in different reintroduction and translocation programmes in poland .
the aim of the present study was to determine the selected innate immunity parameters in eurasian beavers inhabiting natural ecosystems .
beavers were captured in the north - east territory of poland ( wiajny ) in november 2012 .
the animals were collected upon the approval of the regional director of environmental protection in olsztyn ( decision no . rdo-28-oop-6631 - 0007 - 638/09/10/pj ) and resolution of the local ethics committee for animal experiments no .
the age of animals was assessed based on the work of rossell et al . , which allowed to divide individuals into two age groups : juveniles ( < 3 years old ) and adults ( > 3 years old ) .
basic veterinary examination as well as autopsy showed that all animals were healthy and in good physical condition at the time of capture .
the blood was collected from 8 free - ranging beavers , of which 4 were young ( 2 male and 2 female ) and 4 adult ( 2 male and 2 female ) , from the caudal vein by the vacutainer system to the two tubes : heparinized and non - heparinized tubes ( vacutainer set
the blood leucocytes were isolated by centrifugation at 2000 g for 30 min at 4c on the gradisol g gradient ( polfa ) or lymphoprep ( sigma ) , washed three time in pbs and re - suspended in rpmi 1640 medium ( sigma ) supplemented with 10% fcs ( foetal calf serum , gibco - brl ) at a stock concentration of 2 10 cells / ml of medium .
viability of cells was checked by supravital staining with 0.1% w / v trypan blue ( 1 : 1 mixture of cell suspension and trypan blue solution ) .
two hundred cells were counted and only samples containing at least 90% of viable cells were used for experiments .
the metabolic activity of blood phagocytes was determined based on the measurement of intracellular respiratory burst ( rba ) after stimulation by pma ( phorbol myristate acetate , sigma ) , as described by siwicki et al . .
the potential killing activity ( pka ) of blood phagocytic cells was determined according to the method presented by siwicki et al . .
the proliferative response of the blood lymphocytes ( lp ) stimulated by mitogen concanavalin a ( cona , sigma ) or lipopolysaccharide ( lps , sigma ) were determined by mtt assay previously described by wagner et al . .
the lysozyme activity in plasma was measured by a turbidimetric assay presented by siwicki and anderson .
the assay is based upon the lysis of the lysozyme - sensitive gram - positive bacterium micrococcus lysodeikticus ( sigma ) which is obtained freeze - dried from major chemical suppliers .
the ceruloplasmin activity in the plasma was determined spectrophotometrically with modifications for micro - methods .
analysis of total protein and -globulin levels in serum was based on the lowry micro method ( sigma , diagnostic kits ) .
the total -globulin level was measured using lowry micro method presented by siwicki and anderson .
this method requires first precipitating the -globulin out of the serum with polyethylene glycol ( 10 000 kda ) .
the table illustrates the means , standard deviation and levels of significance p < 0.05 .
the innate cellular and humoral defence mechanisms in young and adult eurasian beavers are presented in table 1 .
the analyses of the results showed that phagocytic ability ( rba ) and potential killing activity ( pka ) of blood phagocytes were statistically significantly higher ( p < 0.05 ) in adult animals compared to the young ones .
a similar pattern was observed in proliferative response of blood lymphocytes stimulated by mitogens cona or lps .
the results showed that the proliferative response of lymphocytes was statistically significantly higher ( p < 0.05 ) in adult beavers .
the results showed that in adult eurasian beavers higher cell mediated immunity was observed and suggested that they has a solid and longer time contact with different pathogens and intensively activate the innate cellular immune response , important line of defence mechanisms and protection against diseases .
the innate cellular and humoral immunity in healthy eurasian beavers from natural conditions ( mean sd ) statistically significant p <
0.05 the results of the studies of the humoral innate immunity indicate that the lysozyme activity in plasma and gamma - globulin levels in serum were statistically significantly higher ( p < 0.05 ) in adult beavers compared to the young animals . also statistically significantly higher ( p < 0.05 )
but the ceruloplasmin activity in plasma was on the similar levels in adult and young eurasian beavers .
the objective of the present study was to determine the values of the innate cellular and humoral defence mechanisms in eurasian beavers , which are bred in natural conditions .
this basic examination provides very important information about physiological levels of nonspecific humoral and cellular protection against pathogens in different environmental conditions . in this study
we present for the first time innate defence mechanisms in adult and young eurasian beavers living in natural conditions .
the basic information regarding innate cellular and humoral defence mechanisms in healthy animals gives the possibility to monitor health of beavers by immunological parameters .
these studies are very important to develop effective methods of prevention of infectious diseases and to reduce mortality in different reintroduction and translocation programmes in poland .
| for the first time we tried to examine the basic parameters of innate immunity in beavers for developing the new methods of prevention against infectious diseases in different reintroduction and translocation programmes in poland .
the aim of the present study was to determine the selected innate immunity parameters in eurasian beavers living in natural conditions .
the analyses of the results showed that the phagocytic ability ( rba ) and potential killing activity ( pka ) of blood phagocytes were higher in adult beavers compared to the young animals .
the similar pattern was observed in proliferative response of blood lymphocytes stimulated by mitogens concanavalin a ( con a ) and lipopolysaccharides ( lps ) . the highest proliferative response in adult eurasian beavers
was observed .
the ceruloplasmin activity in plasma was on similar levels in adult and young eurasian beavers .
the results of humoral mediated immunity showed that the lysozyme activity , total protein and gamma - globulin levels in serum were higher in adult beavers compared to the young beavers .
the results of this preliminary study are important in comparative and clinical immunology . |
Kara Tippetts went Home to Jesus on March 22, 2015, after a long battle with breast cancer.
Born Kara Lynne Thewlies on July 14, 1976, she grew up in Noblesville, Indiana, and earned her BS in English Education at Indiana University. She met her husband Jason Tippetts at Eagle Lake Camp, a Christian camp located in Colorado Springs, Colorado. They were married on May 16, 1998.
Kara was led to Christ in high school after a youth leader read her a tract about Christianity and a friend invited her to youth group. Hearing a message about forgiveness prompted her to seek a relationship with Jesus, where she found total acceptance, kindness, and Grace. While she didn’t experience instant change in her life, dramatic changes were softly, slowly occurring in her heart as she trusted Christ’s love for her and allowed it to alter how she viewed the world and the people around her. She saw the difference a gentle word could make in response to an ugly remark, how an outstretched hand could break barriers of a hardened heart. Kindness became Kara’s passion; it defined her relationship with Jason, and then her four children: Eleanor, Harper, Lake, and Story Jane.
Answering a call to plant Westside Church in 2012, the Tippetts moved to Colorado where they soon after had to evacuate their home due to the Waldo Canyon Fire. It was this same summer that Kara received her breast cancer diagnosis. Despite beginning aggressive treatment for the cancer, Kara put her whole heart into growing and developing the new community that would become Westside, reaching out to others and teaching by example how to love and care for people well and sacrificially. An extrovert with a big, warm personality, Kara befriended neighbors, grocery baggers, those in line with her at Starbucks, other moms from her children’s school. She never hesitated to share a smile and a kind word. Her personality was magnetic, attracting people of all kinds, and she treated each friend as though they were her very favorite.
Her well known blog Mundane Faithfulness, where she originally posted about motherhood and living in kindness, became a blog about looking for God’s Grace to show up even in the hardest, messiest, ugliest places. It was a window into her life of chemo, church planting, spontaneous dance parties in the kitchen with her littles, her passion for Jason, her passion for those who don’t know Jesus, and her struggle to accept her growing cancer as God’s story for her life. Her self-described “mundane” life appeared anything but mundane to her readers who inevitably fell in love with her inviting, joyful personality and her love for and trust in Jesus; readers were attracted to her honesty, vulnerability, sense of humor, and simple faith. She never hesitated to share the hard moments, but she always pointed her readers—and herself—back to Jesus.
As the cancer spread, Kara courageously embraced her situation, trusting in a Sovereign God. She believed that cancer was not the point, but Jesus was; how she responded and trusted Christ in the midst of this hard was where she would find Grace. As Kara and her family processed what God was calling them to live out, she invited her community to join her journey through this seemingly impossible ordeal—how would she trust God in the midst of sickness? And then, how would she trust God in the midst of dying?
In the fall of 2014, David C. Cook published her story, The Hardest Peace. The response to Kara’s book has been overwhelming. In high demand, Kara toured and spoke as her physical condition allowed, touching even more people with the gift of her story and perspective. Christmas neared, and the physical became more difficult. Kara fought harder than ever to live well and love others well and with intentionality, especially Jason and their children. She refused to be defined by cancer and considered every moment a gift and an opportunity to learn more about Grace and trusting God; she believed suffering was not an absence of beauty, but an opportunity to understand God’s love on a deeper level. Kara recently wrote, My little body has grown tired of battle, and treatment is no longer helping. But what I see, what I know, what I have is Jesus. He has still given me breath, and with it I pray I would live well and fade well. By degrees doing both, living and dying, as I have moments left to live. I get to draw my people close, kiss them and tenderly speak love over their lives. I get to pray into eternity my hopes and fears for the moments of my loves. I get to laugh and cry and wonder over Heaven. I do not feel like I have the courage for this journey, but I have Jesus—and He will provide. He has given me so much to be grateful for, and that gratitude, that wondering over His love, will cover us all. And it will carry us—carry us in ways we cannot comprehend.
Kara is survived by her husband Jason; her children Eleanor Grace, Harper Joy, Lake Edward, and Story Jane; her parents Carolyn and Dennis Thewlies; her sister Jonna McMahon (Mike) and their three daughters; her brother Dennis Thewlies, Jr., and his son and daughter; and countless other loving family members, in-laws, mentors, friends, and her Westside Church family.
In lieu of flowers, donations may be sent to a fund benefitting the Tippetts children:
Jason Tippetts
P.O. Box 49727
Colorado Springs, CO 80949 ||||| You may have read the poignant & powerful, CNN front-page story of cancer patient Brittany Maynard, 29, who has scheduled her death for Nov. 1? Come November 1, Maynard plans to take a pill given to her by her doctors as she wants to choose her own death and avoid hospice and the suffering her brain-tumor cancer may entail — Her story-gone-viral speaks of her plan to swallow the pill and choose death on her own terms in her own bedroom with her husband beside her and her favorite music playing in the background. Her story is raw — and she has all our love and prayers…. Before she dies by assisted suicide, Brittany states that she wants to use the rest of her time on earth to lobby for every American to have access to assisted suicide services. After I read Brittany’s story yesterday… my friend Kara Tippetts dropped an email into my inbox — Kara was diagnosed with breast cancer at age 36. She has 4 young children. She continues to battle that cancer two years later as it has crossed the blood/brain barrier and has metastasized into her entire body. I’ve been reading Kara’s journey since the beginning, profoundly moved by this woman’s courage to embrace all of her life as it comes to her… Kara’s exceptional book released this week, The Hardest Peace: Expecting Grace in the Midst of Life’s Hard — and Kara humbly speaks important words into this current news story and national conversation about assisted suicide with a tender weight & compassionate gravity that only someone, a mother, a wife, a daughter, bravely facing terminal cancer can — we earnestly love and pray for both women as they each share own their stories:
by Kara Tippetts
Dear Brittany Maynard,
This morning my best friend and I read your story.
My heart ached for you, and I’m simply grieved by your terminal brain tumor, for the less than 6 months the doctor’s gave you, you just past your 29th birthday.
With a heavy heart, I left my home and headed for my oncologist. I too am dying, Brittany.
My oncologist and I sat for a long time with hurting hearts for your story. We spoke in gentle tones discussing the hard path you are being asked to travel.
I came home and my friend and I sat on the bed of my five year old and prayed for you. We simply prayed you would hear my words from the most tender and beautifully broken place of my heart.
We prayed you would hear my words that are on paper coming from a place of tender love and knowing. Knowing what it is to know the horizon of your days that once felt limitless now feels to be dimming.
So hear these words from a heart full of love for you.
Brittany, your life matters, your story matters, and your suffering matters. Thank you for stepping out from the privacy of your story and sharing it openly.
We see you, we see your life, and there are countless lovers of your heart that are praying you would change your mind.
Brittany, I love you, and I’m sorry you are dying. I am sorry that we are both being asked to walk a road that feels simply impossible to walk.
I think the telling of your story is important.
I think it is good for our culture to know what is happening in Oregon.
It’s a discussion that needs to be brought out of the quiet corners and brought brightly into the light. You sharing your story has done that. It matters, and it is unbelievably important. Thank you.
Dear heart, we simply disagree. Suffering is not the absence of goodness, it is not the absence of beauty, but perhaps it can be the place where true beauty can be known.
In your choosing your own death, you are robbing those that love you with the such tenderness, the opportunity of meeting you in your last moments and extending you love in your last breaths.
As I sat on the bed of my young daughter praying for you, I wondered over the impossibility of understanding that one day the story of my young daughter will be made beautiful in her living because she witnessed my dying.
That last kiss, that last warm touch, that last breath, matters — but it was never intended for us to decide when that last breath is breathed.
Knowing Jesus, knowing that He understands my hard goodbye, He walks with me in my dying. My heart longs for you to know Him in your dying. Because in His dying, He protected my living. My living beyond this place.
Brittany, when we trust Jesus to be the carrier, protecter, redeemer of our hearts, death is no longer dying. My heart longs for you to know this truth, this love, this forever living.
You have been told a lie. A horrible lie, that your dying will not be beautiful. That the suffering will be too great.
Today my oncologist and I spoke of your dying, of my dying, and of the beautiful partnership I have with my doctors in carrying me to my last moments with gentle care. For two thousand years doctors have lived beside the beautiful stream of protecting life and lovingly meeting patients in their dying with grace.
The doctor that prescribed you that pill you carry with you that will hasten your last breath has walked away from the hippocratic oath that says, “first, do no harm.” He or she has walked away from the oath that has protected life and the beautiful dying we are granted. The doctors agreeing to such medicine are walking away from the beautiful protection of the hippocratic oath.
There are also people who are speaking in ugly tones that make those of us who believe in Jesus seem unsafe, unkind, or unloving. Will you forgive us for the voices that feel like they are screaming at you from a heart that isn’t loving.
But in my whispering, pleading, loving voice dear heart- will you hear my heart ask you, beg you, plead with you — not to take that pill. Yes, your dying will be hard, but it will not be without beauty. Will you please trust me with that truth.
More importantly, will you hear from my heart that Jesus loves you. He loves you. He loves you. He died an awful death upon a cross so that you would know Him today that we would no longer live separate from Him and in our death. He died and His death happened, it is not simply a story.
He died and He overcame death three days later, and in that overcoming of death He overcame the death you and I are facing in our cancer. He longs to know you, to shepherd you in your dying, and to give you life and give you life abundant- eternal life.
For everyone living knowing death is eminent- that we all will one day face this it – the question that is most important. Who is this Jesus, and what does He have to do with my dying? Please do not take that pill before you ask yourself that question.
It’s a question we all must ask, as we are all dying.
I recently wrote a book, The Hardest Peace, and I also blog about my journey of my living and my journey towards my last breath. It is not simply a story of dying of cancer, but of living this breath. It’s a book for each of us that has breath still to breath, to embrace our living, and to look upon our dying with grace. Living in BIG LOVE and meeting my end in love. Stunning, important, love.
But more than my book, I would jump on a plane tomorrow to meet you and share the beautiful brokenness of my story and meet you in yours if you would ever consider having me.
I pray my words reach you.
I pray they reach the multitudes that are looking at your story and believing the lie that suffering is a mistake, that dying isn’t to be braved, that choosing our death is the courageous story.
No – hastening death was never what God intended.
But in our dying, He does meet us with His beautiful grace.
The hippocratic oath matters, and those that are choosing to walk away from it need to be challenged.
My heart hurts that they have decided to swim from the shores of grace that it protected in our living and dying.
I get to partner with my doctor in my dying, and it’s going to be a beautiful and painful journey for us all.
But, hear me — it is not a mistake —
beauty will meet us in that last breath.
photo credits: Jen Lints Photography |||||
Kara Tippetts, an author and mother of four, has terminal breast cancer at the age of 38. (Photo by Jay “Napoleon” Lyons)
A Christian author and blogger with terminal cancer who tried to convince Brittany Maynard to reconsider her November decision to die through doctor-assisted suicide is facing her own death. [Update on 3/22: Tippetts has died]
Maynard made headlines as the 29-year-old who chose to die on Nov. 1 by taking a legal lethal prescription as she faced an aggressive cancerous brain tumor.
Kara Tippetts, an author and mother of four, has terminal breast cancer at the age of 38.
Kara Tippetts, a Colorado Springs wife of a pastor and 38-year-old mother of four who was diagnosed two years ago with stage four breast cancer, has become the poster face of an opposite view. Her book publicist confirmed on Thursday that her family believes she is close to death.
Tippetts’s open letter to Maynard on Ann Voskamp’s popular blog went viral in many Christian circles. “Dear heart, we simply disagree,” Tippetts wrote. “Suffering is not the absence of goodness, it is not the absence of beauty, but perhaps it can be the place where true beauty can be known. In your choosing your own death, you are robbing those that love you with the such tenderness, the opportunity of meeting you in your last moments and extending you love in your last breaths.”
Tippetts argued in her post that hastening death is not what God intended.
I get to partner with my doctor in my dying, and it’s going to be a beautiful and painful journey for us all. But, hear me — it is not a mistake — beauty will meet us in that last breath.
Her story was picked up by Ross Douthat, who wrote about the debate represented by Maynard and Tippetts.
“The future of the assisted suicide debate may depend, in part, on whether Tippetts’s case for the worth of what can seem like pointless suffering can be made either without her theological perspective, or by a liberalism more open to metaphysical arguments than the left is today,” Douthat wrote.
Kara Tippetts, a mother of four with terminal breast cancer, is in hospice care. (Jay “Napoleon” Lyons)
Tippetts was admitted into hospice care in December. On Friday, her husband Jason Tippetts wrote about his wife’s final days.
“I have an us that cannot be lost,” Jason Tippetts wrote. “And I still get small moments where we are us. But I grieve as I watch her fade. The peace that is in our house is amazing, peace in the midst of tears, peace in the midst of impending loss, but it is peace.”
Jay Lyons, a producer who is a friend of the Tippetts, raised more than $15,000 of his goal of $13,750 to create a documentary.
Before her death in November, Maynard became an advocate for laws for legal protections for terminally ill patients who want to die with medical assistance. Voters in Oregon and Washington passed ballot measures allowing the practice, while legislators in Vermont and judges in Montana and New Mexico have authorized it.
“Goodbye to all my dear friends and family that I love. Today is the day I have chosen to pass away with dignity in the face of my terminal illness, this terrible brain cancer that has taken so much from me … but would have taken so much more,” she wrote on Facebook before her death.
Brittany Maynard, a 29-year-old with terminal brain cancer, tells her story and explains why she plans to ingest a prescription that will end her life on Nov. 1 in this video from advocacy group Compassion & Choices. (Compassion & Choices via YouTube)
NPR host Diane Rehm has emerged as a key force in the end-of-life debates. Americans are divided on the role of medicine in the issue, according to recent Pew Research surveys. When asked about end-of-life decisions for other people, two-thirds of Americans say there are at least some situations in which a patient should be allowed to die, while nearly a third say that medical professionals always should do everything possible to save a patient’s life. Of those polled, 47 percent approved and 49 percent disapproved of laws that would allow a physician to prescribe lethal doses of drugs for a terminally ill patient.
Interested in more religion stories? Read more from Acts of Faith:
Behold! What Shakespeare’s words on mercy can teach us about Internet shaming
Can one pastor bridge deep divides between evangelicals and mainline Protestants?
Presbyterian Church (USA) changes its constitution to include gay marriage ||||| The seed for Wide00014 was:
- Slash pages from every domain on the web:
-- a ranking of all URLs that have more than one incoming inter-domain link (rank was determined by number of incoming links using Wide00012 inter domain links)
-- up to a maximum of 100 most highly ranked URLs per domain
- Top ranked pages (up to a max of 100) from every linked-to domain using the Wide00012 inter-domain navigational link graph | – A Christian writer who fueled the debate over assisted suicide and refused to cut her own life short in the face of terminal cancer died yesterday, according to a post on her blog. Kara Tippetts, 38, a pastor's wife and mother of four in Colorado Springs, Colo., was admitted in December to hospice care, the Washington Post had earlier reported. "I grieve as I watch her fade," wrote her husband Jason. "The peace that is in our house is amazing, peace in the midst of tears, peace in the midst of impending loss, but it is peace." Diagnosed with stage four breast cancer two years ago, Tippetts made a stir with her open letter to Brittany Maynard, the 29-year-old who took her own life rather than suffer what she called "a terrible" death by stage four glioblastoma. In her letter, Tippets wrote: "Dear heart, we simply disagree. Suffering is not the absence of goodness, it is not the absence of beauty, but perhaps it can be the place where true beauty can be known. In your choosing your own death, you are robbing those that love you with ... such tenderness, the opportunity of meeting you in your last moments and extending you love in your last breaths." In a blog post titled "Homecoming," Tippetts is recalled as "an extrovert with a big, warm personality ... [who] never hesitated to share a smile and a kind word. Her personality was magnetic, attracting people of all kinds, and she treated each friend as though they were her very favorite." She is survived by husband Jason; her children Eleanor Grace, Harper Joy, Lake Edward, and Story Jane; and "countless other" family members and friends. One of those friends, a producer, has raised more than $15,000 to make a documentary about her ordeal. See the trailer here, or why the "right to die" debate is personal for an NPR host. |
the introduction of the microscopic discectomy by caspar w and yasargil mg in 1977 ( 2 , 3 ) the infection rate of the procedure has been significantly reduced , mainly due to the less damage to the tissue . at the moment
, the reported rate of infection after disc surgery is between 1 % and 15 % ( 4 ) .
infection can be disabling , it requires a long time treatment with bed rest and antibiotics , deformity , chronic pain , even death .
it is well known that systemic antibiotics prophylaxis reduced the incidence of infection ( 5 ) .
however , there is little evidence for the effect of the local irrigation of operative field with antibiotics at the end of procedure at the infection rate in herniated disc patients .
this paper , based on the experience of a busy neurosurgical department is an attempt to contribute to the wide discussion on this matter .
in this retrospective study we analyzed patients operated for lumbar discectomy , from 20092012 in our institution . during this period
604 patients were operated , including patients operated for the first time , those with recurrent disk disease .
preparation for operation necessarily includes routine laboratory tests , ers and crp , lumbar radiography , spine ct and mri of the lumbar region .
all of the patients , who were operated , did nt present with any signs of infectious focus elsewhere before surgery .
a patient with epidural abscess after lumbar discectomy is excluded from our study because the resident has forgotten a part of the cotton in epidural space .
we use amikacin sulfate injection diluted with saline solution for irrigation and systemic antibiotic cefazolin iv 2.0 , 30 min prior to surgery or 600 mg clindamycine in patients allergic to b - lactam antibiotics ( 15 patients ) .
we stop the antibiotics after third dose in patients without drainage . in patients with drainage antibiotic
the infection is judged by neurosurgeon during regular ambulatory visits , with laboratory analysis , white blood count , ers , crp , radiological imaging , mri for suspicious cases .
a total of 604 patients , 285 ( 47.2% ) were females and 319 males ( 52.8% ) .
gender of the patients in the study level of the herniation of the lumbar disc infection : 3 patients with infection of the wound , two male patients with superficial infection and 1 female diabetic patient with deep infection .
all infected patients were smokers and did nt stop smoking even for short time . with
the wound swab staphylococcus aureus is isolated to the three cases ; two patients had superficial wound infection and were treated with oral tablets , cefuroxime 500 mg 21 for 10 days , according to sensitivity with antibiograme , the patient with deep wound infection was treated with vankomycine amp .
. the surgeon must be very vigilant to reduce their incidence as much as possible . according to the previous similar study in our institution with only systemic antibiotic prophylaxis ,
at that period the infection rate after lumbar discectomy was 2.7 % ( 1.6% discitis and 1.1% wound infections ) .
results obtained in this study show us that the addition of local antibiotic is effective in reducing the rate of infection after lumbar discectomy compared with the rate of infection after prophylaxis with systemic antibiotics only .
our results are similar to studies done worldwide regarding infections after lumbar discectomies 1 % -10 % ( 4 ) . the idea for choose amikacin sulfate was : local activity , effective against staphylococcus and gram negative bacteria , the most common agents of infections after these procedures . as in other studies
diabetes and smoking was a risk factor for infection ( 8 , 9 ) , due to the impaired function of leukocyte , the angiopathy , and poor supply of oxygen to the tissues and poor penetration of the antibiotic in area .
meticulous surgical work , good fascial closure , correct hemostasis , frequent space irrigation with saline , treatment of high blood sugar ( 8) , abstinence of smoking ( 9 ) , good nourishment ( 10 ) are very important factors which together with systemic and local antibiotic prophylaxis help to prevent infections after lumbar discectomies .
our study showed that systemic antibiotic prophylaxis and addition of local antibiotic irrigation of space is effective in reducing the rate of infection after surgery for herniated lumbar disc compared with the rate of infection after prophylaxis with systemic antibiotics only . | introduction : reported rate of infections after lumbar discectomy is 1%15 % .
this complication may result in disability or even the death.aimthe aim of the study is to assess the rate of infection associated with lumbar discectomies when combined systemic and local antibiotic prophylaxis was employed.patients and methods : in this retrospective study we analyzed all patients operated for herniated lumbar disc from 2009 -2012 in our institute . beside of receiving systemic prophylaxis with 2 g of cefazoline , all patients had their operative field irrigated at the end of operation with amikacin sulfate injection .
wound was considered infected when local and systemic signs of infection were revealed and were associated with elevated esr , leukocytosis and elevated crp .
assessment of infection is done by neurosurgeon during the hospitalization and later at outpatient s clinic along postoperative course of three months.results:a total of 604 patients were operated , of those 285 patients ( 47.2 % ) females and 319 males ( 52.8 % ) , 12 patients were operated on two levels ( 1.98 % ) .
average patient age was 32.5 years ( range 2065 years ) localization of herniated disc was : in l/2-l/3 20 patients or 3.3 % , the l/3-l/4 level 42 patients or 7 % , the l/4 -l /5 262 patients or 43.3 % at the level l / v- s/1 280 patients or 46.3 % .
three patients ( 0.49% ) developed wound infection , two of them superficial infection only with local signs : local pain , redness and leakage .
they were treated with oral antibiotics .
one with deep wound infection .
he presented with local and systemic signs and treated with i.v antibiotics .
all the cultures from wound swab revealed staphylococcus aureus.conclusion:prophylaxis with systemic antibiotic ( cefazoline 2.0 ) intravenous administration 30 minutes before the incision and irrigation of operative field with local antibiotic amikacine sulfate at the end of procedure reduces the infection rate in patients operated for herniated lumbar disc when compared with systemic antibiotic prophylaxis only . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``HIV Partner Protection Act''.
SEC. 2. PROGRAM FOR HIV HEALTH CARE SERVICES; AMENDMENT REGARDING STATE
PROGRAMS OF PARTNER NOTIFICATION.
Subpart I of part B of title XXVI of the Public Health Service Act
(42 U.S.C. 300ff-21 et seq.) is amended by inserting after section 2616
the following section:
``SEC. 2616A. PARTNER NOTIFICATION.
``(a) In General.--Subject to subsection (d), for fiscal year 2000
and subsequent fiscal years the Secretary shall not make a grant to a
State under this part unless the State demonstrates to the satisfaction
of the Secretary that the law or regulations of the State are in
accordance with the following:
``(1) The State requires that the public health officer of
the State carry out a program of partner notification to inform
partners of individuals with HIV disease that the partners may
have been exposed to the disease.
``(2) In the case of a health entity that provides for the
performance on an individual of a test for HIV disease, the
State requires that the entity confidentially report positive
test results to the State public health officer, including the
name of the individual, together with any additional
information necessary for carrying out such program.
``(3) The program is carried out in accordance with the
following:
``(A) Partners are provided with an appropriate
opportunity to learn that the partners have been
exposed to HIV disease, subject to subparagraph (B).
``(B) The State does not inform partners of the
identity of the infected individuals involved.
``(C) Counseling and testing on HIV disease are
made available to the partners and to infected
individuals, and such counseling includes information
on modes of transmission for the disease, including
information on prenatal and perinatal transmission and
preventing transmission.
``(D) Counseling for infected individuals includes
the provision of information regarding therapeutic
measures for preventing and treating the deterioration
of the immune system and conditions arising from the
disease, and providing other prevention information.
``(E) Referrals for appropriate services are
provided to partners and infected individuals.
``(F) Notifications under subparagraph (A) are
provided in person, unless doing so is an unreasonable
burden on the State.
``(G) There is no criminal or civil penalty on, or
civil liability for, an infected individual if the
individual chooses not to identify the partners of the
individual, or if the individual does not otherwise
cooperate with such program.
``(H) There is no criminal or civil penalty on, or
civil liability for, a person who in good faith makes
errors in submitting reports or making disclosures
under such program.
``(I) The failure of the State to notify partners
is not a basis for the civil liability of any health
entity who under the program reported to the State the
identity of the infected individual involved.
``(J) The State provides that the provisions of the
program may not be construed as prohibiting the State
from providing a notification under subparagraph (A)
without the consent of the infected individual
involved.
``(b) State Insurance Laws With Respect to Undergoing Testing.--
``(1) In general.--Subject to subsection (d), for fiscal
year 2000 and subsequent fiscal years the Secretary shall not
make a grant to a State under this part unless the State
demonstrates to the satisfaction of the Secretary that, with
respect to an individual who learns that the individual has
been exposed to HIV disease and then undergoes testing for such
disease, State insurance laws prohibit an insurer from taking
any action against the individual solely on the basis that the
individual has been tested for the disease.
``(2) Rule of construction.--A statute or regulation shall
be deemed to regulate insurance for purposes of paragraph (1)
only to the extent that such statute or regulation is treated
as regulating insurance for purposes of section 514(b)(2) of
the Employee Retirement Income Security Act of 1974.
``(c) Definitions.--For purposes of this section:
``(1) The term `infected individual' means an individual
with HIV disease.
``(2) The term `partner' includes the spouses or other
sexual partners of infected individuals; the partners of such
individuals in the sharing of hypodermic needles for the
intravenous injection of drugs; the partners of such
individuals in the sharing of any drug-related paraphernalia
determined by the Secretary to place such partners at risk of
HIV disease; and any other individual whom the infected
individual exposed to HIV disease.
``(d) Delayed Applicability for Certain States.--In the case of a
State whose legislature does not convene a regular session in fiscal
year 1999, and in the case of a State whose legislature does not
convene a regular session in fiscal year 2000, the requirements
described in subsections (a) and (b) as a condition of the receipt of a
grant under this part applies only for fiscal year 2001 and subsequent
fiscal years.''.
SEC. 3. GRANTS TO STATES TO ASSIST WITH COSTS OF REQUIRED LAW.
(a) In General.--The Secretary of Health and Human Services may
make grants to States to assist the States with the costs of carrying
out the program of partner notification with respect to the human
immunodeficiency virus that is required in section 2616A of the Public
Health Service Act (as added by section 2 of this Act).
(b) Authorization of Appropriations.--For the purpose of carrying
out subsection (a), there is authorized to be appropriated $10,000,000
for each of the fiscal years 2000 through 2004. | HIV Partner Protection Act - Amends the Public Health Service Act to prohibit a grant to a State under provisions relating to human immunodeficiency virus (HIV) care grants unless the State: (1) carries out a program of notification of sex or needle sharing partners of individuals with HIV disease that the partners may have been exposed; (2) requires HIV testing entities to confidentially report positive test results, including the individual's name, to the State; (3) does not inform partners of the infected individual's identity; (4) meets certain counseling, testing, and referral requirements; (5) there is no criminal or civil penalty or civil liability for an infected individual if the individual chooses not to identify their partners or for an individual who makes a good faith error in submitting reports or making disclosures; and (6) the failure of the State to notify partners is not a basis for civil liability of any health entity who reported to the State the identity of the infected individual.
Prohibits such a grant unless a State prohibits insurers from taking any action against an individual solely on the basis that the individual has been tested for HIV disease.
Authorizes grants to States to assist with the costs of carrying out the program. Authorizes appropriations. |
papers by the two physicians e. timoni and g. pilarini , published in philosophical transactions in 1714 , made the technology known to savants .
the wife of the english ambassador in constantinople , she had her young son treated in 1718 .
when the family returned to england , his sister was inoculated by the surgeon maitland in 1721 .
not least after lady mary had convinced the princess of wales to have her children inoculated as well , and experiments to check the safety of the method had been carried out on seven prisoners from newgate prison , the innovation became the talk of the town . in 1722 inoculation
massey identified the scourge cast by the lord on job as smallpox , and denounced inoculation as diabolical .
the arguments were answered by maitland , and soon also by men of the church . refuting the religiously based arguments launched by massey and others nonetheless remained a staple element of pro - inoculation literature throughout the century , in england and elsewhere .
the defenders put much energy into not only denouncing the attack , but also presenting pro - inoculation arguments of a religious kind .
most fundamental was the claim that inoculation was a gift from god , given to man to enable him to protect himself .
what was sinful was not to inoculate , but to abstain from it , as this meant refusing god s gift .
moreover , by way of saving lives , inoculation would contribute to population growth , which also agreed with the wishes of god ( and contemporary economic thought ) .
the earliest pro - inoculation text published in norway was a translation of an article by the german theologian johann andreas cramer from 1759 . in his defence against the religiously based objections , cramer drew heavily on the ideas of the german demographer johann peter smilch , who saw population growth as god s will .
hence , inoculation became a means to comply with divine will , while not protecting one s children in this way was regarded a sin of omission .
norway , where a number of subsequent publications reproduced substantial parts of cramer s text verbatim .
another , less biblically based objection was that inflicting a potentially fatal disease on healthy persons who might otherwise never be attacked by it was not ethically defensible .
advocates of inoculation responded that hardly anybody escaped smallpox during his or her life , and that the disease normally was even more dangerous when contracted at a mature age . in comparison ,
the longevity of the debate and the numerous arguments indicate the significance of the religious and ethical challenge posed by inoculation .
even if some enlightenment radicals would ridicule biblical arguments of the kind presented by massey , religious and ethical considerations obviously remained an issue that was not to be treated lightly . among the twelve objections against inoculation discussed by the swiss physician s.a.d .
tissot in his linoculation justifie from 1754 , the first six concern ethical and religious arguments .
the article on inoculation written by the swiss physician thodore tronchin for the encyclopdie presents altogether thirteen objections to inoculation , the last seven of which are religious and ethical .
in his analysis of inoculation , mainly a medical treatise ,
the british physician james kirkpatrick presents and counters the religious and ethical objections in the preface .
his arguments in defence of the method are in part religious inoculation is a gift from god and consist in part of references to past medical authorities who undoubtedly would have been in favour of inoculation and would have acknowledged its providential origin had they only known about it , he declares .
however , taking eighteenth - century public arguments seriously , as they were presented in the public debate and in inoculation literature , it appears that what was felt to represent something dramatically different from traditional medicine were the religious and ethical implications rather than the medical aspects .
defending or advocating inoculation meant countering these arguments just as much as entering into a medical discussion .
parallel to this , and supporting the argument , discussions of how inoculation worked are relatively scarce .
texts trying to explain how the new remedy worked and what its active principles were normally did so within the frames of traditional , philosophical medicine .
inoculation was explained as a treatment working along the same lines as other cures and remedies .
even if it was a novelty in europe , it was not perceived as a challenge to traditional medical principles .
it was surprisingly effective and represented a far better remedy in cases of smallpox epidemics than any other cure or method , but it was not originally seen as fundamentally different from established medicine .
one reason for this was that inoculation was not necessarily perceived as a means to prevent smallpox , but rather as a way of producing a mild and benign case of the disease .
the encyclopdie defines it as the operation by which smallpox is artificially communicated , with the aim of preventing the dangers and damages caused by this disease when it is contracted in the normal fashion.
the danish physician c.f .
rottbll calls it the best way to cure smallpox , and the norwegian vicar a. smith calls it a medication .
tissot s main argument in favour of inoculation was the possibility it gave of controlling the course of the disease .
smallpox in itself was a mild and not very dangerous kind of disease , he contended .
the age of the patient and his or her constitution , as well as the time of year and the weather conditions , not least the air , all contributed to risk , uncertainty and malignant cases .
inoculation solved these problems , as it made it possible to choose the most suitable age and season and to prepare the patients for it in the ways their individual constitutions demanded .
nonetheless , tissot also warned against measures that might make the illness too light in such cases inoculation will not protect against further attacks of the disease , he maintained .
the idea that smallpox was not really a dangerous disease was not widespread , but the understanding that one of the main advantages of inoculation was the possibility of choosing when to get ill , and to prepare for it , is expressed by a majority of the authors advocating the method .
scholars working on the history of vaccination in nineteenth - century india have argued that the reason why the modern practice of vaccination did not easily supplant the older variolation ( inoculation ) , was that while the former worked as a prophylactic , the latter was conceived of as part of a therapeutics .
its context of religious ritual was long seen as the explanation for the indian preference for variolation and corresponding reluctance toward vaccination .
more recent research has recast this debate in new terms . rather than presenting an opposition between the indigenous , religious and superstitious tradition on the one hand , and the european , scientific and effective practice on the other , two different approaches to the challenge raised by smallpox
are now described : one therapeutic , the other prophylactic .
traditional medical history has tended to see european eighteenth - century inoculation as a prophylactic .
close reading of texts from the period show it rather to be part of a therapeutics .
its important difference from the indian parallel , however , is that the ritual context of the european treatment was not religion , but learned medicine itself .
the great emphasis that was put on preparations is an important key to this medical understanding .
the first concerned preparation , which meant both choosing the most suitable time and preparing the patient .
the next phase treated the insertion of variolous matter , while the final phase included the course of the subsequent disease and the care of the patient .
the issue of time related in part to the age of the person to be treated .
infants were normally not inoculated , and the minimum age was discussed . in the case of an epidemic , parents were often anxious to have even their newborn treated , but most inoculators set a minimum age of at least two years .
an epidemic could dispel theoretically based concerns about treating individuals over thirty years of age .
it was generally recommended not to inoculate menstruating or pregnant women .
for the time of year , spring and autumn
it was also important to choose a period without the threat of other perilous diseases .
the preoccupation with weather , season and temperature can be understood as part of eighteenth - century neo - hippocratic medicine and its interest in the non - natural things. above all , physicians of the period ascribed great importance to air , smell and climatic conditions as determining factors for health and as causes for disease .
the treatment of the danish crown prince christian ( later christian vii ) was , for instance , reported to have taken 84 days .
medical as well as more popular literature on inoculation gives much attention to the preparatory procedures .
the number of clysters to be given , would vary according to the constitution or
tissot advises against bleeding , unless the patient has a very blood - rich constitution .
women are usually inoculated immediately after their period , hence they do not need to be bled .
kirkpatrick is vehement that the diet is fundamental because it produces changes in our fluids and solids that are gradual and hence without violence to the constitution.
during a period of six weeks or even two months in the cases of very unfavourable dispositions the patient ought to follow a regime of very light food .
kirkpatrick gives detailed descriptions fit for different constitutions , the most demanding one being that of black jaundice ( black bile ) .
the procedures were thought to call for all the caution as well as knowledge , of the physician.
knowing this art well , however , every ingenious and experienced physician , who has considered this matter well , may have sufficient reason to infer , that on availing his patients of all good circumstances , persons of naturally unpromising temperaments , and less convenient ages for the accidental disease , may have a reasonable expectation of passing very tolerably through that by inoculation.
children were generally thought to need less preparation than adults : a few days of diet and one or two mild purgings were generally held to suffice .
kirkpatrick as well as the swedish physician lars montin observe that children frequently suffer from worms .
kirkpatrick s advice is to drive them out with calomel powder and some grains of rhubarb .
older children ( from six or seven years ) may also be given laxatives like glauber salt or cream of tartar .
the attention given to preparations and the large room given to the issue in texts , medical as well as popular , indicate their importance .
preparations loom large in the medical practice that is described , and were equally fundamental to the understanding of what the new method was all about .
kirkpatrick s words quoted above underscore that it was the work with preparations where the competence , experience and art of the physician really entered into the picture .
it was the physician s learning that made it possible for him to alter the specific constitution and stamina of the patient , and to lead him or her safely through the dangers .
this learning and the art it produced are firmly situated within the frames of traditional pathology , with its teachings on constitutions and temperaments , bodily fluids or humours . what can be read from the argument , then
, is that the reason why physicians could succeed in their work as inoculators was because they knew how the humours interact inside the body and how they constitute the temperament of each individual .
moreover , this also supplied a reason why inoculation ought to be the privilege of the physicians .
such a claim can be seen as a strategy to stop lay inoculators , but was just as probably an argument directed against surgeons .
they were the experts on wounds and operations , and might be called upon to dress the incision made by the inoculator s lancet . nonetheless , the weight put upon preparations defined inoculation securely as a matter for the physicians .
roger french has pointed out that when aristotelian natural philosophy fell into decline during the seventeenth century , medicine was deprived of its philosophical base and faced the risk of being reduced to a mere art of healing .
he argues that a number of attempts were made during the eighteenth century to give medicine a new philosophical or scientific base , which did not really succeed until the development of modern anatomical pathology .
the texts on inoculation demonstrate the vitality of the old ways of thinking . in the same way
as a modern understanding of blood circulation did not preclude traditional ideas about the usefulness of bleedings , humoral pathology was fully able to incorporate inoculation into the world view it represented .
it dictated the practice of inoculation as well as the way it was spoken about .
both reflected that what was held important and what defined the distinct qualification of the learned physician was his ability to work on the patients constitutions .
this facility by which inoculation was incorporated into traditional pathology made discussions of its working principles superfluous .
, texts on inoculation normally describe the operation itself . the original method used in europe consisted of making small incisions , normally one on each arm of the patient , and placing a thin thread that had been saturated with variolous matter .
the thread was kept in place by a bandage and then removed after about 48 hours .
the important development in the 1760s was that the scratches now were made merely cutaneously , and frequently in one arm only .
fresh pus from another patient replaced the saturated thread , and no bandage was needed .
the new method reduced the risk of infected wounds , and also produced milder attacks of smallpox , hence increasing the survival rate . along with these innovations ,
other new ideas were the extensive use of fresh air and cold drinks during the subsequent illness
it had formerly been thought that too fresh pus did not bring about the desired effect when transferred to another person .
several of these developments , and not least their organisation into a system , were due to the english surgeon daniel sutton . with the motto
safely , quickly and pleasantly , he made his methods a commercial success in the 1760s , setting up inoculation clinics in the countryside .
similar innovations were advocated by thomas dimsdale who in some cases was also heralded as their inventor .
his 1767 book the present method of inoculating for the small - pox saw five subsequent editions in as many years .
some physicians worried that the new methods would not produce a sufficient cleansing of the body during the subsequent illness , and also found it hardly defensible to decrease the preparatory period .
others defended the innovations , even if opinion varied as to which of the elements was the most significant .
for some physicians , like dimsdale and the sutton family , the new and efficient method resulted in considerable economical gain .
others seem to have adopted the new ways mainly because of the possibility of treating more people cheaply and rapidly , which was important not least during epidemics .
the last phase of inoculation texts describes the care of the patient during the period of illness . about a week
fever normally appeared after seven or eight days , and decreased again when pustules broke out about ten days after the operation . inoculated smallpox normally gave a smaller number of pustules than the natural version .
their development was nonetheless closely followed , as even inoculated smallpox could lead to fatal cases .
a rich crop of pustules circling the scratches where the pus had been inserted was seen as indication of good cleansing : most of the
poison of the disease was then thought to be eliminated through the incisions rather than disfiguring the patient s face or other parts of the body .
cold treatment during the fever , fundamentally based on the principles described by thomas sydenham in 1666 .
dimsdale describes it applied to smallpox cases : instead of confining the patient to his bed , or his room , when the symptoms of the eruptive fever come on , he is directed , as soon as the purging medicine has operated , to keep abroad in the open air , be it ever so cold , as much as he can bear , and to drink cold water , if thirsty ; always taking care not to stand still , but to walk about moderately while abroad .
instead of confining the patient to his bed , or his room ,
when the symptoms of the eruptive fever come on , he is directed , as soon as the purging medicine has operated , to keep abroad in the open air , be it ever so cold , as much as he can bear , and to drink cold water , if thirsty ; always taking care not to stand still , but to walk about moderately while abroad .
spokesmen for the method seem to have considered the introduction of fresh air and cold drinks during illness just as fundamental to the success as the new ways of inserting pus .
smallpox patients had traditionally been covered up and kept as warm as possible in heated rooms with no airing .
its reputation to alleviate or cure the disease was so large that it was even considered to save lives in cases of natural smallpox .
moreover , the cold treatment agreed well with the neo - hippocratic medicine of the period .
their common base in principles of humoral pathology was also what made the regimes for preparation and the subsequent care of the patient so similar .
what mattered was to work on the constitution of the patient during preparation to make the body fit for the imminent treatment and during illness to help it regain its normal , healthy balance of humours .
another reason for this similarity was that smallpox itself was seen as a purging of the body , making it sensible to let the treatment consist of remedies aimed at aiding this process both before and during illness : purgings and bleedings .
the idea is , for instance , expressed by dimsdale when he terms the inoculated matter a purging medicine ( above ) .
notions of illness as purgings were central to humoral pathology in general , but had specific implications when it came to smallpox .
la condamine begins his influential treatise in defence of inoculation by describing smallpox as a terrible and gruesome disease , whose seed we carry in our blood.
the understanding of the cause of smallpox as something inherent in the individual also forms the basis of his answer to the objections against the new method .
it is not correct , he contends , that inoculation means inflicting disease on persons who would otherwise not have been attacked by it . only those who can have smallpox
the one who does not have the growth or seed of smallpox within him does not suffer more than an operation smaller than a bleeding but even he will gain the freedom from worry and fear to be taken ill .
in his discussion of the efficacy of inoculation to protect against future attacks , la condamine argues that even a person who has had natural smallpox in a very light way may suffer a new attack if the illness has insufficiently brought forward the seed or growth that make smallpox break out.
tronchin quotes la condamine s assertion that smallpox is inevitable to the majority of persons ,
and thus seems to share the understanding .
the swiss physician jean - antoine butini expresses the same ideas more explicitly , explaining that the foyer of smallpox is brought into us at birth .
it does not in itself harm the body , but it remains there through our entire lives if it is not exhausted and eradicated through a smallpox attack .
impurities , miasmas , set this matter into motion , which is what causes the disease .
even if butini admits that the exact localisation of the smallpox seed has not been identified , he is able to present a quite detailed explanation of how the infected matter is produced in the blood and gradually seeks its way out of the body , causing pustules and penetrating the skin .
the extreme consequence of this view was an understanding of smallpox as a process similar to secondary dentition or menstruation , and a part of the biological development of the individual .
kirkpatrick argues against this stance , which had been defended by the german physician and philosophe j.g .
a main argument against the theory was that if the seed or poison of smallpox was inherent in all human beings from birth , the disease would exist in all historic periods and in all parts of the world which it did not .
the objections did not , however , imply that kirkpatrick had a very different conception of the cause of smallpox .
even he considered it to be caused by some impurity in the blood , but he was not able to identify its precise location , quality or origin .
as has already been pointed out , the method could easily be incorporated into the range of purgative means that were already at the disposal of the competent physician . whether smallpox was considered the necessary cleansing from congenital impurity or as a purging of another kind of pathogenic poison , inoculation was a tool to carry out the process in a more controlled and less dangerous way than the natural disease . moreover
the physician had to come to terms with the constitution of the individual patient , and use his skills to temper it : healing a sick person meant repairing the disturbed balance and harmony of his or her specific constitution , and inoculating to adapt the patient s constitution to the onslaught of smallpox in the most benign way .
historian of medicine anne kveim lie has pointed out that eighteenth - century medicine always saw the state of illness in a body as individual in principle , and argues that this also lay behind the opposition against panaceas offered by quacks : it was not so much caused by a disbelief that all diseases could be cured by one and the same remedy as by a fundamental reluctance to accept the possibility that all patients could be cured by the same treatment .
these two factors understanding smallpox as a near - unavoidable purge , and a concept of illness and health centred on individual constitutions did not merely help to shape the way inoculation was integrated into existing medical thought in europe .
they also explain why ideas of defeating , or even eradicating , smallpox as a disease were very far from a necessary consequence of the new technology .
the freedom to choose the most suitable time and conditions to expose oneself to smallpox was heralded as one of the main advantages of inoculation .
nonetheless , it seems that burgeoning epidemics have most often spurred the interest in inoculation .
available accounts of actual practice indicate that emerging epidemics were normally the catalyst for introducing inoculation into a region or town .
a detailed description can be found in one of the appendices to rottbll s treatise .
the danish studiosus medicus georg wilhelm barfod had received a letter of inquiry from the authorities about his practice as an inoculator in jutland in the mid-1750s .
one of the queries concerned the number of persons he had treated , and barfod had to admit that he did not know .
the young man had been visiting his friend , the vicar of gunderup in jutland , when a raging epidemic prolonged his stay and made him seek recourse to the method that he so far knew only from reports and textbooks .
people from all parts of the region flocked in great numbers to be treated , one family succeeding the other , all with their children .
barfod was deeply aware that he was running in a race that he was not sure he could win .
the challenge was to inoculate the children before they fell prey to the epidemic , and barfod was emphatic that he could not always know if the disease was caused by inoculation or by natural smallpox .
the operation itself , on the other hand , was uncomplicated and so easy , that i have at times executed it on some while they were asleep.
this was obviously not the time for considering the air and the season , nor for elaborate preparations .
more metaphorically , a similar situation is evoked in the vicar axel smith s text advocating the use of inoculation among norwegian peasants .
he paints the image of a group of people settled on a plain that each year is submerged by a powerful flood of water , killing off many of their number .
those who climb on are saved from the flood , while those who refuse perish as before .
smith was among the authors who relied heavily on cramer s argument ( above ) to refute religiously based objections to inoculation .
he concludes that only fools refuse to use such a life - saving remedy that the raft represented , and that rejecting the new tool that god has given us to save us from smallpox is equally foolish or even impious .
the risk occurs on a regular basis ; smith describes the flood as an annual event .
nonetheless , the raft is not introduced to be prepared for the flood ( or prevent it from coming ) , but to save lives when the water mass comes flooding .
it is possible that the constant availability of fresh pus this produced may have made inoculation less dependent on epidemics in the large cities .
children ( and others who had previously not been exposed ) would not live long before the risk of catching smallpox was imminent .
this was why smallpox was considered a children s disease , and also why children were the main target for inoculation .
going through life without being stricken by smallpox was unusual , save in very isolated areas . here
an epidemic would have correspondingly disastrous effects on a population not protected by acquired immunity .
the frequency of epidemics and the omnipresence of the disease was one reason for the belief that smallpox was due to an impurity congenital to all humans the illness appeared unavoidable .
this also served to blur the distinction between understanding inoculation as a prophylactic , ie .
a means to avoid illness sometime in the future , and as a remedy for addressing an acute threat . to most people ,
the threat of smallpox was too imminent to invite long - term perspectives . during an epidemic
, inoculators would work hard to save as many people as possible , struggling to forestall the disease in the way barfod described ( see above ) . to judge from the reports of barfod and others
it is significant to note , however , that for a long time this was conceptualised in terms of saving lives , not of stopping the epidemic .
smith does not present the raft in his parable as a means to prevent the flood from coming , but as an aid to survive it .
one reason was the understanding of smallpox as a cleansing agent . for those subscribing to the view of smallpox being due to congenital impurity , such as la condamine , tronchin , hahn and butini , the idea of eradicating the disease , or even stopping an epidemic , would be paradoxical .
however , even without this specific belief , humoral pathology with its understanding of disease in terms of the individual had similar implications .
the eighteenth century is generally considered to be the heyday of miasmatic theories , implying that epidemic disease was seen as caused by impurities in the air . in the case of smallpox , the miasmas were thought to activate the
people who had already been cleansed of it had nothing to fear , but for others the miasma would set off the disease .
the disease was produced by a certain impurity in the air which may be more or less malignant and more or less abundant .
it is contagious through contact with patients , but represents a threat only to persons not yet cleansed of their impurity .
diseases whose exhalations , or those from the humours , when they are introduced into healthy bodies , will give the same disease , those are the ones that are called contagious. nonetheless , different constitutions as well as changes in their humoral balance mean that different persons will be affected by the contagion in very different ways .
hence , smallpox will be more dangerous to some constitutions or temperaments than to others .
tissot also argues that the main factor setting off an epidemic will be infected air .
in some cases
the bad air of the miasma will produce particularly malignant cases of smallpox , for instance when it occurs during very warm summers .
for this reason , smallpox is a more dangerous disease in southern france than in the northern regions , according to tissot .
the implication of these arguments concerning the causes and workings of epidemics is that even during an epidemic , illness will vary considerably according to the particularities of the individual , the season and the location . moreover , the internal causes , ie . the inherent impurity together with the patient s specific constitution , are far more important to the development of each case than the external cause that sets off the disease .
the aim was to save as great a number as possible , not least children . nonetheless , the argument for mass treatment built on other premises than those of modern vaccination propaganda .
even inoculators who proudly could claim to have treated a very great number of persons seem for a long time to have conceptualised this solely as a matter of individual lives .
french historian catriona seth has pointed out that even if inoculation was argued to serve the common good , for a long time this was conceptualised in terms of individuals , not institutions , and even less in terms of nations or states .
the number of lives saved was identical with the number of individuals treated .
butini argues that inoculation will save the life and health of a large number of people , who will succumb to smallpox without it , or who will suffer miserably from the effects of the disease. he goes on to state that inoculation will not merely prevent a decrease in population , but also diminish the costs for poor relief : the number of disabled and fatherless persons , unable to provide for themselves , will be reduced .
cramer describes inoculation as a means to the conservation and prolongation of our lives.
in his article in the encyclopdie , tronchin s argument on the advantages of inoculation is centred on accounts of smallpox mortality in a number of european cities which he compares to the reduced mortality after the introduction of inoculation .
the aim of inoculation was to bring as many people as possible safely through the onslaughts of a practically unavoidable epidemic disease .
when speaking of the future effects of the method , tronchin expresses his strong hope that enlightened thought will triumph , and inoculation will become a general practice .
people who have been inoculated will not succumb to an early epidemic , and hence increase their chances of living to old age , the argument goes .
only rarely are other kinds of future effects discussed , and even here the focal point is the individual rather than the population .
the argument is that saving one life through inoculation also means saving the children , grandchildren and so on that this person might have in the future . in this way the argument even includes people who have not yet been born , but these individuals are always conceptualised as the offspring of actual , living persons .
a similar argument may be presented in more general terms when inoculation is depicted as a patriotic means to increase the population , not merely to prevent its decrease . in these calculations the consequences of inoculation have been lifted from the individual to offspring and lineage .
the potentiality of the new method is nonetheless conceptualised in the organic and quite concrete terms of generational succession , not generalised into more abstract ideas about population or society .
comparing smallpox mortality to that caused by inoculation was a key part of the pro - inoculation argument .
the questions posed to barfod by the authorities in copenhagen ( above ) considered the number of people he had treated and the portion that had developed fatal cases .
authors who were not themselves practitioners reported the results of others . among these , the work of the english doctor james jurin held a special position and was cited as an authority . in a series of pamphlets from the 1720s
he had published reports that systematically compared the danger of the natural small pox , and of that given by inoculation. in philosophical transactions ( 172223 ) he provided an overview of the number of people who had been inoculated in england , based on reports from a number of surgeons and physicians . from the 182 cases reported
one out of 91.
the second part of his work was based on a comparison between this result and the figures that could be read out of the annual bills of mortality , going back to 1667 .
jurin had found that the proportion between those who died from smallpox and the total number of burials remained very nearly the same for the years he investigated .
hazard of dying from smallpox in different periods of life , also noting that those who die without ever having had smallpox were mainly very young children .
jurin was then able to conclude : allowing therefore , that out of every 1000 children that are born , 386 die under one or two years of age , without having the small pox , and 72 do some time or other die of that distemper ; it follows , that the hazard of dying of it , to the remainder of mankind , above one or two years of age , who are all supposed to undergo that disease sooner or later , is that of 72 out of 614 , or nearly 2 out of 17 , so that no more , than between 7 and 8 , can recover from that disease , for one that dies of it .
allowing therefore ,
that out of every 1000 children that are born , 386 die under one or two years of age , without having the small pox , and 72 do some time or other die of that distemper ; it follows , that the hazard of dying of it , to the remainder of mankind , above one or two years of age , who are all supposed to undergo that disease sooner or later , is that of 72 out of 614 , or nearly 2 out of 17 , so that no more , than between 7 and 8 , can recover from that disease , for one that dies of it .
jurin s work was carried out in the tradition of john graunt , the first to use mortality bills to develop statistical information on public health .
jurin supplemented this information with reports that he systematically collected from inoculation practitioners throughout the country .
jurin was very much aware that the risk of dying of smallpox varied during life , and endeavoured to incorporate this fact into his calculations .
what captured the most attention were his conclusions and the figures he presented , while his method of collecting information and his concerns over method and calculations generally were ignored .
even when numbers and figures from his work are cited correctly , the emphasis on them alone serves to alter the perspective somewhat .
cleansed of jurin s original methodological reservations , the numbers stand out as witnesses to unwavering truths .
some authors supplemented jurin s numbers with similar information from their own cities or countries , though frequently without making it clear from what sources the numbers were abstracted or how the other calculations had been carried out .
after having quoted jurin and others who compare smallpox mortality with that of inoculation , la condamine declares that even if there may be some confusion in the numbers we have presented , the conclusion can not be any other , and one sees that there is a great difference between the danger one runs in the two cases , and that inoculation keeps all its advantage and excellence.
la condamine s own text contained no tables or statistics , and his use of numbers obviously owes more to rhetoric than to mathematics .
the numbers become metaphors . on the one hand , then , there are strong grounds for claiming that smallpox and the debate over inoculation represented one of the very first examples of statistics used in matters of public health .
correspondingly , inoculation was among the earliest practical applications of the new calculus of probability , as it was developed from the 1660s onwards
.
on the other hand , it may be worthwhile to look more closely into the use of numbers , accounts and ( more or less rudimentary ) statistics in the pro - inoculation literature .
what kind of meaning did the numbers carry , and how were the risks and probabilities they referred to understood ?
problems presented by games of chance were central to the new ideas of probability , developed by the mathematicians pascal , bernoulli and others .
questions of fair contracts , annuities and insurance were other early fields of probabilistic reasoning and application .
lorraine daston has argued that such problems not only were the testing grounds for the new calculus , but also deeply influenced the new ideas about what probability was all about .
she points out that what was developed by mathematicians and philosophes was a calculus of expectation rather than one of probabilities , and that ideals of fair games and contracts as well as equal expectation were taken as the point of departure .
it can be added that seeing probability this way also implied taking the individual s perspective .
accounts and calculations concerning inoculation were not read as attempts to ascertain the effects of the method among a population at large , but to estimate a specific person s chances of survival .
risk did not come into general use until the early eighteenth century .
before this the usual terms were
providence , luck or fate.
jurin and other eighteenth - century pro - inoculation writers generally preferred the word
tronchin reproduced it verbatim in the encyclopdie : it is an enforced lottery , in which we are involved despite ourselves : each of us has his ticket , the later it is drawn , the more the danger increases . in paris , fourteen hundred tickets are drawn each year , whose prize is death .
the conditions of this lottery are changed , the number of unlucky tickets reduced : one of seven , and in the best climates one of ten , used to be fatal , it remains not more than one of three hundred , one of five hundred , soon it will not be more than one of one thousand
it is an enforced lottery , in which we are involved despite ourselves : each of us has his ticket , the later it is drawn , the more the danger increases . in paris , fourteen hundred tickets are drawn each year , whose prize is death .
the conditions of this lottery are changed , the number of unlucky tickets reduced : one of seven , and in the best climates one of ten , used to be fatal , it remains not more than one of three hundred , one of five hundred , soon it will not be more than one of one thousand
the imagery very explicitly evokes the close relationship thought to exist between inoculation and the games of chance so central to probabilistic reasoning .
the use of quantitative material concerning inoculation thus served to strengthen the focus on the individual and his / her luck , rather than to weaken it through an emphasis on the epidemic in itself .
initially , quantification came to be perceived as a means to predict the risk or chance of the individual in the very literal lottery of life conjured up by la condamine .
quantification was nonetheless among the factors that contributed to new ideas about smallpox and changed the understandings of the future potentiality of inoculation .
andrea a. rusnock has pointed out that once something has been turned into numbers , it can easily be compared .
for this reason , decisions about what to count are vitally important : essential to quantification broadly conceived as the process of assigning numbers to represent things is categorisation . in order for jurin to quantify the success of smallpox inoculation
, he had to develop categories to enumerate.
rusnock shows how jurin worked to draw quantifiable information from the reports he received from local medical practitioners .
similar efforts as well as the problems to be encountered can be found in rottbll s treatise .
a number of the reports he published as appendices to his own text reflect the respective authors greater interest in the social standing of the patients than in their actual number .
the inoculators who wrote the reports cite names and titles of their most distinguished patients , and lump the rest into entries like and a flock of peasants children. rottbll himself strived to transform the illustrious names of princes and counts into numbers .
the groups of unnamed poor remained problematic , not due to their lack of social standing but because they had not been counted and did not represent numbers .
the work that goes on in his texts gives a very clear illustration of the process that nicolas jewson has called the vanishing of the sick man from medical cosmology.
this kind of work not only produced tables that deprived individual patients of their names and said nothing about their social standing , but also disregarded the particularities of each case .
accounts and statistics had little room for the particularities of constitution , climate and season , or for details of the careful and individually adapted procedures of preparation intended to produce gradual changes in the patient s fluids and solids. quantification contributed to objectifying disease and making it possible to speak about it without speaking about specific patients .
some of them were caused by the urgency of epidemics , as in the case of barfod ( above ) .
the simplification of preparations led to an understanding that most patients could be treated in a similar way . in his book on the
new method dimsdale was very emphatic that with minor adjustments it could be applied to all patients , given that their general state of health permitted inoculation at all .
dimsdale s book was above all a manual describing how the successful doctor should proceed .
it did not go into theoretical considerations on the nature of the disease or the workings of inoculation .
moreover , it can also be read as a piece of marketing claiming dimsdale as the inventor of the method that was also used by the sutton family , and in both cases brought considerable commercial success due to the private inoculation houses that were established .
nonetheless , the new methods would hardly have been conceivable without the medical debate on the nature of smallpox . was the impurity that produced smallpox congenital and general or was it acquired on an individual basis ? and which were the most decisive causes of the disease the external or the internal factors ?
the two medical treatises investigated here , by kirkpatrick and rottbll respectively , both discuss the matter , and both tend to put greater weight on the external causes .
what makes them particularly interesting is that adherence to traditional miasmatic theories about epidemics only plays a minor role .
he nonetheless concludes that the poison of smallpox ( the exact quality of which he declares himself unable to explain ) , would not be infectious if it did not meet some predisposition in the patient s body .
one argument in favour of this stance is , according to kirkpatrick , that persons who once have contracted smallpox never will be attacked by the disease again : when the internal cause or poison once has been cleansed out , the contagion can do no harm .
smallpox is among the diseases that are produced solely through contagion , he writes , but a certain predisposition in the body is also required .
he points to the fact that during an epidemic , some patients develop mild cases , while others die from the disease .
nonetheless , rottbll also argues that the contagion itself may vary between epidemics .
in this way , rottbll s argument is very close to defining the contagion as the only cause of smallpox , while the traditional internal causes merely contribute to the severity of the case .
his text illustrates how the debates over the internal as opposed to the external causes of the disease gradually served to move the causal factors from the individual body to the contagion .
together with the realisation that the procedure of inoculation did not require much individual adjustment , this move contributed greatly to an understanding of the disease as an object or entity in itself that could be investigated and spoken of without involving all particularities of specific cases . with this shift that seems to have occurred gradually from the 1760s it became possible to conceptualise inoculation as a means to combat smallpox rather than as a way to cure or save individuals .
a very clear expression of the idea that smallpox epidemics might be stopped is found in a text published in france in 1767 . in his pamphlet
un projet pour danantir la petite vrole , the physician antoine le camus suggested that strict quarantine regulations should be imposed when an epidemic broke out .
his argument was that because no effective medical remedy had been found , smallpox must instead be fought with political means .
this argument implies that le camus did not consider nor in fact did he even mention inoculation as a means to combat epidemics .
the regulations he suggests are closely related to traditional measures taken to stop epidemics , not least the plague , by a mixture of isolation and flight .
le camus s proposal does not seem to have had much influence and was not adopted as a programme , either nationally or locally . in 1778 , the physician john haygarth presented a similar but more elaborated scheme in england .
advocating the establishment of a
his belief in quarantine regulations was based on a firm conviction that smallpox only spread by contagion .
the rules of prevention that he proposed would impose very strict isolation on persons infected by the contagion , as well as give utmost attention to cleanliness , both during and after cases of smallpox disease . in 1784 ,
haygarth s text an inquiry how to prevent smallpox was published , and a smallpox society was established in chester .
despite local success
as well as growing international fame , haygarth s ideas were not developed into the national programme that he himself advocated .
musing over the reason for this , christopher booth writes that haygarth s ideas were eclipsed by jenner s vaccine only a few years later .
correct as this observation may be , it can also be argued that the new ways of thinking about disease and epidemics that were so clearly articulated by haygarth contributed heavily to jenner s success and the ways vaccination came to be practised .
the idea that a new remedy in this case vaccination could be applied as a general programme , aimed at epidemic disease as such , did not stem from the technology itself but had emerged gradually from a number of interacting developments , with haygarth s ideas as a keystone .
the so - called general inoculations that had been held in english towns and villages since the 1770s were an inspiration for haygarth s plan .
the improved methods of inoculation developed by dimsdale and sutton not only made the treatment accessible to a greater number of people , but also in some ways tarnished the reputation of the method .
while the simpler procedures and safer method may appear the most significant improvements today , the cold treatment was seen as equally important at the time .
it implied that the patients were not confined to bed or even isolated , but rather encouraged to seek exercise and fresh air . a consequence of this was an increased number of inoculated and potentially contagious persons circulating amongst the general public .
inoculation came to be accused of spreading the disease , increasing rather than reducing the risk of contracting the disease during an epidemic .
mass inoculations were initiated to counter the situation : when an epidemic threatened , inoculation of all inhabitants likely to be attacked was arranged .
the idea was still to stop the epidemic from reaching one s community , and can be compared to traditional plague measures like closing the city gates or stopping ships in the harbour . nonetheless , it had the potential to create herd immunity .
contrary to these traditional measures of isolation , the general inoculations produced enclaves of people who would not be attacked again : when the next epidemic threatened , only the newborn needed further protection .
initiated as acute treatment in situations of immediate threat , the general inoculations revealed themselves to be veritable prophylactic schemes .
moreover , general inoculations contributed to the understanding that effective protection against smallpox needed to be organised on a collective , societal level ; it was a matter for political measures , as le camus had argued .
even if this happened only late in the century , and shortly before vaccination took much of its role , inoculation contributed to shaping the idea of public health as an political issue .
inoculation was a radical novelty when it was introduced in europe in the 1720s . during the period that has been discussed here ,
the years between 1750 and 1775 , the method itself underwent important changes , making inoculation less dangerous and more available to a greater number of persons .
the close reading of texts has nonetheless demonstrated that inoculation was very far from being conceptualised as a herald of modern epidemic control . despite the practical improvements , inoculation remained mainly therapeutic .
it was seamlessly incorporated into traditional , learned medicine and understood within the frames of humoral pathology and neo - hippocratic thinking .
the old humoral pathology showed itself highly capable of swallowing up the new practice and shaping it according to its own principles : inoculation remained a therapeutics centred on evacuation and cleansing .
the medical questions it raised were produced by this context rather than by the novelty or potentiality of inoculation itself .
neither did new understandings seem to have been produced by the practice as such , but developed along with medical theory more generally , and the weakened understanding of disease as intrinsically individual .
shallower incisions , the use of fresh pus and the cold method in the treatment of the patients were not in themselves sufficient to change the fundamental understanding of inoculation .
safer , simpler and more pleasant , not as a way to avoid smallpox altogether .
far more important would appear to be the discussion over internal versus external causes of disease , enabling perspectives that did not make the individual constitution the key to illness . alongside this development ,
the emerging quantitative thinking contributed to changing the understanding of inoculation and helping the process of the vanishing of the sick man. the contribution was nonetheless less radical than may be thought .
as conceptualised in this period , calculation was more about expectation than about probability , more about luck and hazard than about risk , and far more about individual chance than about general demographic development .
the issue raised by inoculation , as expressed by the eighteenth - century texts examined here , concerned the individual s chances of surviving a dangerous and practically unavoidable illness . by implication
, it also concerned what right or what responsibility the individual had to intervene in questions of life and death , using a remedy that might in the worst case bring about the death it was supposed to prevent .
even if the religious objections against inoculation were refuted as soon as they were first presented in the 1720s , the texts that have been investigated here show clearly that they continued to be a concern of great importance through the century .
the texts advocating inoculation are unanimous in their refutation of religious or ethical objections , but the issue appears nonetheless far too important to be ignored .
this can not be reduced to a simple conflict between conservative theologians and radical philosophes .
firstly , a number of theologians supported inoculation . secondly , not even radicals touched lightly upon the moral implications of inoculation . neither is this a matter of ( reactionary , superstitious ) popular resistance to ( scientific ) medical innovation .
firstly , again , the risk of producing fatal cases through inoculation was too real to be ignored .
what appears from the texts examined above was that the novelty of inoculation as a new and effective therapeutics
when looking for the meaning of inoculation to eighteenth - century agents , this complex of ethical , religious , medical and , to some degree , societal concerns is what presents itself . | the idea that smallpox could be eradicated was not necessarily the ultimate aim when inoculation was introduced in europe in the 1720s .
this potentiality was not clearly articulated as an aim until the end of the eighteenth century .
this article argues that during most of the eighteenth century , the main aim of inoculation was to lead people as safely as possible through what was regarded as an unavoidable disease .
inoculation became safer , simpler and less expensive from the 1760s , but the changing ideas about its potentiality had more complex roots .
a new understanding was produced through an interaction between inoculation practice , more general medical theory and developments within probabilistic thinking and political arithmetic .
the first part of the article explores how smallpox inoculation was incorporated into existing medical thinking based on traditional humoral pathology .
inoculation was a new technology , but as it was perceived in the early eighteenth century , the innovation did not first and foremost concern the medical principles of the treatment .
the second part of the article investigates arguments about why and when to inoculate : what kind of remedy was inoculation for eighteenth - century agents ?
the article concludes with a discussion on changes emerging towards the end of the century , and relates them to developments during the preceding decades rather than seeing them as inspired precursors of events and ideas to come . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Women and Children's HIV Protection
Act of 2003''.
SEC. 2. FINDINGS.
The Congress finds as follows:
(1) Perinatal transmission is the leading cause of
pediatric HIV infections, including AIDS cases.
(2) The Centers for Disease Control and Prevention
(``CDC'') estimates that nearly 7,000 HIV-infected women give
birth in the United States each year and as many as 400 babies
continue to be born with HIV infection each year.
(3) Medical advances have made it possible to nearly
eliminate perinatal HIV transmission.
(4) Research studies have demonstrated that the
administration of antiviral medication during pregnancy, during
labor, and immediately following birth can significantly reduce
the transmission of HIV from an infected mother to her baby.
Caesarean section further reduces the risk of transmission.
(5) Even if treatment begins shortly after birth,
antiretroviral therapy can substantially reduce the chance that
an HIV-exposed infant will become infected.
(6) Breastfeeding by HIV-infected mothers poses additional
significant risk of infection to babies.
(7) The Institute of Medicine (``IOM'') has recommended the
adoption of a national policy of universal HIV testing, with
patient notification, as a routine component of prenatal care.
However, 15 percent of HIV-infected pregnant women receive no
prenatal care according to the IOM.
(8) The CDC has recommended since 1995 that all pregnant
women be counseled and offered voluntary HIV testing. Yet
nearly half of pregnant women are still not tested according to
the CDC. The CDC has found that mandatory testing of newborns
and universal HIV testing of pregnant woman are the best
approaches for identifying, treating, and preventing HIV among
pregnant women and children.
(9) The American Medical Association recommends mandatory
HIV testing of all newborns with appropriate treatment for
affected mothers and children.
(10) Testing newborns whose mothers' status is unknown
ensures that every child at risk for HIV is identified.
(11) More than a third of the HIV infections that occur
annually among newborns in the United States could be prevented
with routine HIV testing of pregnant woman or newborns
according to a 2002 report by the Inspector General of the
Department of Health and Human Services. This represents over
100 babies born every year that are needlessly infected.
(12) The provision of testing of pregnant women and
newborns with appropriate counseling and treatment can
significantly reduce the number of pediatric HIV infections,
including AIDS cases, can improve access to and medical care
for the woman and children, and can provide opportunities to
further reduce transmission among adults.
(13) The provision of such testing, counseling, and
treatment can reduce the overall cost of pediatric HIV
infections, including AIDS cases.
(14) New York State has required mandatory HIV counseling
and voluntary testing for pregnant women and mandatory HIV
testing of all newborns since February 1997. As a result, the
perinatal HIV transmission rate in the State has dropped from
25 percent to an all time low of 3.5 percent and over 99
percent of HIV-infected women and their children have been linked to
care.
(15) For the foregoing reasons--
(A) universal routine HIV testing of pregnant women
and newborns should be the standard of care; and
(B) the relevant medical organizations, as well as
public health officials, should issue guidelines making
such testing, counseling, and treatment the standard of
care.
SEC. 3. GRANTS REGARDING COUNSELING AND TESTING OF PREGNANT WOMEN AND
NEWBORN INFANTS.
Subpart II of part B of title XXVI of the Public Health Service Act
(42 U.S.C. 300ff-33 et seq.) is amended by inserting after section 2625
the following section:
``SEC. 2625A. GRANTS REGARDING COUNSELING AND TESTING OF PREGNANT WOMEN
AND NEWBORN INFANTS.
``(a) In General.--Of the amounts appropriated under section 2677
for a fiscal year for carrying out this part, exclusive of amounts
available for grants under section 2618(a)(2)(I), the Secretary,
subject to subsection (b)(2), shall reserve $82,875,000 for making
grants to each State that demonstrates that the law or regulations of
the State are in accordance with the following:
``(1) That all pregnant women receiving prenatal care in
the State be offered counseling and testing regarding HIV
disease.
``(2) In the case of prenatal testing for such disease that
is conducted in the State, that the results of such testing be
promptly disclosed to the pregnant woman involved.
``(3) In the case of newborn infants who are born in the
State and whose biological mothers have not undergone prenatal
testing for HIV disease, that each such infant undergo testing
for such disease.
``(4) That the results of such testing of a newborn infant
be promptly disclosed in accordance with the following, as
applicable to the infant involved:
``(A) To the biological mother of the infant
(without regard to whether she is the legal guardian of
the infant).
``(B) If the State is the legal guardian of the
infant:
``(i) To the appropriate official of the
State agency with responsibility for the care
of the infant.
``(ii) To the appropriate official of each
authorized agency providing assistance in the
placement of the infant.
``(iii) If the authorized agency is giving
significant consideration to approving an
individual as a foster parent of the infant, to
the prospective foster parent.
``(iv) If the authorized agency is giving
significant consideration to approving an
individual as an adoptive parent of the infant,
to the prospective adoptive parent.
``(C) If neither the biological mother nor the
State is the legal guardian of the infant, to another
legal guardian of the infant.
``(D) To the child's health care provider.
``(5) That, in disclosing the test results to an individual
under paragraph (2) or (4), appropriate counseling on HIV
disease and appropriate referrals for health care be offered to
the individual (except in the case of a disclosure to an
official of a State or an authorized agency, or to a health
care provider).''.
``(b) Date Certain for Making Grants; Limitation on Reservation of
Funds.--
``(1) Date certain for making grants.--Not later than the
end of the three-month period beginning on the date on which
appropriations first become available for a fiscal year for
grants under section 2611, the Secretary shall make grants
under subsection (a) for such fiscal year to all States that
seek such grants and meet the condition described in such
subsection for the grants.
``(2) Limitation on reservation of funds.--Effective upon
the expiration of the period described in paragraph (1) with
respect to a fiscal year, the unobligated portion of the amount
reserved under subsection (a) for the fiscal year is available
for grants under section 2611 for the fiscal year.
``(c) Amount of Grants.--Each grant under subsection (a) for a
fiscal year shall be made in the amount of $1,500,000, except that the
amount of such a grant for a territory of the United States shall be
$375,000.
``(d) Authorized Expenditures.--A grant under subsection (a) may be
expended for any purpose for which a grant under 2611 is authorized to
be expended.
``(e) Definitions.--For purposes of this section, the terms `State'
and `territory of the United States' have the meanings that apply to
such terms for purposes of grants under section 2611 (including the
meanings that apply for purposes of section 2618).''. | Women and Children's HIV Protection Act of 2003 - Amends the Public Health Service Act to provide for grants regarding the counseling and testing of pregnant women and newborn infants out of moneys appropriated under the care grant program. Prohibits making a grant to a State unless the State demonstrates that the law or regulations of the State require specified testing and services for pregnant women and newborn infants regarding HIV disease. |
the quest to identify and understand protostars has long been a key but stubborn problem for star formation research @xcite .
the primary factor hindering the investigation of protostellar objects has been the fact that such sources are deeply embedded in dusty molecular gas and are heavily extincted . as a result most of the luminosity generated by a protostar
is absorbed and scattered by dust and radiated in the infrared , rendering the object very difficult , if not impossible , to detect at optical wavelengths .
consequently , progress toward achieving a physical understanding of the nature of protostars had to wait for the development of observing capabilities at longer wavelengths .
significant progress in understanding the physical nature and evolutionary status of protostars has been achieved from measurements of the broadband photometric infrared spectral energy distributions ( seds ) of low - luminosity young stellar objects ( ysos ) in star forming molecular clouds @xcite .
these studies established that the shape of the sed of a yso is linked to its evolutionary state .
class i ( and class 0 ) sources were characterized by strong infrared excesses and steeply rising seds from near- to far - infrared wavelengths .
these sources were found to be distinctly different from class ii sources .
these latter objects were characterized by smaller infrared excesses and seds that decreased from near- to far - infrared wavelengths and could be well - explained by models of pre - main sequence ( pms ) stars surrounded by circumstellar disks ( i.e. classical t - tauri stars ) .
class ii sources , in turn , were differentiated from class iii sources which displayed no infrared excess and whose seds could be explained by normal stellar photospheres of classical pms stars .
class i seds were found to be consistent with , and well - fit by , theoretical models of protostellar envelopes .
moreover , other lines of evidence , such as the intimate association of class i ( and 0 ) sources with molecular outflows , molecular hydrogen emission , fu ori phenomenon , etc . strongly suggested an extreme youth and possibly protostellar nature for these objects .
little is known about the underlying stellar component of protostars since these objects are typically undetectable in visible light rendering the traditional methods of optical spectroscopy that are used to measure stellar physical properties not generally applicable .
however advances in technology over the past dozen years have enabled spectroscopic observations of class i sources at near - infrared wavelengths . in a pioneering paper , @xcite obtained low resolution ( r @xmath6 300 ) spectra at 2 @xmath1 m of a sample of ten bright class i and class ii sources in ophiuchus and found class i sources to exhibit a featureless continuum , unlike class ii sources which displayed photospheric absorption lines .
this result was confirmed by a subsequent low resolution ( r @xmath6 500 ) near - infrared spectroscopic survey of a significantly larger sample of @xmath6100 low luminosity ysos in ophiuchus and taurus @xcite . the absence of photospheric absorption lines in class i sources was interpreted as being the result of high veiling due to strong infrared excess emission produced by disk accretion and reprocessing in circumstellar envelopes .
this provided strong supporting evidence for a protostellar nature for class i objects .
however , the high veilings of class i sources indicated that very high signal - to - noise and high spectral resolution observations would be required to detect photospheric features and measure the physical parameters of the embryonic stellar core at the heart of a protostellar object .
@xcite obtained the first such deep and high resolution ( r @xmath6 20,000 ) infrared spectra and detected photospheric absorption features in a sample of several flat - spectrum protostars .
these embedded sources exhibit seds with shapes between those of class i and ii objects and are believed to be in transition between the class i and ii evolutionary states .
flat - spectrum sources are likely to be extremely young and can be considered the least obscured candidate protostars .
these objects were found to have late ( m0 or later ) spectral - types confirming their nature as low mass stellar objects and to be relatively fast rotators compared to class ii sources , an unexpected result .
@xcite also obtained spectra of five class i sources , and all presented featureless spectra indicating that even more sensitive infrared observations would be necessary to detect the photospheres of these objects . using the 10 meter keck telescope , @xcite were able to obtain yet deeper observations and detect the first photospheric absorption lines in a heavily veiled accreting protostellar source , ylw 15 .
these observations enabled determinations of the central source s spectral - type , veiling , stellar luminosity and allowed its placement on the hertzsprung - russell ( h - r ) diagram .
although most class i sources are deeply buried in dusty envelopes , visible light scattered off cavities in these envelopes can in some cases be detected at optical wavelengths with large ground - based telescopes .
@xcite performed an i - band spectroscopic survey of 13 class i sources in taurus that were optically visible .
they were able to detect photospheric features in 5 of these sources and found them to display late ( m ) spectral - types and to lie in the same general region of the h - r diagram as class ii sources .
the optically - selected sample of taurus class i sources also did exhibit stronger and more frequent forbidden - line emission than class ii sources , suggesting higher mass outflow and accretion rates . a recent higher resolution , more sensitive optical spectroscopic survey of optically detected class i sources in taurus by @xcite produced spectral - types of 11 objects and generally confirmed the trends observed by @xcite , although the @xcite observations suggest similar accretion and rotation rates for class i and ii objects in their sample .
these observations suggest that optically detectable class i sources may be in a more advanced state of evolution than the more common optically invisible class i protostars which are more deeply embedded .
sensitive high resolution infrared and optical spectroscopy of flat - spectrum and class i sources represent a significant advance in protostellar studies and clearly have demonstrated the utility and potential of such observations for investigating protostellar evolution .
a number of interesting issues have been raised by these observations .
do the optically detectable class i sources represent the end stages of protostellar evolution ?
are their physical properties similar to those of the optically invisible class i objects or is there a significant range in evolutionary states among class i objects from accretion active to accretion anemic objects ?
to better define the physical properties and nature of class i sources and achieve a more complete understanding of protostellar evolution we have conducted the first extensive and systematic near - infrared spectral survey of deeply embedded class i and flat - spectrum objects carried out at high resolution and with the high sensitivity afforded by a 10 meter class telescope
. we were able to obtain high quality spectra for more than 50 class i and flat - spectrum sources in three nearby regions of active star formation .
photospheric absorption features were detected with good signal - to - noise in the vast majority of these sources . in order to derive the physical parameters that characterize these young stellar objects we have employed synthetic model atmospheres following the techniques successfully developed by @xcite ( hereafter dj03 ) in their recent study of infrared class ii sources in ophiuchus @xcite . in this paper
we present the basic observational results of the survey . in @xmath7 2
we describe the instrumentation and observing procedures used to obtain our data and discuss our data reduction methods . in @xmath7 3
we present the results and analysis of our observations . in @xmath7 4
we discuss the implications for the nature of class i and flat - spectrum sources in the context of protostellar evolution and in @xmath7 5 we summarize the results and conclusions of this contribution .
this paper is the first in a series of three papers dealing with the results of our survey .
two subsequent papers will respectively deal with the analysis of the rotational properties @xcite and radial velocities @xcite of this sample .
ysos were selected from nearby star forming regions of @xmath2 oph , taurus , serpens , perseus , and corona australis using the following criteria : ( 1 ) objects with rising or flat spectral energy distributions across 2
@xmath810 @xmath1 m , indicative of excess emission at infrared wavelengths ( @xmath9 ) ; and ( 2 ) except for a few fainter sources in ophiuchus , our targets were generally k @xmath10 11 , in order to obtain high signal - to - noise spectra ( s / n @xmath11 100 ) in a reasonable amount of time ( @xmath10 120 minutes ) at the telescope . in total ,
our sample was comprised of 52 flat - spectrum or class i protostars : 2 in perseus , 13 in taurus , 20 in ophiuchus , 13 in serpens , and 4 in corona australis ( table [ tbl-1 ] ) .
these sources were selected from @xcite .
in addition , 28 late - type giant and dwarf mk spectral standards were observed for calibration of our spectral synthesis models .
near - ir spectra of the protostellar sample and mk spectral standards were acquired on 2000 may 29 30 , 2001 july 7 10 , 2001 november 4 6 , and 2003 june 19 21 ut . all data were acquired with the 10-m keck ii telescope on mauna kea , hawaii , using the nirspec multi - order cryogenic echelle facility spectrograph @xcite .
spectra were acquired with a 058 ( 4 pixel ) wide slit , providing spectroscopic resolution @xmath12 = 18,000 ( 16.7 km s@xmath13 ) .
the plate scale was 020 pixel@xmath13 along the 12@xmath14 slit length , and the seeing was typically 05 06 .
the nirspec gratings were oriented to allow orders containing the 2.1066 @xmath1 m mg and 2.1099 @xmath1 m al lines , the 2.1661 @xmath1 m hi br
@xmath4 line , the 2.2062 and 2.2090 @xmath1 m na lines , and the 2.2935 @xmath1 m co bandhead regions to fall onto the instrument s 1024 @xmath15 1024 pixel insb detector array .
the instrument s nirspec-7 blocking filter was used to image these orders on the detector .
nirspec was configured to acquire simultaneously multiple cross - dispersed echelle orders 31 36 ( 2.08 2.45 @xmath1 m , non - continuous ) for most objects , but some objects were observed in orders 32 38 ( 1.97 2.38 @xmath1 m , non - continuous ) .
each order had an observed spectral range @xmath16 ( @xmath17 4450 km s@xmath13 ) .
the internal instrument rotator was used to maintain a fixed position angle on the sky when observing on 2000 may 29 30 .
unfortunately vibration from the rotator caused slight changes in the echelle grating angle during those nights , but we removed the resultant wavelength shifts during the data reduction process .
the slit was held physically stationary and thus allowed to rotate on the sky ( as the non - equatorially - mounted telescope tracked ) when observing at all other times .
data were acquired in pairs of exposures of durations from less than 1 second ( for giant mk standards ) to up to 900 s ( for the protostars ) each , with the telescope nodded @xmath18 along the slit between frames so that object spectra were acquired in all exposures .
early - type ( b7 a2 ) dwarfs were observed for telluric correction of the protostellar and mk standard stellar spectra .
the telescope was automatically guided with frequent images from the nirspec internal scam ir camera during all exposures of more than several seconds duration .
spectra of the internal nirspec continuum lamp were taken for flat fields , and exposures of the ar , ne , kr , and xe lamps were used for wavelength calibrations .
the observation dates , total integration times , signal - to - noise , and other parameters of the observed objects are given in table [ tbl-1 ] .
all data were reduced following standard procedures with iraf packages @xcite .
bad pixels and cosmic rays were removed with the cosmicray task images were cleaned once to remove cosmic rays and bad pixels , then inverted and cleaned again to remove cold pixels before being returned to positive flux .
frames were then flatfield divided and sky subtracted before spectra were extracted with the apall task .
extracted spectra were wavelength calibrated using 4th order fits to lines in arc lamp exposures , and all spectra of objects at the same slit position and similar airmasses were coadded .
instrument vibration during the may 2000 observing run caused the echelle grating to shift slightly between lamp and object spectra exposures .
corrections for the shift of the wavelength solution between objects were applied by using the fxcor task to find the pixel shift between object spectra and telluric standards observed closely after lamp spectra .
this appears to have improved the wavelength solutions of the may 2000 data considerably , but radial velocities derived for objects observed during may 2000 will be significantly more uncertain than those objects observed on later runs .
instrumental and telluric features were removed by dividing wavelength calibrated object spectra by spectra of early type stars observed at similar airmass and slit position .
spectral orders containing the hi br @xmath4 line ( 2.1661 @xmath1 m ) were corrected for telluric absorption with the use of the xtellcor idl routine developed by @xcite .
this routine creates and then removes a pure telluric spectrum generated by dividing an observed early - type stellar spectrum by a synthetic model of vega ( modified to include line broadening ) .
combined spectra were then produced by summing the spectra of both slit positions for each object .
wavelength shifts have not been applied to correct for earth and solar system motions ; rather , radial velocities have been measured and then converted to radial velocities with respect to the local standard of rest . finally , the spectra of each wavelength sub - interval used in our analysis ( see @xmath7[sec - diaglines ] ) , was flattened and continuum normalized to one by linear function , so as to be directly comparable to the intrinsically flat continua of our synthesis models . in order to view the true continuum shape within the three k - band orders where we analyze photospheric lines , we multiply the spectra of our ysos and mk standards by a 10,000 k blackbody following the telluric division by a hot ( b7 a2 ) telluric standard star . all these spectra are displayed in appendix [ sec - spectra ] ( figs .
[ fig-all.spectra1 ] [ fig-stands.spectra4 ] ) .
our high resolution spectra reveal numerous absorption and emission lines in our class i and flat - spectrum sample ( listed in table [ tbl-1 ] ) . in 41/52 sources , we detect photospheric absorption lines ( @xmath7 [ sec - diaglines ] ) sufficient to carry out an analysis of their stellar properties .
additionally , ten of these sources show hi br @xmath4 absorption , superposed on a br @xmath4 emission peak in 6/10 cases ( see @xmath7 [ sec - brgemis ] )
. the existence of infrared emission lines indicative of accretion , in - fall , and outflows may distinguish between class i and class ii yso populations @xcite .
our flat - spectrum / class i study shows the presence of such lines in some of our sample : 34/52 have hi br @xmath4 , 8/52 show @xmath19co overtone emission , and 23/52 have h@xmath3 1 - 0 s(0 ) emission .
table [ tbl-2 ] lists these statistics grouped by individual star forming region . in the 11 sources for which we do not detect photospheric lines sufficient for our following analysis , 10 show br @xmath4 emission , while the remaining one ( crbr 85 ) has marginal co absorption evident in its lower signal - to - noise spectrum . in this section 3 ,
we describe the method by which we compare spectral synthesis models to observed protostellar spectra and produce the best multi - line fit to numerous k - band lines that diagnose fundamental stellar or circumstellar properties .
in particular , the resolved line shapes , depths , and positions permit us to measure the effective temperature ( t@xmath20 ) , surface gravity ( @xmath21 ) , rotational broadening ( @xmath22 ) , and radial velocity ( v@xmath23 ) of an embedded yso , as well as the amount of continuum veiling ( r@xmath24 @xmath25 f@xmath26/f@xmath27 , the ratio of non stellar excess over the stellar flux at k ) arising in its circumstellar disk .
this method is based on a routine originally presented in dj03 , but has been substantially expanded to include simultaneous fitting of multiple wavelength regions and is thus discussed here in detail . @xmath7 [ sec - diaglines ] describes the photospheric lines utilized by this spectral fitting routine and the stellar parameters to which each line is most sensitive . @xmath7
[ sec - synthgrid ] explains the creation of a grid of synthetic spectra for various values of t@xmath28 and @xmath21 , while @xmath7 [ sec - fittingroutine ] reviews the routine which extends the spectral grid to cover a range of @xmath22 , r@xmath29 , and v@xmath23 , as well as selecting the set of parameters which minimizes the overall residuals between the model grid and the observed protostellar spectrum to find the best - fit stellar parameters . in @xmath7 [ sec - qualityfits ]
we explore the sensitivity of the model results to both random and systemic errors , while in @xmath7 [ sec - standsfits ] we verify the accuracy of the stellar parameters determined by the fitting routine for spectra of well - studied mk standards . @xmath7
[ sec - radvels ] corrects the routine for a slight ( @xmath30 ) bias in the detected radial velocity .
finally , in @xmath7 [ sec - photlums ] we describe the way we derive stellar luminosities from photometry , pointing out issues and uncertainties associated with using this traditional approach for placing ysos on the h
r diagram .
we focus our analysis on key diagnostic absorption lines whose sensitivity to stellar parameters we have identified and tested with late - type spectra of mk dwarfs and giants .
the cross dispersed wavelength coverage afforded by nirspec enables the detection of photospheric lines across multiple echelle orders .
we select strong absorption lines of neutral metals and the molecular overtone band of ( 2 - 0 ) @xmath19co , present in three k - band echelle orders , to diagnose the physical state of our embedded protostars , by measuring effective temperature ( t@xmath20 ) , surface gravity ( @xmath21 ) , projected rotation ( @xmath22 ) , continuum veiling ( r@xmath29 ) , and radial velocity ( v@xmath31 ) . at 2.21 @xmath1 m ( order 34 )
, we utilize neutral atomic lines of na , si , and sc ( hereafter , the na interval ) , proven diagnostics of t@xmath28 in mk standard stars ( dj03 ) . at 2.11 @xmath1 m ( order 36 ) , lines of neutral mg and al ( hereafter , the mg / al interval ) are also present in k and m spectral - type stars , and are sensitive to changes in t@xmath20 and @xmath21 .
the first overtone of the @xmath19co bandhead at 2.29 @xmath1 m ( order 33 , hereafter the co interval ) is also prominent in the photospheres of cool , late - type stars .
changes in t@xmath20 and @xmath21 affect the depth of the bandhead and r branch lines , without broadening the feature ( i.e no pressure broadening ) .
furthermore , co is not affected by zeeman broadening seen in k - band atomic lines of t - tauri stars with strong magnetic fields @xcite .
therefore , our most reliable measurement of @xmath22 in our protostars comes from spectral fits to the co interval . at cool effective temperatures ( t@xmath20 : 3200k 4500k ) and sub - dwarf surface gravities ( @xmath32 ) , the na lines in the na interval grow and broaden as t@xmath20 decreases and @xmath21 _ increases _
( see figs .
[ fig-stands.spectra1 ] & [ fig-stands.spectra2 ] in appendix [ sec - spectra ] ) .
conversely , the mg lines ( a close triplet ) in the mg / al interval are degenerate between temperature and gravity , but in the opposite sense as are the na lines ( i.e. a decrease in t@xmath20 trades off with a _ decrease _ in gravity ) .
earlier studies have identified the strength of the co overtone band at 2.2935 @xmath1 m as being diagnostic of luminosity and surface gravity @xcite in stars that have already evolved to the main - sequence and beyond , and in class ii pms stars ( dj03 ) that are less likely to have contamination by co emission arising from disks or in outflow winds . for our class
i and flat - spectrum ysos , we avoid using fits to the co interval to constrain temperature and gravity , since the strength of the bandhead absorption may be altered by non - stellar components .
we develop a multi - parameter grid of synthetic spectra in which we search to find the best simultaneous fit to the wavelength intervals described in @xmath7 [ sec - diaglines ] , extending the spectral fitting techniques pioneered by dj03 to include these three distinct wavelength regions .
the spectral synthesis code moog @xcite is used to generate a high resolution ( r = 120,000 ) k - band spectrum of each wavelength interval based on lte radiative transfer through a nextgen @xcite stellar atmosphere profile ( see dj03 ) .
each moog synthesis generates a model spectrum specific to a particular t@xmath20 , @xmath21 , and metallicity .
we restrict our spectral search to objects with solar abundances @xcite , though , in principle , spectral fits using metallicity as another free search parameter have potential for future work when more diagnostic lines are present .
physical constants ( i.e. oscillator strengths and damping coefficients ) are needed in order to model the correct depth and width for each absorption line transition in the synthetic spectra .
for our spectral syntheses in the na and co intervals , we use atomic and molecular line constants published by @xcite and @xcite , respectively .
however , no published oscillator strengths or damping coefficients were available in the literature or on - line ( i.e. vald or nist ) for the mg line transitions ( 3s4f@xmath33f@xmath343s7g@xmath35g@xmath36 ) at 2.1061 @xmath1 m in the mg / al interval .
therefore , we determined these values empirically by fine tuning the models to best fit our observed spectra of several mk standard stars for which t@xmath20 , @xmath21 , and [ fe / h ] was known .
we use solar micro - turbulence values ( 1 km s@xmath13 ) , appropriate for our models of late - type stars with dwarf and sub - dwarf gravities ( dj03 ) .
damping of the na lines , which are noticeably pressure broadened in the na interval in dwarf standards , has been tuned to best match an observed solar spectrum ( dj03 ) .
once the basic synthesis grid has been created , a spectral search routine ( dj03 ) steps through each model spectrum , modifying it by incrementally adding rotational broadening ( @xmath22 ) , continuum veiling ( r@xmath29 ) , and fractional pixel wavelength shifts ( @xmath37 ) . broadening by stellar rotation is modeled by convolving our model spectra with a rotational broadening profile and an assumed limb - darkening coefficient of 0.6 @xcite .
we simulate the amount of 2 @xmath1 m continuum veiling ( r@xmath29 ) by adding successive amounts of non - photospheric flux , assumed to be spectrally flat and featureless .
a coarse value for the topocentric radial velocity is estimated by eye for each observed spectrum .
then , 0.8 km s@xmath13 shifts ( @xmath61/5 of a pixel ) are each tested over a @xmath385 km s@xmath13 range to find the best radial velocity fit to each protostellar spectrum . the search routine steps through a selected region of parameter space , modifying the spectral synthesis templates of all three wavelength intervals by modeling each unique combination of the five search parameters within the following range of values : 3000k 6000k ( t@xmath20 ) , 3.5 5.0 cm s@xmath39 ( @xmath21 ) , 0 80 km s@xmath13 ( @xmath22 ) , 0 6.0 ( veiling , r@xmath29 ) , and @xmath385 km s@xmath13 ( v@xmath23 ) .
each unique model spectrum is compared to the observed yso spectrum .
wavelength sub - intervals in the observed spectrum are selected by eye to isolate only those photospheric lines which will be compared to their model counterparts .
the quality of the fit between the observed protostellar spectrum and each spectral synthesis model is then quantified from the aforementioned selected wavelength sub - intervals as the root mean square ( rms ) of the residuals in the data - to - model comparison ( dj03 ) .
the overall best - fit model is automatically selected by the search routine as the one with the lowest rms value over the entire search grid . fig .
[ fig-rmscontour.teff ] illustrates the rms error space in the veiling / effective temperature plane for the model fits to dg tau .
the elongation in the error space stretching from upper left to lower right in the lower panel shows that there is still a bias for lines with higher amounts of veiling to trade off with lines of cooler temperature stars .
the range of the search grid in t@xmath20 and @xmath21 is constrained by the availability of the nextgen models @xcite which we use to generate the spectral synthesis templates .
rms values corresponding to each of the fits in the three wavelength intervals are combined in the following way after validating this technique with the fits to mk standards of known t@xmath20 , @xmath21 , and @xmath22 ( @xmath7 [ sec - standsfits ] ) .
( 1 ) we use the na and mg / al wavelength intervals together as combined diagnostics of temperature , gravity , and veiling in an iterative process .
initially , gravity is held fixed , while the best fit for temperature and veiling is found .
then , temperature is fixed at the previous best - fit value while gravity and veiling were varied to find the best fit .
this process is iterated until a best fit for all three parameters is found . by fitting both na and mg / al wavelength intervals
simultaneously we usually converge to a unique value for effective temperature , gravity and veiling where the combined rms value from both na and mg / al intervals is lower and the error space more sharply defined than when either interval is used alone .
therefore , we use both intervals weighted together , equally , as strong diagnostics for t@xmath20 and @xmath21 , as well as r@xmath29 .
( 2 ) the broadening of the bandhead in the co interval is determined to be the most sensitive indicator of projected @xmath22 rotation of all our diagnostic lines .
therefore @xmath22 is solely determined by the best fits to the co interval by first imposing the best t@xmath20 and @xmath21 from the na and mg / al intervals , while leaving the amount of veiling unconstrained , in favor of finding the best rotationally broadened spectral fit .
this amount of broadening is likewise imposed on the fits in the other two intervals .
radial velocities for each object are found as the mean of the velocity shifts between the observed and the best - fit synthetic spectra for each of three spectral regions independently .
occasionally one of the three orders had a widely divergent derived velocity shift ; in these cases the discrepant point is discarded from the mean .
the derived velocities are adjusted using the iraf package rvcorrect to account for motions due to the earth s solar and galactic orbits , allowing a calculation of v@xmath40 and v@xmath31 for each object .
random errors present in the rms best - fit value of the spectral fits are due to the finite signal - to - noise present in our data . in order to calibrate a 3 @xmath41 change in the rms parameter search space
, a test model spectrum was constructed using a particular synthesis model , representative of a typical yso fit in our sample : ( t@xmath28 = 3600k , @xmath21 = 4.0 , @xmath22 = 40 , and r@xmath29 = 3.0 ) .
random gaussian noise was added to the test spectrum to achieve s / n = 200 pixel@xmath13 before it was then run through the standard fitting routine .
this was done many times with random noise seeds .
a 1 @xmath41 variation in the best - fit rms value over many trial fits to the same spectrum with noise was @xmath42rms = 10@xmath43 . using this number
, we calibrate the errors due to noise in each of the physical parameters using the rms error contour plots ( output by the spectral fitting routine for each fit ) . a change in the rms from the lowest value ( i.e. the best fit ) to a value that is bigger by 3 @xmath15 10@xmath43
, then corresponds to the 3 @xmath41 random error along that new error contour line .
for example , fig .
[ fig-rmscontour.logg ] shows the error space contours in the @xmath21 vs r@xmath29 and @xmath21 vs @xmath22 planes corresponding to the best fits of these quantities in dg tau .
the asterisks mark the minima in the error space ( rms = 4.2 @xmath15 10@xmath44 and 4.5 @xmath15 10@xmath44 ) and each contour interval corresponds to an _ increase _ of 3 @xmath15 10@xmath43 ( 3 @xmath41 contours ) , resulting in a calibrated change for each parameter .
therefore , the error space in each of four parameter fit planes ( t@xmath20 vs @xmath22 ) , ( t@xmath20 vs r@xmath29 ) , ( @xmath21 vs @xmath22 ) , ( @xmath21 vs r@xmath29 ) is characterized by changes of 10@xmath43 ( 1 @xmath41 ) from the best - fit rms value .
random errors in the four parameters are generally smaller than systematic errors . the best model fit to each observed protostellar spectrum is associated with an initial seeded @xmath21 value , where the initial seed value for @xmath21 is assumed and held fixed while the spectral fitting routine then finds the best - fit t@xmath20 . following this
, the routine then holds the new best - fit t@xmath20 fixed and searches for the corresponding best fit for @xmath21 , and so forth .
thus , the routine finds an rms minimum within the 5 parameter search space , iterating between the t@xmath20 and @xmath21 search planes . sometimes there is more than one local minima in the solution and different initial seed values for @xmath21 fit to different best - fit solutions . in this case , differences in the different rms minima are compared and the overall best solution is taken as the global minimum of all different seeded best fits .
uncertainties ( 1 @xmath41 ) in the physical parameters ( t@xmath20 , @xmath45 , r@xmath29 , and @xmath46 ) derived from the spectral fits are computed by measuring the changes in each quantity that produced a change of @xmath47 in the rms fit residual , about the global minimum rms fit .
systematic errors in the best - fit parameters are then gauged by changes in best - fit solutions that are below our ability to discern real changes in the fits appropriate to the signal - to - noise of our spectra .
changes in the equivalent widths of lines are evident in the spectra of young stars with differing t@xmath20 , @xmath21 , and r@xmath29 . at high resolution
the changes to the lines whose shapes are fully resolved can distinguish between different physical diagnostics ( i.e. line damping and large @xmath22 rotation ) , but degeneracies in the fits to spectral models in t@xmath20 , @xmath21 , and r@xmath24 persist even at high spectral resolution , especially in unsaturated lines .
the elongation in the error space in figures [ fig-rmscontour.teff ] and [ fig-rmscontour.logg ] ( bottom panels ) show how t@xmath20 and @xmath21 are both somewhat degenerate with veiling , though in opposite senses .
also , surface gravity and effective temperature are together degenerate ( dj03 ) in the sense that lower effective temperatures fit to lower @xmath21 spectra ( see further discussion in @xmath7 [ sec - standsfits ] ) .
the degeneracy is less pronounced when simultaneous fits to more spectral lines can be performed , as has been done here with the nirspec echelle spectra . in particular
, the na fits and mg / al fits together constrain gravity and temperature better than using only one interval , despite systematic errors that can dominate the accuracies of the best - fit model . to validate the quality of the spectral synthesis models and our ability to accurately fit them to actual data
, we apply our fitting routine ( @xmath7 [ sec - fittingroutine ] ) to our nirspec observations of mk standards . using our standard fitting procedure to the synthesis model grid ,
we determine the best - fit values for t@xmath20 spanning g8 m5.5 spectral - types ( 5300k to 3100k ) in our standard stars .
we find a very good agreement ( correlation coefficient of 0.99 ) between our near - ir temperatures and those inferred from the optical spectral - types ( fig . [ fig-teff.fitstands ] )
using the relation quoted by @xcite .
the surface gravities we derive in the standards are consistent with those of late - type dwarfs ( @xmath21 = @xmath64.4 5.0 ) with some scatter due to the uncertainties in the conversion from the standards spectral - types to surface gravities .
all but 2 of our late - type standards have @xmath22 rotational velocities well below our resolution limit ( r = 18,000 , 17 km s@xmath13 ) .
the average @xmath22 value derived for these slow rotating standards is 10.8 km s@xmath13 , which we adopt as a measure of the instrumental broadening through our 4 pixel wide slit .
we remove this value in quadrature from the @xmath22 values we measure in two standards ( gliese 791.2 & 1245a ) whose velocity broadened lines we resolve and compare with independent derived optical measurements of 32 and 22.5 km s@xmath13 , respectively @xcite .
our near - ir derived @xmath22 values are in excellent agreement with the optical study , where we measure , 34.3 and 22.5 km s@xmath13 , respectively .
we expect our mk standard stars that are in the field to be completely unveiled .
however , when we allow veiling to be fit as a free parameter along with t@xmath20 , @xmath21 , and @xmath22 , we find the best - fit value has an average veiling of r@xmath48 = 0.2 , weighted toward more veiling in later type spectral standards .
we also see a similar effect in the co order .
if this is an instrumental effect caused by scattering or leaking some of each object s own light , then the amount of this excess instrumental veiling is @xmath42r@xmath49 ) where r@xmath29 is the object s true veiling .
we correct the best - fit veiling values r@xmath50 of the ysos ( as derived from the na and mg / al intervals ) to true intrinsic veilings ( r@xmath29 ) with this relation and report only these corrected values in this publication : @xmath51 after validating our technique with the standards , and establishing the veiling correction needed in our nirspec data , we fit 41 spectra of class i and flat - spectrum sources to the synthesis models following the procedure described in @xmath7 [ sec - fittingroutine ] .
at least 1 echelle order displayed photospheric absorption lines in all of these 41 sources from which we were able to derive key physical properties directly from the spectra .
these results are listed in table [ tbl-3 ] along with the 1 @xmath41 uncertainties ( @xmath7 [ sec - qualityfits ] ) .
we do not apply our fitting routine to 11 stars in our sample due to the absence of photospheric lines in their spectra . as a check to the effective temperatures , rotational broadening and veiling values
that we derive using our spectral synthesis models , we evaluate fits to our protostellar spectra using the observed standard spectra ( that have been spun - up and veiled ) , where the best fit is found qualitatively by eye .
we compare the best model fit to the best standard fit after converting the spectral - type of each best - fit dwarf mk standard to an effective temperature @xcite .
the @xmath22 and r@xmath29 values both show some scatter that is roughly symmetric about a perfect - fit line .
the t@xmath20 values show a systematic offset toward higher derived effective temperatures ( @xmath52 ) .
this temperature difference is likely due to differences in surface gravities between the dwarf standards ( @xmath53 4.3 4.7 ) and our yso models ( mean @xmath21 = 3.8 ) . in general
, effective temperatures increase by @xmath6 200k for each increase of 0.5 in @xmath21 for late - type stars ( dj03 ) , so the sign and magnitude of the temperature offset is correct .
the @xmath22 rotation velocities and r@xmath29 continuum veilings for each of the 41 objects fit in our sample ( table [ tbl-3 ] ) are shown in figure [ fig-vsini.veil ] .
this figure also shows 2 curves which plot our expected sensitivity to @xmath22 and r@xmath29 for t@xmath20 = 3500k and 4600k stars with signal - to - noise representative of our object sample ( s / n = 180 ) .
we should detect photospheric absorption lines in objects which lie to the left of those curves , and we are insensitive to detecting photospheric absorption features in objects which lie to the right of these curves .
the curves and points show that we are least sensitive to objects with high r@xmath29 and high @xmath54 and most sensitive to ones with low r@xmath29 and low @xmath22 ; high veilings and fast rotation velocities both reduce the depths of absorption features relative to continua .
k - band veilings and rotation velocities do not appear strongly correlated in figure [ fig-vsini.veil ] . we detect objects which span nearly the entire range of @xmath22 and r@xmath29 to which we expect to be sensitive . however , there are no objects in the region near the line defined by the points r@xmath29 = 1 , @xmath22 = 0 km s@xmath13 and r@xmath29 = 4 , @xmath22 = 40 km s@xmath13 . it is unclear whether this gap is due to a physical effect or else a characteristic of our finite object sample . to determine the accuracy of our derived radial velocities , we compare our derived heliocentric radial velocities to those in the literature for well - observed spectral - type standards .
figure [ fig-radvel.offset ] shows a histogram ( solid line ) of the residuals of our derived velocities less the previously determined value for spectral - type standards with precise ( error @xmath10 2 km s@xmath13 ) heliocentric velocities @xcite .
the best fit gaussian to the histogram , binned in the same manner , is shown as the dashed line .
the mean of the gaussian fit is 1.8 km s@xmath13 , indicating the presence of a slight offset in our derived velocities . to correct for this systematic observational artifact ,
a + 1.8 km s@xmath13 shift has been applied to all derived velocities presented in this work ( table [ tbl-3 ] ) and @xcite .
the width of the gaussian fit in fig . [ fig-radvel.offset ] also provides an indication of the level of accuracy with which we can determine the velocities of targets ( @xmath55 2 km s@xmath13 ) .
the true distribution appears to have slightly broader wings than the gaussian fit .
we therefore consider the size of our true velocity error as 1.5 @xmath41 , or @xmath6 3 km s@xmath13 .
in addition to the surface gravities we measure directly from the spectra , we derive stellar luminosities for our sources in ophiuchus , taurus , and serpens based on published h and k - band apparent magnitudes @xcite .
many of our objects do not have j - band photometry , so we are unable to de - redden these sources individually on a color - color diagram .
instead , we estimate the extinction at k by de - reddening all our objects to an intrinsic h k color of 0.6 , which is midway between the end of the classical t - tauri star locus ( h k = 1.0 , * ? ? ? * ) and the average intrinsic color for late - type dwarfs ( h k @xmath56 0.2 , table a5 of * ? ? ?
* ) . to account for the presence of scattered light
, we increase each of our derived extinctions by 0.88 magnitudes ( see paragraph below ) .
absolute k magnitudes were computed from observed k magnitudes corrected for extinction ( employing the extinction law of * ? ? ?
* ) , excess emission that is measured spectroscopically though veiling in this work ( see table [ tbl-3 ] ) , and distance to the star forming cloud ( tau = 140 pc , oph = 145 pc , ser = 259 pc ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
the stellar luminosity is found by converting the absolute k magnitude to a v magnitude adopting a v
k color and a bolometric correction appropriate to a late - type dwarf having our derived effective temperature ( table a5 , * ? ? ?
* ) . using the photometric luminosities and spectroscopic effective temperatures ,
these objects are plotted on an observational h - r diagram , and show a spread in t@xmath20 and luminosity ( fig .
[ fig-hrd.lstar ] ) .
this stellar luminosity should be representative of the pms star and not include any accretion luminosity .
the flux measured within a photometric aperture toward a class i object contains contributions from sources other than the direct light from the extincted stellar photosphere .
these other sources of emission include the surrounding accretion disk , hot dust in the inner envelope and scattered light from holes or cavities in the envelope . indeed , observed high polarizations of many class i sources in taurus suggest that the observed fluxes are dominated by scattered light @xcite . in this case
extinction estimates based only on de - reddened colors are underestimates since they represent the extinction to the scattering surface and not the protostellar object itself .
in some cases this could lead to severe underestimates in the source luminosity .
we compare our derived extinction estimates to those derived by @xcite from a more careful analysis using polarimetric observations and radiative transfer models of class i envelopes to derive more realistic extinctions to individual protostellar objects in the taurus cloud .
seven of those objects are also in our sample , and we find that the @xcite k - band extinctions are 0.88 magnitudes higher ( mean value ) than the extinctions we compute from the h
k colors of those same objects . therefore in an attempt to account for the extinction produced by the presence of scattered light , we increase the derived extinctions in all of our class i and flat - spectrum sources by 0.88 magnitudes .
the luminosity error bars depicted in figure [ fig-hrd.lstar ] are the quadrature sum of uncertainties due to distance to the cloud , observed photometry , slope of the extinction power law , the ( assumed ) intrinsic ( h k ) color , and the presence of scattered light .
the last two quantities are highly uncertain due to the complexities of the circumstellar environments typical of class i objects .
the largest uncertainty in our luminosity calculation arises from the intrinsic colors of protostars ( h k = 0.6 @xmath57 ) which may not resemble those of dwarfs . to quantify the luminosity uncertainty due to scattered light
, we examine the uncertainty of the 0.88 magnitude offset of the k band extinction values , the mean difference between the extinctions derived by @xcite and us for the seven objects in taurus that we had in common .
we determine the uncertainty of this offset from the standard deviation of the mean ( 0.39 magnitudes in a@xmath29 ) .
ascertaining appropriate extinctions and disentangling the effects of scattering , source geometry and veiling from disks and envelopes likely requires detailed modeling of the envelopes of individual sources in order to derive meaningful luminosities for the central embryonic stars . in the absence of such modeling one
must regard our derived luminosities of class i objects as being highly uncertain .
the placement of class i and flat - spectrum sources in h - r diagrams is one of the main goals of this study .
coupling our determinations of t@xmath20 and @xmath21 with estimates of individual source luminosities derived from existing photometric observations , we are able to place our object sample on the h - r diagram .
we present the individual h - r diagrams for ophiuchus , taurus and serpens in figure [ fig-hrd.lstar ] . for comparison we also plot one set of theoretical pms evolutionary tracks @xcite on an accompanying h - r diagram .
we find the flat - spectrum / class i stars to lie in a relatively broad band , parallel to and well above the main - sequence , but below the expected birth - line for ysos @xcite . in figure [ fig-hrd.lstar.classii ]
we show the locations on the h - r diagram of class ii sources from the same clouds .
comparison of the two plots shows that class i and flat - spectrum central stars span a very similar range of luminosity and effective temperature as class ii sources . for both types of sources
there is a relatively large scatter in their positions on the h - r diagrams .
these findings are similar to those derived from optical spectroscopy of class i sources in taurus @xcite .
classical pms theory would suggest that class i sources should appear at or near the birth - line , however pms models that include the effects of accretion indicate that accreting stars evolve more quickly down hayashi tracks than non - accreting stars and should appear at lower luminosities than non - accreting stars of the same age @xcite . thus the locations of class i sources below the birthline are consistent with expectations for accreting stars .
however , because class i sources should be systematically younger than class ii objects the class i stars should on average be more luminous than the class ii sources which does not appear to be the case for the objects we observed .
however as discussed below large uncertainties in both derived source luminosities and the locations of theoretical tracks on the h - r diagram may mask such an effect . in figure [ fig-hrd.logg ] , we plot the surface gravities vs effective temperatures for class i and flat - spectrum sources in the same clouds along with the predictions of theoretical models of pms evolution .
the surface gravities we derive from spectroscopy are correlated with the photometrically determined luminosities using evolutionary model tracks to infer the stellar mass .
we find that our protostellar sample are characterized by sub - giant surface gravities that are significantly lower than those of main - sequence dwarfs .
there is a relatively large scatter in distribution of the class i and flat - spectrum surface gravities .
if we compare the positions of our ysos on the h - r diagram and on the surface gravity plots with the predictions of classical pms theory we find these ysos appear to span an age range of @xmath6 10@xmath58 years , similar to that of class ii objects .
this is almost certainly an unphysical result .
for example from statistical arguments the class i phase is thought to be only about 10@xmath59 years in duration , considerably shorter than the spread of sources on the h - r and surface gravity diagrams would suggest .
moreover , the observed color - magnitude diagrams of slightly older ( @xmath60 myr ) young clusters exhibit very well - defined pre - main sequences with nearly coeval age spreads of typically less than 23 myr @xcite .
together these facts suggest that the observed spreads on the h - r diagrams for a very young stellar population ( @xmath6 13 myr ) are a result of factors other than age , factors that introduce systematic uncertainties in the locations of stars on the h - r diagram .
these factors include intrinsic source variability , uncertainty in extinction corrections , binarity ( e.g. , * ? ? ?
* ) as well as effects of accretion on the positions of accreting stellar objects on the h - r diagram @xcite .
protostellar luminosities are dominated by scattering and disk accretion and thus determination of the stellar component of the luminosity from observed photometry is likely one of the largest sources of uncertainty in the vertical positions of class i and flat - spectrum objects on the h - r diagram .
errors in stellar luminosities derived from near - ir photometry in our sources are dominated by uncertainties in judging the intrinsic near - ir colors of these embedded sources ( @xmath7 [ sec - photlums ] ) .
relying on the assumption that these objects are radiating isotropically is problematic since the stellar light can be partially blocked by disks or scattered through cavities .
@xcite find that the stellar luminosity in t - tauri stars can be underestimated by up to @xmath6 50% ( factor @xmath62 in age ) due to occultation by opaque disks at various inclination angles .
luminosities of class i sources in taurus report uncertainties of @xmath633% - 50% for objects
whose optical spectra are seen only in scattered light @xcite .
the geometry of protostellar disks is clearly important to making accurate measurements of the luminosity emanating from an embedded source , and overestimates in the apparent age can result if this is not accounted for .
this effect has been seen by others as well ; the h - r diagrams of @xcite show that class i ysos and ysos driving herbig - haro flows in taurus - auriga which have edge - on disks have low luminosities making them to appear to have very high ages , on the order of 10@xmath61 yr .
uncertainties in our spectroscopic measurements of gravity stem from our fits to key photospheric lines ( see @xmath7 [ sec - qualityfits ] ) , whose shapes and depths are affected by combinations of physical parameters ( i.e. t@xmath20 , @xmath21 , r@xmath29 ) that are difficult to completely separate in finite signal - to - noise data .
a theoretical uncertainty in using h - r diagrams to measure masses and ages lies in the reliability of the placement of evolutionary model tracks which permit us to convert observables into fundamental intrinsic properties .
the presence of accretion delays the formation of a radiative core @xcite , which offsets the isochrones toward lower luminosities and higher gravities in cool ( t@xmath62 5800k ) ysos @xcite . depending on the accretion history , and initial mass , overestimates in the ages vary between 30% and a factor of 5 when compared to models without accretion ( i.e. * ? ? ?
it is quite likely therefore that the large spreads in the stellar luminosities and gravities that we find for our class i and flat - spectrum sources are not due to real spreads in age , but represent uncertainties in the intrinsic colors , extinctions , and emitting geometry of each star , along with observational uncertainties in their spectra .
therefore differences in the stellar luminosities of class i / flat - spectrum and class ii sources are extremely difficult to detect in observational h - r diagrams and comparisons of derived luminosities and ages between these objects are not likely meaningful . moreover ,
when the observational uncertainties are coupled with uncertainties in the pms evolutionary tracks it is evident that class i and flat - spectrum ages can not be confidently extracted from h - r diagrams .
near - ir co emission has been observed in a number of ysos @xcite , although it is less common in low luminosity objects ( e.g. * ? ? ?
* ; * ? ? ?
co emission has been used as a probe to study the kinematics of the inner disk region around ysos @xcite , since relatively warm ( t@xmath63 = 2500k 4500k ) and dense ( n @xmath64 cm@xmath44 ) neutral gas is needed to collisionally excite co , where the origin of the emission may likely be from a temperature inversion in the inner disk atmosphere . while another source of this emission could be outflows of neutral gas in winds ( e.g. svs 13 , * ? ? ?
* ) , most co overtone emission fits profiles of rapid keplerian rotation ( up to 400 km s@xmath13 ) originating from an inner disk @xcite .
the rotation profile of a disk is distinctly double peaked in velocity space @xcite because different disk regions have different keplerian velocities and different co emission strengths .
when this profile is convolved with the first overtone co bandhead and r branch lines , the result is an asymmetric profile having a blue wing , a shoulder , and a peak redward of the bandhead rest velocity @xcite . in contrast , a stellar rotation profile @xcite has a single symmetric peak centered at the rest velocity , with the higher velocity components contributing less as the projected emitting area decreases outward toward the limb .
we detect co emission in 8 of our sources ( 15% of our sample ) , which is accompanied by br @xmath4 emission in all cases , and na emission at 2.2062 @xmath1 m & 2.2090 @xmath1 m in 5 cases . except for 2 sources ( ec 129 & ec 38 , see appendix [ sec - indivsources ] ) , the broadened co emission ( @xmath10 100 km s@xmath13 ) shows a velocity structure that is consistent with spectral models of keplerian rotation @xcite from an optically thin disk .
two sources have both co and br @xmath4 absorption superposed on corresponding emission features in these two lines .
we detect hi br @xmath4 emission ( 2.1661 @xmath1 m ) in 34 of 52 ysos observed in our sample ( 65% , shown in figs .
[ fig-brg.spec1 ] & [ fig-brg.spec2 ] ) . in general , the emission profiles are broad ( @xmath695 320 km s@xmath13 , fwhm ) , consistent with what is seen in low luminosity embedded ysos and active t - tauri stars @xcite . in 4 cases ( i.e. ec 129 ,
gy 224 , irs 67 , irs 43 ) , the emission is significantly blue - shifted relative to the stellar systemic velocity , indicative of an outflow .
these sources are among those that are marked with dashed vertical line indicating the objects where we measure photospheric radial velocities ( figs .
[ fig-brg.spec1 ] & [ fig-brg.spec2 ] ) . in 6 cases , there is accompanying br @xmath4 absorption that is superposed near the peak of the emission profile ( left panel of fig . [ fig-brg.spec1 ] ) , but red - shifted by @xmath615 65 km s@xmath13(i.e .
04016 + 2610 , ec 129 , gy 21 , ec 94 , irs 63 , svs 20a ) .
emission with blue - shifted absorption , which would be explained by an expanding wind @xcite , is absent in our sample .
instead , the red - shifted absorption minimum is characteristic of material in - falling from the disk onto the photosphere @xcite , perhaps along magnetic accretion columns in cases of greater velocity red - shifts where in - falling material can reach free fall velocities .
inverse p - cygni profiles in classical t - tauri stars indicative of in - fall are ubiquitous @xcite , and have been explained by free falling gas along the magnetosphere @xcite .
the modest red - shifts ( v@xmath66 65 km s@xmath13 ) we observe in these br @xmath4 absorption components ( relative to the emission peak ) suggests that accretion may be occurring through the inner disk in this stage before it could become disrupted and truncated in a later evolutionary stage @xcite .
four ysos have br @xmath4 absorption without the presence of any emission . the strongest and broadest of these is 03260 + 3111a , whose equivalent width ( 3.4 @xmath67 ) and broadened line wings are consistent with br @xmath4 absorption we see in late g - type dwarf standards , confirming its relatively warm t@xmath20 ( 5600k ) derived from spectral fits to photospheric lines in the na and mg / al intervals .
only one other source is warm enough ( svs 20a , see appendix [ sec - indivsources ] ) , to allow a photospheric origin for the absorption . for the other 3 sources that show only br @xmath4 in absorption ( ec 53 , ec 92 , ec 95 )
, we see equivalent widths that are significantly greater than what is observed in the mk standards of comparable spectral - type .
the likely explanation for this is that either the br @xmath4 absorption arises from a non - photospheric mechanism @xcite , or else these are binary systems with both early and late - type components .
if the latter is true , then the early - type star must cause significant veiling of the k - band photospheric features of the late - type star in each system , by nature of their relative temperatures and the larger radii of the early - type stars . this does not apply for ec 92 and ec 95 which have veiling r@xmath29 = 0.0 and 0.1 , respectively . in the case of ec 53 which has veiling r@xmath29 = 1.8 , an earlier spectral - type binary component that is warm enough to have photospheric br @xmath4 absorption lines ( i.e. t@xmath20 @xmath11 4200k ) would mask the lines ( r@xmath68 ) of the cooler star ( t@xmath20 = 3400k ) .
therefore we conclude that the br @xmath4 absorptions of ec 53 , ec 92 and ec 95 most likely arise from another mechanism .
the radial velocities of all the br @xmath4 absorption lines lie at the stellar systemic velocity to within one resolution element of our observations ( 17 km s@xmath13 ) .
k - band veiling traces thermal emission from circumstellar material .
moderate amounts of veiling ( @xmath69 ) can be produced by circumstellar disks , depending on their structures , activities , and geometries .
circumstellar envelopes are usually responsible for larger amounts of veiling ( see * ? ? ?
young stars with large r@xmath29 values have more warm circumstellar material than less veiled ones .
k - band veiling may also be a good indicator of mass accretion because matter close to a young star is attracted to it by gravity .
we now use r@xmath29 measurements to investigate whether the class i and flat - spectrum objects in our sample have more warm circumstellar material than class ii and t - tauri stars .
we start by compiling mean veiling values for each of the 3 major star forming regions which we have studied .
we compute these values from the r@xmath29 results presented in table 3 , but we also correct for the objects for which we were not able to determine physical parameters .
eight of these objects ( 2 in tau - aur , 3 in @xmath2 oph , and 3 in serpens ) were observed with high signal - to - noise , so we assign them the value r@xmath29 = 4.0 .
we determined this value to be their likely lower limits using our observed veiling / rotation completeness limit assuming a typical rotation velocity @xmath22 = 35 km s@xmath13 ( see fig .
[ fig-vsini.veil ] ) . the other 2 objects ( crbr 85 in oph and ec 89 in ser ) show weak na and co absorption features ( too weak for analysis ) in moderate signal - to - noise spectra , so we assign them both r@xmath29 = 1.5 , typical for the object sample . with these corrections ,
our entire class i and flat - spectrum object sample has a mean veiling @xmath70 = 1.83 .
the objects in tau - aur and ser both have @xmath70 = 1.54 ( @xmath381.21 for tau - aur and @xmath381.49 for ser ) , while the @xmath2 oph objects are characterized by @xmath70 = 2.21 @xmath381.35 .
we evaluated the likelihood that objects in these different regions have statistically significant veiling differences by performing ks tests on their r@xmath29 values .
we found that the ser and tau - aur objects are likely to be drawn from the same veiling distribution ( 88% probability ) , while the tau - aur and @xmath2 oph probability was 18% and the ser and oph probability was 24% .
thus all the objects in the 3 major star forming regions have similar veiling values , with @xmath2 oph and tau - aur showing some evidence for being different ( at the 1.3 @xmath41 level ) .
we infer similar conclusions about the similarity of circumstellar material around these objects .
next we compare these results to the veilings of class ii ysos in order to evaluate whether objects in our study have significantly more circumstellar material . of the 3 major star formation regions in our study ,
only the @xmath2 oph region has a significant number of class ii ysos for which r@xmath29 values have been determined .
we compute that the mean veiling of class ii objects in @xmath2 oph is @xmath71 = 0.94 @xmath381.03 from data presented by @xcite ( 10 objects ) and @xcite ( 15 objects ) .
this is about half that of the @xmath2 oph objects in our class i and flat - spectrum sample .
furthermore , the ks test reveals that the r@xmath29 values of the class i / flat - spectrum and the class ii samples in @xmath2 oph have less than a 1% chance of being drawn from the same parent population .
therefore we conclude that class i and flat - spectrum objects have significantly more veiling than class ii ysos .
the class i and flat - spectrum objects must have more warm circumstellar material , making it likely that they are in a more embedded and younger evolutionary state .
@xcite have shown that hi br @xmath4 emission is well - correlated with mass accretion in t - tauri stars , and we now evaluate whether r@xmath29 and br @xmath4 emission are correlated in our class i and flat - spectrum sample . in figure [ fig-brg.veil ]
we plot br @xmath4 line luminosity ( after correcting for extinction and distance ) for sources where we also were able to measure r@xmath24 .
these two parameters are positively correlated , but fig .
[ fig-brg.veil ] shows too much scatter ( perhaps due to uncertain extinction corrections or asymmetrically distributed circumstellar material ) to confirm that both r@xmath29 and br @xmath4 emission are reliable mass accretion diagnostics for class i and flat - spectrum ysos .
using our measured br @xmath4 luminosities , the @xcite relation suggests that our @xmath2 oph sources have accretion luminosities 10@xmath72 , while taurus and serpens have about an order of magnitude less .
however , we note that many of the objects in our sample have been observed to have significantly higher bolometric ( accretion ) luminosities @xcite , and the @xcite relation was derived for class ii objects with low accretion luminosities
. therefore the absolute accretion luminosities derived from br @xmath4 fluxes are likely to be underestimates , although the relative difference between @xmath2 oph and the other regions is interesting and may be real .
the above discussion has demonstrated that analysis of spectroscopic features provides much more detailed information on the natures of ysos than can be ascertained from sed shapes alone .
we now examine the extent to which the aggregate of information derived from our spectra provides insight into the true physical natures and evolutionary status of class i and flat - spectrum ysos . as part of this effort
, we also assess whether this new information supports the established paradigm that class i objects are protostars near the ends of their bulk mass accretion phases that then evolve to class ii or class iii ysos .
our analysis has shown that class i and flat - spectrum ysos have some astrophysical properties which are similar and some which are considerably different from class ii and iii ysos . as noted in @xmath7 [ sec - hrdiags ] , our class i and flat - spectrum sample
have effective temperatures , surface gravities , and stellar luminosities which are similar to those of class ii pms stars .
this is not completely unexpected given the relatively large uncertainties in stellar luminosities determined for class i and flat - spectrum objects ( @xmath7 [ sec - photlums ] ; see also figure [ fig-hrd.lstar ] ) , and the stellar cores of steadily accreting protostars are expected to be in near hydrostatic equilibrium with radii and central temperatures similar to t - tauri stars @xcite . however , other intrinsic astrophysical properties of class i and flat - spectrum objects do differ significantly from class ii or class iii pms stars . in @xmath7 [ sec-cont.emis ]
, we determined that the k - band veilings of @xmath2 oph class i and flat - spectrum ysos are significantly higher than those of @xmath2 oph class ii objects , indicating more circumstellar material and higher mass accretion in class i and flat - spectrum objects .
also , our class i and flat - spectrum sample has significantly higher @xmath73 sin @xmath74 rotation velocities and angular momenta than class ii and t - tauri pms stars the tau - aur and @xmath2 oph regions . if a young star is magnetically locked to its disk via its magnetic field , popular magnetospheric accretion models predict that the disk coupling radius is proportional to @xmath75 , where @xmath76 is the mass accretion rate onto the star @xcite .
this means that ysos with higher accretion rates should be rotating faster than low accretion rate objects , with angular velocities @xmath77 ( for a full discussion see * ? ? ?
* ) . in summary ,
all fundamental astrophysical properties derived in this study appear to support the paradigm that class i and flat - spectrum ysos are accreting protostars . in this respect
our results appear to differ from those of @xcite who found that most optically - selected class i ysos in tau - aur have mass accretion rates , accretion luminosities , and rotation velocities that are not significantly different from class ii and t - tauri stars in the same region .
furthermore , @xcite conclude that the similarity of class i and class ii / t - tauri spectral - types and stellar luminosities imply that these objects have similar ages and masses .
therefore @xcite argue that class i and ii ysos are not in different evolutionary states and that class i objects are no longer in their main mass accretion phases of evolution .
we note that we argued in @xmath7 [ sec - hrdiags ] that conventional pms models can not yield ages of class i and flat - spectrum ysos because they lack accretion physics . in an attempt to reconcile these results ,
we first investigate whether the optical spectroscopy analysis technique of @xcite yields the same parameters as our analysis for objects observed in both studies .
eight objects were observed in both studies , and we derive astrophysical parameters for all of them .
the six sources with astrophysical properties derived in both studies are 04016 + 2610 , 04158 + 2805 , dg tau , gv tau , haro 6 - 28 , and 04489 + 3042 . both studies derive similar effective temperatures ( within 350k ; converted from the spectral - type designations of * ? ? ?
* ) for all 6 objects except dg tau , which @xcite find to be significantly earlier ( about 650k warmer ) than we do ( table [ tbl-3 ] ) .
the high optical and ir veilings of this object may contribute to uncertainties in the spectral - type and effective temperature derived for this object .
the @xmath22 rotation velocities of 5 of these 6 objects also agree well ( to several km s@xmath13 ) , with the exception of 04016 + 2610 .
@xcite derive @xmath78 km s@xmath13 for this object , while we report 46 km s@xmath13 .
we suggest that the very low signal - to - noise in the optical spectrum ( s / n @xmath6 2 ) may be responsible for this discrepancy , and it is likely that our higher signal - to - noise spectrum ( s / n @xmath0 240 ) yields the less uncertain value .
overall it appears that both studies yield similar astrophysical parameters for common sources .
the differences in the conclusions between the two studies may be due to differences in the underlying physical properties of the ir and optically - selected samples that were analyzed .
@xcite find that class i ysos do not have higher rotation velocities or higher mass accretion rates ( as inferred from veiling and luminosity measurements ) than class ii objects .
they do not derive astrophysical parameters for two of the eight objects common in both studies , l1551 irs5 and 04295 + 2251 .
interestingly , we find that the @xmath22 rotation velocities of these objects are 31 and 51 km s@xmath13 , considerably higher than the median rotation velocity of 19.8 km s@xmath13 of the @xcite class i sample ( see their table 3 ) .
the five class i or flat - spectrum tau - aur ysos in our sample which were not observed by @xcite are not optically visible , and we find 4 of the 5 to be highly veiled r@xmath79 , with 2 of those veiled to the point where they have no discernible absorption features ( r@xmath80 ; see figure [ fig-vsini.veil ] ) .
this suggests that optically - selected class i ysos may have less veiling and less accretion luminosity than ir - selected ones .
also , tau - aur ysos have been known to have lower bolometric luminosities @xcite , and presumably lower mass accretion luminosities and rates than those in the @xmath2 oph star forming region @xcite .
finally , we note that @xcite did not account for the fact that several of their class i objects ( and a few of their class ii ones ) were too veiled to determine their astrophysical parameters , so they did not compute mass accretion rates or rotation velocities for these objects
. therefore the median mass accretion rates and rotation velocities computed in that study are likely biased by these omissions .
the above discussion suggests that class i sources span a wide range of stellar and circumstellar properties , from actively accreting to relatively quiescent objects .
we do believe that our large sample of ir - selected class i and flat - spectrum ysos from several star forming regions does give the most accurate picture to date of their true natures as accreting protostars .
we have acquired high resolution near - ir spectra of a sample of 52 class i and flat - spectrum ysos located in the tau - aur , @xmath2 oph , ser , and other nearby dark clouds .
we have derived their fundamental astrophysical properties via fitting their spectra to theoretical spectra synthesized from the nextgen @xcite pms models and make the following conclusions : 1 .
we detect absorption lines in 41 of the 52 objects .
this is a much higher number and fraction than earlier studies because of the high sensitivity and spectral resolution of the keck ii telescope and its nirspec spectrograph .
twenty - three of the objects show 2.2235 @xmath1 m h@xmath3 emission lines . 2 .
thirty - four objects show hi br @xmath4 emission lines , and 6 of these show br @xmath4 absorption as well .
the absorptions are modestly red - shifted in all cases , indicating accretion in those objects .
@xmath5 co emission is seen in 15% of the objects , indicating that co emission and active circumstellar disks are more common than expected from earlier studies .
the absorption spectra are fit well by the synthetic spectra , indicating that the objects have effective temperatures and surface gravities which are consistent with pms stars .
the spectral fitting procedure also yields rotation velocities , radial velocities , and k - band veilings .
the objects show a wide range of effective temperatures and stellar luminosities , and these values overlap with those of class ii and t - tauri stars when placed in h - r diagrams .
the class i and flat - spectrum objects have low masses which span the same range as class ii and t - tauri stars , but significant observational and theoretical uncertainties preclude deriving meaningful and accurate luminosities and ages for protostellar sources from placement on the h - r diagram and comparison with conventional pms models .
we find that the mean k - band veiling of class i and flat - spectrum ysos in @xmath2 oph is significantly higher than for class ii objects in this region .
this indicates that the class i and flat - spectrum objects are accreting at higher rates , which is bolstered by an analysis of their angular momentum properties in a companion paper @xcite .
we also find that k - band veilings vary somewhat between class i and flat - spectrum ysos in different regions , with the @xmath2 oph objects having the highest veiling values , @xmath81 .
we conclude that class i and flat - spectrum ysos are indeed actively accreting protostars , although they span a wide range of accretion activity .
high resolution near - ir spectra provide sufficiently detailed information to diagnose the stellar and circumstellar properties of nearly any class i or flat - spectrum yso .
the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community .
we are most fortunate to have the opportunity to conduct observations from this mountain .
we also thank the staff of the keck observatory for excellent support in the operation of the telescope and nirspec .
we thank russel white for his careful reading of this manuscript and valuable comments .
we thank dan jaffe and amanda kaas for helpful discussions .
we are grateful to the referee , barbara whitney , whose insightful comments helped improve the manuscript .
we acknowledge support from nasa s origins of solar systems program via upn 344 - 39 - 00 - 09 .
g.w.d . gratefully acknowledges support from the national research council . k.r.c
gratefully acknowledges the support of nasa grant 80 - 0273 .
this research utilizes nasa s astrophysics data system bibliographic services , the simbad database , operated at cds , strasbourg , france , and the vizier database of astronomical catalogs @xcite .
ec 38 : of all our sources which show co overtone emission , ec 38 is the only one with an extremely narrow co emission profile ( @xmath630 km s@xmath13 ) , perhaps the most narrow observed co overtone emission profile seen in any embedded source .
furthermore , there are two resolved bandhead peaks ( separated by 64 km s@xmath13 ) , with evidence of beating in the r branch lines . a conical high velocity neutral wind in the plane of the sky viewed at low inclination angles @xcite might explain the well - separated blue and red - shifted bandhead components .
however , narrow co disk emission lines ( 4050 km s@xmath13 wide ) have only been observed in one other yso ( svs 13 ) , but are too narrow to fit emission models for either a circumstellar disk or outflow @xcite , unless there is rotational coupling between the star and inner disk or if co originates from a lower velocity flow .
strong br @xmath4 emission is also observed in this source .
a model that includes in - falling material from a truncated disk accompanied by a outflowing wind might best describe these observations .
svs 20a : we detect broad br @xmath4 and co emission , along with br @xmath4 absorption .
a marginal detection of weak co absorption may also be present with the co emission .
the relatively warm t@xmath20 ( 5900k ) we derive from photospheric lines in the na and mg / al intervals and the presence of br @xmath4 absorption at the same radial velocity , argues that the origin of the br @xmath4 absorption is photospheric .
if co absorption is also present , it must originate in a disk or a wind , since photospheric co is dissociated in warmer stars .
if the co feature is due to emission only , then its broadened double peaked profile suggests that it may originate in a wind at a high inclination angle @xcite .
the radial velocity of co is blue - shifted ( @xmath870 km s@xmath13 ) relative to the systemic stellar velocity , in support of an outflow origin for the co emission .
this object is the warmest and most luminous protostar that we measure stellar properties for . without making a correction for scattered light ( see @xmath7 [ sec - photlums ] ) , we derive a stellar luminosity of 24.7 l@xmath82 , based on the apparent flux at k from the north component ( m@xmath83=8.7 , * ? ? ?
* ) , adopting an h
k color of 2.16 observed in the total svs 20 system @xcite .
ec 129 : this source displays emission and absorption components in both co and br @xmath4 lines . ec 129 is cool enough ( t@xmath20= 4400k ) for co to exist in the photosphere , though the blue - shifted radial velocity ( @xmath655 km s@xmath13 ) relative to the systemic velocity of the star , argues against the presence of photospheric co. alternatively , co can exist in absorption in the disk if the effective temperature of the disk increases faster than the surface temperature , favored in cases of high mass accretion @xcite .
the co emission ( blue - shifted even more than the absorption ) could then be formed in an outflow wind , while the red - shifted ( @xmath650 km s@xmath13 ) br @xmath4 absorption line indicates in - falling material and accretion .
dg tau : we do not detect any sign of co overtone emission in our nov .
2001 spectrum , as has been reported in the past ( e.g. * ? ? ?
* ) , though this source is known to have variable emission on week long time scales ( reported in private communication ) .
we find a good fit to the absorption lines , deriving an effective temperature of 4000k and @xmath21 = 4.0 , with little @xmath22 rotation ( 24 km s@xmath13 ) , but significant veiling ( r@xmath24 = 2.0 ) .
l1551 irs5 : this prototypical bipolar molecular outflow has been well - studied for over 20 years ( see review by * ? ? ? * ) . though we did not detect hi br @xmath4 emission or absorption in november 2001 , this source has displayed a p - cygni h@xmath84 profile early - on , suggesting that it is an fu orionis class yso @xcite .
we detect strong h@xmath3 emission with a complex velocity structure at 2.2235 @xmath1 m , indicating kinematically active shocked molecular gas .
based on k - band absorption lines of na , mg , and al , we derive an effective temperature of 4800k , consistent with earlier estimates of its spectral type from spectroscopy and photometry @xcite .
we also derive a slow rotation rate ( @xmath22 = 31 km s@xmath13 ) and moderate veiling ( r@xmath29 = 1.0 ) in this embedded binary source .
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williams , c. g. 1982 , , 20 , 587 04016 + 2610 & tau & 4 4 43.10 & 26 18 57.9 & 4-nov-01 & 25.0 & 240 & yes + 04108 + 2803b & tau & 4 13 54.89 & 28 11 30.5 & 6-nov-01 & 20.0 & 110 & yes + 04158 + 2805 & tau & 4 18 58.17 & 28 12 23.7 & 6-nov-01 & 40.0 & 70 & yes + 04181 + 2655 & tau & 4 21 10.94 & 27 2 5.9 & 6-nov-01 & 30.0 & 120 & yes + dg tau & tau & 4 27 4.77 & 26 6 17.4 & 6-nov-01 & 4.0 & 240 & yes + gv tau s & tau & 4 29 23.66 & 24 33 2.0 & 6-nov-01 & 16.0 & 220 & yes + 04264 + 2433 & tau & 4 29 30.01 & 24 39 55.6 & 6-nov-01 & 48.0 & 190 & yes + l1551 irs5 & tau & 4 31 34.10 & 8 8 8.0 & 6-nov-01 & 20.0 & 100 & yes + 04295 + 2251 & tau & 4 32 32.07 & 22 57 30.3 & 5-nov-01 & 33.3 & 205 & yes + haro 6 - 28 & tau & 4 35 56.77 & 22 54 36.5 & 5-nov-01 & 20.0 & 110 & yes + 04361 + 2547 & tau & 4 39 13.43 & 25 53 19.2 & 5-nov-01 & 44.0 & 230 & no + 04365 + 2535 & tau & 4 39 34.99 & 25 41 46.7 & 4-nov-01 & 60.0 & 210 & no + 04489 + 3042 & tau & 4 52 6.87 & 30 47 17.2 & 4-nov-01 & 16.7 & 120 & yes + + crbr 12 & oph & 16 26 17.23 & -24 23 44.6 & 20-jun-03 & 50.0 & 50 & yes + crbr 85 & oph & 16 26 17.23 & -24 23 44.6 & 20-jun-03 & 120.0 & 15 & no + gss 30 & oph & 16 26 21.42 & -24 23 6.3 & 8-jul-01 & 30.0 & 395 & no + gy 21 & oph & 16 26 23.56 & -24 24 38.2 & 10-jul-01 & 16.7 & 170 & yes + 162636 & oph & 16 26 36.90 & -24 15 54.0 & 10-jul-01 & 15.0 & 100 & yes + gy 91 & oph & 16 26 40.43 & -24 27 15.1 & 21-jun-03 & 40.0 & 55 & yes + wl 12 & oph & 16 26 44.10 & -24 34 47.8 & 7-jul-01,8-jul-01 & 87.3 & 215 & yes + wl 1 & oph & 16 27 3.98 & -24 28 27.5 & 30-may-00 & 30.0 & 35 & yes + wl 17 & oph & 16 27 6.69 & -24 38 15.3 & 10-jul-01 & 30.0 & 140 & yes + gy 224 & oph & 16 27 11.25 & -24 40 47.0 & 10-jul-01 & 50.0 & 150 & yes + wl 19 & oph & 16 27 11.60 & -24 38 32.0 & 30-may-00 & 20.0 & 85 & yes + wl 3 & oph & 16 27 19.20 & -24 28 40.5 & 10-jul-01 & 40.0 & 95 & yes + wl 6 & oph & 16 27 21.62 & -24 29 51.3 & 19-jun-03 & 40.0 & 150 & no + irs 43 & oph & 16 27 26.96 & -24 40 50.0 & 7-jul-01 & 73.3 & 330 & yes + ylw 16a & oph & 16 27 27.84 & -24 39 31.9 & 8-jul-01,9-jul-01 & 38.0 & 170 & yes + ylw 16b & oph & 16 27 29.29 & -24 39 15.8 & 30-may-00 & 20.0 & 180 & no + vssg 17 & oph & 16 27 30.39 & -24 27 43.7 & 10-jul-01 & 6.0 & 160 & yes + irs 51 & oph & 16 27 39.53 & -24 43 14.1 & 8-jul-01,20-jun-03 & 50.0 & 330 & yes + irs 63 & oph & 16 31 35.53 & -24 1 28.3 & 30-may-00 & 30.0 & 140 & yes + irs 67 & oph & 16 32 1.05 & -24 56 44.6 & 7-jul-01,8-jul-01 & 80.0 & 330 & yes + + ec 38 & ser & 18 29 49.50 & 1 17 7.0 & 20-jun-03 & 90.0 & 70 & yes + ec 53 & ser & 18 29 51.20 & 1 16 42.0 & 7-jul-01,19-jun-03 & 104.0 & 120 & yes + svs 2 & ser & 18 29 56.79 & 1 14 46.1 & 29-may-00 & 12.0 & 150 & no + ec 89 & ser & 18 29 57.50 & 1 12 59.0 & 8-jul-01 & 40 & 40 & no + ec 88 & ser & 18 29 57.50 & 1 12 59.0 & 21-jun-03 & 60.0 & 60 & no + ec 91 & ser & 18 29 57.70 & 1 12 28.0 & 20-jun-03 & 60.0 & 50 & yes + ec 92 & ser & 18 29 57.70 & 1 12 52.0 & 7-jul-01 & 46.0 & 195 & yes + svs 20a & ser & 18 29 57.77 & 1 14 7.2 & 30-may-00 & 4.0 & 120 & yes + ec 94 & ser & 18 29 57.80 & 1 12 37.0 & 19-jun-03 & 60.0 & 80 & yes + ec 95 & ser & 18 29 57.90 & 1 12 47.2 & 30-may-00 & 20.0 & 140 & yes + ec 103 & ser & 18 29 58.70 & 1 14 26.0 & 8-jul-01 & 40.0 & 145 & no + ec 125 & ser & 18 30 1.90 & 1 14 1.0 & 21-jun-03 & 30.0 & 45 & yes + ec 129 & ser & 18 30 2.80 & 1 12 28.0 & 8-jul-01 & 38.7 & 210 & yes + + ts 13.1 & cra & 19 1 41.40 & -36 58 34.0 & 29-may-00 & 8.0 & 180 & yes + rcra irs5 & cra & 19 1 48.00 & -36 57 19.0 & 21-jun-03 & 10.0 & 70 & yes + ts 2.6 & cra & 19 1 49.78 & -36 58 12.0 & 29-may-00 & 4.0 & 190 & no + rcra irs9 & cra & 19 1 53.10 & -36 57 4.0 & 21-jun-03 & 53.3 & 90 & yes + + 03260 + 3111a & per & 3 29 10.49 & 31 21 51.2 & 5-nov-01 & 6.0 & 205 & yes + 03260 + 3111b & per & 3 29 10.49 & 31 21 51.2 & 5-nov-01 & 20.0 & 70 & yes + + mk standards + + gl 15a & m2 v & 0 18 18.70 & 44 1 23.3 & 29-may-00 & 1.0 & 110 & yes + gl 28 & k2 v & 0 40 48.40 & 40 11 14.7 & 29-may-00 & 2.0 & 115 & yes + gl 338b & k7 v & 9 14 26.50 & 52 41 15.9 & 30-may-00 & 0.7 & 200 & yes + gl 338a & m0 v & 9 14 28.70 & 52 41 15.3 & 29-may-00 & 2.0 & 185 & yes + gj 402 & m4 v & 10 50 52.40 & 6 48 31.6 & 30-may-00 & 5.0 & 110 & yes + gj 406 & m6 v & 10 56 29.10 & 7 0 56.1 & 30-may-00 & 4.0 & 75 & yes + hr 4358 & k3 iii & 11 14 1.80 & 8 3 38.0 & 30-may-00 & 1.3 & 180 & yes + hr 4496 & g8 v & 11 41 3.20 & 34 12 5.7 & 29-may-00 & 1.0 & 215 & yes +
hr 5150 & m1.5 iii & 13 41 36.70 & -8 42 11.0 & 30-may-00 & 0.2 & 130 & yes + lhs 2924 & m9 v & 14 28 43.22 & 33 10 35.3 & 20-jun-03 & 30.0 & 300 & yes + gj 569b & m8.5 v & 14 54 28.97 & 16 6 4.8 & 19-jun-03 & 16.0 & 265 & yes + gj 569a & m3 v & 14 54 29.31 & 16 6 3.4 & 19-jun-03 & 0.7 & 265 & yes + hd 131976 & m1 v & 14 57 26.79 & -21 24 26.8 & 21-jun-03 & 0.4 & 450 & yes + hr 5568 & k4 v & 14 57 27.90 & -21 24 56.0 & 29-may-00 & 1.0 & 240 & yes + vb 8 & m7 v & 16 55 35.16 & -8 23 45.4 & 21-jun-03 & 6.0 & 260 & yes + hd 157881 & k7 v & 17 25 45.10 & 2 6 37.0 & 21-jun-03 & 0.6 & 350 & yes + hd 166620 & k2 v & 18 9 37.32 & 38 27 26.3 & 21-jun-03 & 0.5 & 315 & yes + hd 168387 & k2 iii & 18 19 9.53 & 7 15 35.1 & 21-jun-03 & 0.1 & 250 & yes + hd 175225 & k1 iv & 18 51 34.88 & 52 58 30.0 & 21-jun-03 & 0.2 & 220 & yes + vb 10 & m8 v & 19 16 57.53 & 5 8 55.5 & 20-jun-03 & 10.0 & 295 & yes + hd 182572 & g8 iv & 19 24 58.22 & 11 56 40.2 & 20-jun-03 & 0.1 & 360 & yes + hd 184489 & m0 v & 19 34 39.96 & 4 34 58.1 & 20-jun-03 & 0.8 & 400 & yes + gj 1245a & m5.5 v & 19 53 54.58 & 44 24 49.8 & 19-jun-03 & 2.7 & 360 & yes + gj 791.2 & m4.5 v & 20 29 48.57 & 9 41 19.6 & 20-jun-03 & 3.0 & 255 & yes + gj 806 & m2 v & 20 45 4.24 & 44 29 57.6 & 19-jun-03 & 2.0 & 175 & yes + hd 201091 & k5 v & 21 6 55.19 & 38 45 9.3 & 21-jun-03 & 0.1 & 250 & yes + gj 4281 & m6.5 v & 22 28 54.52 & -13 25 25.0 & 21-jun-03 & 16.0 & 240 & yes
+ hd 219134 & k3 v & 23 13 17.87 & 57 10 7.1 & 21-jun-03 & 0.4 & 433 & yes + mg / al , na , or @xmath19co ( absorption ) & 11/13 & 16/20 & 9/13 & 3/4 & 2/2 & 41/52 + br @xmath4 ( absorption ) & 1/13 & 2/20 & 6/13 & 0/4 & 1/2 & 10/52
+ br @xmath4 ( emission ) & 9/13 & 13/20 & 9/13 & 3/4 & 0/2 & 34/52 + @xmath19co ( emission ) & 2/13 & 1/20 & 3/13 & 2/4 & 0/2 & 8/52 + h@xmath3 1 - 0 s(0 ) ( emission ) & 10/13 & 8/20 & 3/13 & 1/4 & 1/2 & 23/52 + 04016 + 2610 & 4500 & @xmath3868 & @xmath103.5 & @xmath380.05 & 46 & @xmath382.7 & 0.9 & @xmath380.02 & -12.8 & 4.9 + 04108 + 2803b & 3500 & @xmath3822 & @xmath103.5 & @xmath380.03 & 14 & @xmath383.3 & 1.1 & @xmath380.08 & 5.4 & 0.4 + 04158 + 2805 & 3500 & + 213 , -124 & 3.8 & + 0.40 , -0.11 & 26 & @xmath381.2 & 1.3 & + 0.21 , -0.19 & 5.9 & 0.1 + 04181 + 2655 & 4000 & + 202 , -301 & 4.2 & + 0.30 , -0.50 & 33 & + 1.3 , -0.9 & 0.2 & @xmath380.004 & 5.6 & 1.8 + dg tau & 4000 & + 105 , -33 & 4.0 & + 0.12 , -0.06 & 24 & @xmath382.0 & 2.0 & @xmath380.10 & 7.1 & 5.5 + gv tau s & 4500 & @xmath3825 & 4.4 & @xmath380.06 & 27 & @xmath381.6 & 1.8 & @xmath380.003 & -7.2 & 3.3 + 04264 + 2433 & 4000 & @xmath3841 & 3.9 & @xmath380.12 & 32 & @xmath382.4 & 1.4 & @xmath380.03 & 4.3 & 0.9 + l1551 irs5 & 4800 & @xmath38154 & 4.0 & @xmath380.14 & 31 & @xmath382.4 & 1.0 & @xmath380.30 & 1.2 & 2.6 + 04295 + 2251 & 3400 & @xmath3840 & @xmath103.5 & @xmath380.02 & 51 & @xmath381.9 & 0.3 & @xmath380.01 & 3.7 & 1.2 + haro 6 - 28 & 3400 & + 35 , -106 & 4.1 & + 0.06 , -0.31 & 17 & + 2.2 , -2.4 & 0.6 & + 0.11 , -0.04 & 3.5 & 0.4 + 04489 + 3042 & 3100 & @xmath3819 & @xmath103.5 & @xmath380.07 & 17 & @xmath382.2 & 1.4 & @xmath380.11 & -17.5 & 0.3 + + crbr 12 & 3600 & + 89 , -313 & 4.5 & + 0.09 , -0.71 & 40 & @xmath383.7 & 2.0 & + 0.64 , -0.57 & -8.5 & 1.0 + gy 21 & 3900 & @xmath3837 & 3.8 & @xmath380.09 & 24 & @xmath382.4 & 1.4 & @xmath380.03 & 1.5 & 0.8 + 162636 & 3700 & @xmath3856 & 4.3 & @xmath380.09 & 27 & @xmath384.7 & 1.9 & @xmath380.06 & 3.7 & 0.4 + gy 91 & 3300 & @xmath3830 & 3.7 & @xmath380.03 & 12 & @xmath380.9 & 0.3 & @xmath380.01 & 3.5 & 1.7 + wl 12 & 4000 & + 403 , -46 & 3.6 & + 0.71 , -0.12 & 35 & @xmath383.4 & 2.8 & + 0.71 , -0.12 & 1.2 & 2.1 + wl 1 & 3300 & @xmath3812 & @xmath103.5 & @xmath380.02 & 14 & @xmath380.8 & 0.8 & @xmath380.004 & -12.7 & 0.7 + wl 17 & 3400 & + 203 , -34 & 3.7 & + 0.4 , -0.05 & 12 & + 4.3 , -4.4 & 3.9 & + 0.77 , -0.80 & 4.4 & 1.8 + gy 224 & 3500 & + 306 , -116 & 3.7 & + 0.50 , -0.21 & 10 & @xmath385.1 & 4.4 & @xmath380.75 & 2.2 & 0.7 + wl 19 & 4200 & + 143 , -246 & 4.6 & + 0.19 , -0.44 & 19 & + 3.5 , -3.6 & 3.7 & + 0.31 , -0.37 & -16.6 & 10.3 + wl 3 & 3300 & + 202 , -28 & 3.7 & + 0.41 , -0.08 & 37 & @xmath382.1 & 0.5 & + 0.04 , -0.11 & -2.3 & 2.3 + irs 43 & 4400 & + 118 , -405 & 4.2 & + 0.32 , -0.61 & 48 & + 3.5 , -3.9 & 1.8 & + 0.11 , -0.20 & 1.8 & 19.0 + ylw 16a & 4400 & + 62 , -118 & 4.5 & + 0.10 , -0.22 & 29 & @xmath383.5 & 2.2 & + 0.23 , -0.25 & 3.7 & 9.8 + vssg 17 & 3500 & @xmath3842 & @xmath103.5 & @xmath380.08 & 43 & @xmath381.7 & 0.5 & @xmath380.005 & 1.0 & 9.7 + irs 51 & 4200 & + 208 , -116 & 3.7 & + 0.30 , -0.11 & 44 & @xmath382.8 & 1.8 & + 0.10 , -0.01 & 9.1 & 21.7 + irs 63 & 4200 & + 144 , -103 & @xmath103.5 & + 0.13 , -0.08 & 45 & + 3.1 , -2.9 & 1.7 & + 0.32 , -0.34 & -26.5 & 3.8 + irs 67 & 4300 & @xmath3891 & @xmath103.5 & @xmath380.10 & 55 & @xmath383.0 & 1.0 & @xmath380.02 & -0.7 & 11.6 + + ec 38 & 3400 & + 107 , -37 & @xmath103.5 & + 0.22 , -0.10 & 34 & + 2.5 , -2.7 & 0.9 & + 0.10 , -0.006 & 10.8 & 1.9 + ec 53 & 3400 & + 304 , -47 & @xmath103.5 & + 0.41 , -0.08 & 24 & @xmath384.3 & 1.8 & + 0.40 , -0.26 & 4.3 & 0.4 + ec 91 & 3600 & @xmath3874 & 3.8 & @xmath380.14 & 17 & @xmath380.9 & 1.1 & @xmath380.07 & 4.8 & 1.0 + ec 92 & 4200 & @xmath3817 & @xmath103.5 & @xmath380.02 & 47 & @xmath380.9 & 0.0 & + 0.002 & 9.4 & 6.5 + svs 20a & 5900 & + 205 , -228 & @xmath103.5 & @xmath380.23 & 52 & + 6.0 , -6.1 & 0.7 & + 0.1 , -0.007 & -8.3 & 55.6 + ec 94 & 4000 & + 301 , - 24 & 3.6 & + 0.30 , -0.05 & 36 & @xmath381.6 & 0.5 & @xmath380.004 & 5.8 & 4.3 + ec 95 & 4400 & + 115 , -57 & @xmath103.5 & + 0.10 , -0.03 & 56 & @xmath381.1 & 0.1 & @xmath380.002 & -14.5 & 22.8 + ec 125 & @xmath103000 & @xmath3826 & 4.0 & @xmath380.26 & 30 & @xmath382.4 & 0.8 & @xmath380.09 & 5.7 & 0.2 + ec 129 & 4400 & @xmath3874 & @xmath103.5 & @xmath380.06 & 35 & @xmath382.2 & 0.6 & @xmath380.004 & 10.0 & 5.2 + + ts 13.1 & 4400 & + 69 , -212 & @xmath84.5 & + 0.14 , -0.42 & 34 & + 2.6 , -2.8 & 2.7 & + 0.03 , -0.2 & 14.5 & ... + rcra irs5 & 3700 & + 203 , -107 & 3.7 & + 0.31 , -0.21 & 36 & @xmath381.1 & 0.3 & @xmath380.01 & 1.6 & ... + rcra irs9 & 3800 & + 100 , -9 & 4.1 & + 0.2 , -0.01 & 5 & + 1.9 , -1.6 & 0.0 & @xmath380.01 & 5.3 & ... + + 03260 + 3111a & 5600 & @xmath38112 & @xmath103.5 & @xmath380.13 & 76 & @xmath384.6 & 0.0 & @xmath380.01 & 6.2 & ... + 03260 + 3111b & 3400 & + 39 , -204 & 3.9 & + 0.05 , -0.30 & 23 & @xmath381.6 & 0.3 & @xmath380.04 & 3.9 & ... | we present high resolution ( r @xmath0 18,000 ) , high signal - to - noise , 2 @xmath1 m spectra of 52 infrared - selected class i and flat - spectrum young stellar objects in the taurus - auriga , @xmath2 ophiuchi , serpens , perseus , and corona australis dark clouds .
we detect key absorption lines in 41 objects and fit synthetic spectra generated from pre - main sequence models to deduce the effective temperatures , surface gravities , near - infrared veilings , rotation velocities , and radial velocities of each of these 41 sources .
we find these objects to span ranges in effective temperature , surface gravity , and stellar luminosity which appear similar to those of late spectral - type class ii sources and classical t - tauri stars .
however , due to significant but uncertain corrections for scattering and extinction , the derived luminosities for the embedded protostellar objects must be regarded as being highly uncertain .
we determine that the mean 2 @xmath1 m veiling of class i and flat - spectrum objects is significantly higher than that of class ii objects in the same region where both types of objects are extensively observed ( @xmath2 oph ) .
we find a significant fraction of our protostellar sample also exhibits emission lines .
twenty - three objects show h@xmath3 emission , usually indicative of the presence of energetic outflows .
thirty - four sources show hi br @xmath4 emission and a number of these exhibit profile asymmetries consistent with in - fall .
eight sources show significant @xmath5 co emission suggestive of emission from a circumstellar disk .
overall , these observations indicate that class i and flat - spectrum objects are self - embedded protostars undergoing significant mass accretion , although the objects appear to span a broad range of mass accretion activity . |
in 1967 - 73 , the four vela spacecraft ( named after the spanish verb _ velar _ , to keep watch ) , that where originally designed for verifying whether the former soviet union abided by the limited nuclear test ban treaty of 1963 , observed 16 peculiarly strong events ( klebesadel , olson and strong 1973 , bonnell and klebesadel 1996 ) . on the basis of arrival time differences , it was determined that they were related neither to the earth nor to the sun , but they were of cosmic origin .
therefore they were named cosmic gamma - ray bursts ( grbs hereafter ) .
grbs appear as brief flashes of cosmic high energy photons , emitting the bulk of their energy above @xmath0 0.1 mev .
they are detected by instruments somewhat similar to those used by the particle physicists at their laboratories , but the main difference is that grb detectors have to be placed onboard balloons , rockets or satellites .
the konus instrument on _ veneras 11 _ and _ 12 _ gave the first indication that grb sources were isotropically distributed in the sky ( mazets et al .
1981 , atteia et al . 1987 ) . based on a much larger sample , this result
was nicely confirmed by batse on board the _ cgro _ satellite , launched in the spring of 1991 , an instrument that has revolutioned the grb field ( meegan et al .
1992 ) . since then , batse is detecting about 300 grbs every year , but only very few can be localized accurately .
the apparent isotropy of the bursts in the sky ruled out the models dealing with neutron stars in the galactic plane , and it was rather interpreted in terms of grbs arising at cosmological distances , although the possibility of a small fraction of the sources lying nearby , within a galactic disc scale of few hundred pc , or in the halo of the galaxy , could not be discarded by that time .
another result was that the time profiles of the bursts are very different , with some grbs lasting a few ms and others lasting for several minutes .
in general , there was no evidence of periodicity in the time histories of grbs .
however there was indication of a bimodal distribution of burst durations , with @xmath125% of bursts having durations around 0.2 s and @xmath175% with durations around 30 s. a deficiency of weak events was noticed in the log @xmath2-log @xmath3 diagram , as the grb distribution deviates from the -3/2 slope of the straight line expected for an homogeneous distribution of sources assuming an euclidean geometry .
all these observational data led many researchers to believe that grbs are indeed at cosmological distances . however , the grb distance scale had to remain unknown for 30 years .
a comprenhensive review of these observational characteristics can be seen in fishman and meegan ( 1995 ) .
it was well known that an important clue for solving the grb puzzle was going to be the detection of transient emission -at longer wavelengths- associated with the bursts .
a review on the unsuccessful search for counterparts prior to 1997 can be seen in castro - tirado ( 1998 ) and references therein . here
i will summarize some results concerning nine selected bursts detected by the _ bepposax _ ( _ bsax _ ) and _ rossixte _ ( _ rxte _ ) satellites in 1996 - 98 . see also piran ( 1999 ) .
this was the first grb for which a precise position ( 5@xmath4 error radius ) was obtained by _
( in ' t zand et al . 1997 ) .
the bright radio - loud quasar 4c 49.29 at @xmath5 = 1.038 lies within the tiny grb error box .
the probability to find such object within the error box is 2 @xmath6 10@xmath7 ( greiner and heise 1997 , piro et al .
1997a ) , but no firm relationship could be established .
the position for this grb was rapidly distributed , allowing to perform deep optical imaging only 19 hr after the high energy event .
no optical variability was found within the error box down to b = 23 , r = 22.5 ( castro - tirado et al .
1997 , gorosabel et al .
1998a ) . a careful analysis of the x - ray data revealed a weak fading x - ray source within the grb error box ( feroci et al .
1998a ) , but its association to grb 970111 could not be definetively proven .
thanks to _ bsax _ , it was possible on 28 feb 1997 to detect the first _ clear _ evidence of a long x - ray tail -the x - ray afterglow- following grb 970228 .
a previously unknown x - ray source was seen to vary by a factor of 20 on a 3 days timescale .
the x - ray fluence was @xmath1 40 % of the gamma - ray fluence , as reported by costa et al .
( 1997b ) , implying that the x - ray afterglow was not only the low - energy tail of the grb , but also a significant channel of energy dissipation of the event on a completely different timescale .
another important result was the non - thermal origin of the burst radiation and of the x - ray afterglow ( frontera et al .
the precise x - ray position ( 1@xmath4 ) led to the discovery of the first optical transient ( or optical afterglow , oa ) associated to a grb , identified on 28 feb 1997 , 20 hr after the event , by groot et al .
the oa was afterwards found on earlier images taken by pedichini et al .
( 1997 ) and guarnieri et al .
( 1997 ) , in the rising phase of the light curve .
the maximum was reached @xmath1 20 hr after the event ( v @xmath1 21.3 ) , and followed by a power - law decay f @xmath8 t@xmath9 ( galama et al .
1997 , bartolini et al .
an extended source was seen at the oa position since the very beginning by both ground - based and _ hst _ observations ( van paradijs et 1997 , sahu et al .
hst _ observations taken 6 months after the event were reported by fruchter et al .
both the oa ( at v = 28 ) and the extended source ( v = 25.6 ) were seen .
the extended object surrounding the point - source was interpreted as a galaxy , according to the similarities ( apparent size , magnitude ) with objects in the _ hst _ deep field . despite exhaustive efforts in order to get spectroscopic measurements ,
no emission lines were found , implying that the redshift of this galaxy should lie in the range 1.3 @xmath10 @xmath5 @xmath10 2.5 ( fruchter et al .
1999 ) .
the second oa associated to a grb was discovered by bond ( 1997 ) within the grb 970508 error box , and observed 3 hr after the burst in unfiltered images ( pedersen et al .
the optical light curve reached a peak in two days ( r = 19.7 , castro - tirado et al .
1998a , djorgovski et al .
1997 , galama et al . 1998a ) and was followed by a power - law decay f @xmath8 t@xmath9 .
optical spectroscopy allowed a direct determination of a lower limit for the redshift of grb 970805 ( @xmath11 ) and was the first proof that at least a fraction of the grb sources lie at cosmological distances ( metzger et al .
the flattening of the decay in late august 1997 ( pedersen et al . 1998 , sokolov et al .
1998a ) revealed the contribution of a constant brightness source -the host galaxy- that was revealed in late - time imaging obtained in 1998 ( bloom et al .
1998a , castro - tirado et al . 1998b , zharikov et al .
the luminosity of the galaxy is well below the knee of the galaxy luminosity function , l @xmath0 0.12 @xmath12 , and the detection of deep mg i absorption ( during the bursting episode ) and strong [ o ii ] 3727 @xmath13 emission ( the latter mainly arising in h ii regions within the host galaxy ) confirmed @xmath5 = 0.835 and suggested that the host could be a normal dwarf galaxy ( pian et al .
1998a ) , with a star formation rate ( sfr ) of @xmath1 1.0 @xmath14 year@xmath15 ( bloom et al .
prompt vla observations of the grb 970508 error box allowed detection of a variable radio source at 1.4 , 4.8 and 8.4 ghz , the first radiocounterpart ever found for a grb ( frail et al .
the fluctuations could be the result of strong scattering by the irregularities in the ionized galactic interstellar gas , with the damping of the fluctuations with time indicating that the source expanded to a significantly larger size .
however vlbi observations did not resolve the object ( taylor et al .
the transient was also detected at 15 ghz ( pooley and green 1997 ) and as a continuum point source at 86 ghz with the iram pdbi on 19 - 21 may 1997 ( bremer et al . 1998 ) . a fe k@xmath16 line redshifted at @xmath5 = 0.835 in the x - ray afterglow spectrum
was reported ( piro et al . 1999 ) , and could be attributed to a thick torus surrouding the central engine ( mszros and rees 1998 ) .
this burst was detected by _
( remillard et al . 1997 ) and was followed up by _ asca _ and _ rosat _ ( murakami et al .
1997 , greiner et al . 1997 ) .
the x - ray spectrum as seen by _ asca _ is strongly absorbed ( yoshida et al . 1999 ) , suggesting that the event occurred in a dense medium .
the fact that no optical counterpart down to r = 23.8 was detected between 4 hr and 8 days after the event , could support the idea that the non - detection was due to photoelectric absorption ( groot et al .
an excess at 6.7 kev was foud by _
asca _ in the x - ray afterglow spectrum . if this is due to highly ionized fe , then @xmath5 @xmath1 0.33 ( yoshida et al . 1999 ) .
the third optical transient was related to grb 971214 and identified by halpern et al .
( 1997 ) as an i = 21.2 object that faded 1.4 mag in 1 day .
independently , this source was also noticed as suspicious by itoh et al .
further observations proved that the decay followed a power - law decline ( diercks et al .
1997 , castander et al .
1997 ) with f @xmath8 t@xmath17 , similar to , but steeper than , the previous grbs with optical counterparts .
grb 971214 was detected in the k - band 4 hr after the burst ( gorosabel et al . 1998b ) and rapidly decreasing in the j - band ( tanvir et al .
however , no source was detected at 850 @xmath18 m at the james clerk maxwell telescope .
the upper limit was 1 mjy on dec 17 - 22 ( smith et al .
spectroscopy of the host galaxy ( r = 25.6 ) one month later reveled a strong emission - line attributted to ly-@xmath16 redshifted at @xmath5 = 3.42 ( kulkarni et al .
1998a ) , implying a sfr of 1.0 @xmath19 0.5 @xmath14 year@xmath15 , similarly to other galaxies at comparable redshift .
the emitted energy , assuming isotropic emission , was 3 @xmath6 10@xmath20 erg .
together with grb 970111 , this burst is among the top 2@xmath21 burst with larger gamma - ray fluences as detected by batse .
the detection of a variable radiosource ( taylor et al .
1998 ) within the grb error box led to the indentification of an optical transient ( klose et al .
1998 , palazzi et al . 1998 ) .
the evidence for a dusty host ( r - k = 4.7 ) was confirmed by a scuba detection at 850 @xmath18 m ( smith et al .
1999 ) and fruchter ( 1999 ) proposed that the host could lie at @xmath5 @xmath1 5 . in that case , if the gamma - rays were radiated isotropically , the implied energy would be 5 @xmath6 10@xmath22 erg !
a peculiar supernova ( sn 1998bw ) has been found in the wfc error box for this soft grb ( galama et al .
the sn lies in the galaxy eso 184 - 82 ( at @xmath5 = 0.0085 ) .
the fact that the sn event occurred within @xmath19 1 day of the grb event , together with the relativistic expansion speed derived from the radio observation ( kulkarni et al .
1998b ) strengths such a relationship . in that case , the total energy released would be 8 @xmath6 10@xmath23 erg .
however , the fact that a fading x - ray source -as in _ all _ the previous cases- unrelated to the sn was detected by _
bsax _ in the grb error box ( pian et al .
1998b , piro et al . 1998 ) cast some doubts on the sn / grb association ( graziani et al .
1999 ) .
a variable radiosource was found by frail et al .
( 1998 ) , and the optical counterpart was independently discovered by frail et al .
( 1998 ) and zapatero - osorio et al .
( 1998 ) in the error box provided by _ rxte_. the host galaxy is the brightest one so far detected ( r = 22.5 , h = 20.5 ) according to bloom et al .
( 1998b ) and castro - tirado et al .
optical spectroscopy revealed the [ o ii ] emission line at @xmath5 = 0.966 , as well as some fe ii y mg ii absorption ones .
the derived sfr is @xmath1 63 @xmath14 year@xmath15 ( djorgovski et al .
the released energy during the grb event amounts to @xmath13 @xmath6 10@xmath24 erg .
further x - ray afterglows were observed by _
bsax _ and _ rxte _ in 1998 ( grb 980706 , grb 981220 and grb 981226 ) .
exponents for the power - law decay in the x - rays and in the optical are in the range @xmath16 = 1.10 - 2.25 for a dozen of bursts .
these results are given on table 1 whereas table 2 summarizes the properties of the host galaxies found so far .
see also ( greiner 1999 ) for an updated information .
.grbs detected by _
bepposax _ and _ rxte _ in 1996 - 98 [ cols="<,<,<,<,<",options="header " , ]
the observational characteristics of the grb counterparts can be accommodated in the framework of the relativistic fireball models , first proposed by goodman ( 1986 ) and paczyski ( 1986 ) , in which a compact source releases 10@xmath20 ergs of energy within dozens of seconds .
see also mszros et al .
( 1994 ) , mszros and rees ( 1997 ) , tavani ( 1997 ) , vietri ( 1997 ) , waxman ( 1997 ) and wijers et al .
the opaque radiation - plasma accelerates to relativistic velocities ( the fireball ) .
the blast wave is moving ahead of the fireball , and sweeps up the interstellar matter , producing an afterglow at frequencies gradually declining from x - rays to visible and radio wavelenghts .
an extensive discussion is given by piran ( 1999 ) .
the properties of the blast wave can be derived from the classical synchrotron spectrum ( ginzburg and syrovatskii 1965 ) produced by a population of electrons with the addition of self absorption at low frequencies and a cooling break ( sari , piran and narayan 1998 ) .
thus , the four main quantities involved are : \i ) the synchrotron frequency : the population of electrons has a power - law distribution of lorentz factors @xmath25 following d@xmath2/d@xmath25 @xmath8 @xmath26 above a minimum lorentz factor @xmath25 @xmath27 @xmath28 , corresponding to the synchrotron frequency @xmath29 ; \ii ) the break frequency : if the electrons are energetic they will cool rapidly for a break frequency @xmath30 @xmath31 @xmath29 , and low energy electrons will have always slow cooling for @xmath30 @xmath32 @xmath29 , \iii ) the self - absorption frequency : synchrotron self absorption becomes important below a critical frequency @xmath33 , and \iv ) the maximum flux f@xmath34 .
after some time , the evolution of the blast wave is adiabatic , and @xmath30 @xmath32 @xmath29 implying that f@xmath35 @xmath8 @xmath36 for @xmath29 @xmath10 @xmath37 @xmath31 @xmath30 ; f@xmath35 @xmath8 @xmath38 for @xmath37 @xmath32 @xmath30 y f@xmath35 @xmath8 @xmath39 for @xmath37 @xmath31 @xmath29 . for @xmath33 @xmath40 @xmath29 , f@xmath35 @xmath8 @xmath41 .
the time evolution of the flux as a function of a given frequency is a function of @xmath30 ( @xmath8 t@xmath42 ) and @xmath29 ( @xmath8 t@xmath43 ) . for @xmath37 @xmath10
@xmath30 the flux decays following a power - law with exponent @xmath44 , f @xmath8 t@xmath45 with @xmath16 = ( 2@xmath463@xmath47)/4 , thus allowing to determine @xmath47 . thus , the determination for every grb of the six observables @xmath29 , @xmath30 , @xmath33 , f@xmath34 , @xmath47 ( from the multiwavelength spectrum , see fig .
2 ) and @xmath5 ( from optical or x - ray spectroscopy ) allows to obtain the total energy per solid angle ( e@xmath48 ) , the fraction of the shock energy in electrons ( @xmath49 ) , the fraction of the shock energy in post - grb magnetic fields ( @xmath50 ) and the density of the ambient medium ( @xmath51 ) .
see for example , wijers and galama ( 1998 ) .
how does the grb take place ?
the fireball model is based on the existence of a `` central engine '' .
however , current observations have been unable to give any insight on this issue .
until 1994 , the number of theoretical models amounted up to 150 ( see nemiroff 1994 ) , but once the cosmological nature of grbs was established , only those models dealing with mechanisms able to produce 10@xmath52 erg in a few seconds were taken into consideration .
they can be classified into two groups : \i ) coalescence of neutron stars in a binary system ( narayan et al .
1992 ) : lifes of such systems are of the order of @xmath1 10@xmath53 years , and large escape velocities are usual , putting them far away from the regions where their progenitors were born .
the likely result is a kerr black hole ( bh ) , and the energy released energy during the merger process is @xmath1 10@xmath22 erg .
it is also possible that a @xmath1 0.1 @xmath14 accretion disk forms around the bh and is accreted within a few dozen seconds , then producing internal shocks leading to the grb ( katz 1997 ) .
there are variations of these models where one or two components are substituted for black holes ( paczyski 1991 ) .
\ii ) a `` failed '' type - i sn ( bodenhaimer and woosley 1983 , woosley 1993 ) or _ hypernova _ ( as it has been called by paczyski ( 1998 ) on the basis of the observational consequences ) : very massive stars ( wolf - rayet ) collapse forming a keck bh and a 0.1 - 1 @xmath14 torus .
the matter is accreted at a very high rate and the energy is extracted via the rotational energy of the bh or via the accretion energy from the disk . in any case , a `` dirty fireball '' , is produced reaching a luminosity @xmath1 300 times larger that than of a normal sn .
this would happen every @xmath1 10@xmath54 yr . in this scenario ,
grbs would be produced in dense enviroments near star forming regions ( see also macfadyen and woosley 1999 ) and grbs might be used for deriving the sfr in the universe ( totani et al .
1998 , krumholz et al . 1998 ) .
the existence of x - ray afterglow in _ most _ bursts is confirmed . out ot 15 _ bsax _ pointings , 11 revealed a strong afterglow , and 4 displayed faint ones , leading to the detection of optical / ir / radio counterparts in 1997 - 98 .
very promising seems to be the determination of @xmath5 for the host galaxies by means of absorption edges or emission lines in the x - ray afterglow .
this requires prompt x - ray follow - up , as was achieved for grb 970508 and grb 970828 .
however , only the population of bursts with durations of few seconds has been explored .
short bursts lasting less than 1 s , like grb 980706 , that follow the -3/2 slope in the log @xmath2-log @xmath3 diagram ( in contrast to the longer bursts ) remain to be detected at longer wavelengths .
it is generally believed is that internal shocks produced by the @xmath55central engine@xmath55 are responsible for the @xmath56-ray emission , whereas the slowing down of a relativistic shell on the interstellar medium ( an external shock ) would cause the post - grb emission at longer wavelengths ( the afterglow ) .
energy releases of @xmath1 10@xmath22 erg ( as derived for grb 980329 ) are difficult to reconcile with theoretical models and non - isotropic emission , such as intrinsic beaming appears as the most plaussible resolution of this problem .
_ bsax _ and _ rxte _ have opened a new window in the grb field and it is widely accepted now that most grbs , if not all , lie at cosmological distances .
it is expected that _ bsax _ ,
_ rxte _ and _ cgro _ will facilitate the discoveries of many other counterparts and , together with the new high - energy observatories ( _ axaf _ , _ spectrum x/@xmath57 _ , _ xmm _ , _ integral _ , _ hete 2 _ ) and , hopefully _ swift _ and _ ballerina _ , will help to solve the long - standing gamma - ray burst mystery .
castro - tirado , a. j. 1998 , in _ ultraviolet astrophysics : beyond the iue final archive _ , sevilla , spain , november 1997 , eds : gonzalez - riestra , r. , wamsteker , w. , harris , r. , esa conference proceedings sp-413 , pp .
659 - 668 .
( http://xxx.lanl.gov/abs/astro-ph/9803007 ) | grbs have remained a puzzle for many high energy astrophysicists since their discovery in 1967 . with the advent of the x ray satellites _
bepposax _ and _ rossixte _ , it has been possible to carry out deep multi - wavelength observations of the counterparts associated with the grbs just within a few hours of occurence , thanks to the observation of the fading x - ray emission that follows the more energetic gamma - ray photons once the grb event has ended . the fact that this emission ( the afterglow ) extends at longer wavelengths , has led to the discovery of the first optical / ir / radio counterparts in 1997 - 98 , greatly improving our understanding of these sources .
now it is widely accepted that grbs originate at cosmological distances but while the observed afterglow satisfies the predictions of the relativistic fireball models , the central engines that power these extraordinary events remain still unknown .
detailed results for nine selected grbs are presented as well as a summary of the grb counterparts and host galaxies found so far . |
the cdf ( collier detector at fermilab ) experiment is a general purpose experiment for the studies of @xmath1 collisions at the tevatron collider located at the fermi national accelerator laboratory ( fermilab ) , in batavia , illinois , u.s .. the tevatron accelerator is the highest - energy proton - antiproton accelerator machine in the world .
the tevatron accelerator @xcite and the cdf(d0 ) @xcite detectors have upgraded since the termination of run i experiment in 1996 .
the accelerator complex had added the main injector , replacing the old main ring , to inject higher intensity beams to the tevatron and to produce more anti - protons to be used for collision .
the tevatron beam energy has been increased and it resulted in a center - of - mass energy of 1.96 tev in run ii from 1.8 tev in run i. the instantaneous luminosity has improved steadily since the beginning of run ii , and is marking with a new record .
the record value at this conference was 6.3 @xmath2 10@xmath3 @xmath4s@xmath5 which was about 3 times higher than the run - i record value and is close to the run - iia goal of 8.6 @xmath2 10@xmath3 .
the integrated luminosity delivered to each experiment has exceeded 450 pb@xmath5 , and with about 80% of them recorded by the detector .
the cdf detector has undergone the upgrade of a completely new tracking and forward calorimetry systems , a extension of muon tracking , and lots of minor changes as well as daq upgrades . since the tevatron run - ii program has officially started in march 2001 , the cdf is extensively exploring a new physics beyond standard model . measuring
the high @xmath0 phenomena to establish the sm in electroweak sector is also important in that it may give us a knowledge in nature about symmetry breaking . in this paper , we describe our recent results for the high @xmath0 physics .
since the great success of the standard model in the recent decades , there has been no doubt that the gauge theories are capable to describe the interactions between elementary particles . with larger colliding energy available to probe higher energy scattering events , a high precision measurement may open a beautiful structure among them .
the cdf has performed studies of various aspects of the weak boson properties .
they are cleanly identified with their decays to leptons ( mostly electrons or muons ) .
the leptonicaly decaying z boson is identified by using two clean high @xmath0 lepton candidates within the mass range of z boson . the invariant mass distribution for z boson candidates is shown in figure [ zinvms ] .
the production cross sections are measured to be @xcite @xmath6 in good agreement with a theory prediction of 251.3 @xmath7 5.0 pb at nnlo level with mrst @xcite .
decays of w bosons are distinguished by one high @xmath0 lepton and missing transverse energy from undetectable neutrino .
the transverse mass distribution for w boson candidates is shown in figure [ wtransms ] , where the transverse mass is given as @xmath8 @xmath9 @xmath10}$ ] .
the production cross sections are measured to be @xcite @xmath11 in good agreement with a theory prediction of 2687 @xmath7 54 pb at nnlo level with mrst @xcite . in figure [ cs_vs ]
, we summarize the single boson production cross sections as a function of the center - of - mass energy starting from earlier measurement at cern together with our previous measurements of run i. we can see a good agreement with the theory predictions .
the ratio of the z and w boson production cross sections is used as an indirect measurement of the w boson mass and width .
the ratio is defined as @xmath12 using a theoretical calculation of the ratio of production cross sections and a measured value of the branching ratio of z boson at lep experiment @xcite , we can extract the leptonic branching ratio or total width of w boson , @xmath13 the current world average for the w boson width is shown in figure [ gamma_s ] .
one of remarkable achievements in cdf ii experiment is that the track reconstructions are possible at the trigger level . as a result of this , tau candidate events are able to be triggered , then statistically accessible to study various tau lepton physics .
reconstruction of the tau decay is accomplished by finding an energy cluster in the calorimeter with isolated tracks matched to it .
individual @xmath14 particles from the tau decay are reconstructed using detectors in the calorimeter at shower max , and the combined invariant mass of the cluster is required to be less than the mass of the tau . obtained production cross section of z and w decaying into tau leptons
are @xcite @xmath15 the lepton universality can be measured with three generations of lepton family . calculating the r ratio for each channel separately , we can derive the ratio of the coupling constants , @xmath16 these are all consistent with the sm predictions . in z boson production ,
the forward backward asymmetry yields a measurement of @xmath17 ( mixture with up- and down - type quark in pdf ) and a search for higher mass z bosons .
this is unique tests only at the tevatron .
the asymmetry is defined as @xmath18 where @xmath19 is the polar angle between the incoming proton and the outgoing lepton .
the distributions of the asymmetry around z - pole and in high mass region are shown in figure [ afb_zoom ] and [ afb ] , respectively .
both distributions agree with the sm predictions . extracting @xmath17 from those shape
, we can obtain @xcite @xmath20 an non - abelian gauge theory describing the electroweak interactions induces the three- and four - point self - couplings of gauge bosons .
measurements of the pair production of the gauge bosons is a fundamental tests for those self - couplings .
the cross section for @xmath21 productions has been measured in the _ dilepton _ channel at cdf @xcite .
the azimuthal angle between the missing transverse energy and the closest lepton for it is uesd to enhance the candidate events , which is shown in figure [ wpairdphimet ] .
the measured value is @xmath22 which is consistent with the sm expectations @xcite .
inclusive w@xmath23 and z@xmath23 productions are also studied @xcite .
the photon can be radiated from the initial state quark and final state lepton in addition to from the w boson with the triple gauge coupling which contribution is presumably enhanced in high @xmath24 region .
the @xmath24 spectra probes the anomaly to that triple gauge boson coupling .
in figure [ wgammaphoet ] , we show the photon @xmath24 distribution , and no excess is observed .
the measured production cross sections are @xmath25 those results are compared with the nlo calculation @xcite of 19.3 @xmath7 1.3 pb for w@xmath23 production and 5.4 @xmath7 0.4 pb for z@xmath23 production , and both results are a good agreement with the theoretical calculation
. a more direct test of the gauge couplings can be performed if photon angular distributions of those events are studied and radiation amplitude zero is looked for directly .
since the discovery of the top quark in 1995 by the cdf and d0 collaborations @xcite , the studies of the top quark properties have been the most important mission in run ii physics program .
while the existence of the top quark demonstrates correctness of the standard model , nothing tells us about the hierarchy problem of the mass gap among the quark family and generations .
detailed studies of their properties will reveal something about a fundamental nature of the matter . at tevatron ,
the production mechanism is a top and anti - top quarks pair creation via quark - antiquark annihilation ( 85% ) or via gluon fusion ( 15% ) .
then , the top quark is assumed to decay into w boson and bottom quark immediately .
the final observed signature thus depends on the w bosons decay from top quarks .
the analysis strategy is basically categorized by the _
( @xmath26 , @xmath277% of all @xmath28 events ) , _ lepton+jets _ ( @xmath29 , @xmath2735% ) , and _ all hadronic _
( @xmath30 , @xmath2744% ) channels .
the analysis is also categorized by the b - tagging algorithms , but combined results are only presented in this section .
the _ dilepton _ channel is characterized by two leptons with high transverse momentum and missing energy from the undetected neutrinos and two jets from the b quarks .
this channel is relatively clean to the other channels , but statistically limited . to increase the overall acceptance of two leptons , the selection criteria to identify the leptons
is loosen , while the tight selection does not suffer from the background contamination .
figure [ topdilepton ] shows the jet multiplicity distribution of the candidate events in case of one tight lepton plus isolated track data set .
those combined result for the production cross section is @xcite @xmath31 in good agreement with a theory prediction of 6.7@xmath32 pb at nlo level with assuming the top mass of 175 gev @xcite .
the _ lepton+jet _ channel requires one lepton and 4 more jets in the final state .
the sample size is larger than the _ dilepton _ sample , but there is a significant background contamination from the associated production of w boson with jets . the purity of the sample can be improved by the identification of at least one b - quark jets .
we typically use two different b - tagging algorithms .
the first one makes used of the long lifetime of the b hadrons to reconstruct a displaced secondary vertex .
the second one identifies the soft muon from semileptonic b - decay .
the signal to noise ratio can be further improved by requiring the scalar sum of the energy in the event , @xmath33 , to be greater than 200 gev .
the jet multiplicity distribution of these candidate events by the displaced secondary vertex technique with @xmath33 @xmath34 200 gev are shown in figure [ secvtxttprod ] .
the excess of events in the bins @xmath35 @xmath36 3 bins is nicely described after the inclusion of top contributions .
the production cross sections from both b - tagging algorithms are measured to be @xcite @xmath37 instead of counting signal and background events , one can extract the fraction of @xmath28 events in the lepton + jets sample by fitting one or more kinematic variables in the data to the expected shapes from signal and backgrounds .
as already mentioned , the @xmath33 variable is strong discrimination power of signal to backgrounds .
figure [ htdis ] shows the @xmath33 distribution with the expected shapes of signal and backgrounds .
at least 4 more jets are required for the fitting to @xmath33 in this plot .
the estimated production cross section is @xcite @xmath38 summary of the measured @xmath28 cross section from cdf is presented in figure [ allxsec ] .
note that there are many other measurements using various different methods @xcite .
recent combined result of the top quark mass measurements by cdf and d0 collaboration in run i experiment is reported to be 178.0 @xmath7 4.3 gev @xcite .
global ew fits place a 95% cl upper bound on the higgs mass of @xmath27260 gev @xcite .
the precise measurement of the top quark mass will further constrain the mass bound .
the run ii goal of the mass measurement is to control under an uncertainty of 2 - 3 gev .
the top mass measurement at cdf largely depends on the fitting techniques to reconstruct the event topology .
first , the kinematic equations of the @xmath28 decay chain are imposed , and then some kinematical variables are fold by the measured quantities out of 16 free parameters in each event . in _
lepton+jets _ channel , there are 24 configurations for the jets .
for each configuration , an event @xmath39 is calculated and minimized .
the @xmath39 takes into account the detector resolution on the measured quantities as well as the w boson and top quark widths .
the configuration that yields the minimum @xmath39 is taken as the configuration for the event .
the distribution of the reconstructed mass is compared and fit to monte carlo generated templates with known input top masses .
the cdf has measured the mass of the top quark in _
lepton+jets _ channel using traditional `` template '' methods @xcite , where one mass is reconstructed per event and the resulting mass distribution compared against template distributions from the simulated @xmath28 events of varying masses .
the multivariate templates method @xcite is used weighting events according to the probability for the chosen jet - parton assignment to be correct .
the dynamical likelihood method @xcite uses the probability formed from the @xmath28 matrix element to utilize maximal information from the events .
this method @xcite results in the best value of the top quark mass of @xmath40 figure [ dlmmass ] shows the top mass distribution by dlm analysis .
the systematic uncertainty is dominated by the measurement of the jet energy . in _ dilepton _ channel , due to the presence of two unfold neutrinos , one
more extra conditions driven by the monte carlo simulation are imposed on the kinematical variables for the neutrinos .
the best fit returns @xmath41 by the neutrino weighting method @xcite
. the other top mass measurements using _ dilepton _ channel can be seen in @xcite .
summary of the top mass measurement from cdf is presented in figure [ alltmass ] .
the w boson coming from top decay can be either left - handed ( l ) or longitudinally ( 0 ) polarized . those fraction for both mixture states
is predicted in the standard model as @xmath42 where b - quark mass is neglected and top mass is assumed to be 175 gev .
it is important to check this fraction of the longitudinal component which tells us the symmetry breaking mechanism to give a mass of w boson .
since the polarization state of the w boson controls the angular distribution of the decaying leptons , cdf has precisely measured the lepton @xmath0 spectra and angular distributions .
the estimated @xmath43 value from those distributions constrains to be @xcite @xmath44 which is consistent range of the standard model prediction .
the single top production is linked to the direct measurement of the quark mixing among third generation , @xmath45 , in ckm matrix @xcite .
the dominant production mechanics are s - channel drell - yan production and t - channel associated w boson scattering process .
those production cross sections are proportional to the @xmath45 . if abnormal cross section is observed , it is directory addressed to the coupling with the wtb electroweak interaction .
however , the single top event has lower jet multiplicities than that of @xmath28 production events , which suffers significant backgrounds from w + jets events .
the optimized search is proposed in @xcite .
the cdf has searched the single top candidate events , and no candidate observed .
we set a limit of @xcite @xmath46
there are several reasons to motivate a new physics beyond the standard model : the electroweak symmetry breaking , hierarchy problems , gravitational force , and so forth .
those issues inspire a new theory beyond the standard model such as supersymmetry ( susy ) , grand unified theories ( gut ) , technicolor ( tc ) , and extra dimensions ( ed ) .
these models predict new signatures that can be seen at the experiments with a small production cross section to be compared with the typical qcd events at tevatron .
it is often hard to distinguish new phenomena from the sm background processes . jet based strategies are overwhelmed by the sm processes , so that the cdf has searched lepton based signatures even through the rates are often suppressed . in this section ,
a couple of selected studies are only described .
readers may refer @xcite for details .
a heavy partner of the z boson , z boson @xcite , is a by - product predicted by many models of gut , ed , and little higgs @xcite models .
the cdf has searched the excess in high mass drell - yan process using _ dilepton _ events .
the invariant mass distribution of _ dilepton _ events is shown in figure [ dyeemass ]
. no excess is found , and limits is set the cross section limits as a function of the spin state since the experimental acceptance changes depending their spin state of the resonance particles .
mass limits for the rpv @xmath47 ( spin-0 ) , z @xcite ( spin-1 ) , and rs - graviton @xcite ( spin-2 ) are set @xcite .
the _ dijet _ events are also used to search for the high mass resonance peak , and limits for some models are set from the cross section limit as shown in figure [ dijetmass ] . with high statistic data in run ii , cdf and d0 experiments
will start reaching sensitivity to production of low - mass higgs bosons beyond the limits from lep experiment .
the standard model higgs boson is predominantly decaying into @xmath48 in the low - mass region .
the most promising channel is the associated production with w or z boson followed by leptonically decay . in high - mass region up to about 180 gev , higgs boson produced via gluon fusion might be observable in the decay to ww . in higgs doublet model , the coupling of the higgs bosons to b - quarks
can be significantly enhanced which allows us to search for the higgs bosons produced in association with b - quarks .
the previous sensitivity studies can be seen in @xcite .
the cdf has searched the higgs boson(s ) , and set the cross section limits as a function of higgs mass for the searches of the associated production with w boson ( @xmath49 ) @xcite and higgs ww decay channel ( @xmath50 or @xmath51 ) @xcite .
the analysis strategies are the same as the top quark measurement in _
lepton + jets _ channel and the ww cross section measurement .
the sensitivity plot is shown in figure [ hsen ] .
also , many other higgs searches are on - going .
introduction of supersymmetric particles has attractive features for lots of aspects : higgs self - coupling is converged without fine tuning , all forces except gravity merging in gut scale , and resulting in many new particles in tev region , even in cosmology . in this section
, a search of gauge - mediated susy breaking ( gmsb ) scenario is only described .
many results can be seen in @xcite .
gmsb can produce a final state of two photons and large missing energy from the lightest supersymmetric particle ( lsp ) , where the lightest neutralino can decay into photon and gravitino ( lsp ) .
thus , _ diphoton _
candidate events is used in this analysis .
the dominant background source is qcd jets events which makes fake missing @xmath24 and photon signals due to the mismeasurement of jets and interaction vertices . after requiring large missing @xmath24 with two identified photons ,
no candidate is found , and thus set limits @xcite , @xmath52 where @xmath53 is a susy - breaking scale .
the sensitivity plot is shown in figure [ gmsbsen ] .
the leptoquark ( lq ) model @xcite is natural consequence from gut theories .
the relation between quark and lepton quantum numbers can rule out a triangle anomaly @xcite , so that the theory is renormalizable .
the leptoquarks are color triplet bosons carrying both lepton and quark quantum numbers , they can be scalar or vector bosons . at tevatron
, they can be pair produced through strong interactions and decay either into a charge lepton and a quark ( @xmath54 = 1 ) or a neutrino and a quark ( @xmath54 = 0 ) .
the cdf has searched two scenarios of @xmath54 = 1 and @xmath54 = 0 for the scalar type leptoquarks .
final signatures are @xmath55 ( @xmath54 = 1 ) , @xmath56 ( @xmath54 = 0 ) , and @xmath57 ( @xmath54 = 0.5 ) for the first and second generations of the scalar leptoquarks .
the results are shown in figure [ leptoquarkbeta1 ] and [ leptoquarkbeta2 ] in case of @xmath54 = 1 and @xmath54 = 0 , respectively , and limits is set @xcite .
a search for the third generation leptoquark is also in progress . in the compositeness model for the substructure of quarks and leptons ,
the excited states of those particles are considerable @xcite .
the cdf has searched the excited electron , @xmath58 , which could be produced through either contact interaction or gauge mediated interactions , and decays into an electron and photon .
the signature would be events with @xmath59 with making a mass peak of the excited electron with @xmath60 .
there is no observation of any deviation from the standard model backgrounds .
the upper limits are set at 95% c.l . in the parameter space of the excited electron mass and the @xmath61/@xmath53 for the contact interaction model or @xmath62/@xmath63 for the gauge mediated model @xcite .
figure [ excitedelegm ] and [ excitedeleci ] shows the excluded region for the two models , respectively .
the tevatron run ii program is in progress since 2001 .
the cdf experiment have accumulated roughly five times more data than in run i , with much improved detectors .
many physics results have been produced and more are expected in the near future .
preliminary results on the measurements at cdf are presented , most of all will be published in the near future
. for the electroweak physics , production of weak vector bosons has been measured at a new center of mass energy .
the single boson productions have studied , and some fundamental parameters are very precisely driven .
the w boson mass will be measured with the accuracy of 25 mev with a well - established knowledge of the detector .
pairs of gauge bosons are now being produced in reasonably high statistics , and interactions among gauge bosons will be studied in detail . for the top physics ,
the top quark measurements have been re - established since run i experiment , and new measurements just came out in run ii experiment . the top cross section and mass measurements have improved systematics with various analysis techniques . with large data samples
, the top mass will be measured with the accuracy of 2 gev .
the studies of the top quark property will push forward with the understandings of top physics . for new physics searches ,
many results are improved and marked new limits . in the next a few years , the tevatron is an unique opportunity to directly search for new physics beyond the standard model .
the cdf is aggressively looking for new phenomena .
many other studies not fully covered in this paper are on - going .
we hope to see many exciting results from the tevatron .
the author would like to thank all the people in the cdf collaboration , and especially dr .
pasha murat for the assistance that he provided the information during the conference .
the author would also like to thank the organizers of the conference .
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cdf collaboration , fermilab - pub-04 - 287-e ( 2004 ) , submitted to _ phys | the tevatron run ii program is in progress since 2001 .
the cdf experiment have accumulated roughly five times more data than in run i , with much improved detectors .
preliminary results from the cdf experiment are presented .
we focus on the recent high @xmath0 physics results in tevatron run ii program .
# 1#2#3#4#1 * # 2 * ( # 3 ) # 4 * recent results of high @xmath0 physics at the cdf ii * + soushi tsuno ( cdf collaboration ) + department of physics , faculty of science , okayama university + 3 - 1 - 1 tsushima - naka , okayama 700 - 8530 , japan + |
in last years the study of the properties of @xmath0 mesons and especially its weak decays attracts attention of both theorists and experimenters .
indeed the investigation of such decays is important for the independent determination of the cabibbo - kobayashi - maskawa ( ckm ) matrix elements , studying the @xmath1-violation , testing the standard model and a `` new physics '' models .
new precise data are coming from the experiments on large hadron collider ( lhc ) which significantly extended the number of the observed @xmath0 decay channels @xcite .
in the recent paper @xcite we considered the weak @xmath0 decays to the ground and excited states of charmed mesons .
such decays are the dominant decay channels of the @xmath0 meson .
we calculated the weak decay form factors in the framework of the relativistic quark model with the qcd - motivated interquark potential .
good agreement of our predictions for the semileptonic and nonleptonic decay branching fractions with experimental data has been found .
here we extend our analysis to the consideration of the ckm suppressed @xmath0 decays to strange mesons .
first we calculate the corresponding weak decay form factors .
the characteristic features of the heavy - to - light @xmath2 transitions are the presence of the light @xmath3 meson in the final state and a very broad accessible kinematical region .
therefore it is important to consistently take into account the relativistic effects , which give substantial contributions , and to reliably determine the momentum dependence of the form factors .
it is necessary to point out that most of the available theoretical approaches permit to evaluate the form factors either at some fixed point ( of zero or maximum recoil of a final light meson ) or determine the momentum dependence of the form factors in a restricted kinematical range . as a result
they require ad hoc assumptions about the @xmath4 dependence of form factors or their extrapolations , which also rely on specific models .
the advantage of our model consists in its ability to explicitly determine the corresponding decay form factors as the overlap integrals of meson wave functions in the whole kinematical range without any additional assumptions and extrapolations . in our calculations of the decay form factors we use the wave functions of the @xmath0 and @xmath3 mesons obtained previously in their mass spectra evaluations @xcite .
in table [ tab : smm ] we compare our predictions for the masses of the ground state and lowest orbitally excited strange mesons @xcite with available experimental data @xcite .
we find satisfactory agreement of our predictions with data .
note that in our mass spectrum calculations all relativistic effects , including the spin - dependent and spin - independent contributions to the potential , were treated nonperturbatively in @xmath5 . from table [
tab : smm ] we see that our model predicts that all orbitally excited @xmath6 mesons have masses heavier than 1 gev .
the scalar @xmath7 ( or @xmath8 ) meson is predicted in our model to be a scalar tetraquark @xcite , while some other theoretical approaches assume it to be the scalar quark - antiquark ( @xmath9 ) state .
it is clear that the form factors of the weak @xmath10 transition are significantly different if the @xmath11 meson is the @xmath9 or @xmath12 state .
therefore the resulting rates of the semileptonic and nonleptonic @xmath0 decays to the @xmath11 strongly vary depending on its structure and quantum numbers .
thus the study of the weak @xmath0 decays to the @xmath13 meson can help to reveal the nature of light scalar mesons . in the following
we denote the @xmath11 meson by @xmath13 .
.masses of the ground state and first orbitally excited strange mesons calculates in our model ( in mev ) .
[ cols="^,^,^,^,^",options="header " , ]
the form factors of the @xmath0 weak decays to strange mesons were calculated in the framework of the relativistic quark model based on the quasipotential approach .
decays both to the ground @xmath14 and to orbitally excited @xmath6 mesons were considered .
the form factors were determined as the overlap integrals of the related meson wave functions , found in the previous meson mass spectrum calculations @xcite , in the whole broad kinematical range without additional assumptions about their @xmath4 dependence .
the important relativistic effects , such as transformations of the meson wave functions from the rest to a moving reference frame and contributions of the intermediate negative - energy states , were consistently taken into account .
we used these form factors for the evaluation of the charmless semileptonic @xmath0 decay rates to ground state and orbitally excited @xmath3 mesons .
it was found that total branching fractions of semileptonic @xmath0 decays to ground and first orbitally excited @xmath3 mesons have close values about @xmath15 .
summing up these contributions we get @xmath16 .
this value is almost 2 orders of magnitude lower than our prediction for the corresponding sum of branching fractions of the semileptonic @xmath0 to @xmath17 mesons @xcite as it was expected from the ratio of ckm matrix elements @xmath18 and @xmath19 .
therefore the total semileptonic @xmath0 decays branching fraction is dominated by the decays to @xmath17 mesons and in our model is equal to @xmath20 in good agreement with the experimental value @xmath21 @xcite .
the obtained predictions for charmless semileptonic @xmath0 decays were compared with previous calculations .
it was found that different theoretical approaches yield close values of branching fractions for decays to ground state @xmath14 mesons agreeing within uncertainties , while the ones for the decays to orbitally excited @xmath6 mesons differ significantly from each other .
the latter observation can help to discriminate between theoretical models .
charmless two - body nonleptonic @xmath0 decays dominated by tree diagrams were considered .
the factorization approximation was used which allowed to express the decay matrix elements as the product of weak transition matrix elements and decay constants .
the branching fractions of the nonleptonic decays to ground state @xmath14 or orbitally excited @xmath6 meson and pion or @xmath22 meson , both charged and neutral , were calculated .
the obtained results were confronted with previous theoretical predictions and experimental data , which are available for only few of the considered decays .
good agreement with data and other evaluations is found for the nonleptonic decays to the ground state @xmath14 meson and a light meson , while again for decays involving the orbitally excited @xmath6 mesons significant disagreement between predictions of different approaches is observed .
the authors are grateful to d. ebert , m. a. ivanov , v. a. matveev , m. mller - preussker and v. i. savrin for useful discussions .
this work was supported in part by the _
russian foundation for basic research _ under grant no.12 - 02 - 00053-a .
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d * 80 * , 114026 ( 2009 ) . | the form factors of the weak @xmath0 transitions to the ground state and orbitally excited strange mesons are calculated in the framework of the qcd - motivated relativistic quark model based on the quasipotential approach .
these form factors are expressed through the overlap integrals of meson wave functions found in their mass spectrum evaluations .
the momentum dependence of the form factors is determined in the whole accessible kinematical range without any additional assumptions and extrapolations .
relativistic effects , including the wave function transformation from the rest to a moving reference frame as well as contributions of the intermediate negative - energy states , are consistently taken into account .
the calculated form factors are used for the evaluation of the charmless semileptonic decay rates and two - body nonleptonic @xmath0 decays in the factorization approximation .
the obtained results are confronted with previous predictions and available experimental data . |
in a recent paper moitsheki et al@xcite argued that a method based on lie algebras is suitable for obtaining the solution to nonlinear ordinary differential equations that appear in simple models for heat transfer .
they compared the analytical solutions with other results coming from perturbation approaches like homotopy perturbation method ( hpm ) and homotopy analysis method ( ham)@xcite . it is worth noticing that there is an unending controversy between the users of those fashionable perturbation approaches that arose some time ago@xcite .
the purpose of this paper is to determine the usefulness of the results for the heat transfer systems provided by the lie algebraic method and those perturbation approaches . in sec .
[ sec : exact ] we analyze the exact solutions arising from lie algebras , in sec . [ sec : taylor ] we outline the application of the well known taylor
series approach , in sec .
[ sec : virial ] we derive a simple accurate analytical expressions for one of the models and in sec .
[ sec : conclusions ] we summarize our results and draw conclusions .
the first example is the nonlinear ordinary differential equation@xcite @xmath0u^{\prime \prime } ( x)+\epsilon u^{\prime } ( x)^{2 } & = & 0 \nonumber \\
u(0)=1,\;u(1 ) & = & 0 \label{eq : ex_1}\end{aligned}\ ] ] where the prime denotes differentiation with respect to the variable @xmath1 .
this equation is trivial if one rewrites it in the following way @xmath2^{\prime } = 0$]@xcite and the solution is @xmath3x}-1}{\epsilon } \label{eq : u_ex_1}\ ] ] moitsheki et al@xcite derived exactly this result by means of a rather lengthy algebraic procedure .
it is clear that in this case the lie algebraic method gives us the same answer that we can obtain in a simpler way .
for the second example @xmath4 the authors derived the simple analytical expression@xcite @xmath5 they argued correctly that it satisfies @xmath6 but they were wrong when they stated that `` however , @xmath7 only if @xmath8 '' .
notice that the function @xmath9 that comes from such value of @xmath10 does not have the correct behaviour at @xmath11 .
therefore , in this case the lie algebraic approach led to a wrong result .
other authors have applied hpm and ham to the equation@xcite @xmath0u^{\prime } ( x)+u(x ) & = & 0 \nonumber \\
u(0 ) & = & 1 \label{eq : ex_3}\end{aligned}\ ] ] with the trivial solution @xmath12+x=0 \label{eq : u_ex_3}\ ] ] in the following two sections we discuss some of these problems from different points of view .
if the variable of the nonlinear equation is restricted to a finite interval , one can try a straightforward power
series solution @xmath13 and obtain the unknown model parameter from the boundary conditions . in the case of the example ( [ eq : u_ex_1 ] ) the radius of convergence of this series is @xmath14 $ ] and therefore the approach will be useful for small and moderate values of @xmath10 . as @xmath10 increases the rate of convergence of the taylor series method decreases because the radius of convergence approaches unity from above . however , this example is trivial and of no interest whatsoever for the application of a numerical or analytical method .
this reasoning also applies to example ( [ eq : ex_3 ] ) although in this case we do not have an explicit solution @xmath15 but @xmath16 .
the example ( [ eq : ex_2 ] ) is more interesting because there appears to be no exact solution , and for this reason we discuss it here .
the unknown parameter is @xmath17 and the partial sums for the taylor series about @xmath11@xmath18}(x)=\sum_{j=0}^{n}u_{j}(u_{0})x^{j } \label{eq : u_x_series}\ ] ] enable one to obtain increasingly accurate estimates @xmath19}$ ] as @xmath20 increases .
such estimates are roots of @xmath21}(1)=1 $ ] .
although the rate of convergence decreases as @xmath10 increases it is sufficiently great for most practical purposes .
notice that the ham perturbation corrections for this model are polynomial functions of @xmath1@xcite whereas the hpm has given polynomial functions of either @xmath1@xcite or @xmath22@xcite . however , there is no doubt that the straightforward power
series approach is simpler and does not require fiddling with adjustable parameters@xcite .
the analysis of the nontrivial equations for heat transfer models may be easier if we have simple approximate analytical solutions instead of accurate numerical results or cumbersome perturbation expressions . in the case of the models ( [ eq : ex_1 ] ) and ( [ eq : ex_3 ] ) there is no doubt that the exact analytical expressions should be preferred .
for that reason , in what follows we concentrate on the seemingly nontrivial model ( [ eq : ex_2 ] ) .
we have recently shown that the well known virial theorem may provide simple analytical solutions for some nonlinear problems@xcite .
in particular , we mention the analysis of a bifurcation problem that appears in simple models for combustion@xcite .
the only nontrivial problem outlined above is a particular case of nonlinear ordinary differential equations of the form @xmath23 the hypervirial theorem is a generalization of the virial one .
if @xmath24 is an arbitrary differentiable weight function , the hypervirial theorem provides the following suitable expression for our problem ( [ eq : gen_nonlin ] ) : @xmath25^{\prime } dx & = & w(u(1))u^{\prime } ( 1)-w(u(0))u^{\prime } ( 0 ) \nonumber \\ & = & \int_{0}^{1}\left [ \frac{dw}{du}(u^{\prime } ) ^{2}+w(u)f(u)\right ] dx \label{eq : vt_gen}\end{aligned}\ ] ] in the particular case of the example ( [ eq : ex_2 ] ) we have @xmath26 dx \label{eq : vt_ex_2}\ ] ] when @xmath27 we obtain the virial theorem .
here we also consider the even simpler choice @xmath28 that we will call hypervirial although it is just a particular case .
since @xmath29 we try the ansatz @xmath30 that satisfies the boundary conditions in equation ( [ eq : ex_2 ] ) .
it follows from equation ( [ eq : vt_ex_2 ] ) that the adjustable parameter @xmath31 is a root of @xmath32 when @xmath27 and @xmath33 when @xmath28 .
[ fig : ht1 ] shows @xmath34 for some values of @xmath10 and also the accurate result obtained from the taylor series discussed in sec .
[ sec : taylor ] .
we appreciate that the accuracy of the analytical expression ( [ eq : u_app ] ) decreases as @xmath10 increases .
however , if one takes into account the simplicity of equation ( [ eq : u_app ] ) the agreement is remarkable .
besides , the hypervirial theorem with @xmath35 proves to be more accurate than the virial theorem .
it is curious that there is no such test for the hpm or ham@xcite . as a particular example we consider @xmath36 ( the preferred parameter value for both ham and hpm calculations@xcite ) . from the partial sums of the taylor
series with @xmath37 we obtain @xmath38 . the analytical function ( [ eq : u_app ] ) yields @xmath39 , @xmath40 for @xmath41 and @xmath42 , @xmath43 for @xmath35 that is a reasonable estimate of the unknown parameter .
again we see that the hypervirial approach is better than the virial one .
[ fig : ht2 ] shows accurate values of @xmath15 given by the taylor series with @xmath44 , our approximate analytical virial expression @xmath45 and equation ( [ eq : u_ex_2 ] ) for @xmath46 .
it seems that the accuracy of @xmath45 is somewhat between the ham results of 5th and 10th order@xcite . on the other hand , the equation ( [ eq : u_ex_2 ] ) derived by
the lie algebraic method@xcite exhibits a wrong behaviour . finally , in fig .
[ fig : ht2b ] we compare the numerical , virial ( @xmath41 ) and hypervirial ( @xmath35 ) approaches to the function @xmath15 in a wider scale .
we conclude that the virial theorem is not always the best choice for obtaining approximate solutions to nonlinear problems .
the purpose of this paper has been the discussion of some recent results for the nonlinear equations arising in heat transfer phenomena .
the oversimplified models considered here may probably be of no utility in actual physical or engineering applications .
notice that the authors did not show any sound application of those models and the only reference is a pedagogical article cited by rajabi et al@xcite .
however , it has not been our purpose to discuss this issue but the validity of the methods for obtaining exact and approximate solutions to simple nonlinear equations .
it seems that the particular application of the lie algebraic method by moitsheki et al@xcite has only produced the exact result of a trivial equation and a wrong result for a nontrivial one .
therefore , we believe that the authors failed to prove the utility of the technique and it is not surprising that they concluded that their results did not agree with the ham ones@xcite ( see fig . [ fig : ht2 ] ) . we have also shown that under certain conditions the well known straightforward taylor series method is suitable for the accurate treatment of such nontrivial equations . it is simpler than both ham and hpm@xcite and as accurate as the numerical integration routine built in a computer algebra system@xcite .
finally , we have shown that the well known hypervirial theorem may provide simple analytical expressions that are sufficiently accurate for a successful analysis of some of those simple models for heat transfer systems .
it is surprising that our results suggest that the virial theorem@xcite may not be the best choice . | we analyze some exact and approximate solutions to nonlinear equations for heat transfer models .
we prove that recent results derived from a method based on lie algebras are either trivial or wrong .
we test a simple analytical expression based on the hypervirial theorem and also discuss earlier perturbation results . |
the emerging of ovarian cryopreservation and follicle / oocyte in vitro maturation ( ivm ) as a potential strategy to safeguard fertility in cancer patients [ 1 , 2 ] has increased the attention of the reproductive biology researches in managing long - term ovarian cells culture .
studies using human granulosa - lutein cells ( glcs ) aspirated during oocyte retrieval for in vitro fertilization ( ivf ) procedure may ultimately provide data to further development of adequate milieu for oocyte growth and maturation by coculture of these cells with immature oocytes or preantral follicles . furthermore , physical and metabolic integrity of oocyte and surrounding granulosa cells interaction is essential for the normal course of the folliculogenesis process [ 35 ] , which makes the managing of the in vivo - like granulosa cells function during culture important for the ivm approach success
. microbial contamination of long - term cell culture is a current concern for assisted reproductive techniques ( arts ) laboratories .
although transvaginal oocyte retrieval for ivf is considered to be relatively safe , occasionally microorganisms colonize culture dishes of oocytes and embryos [ 7 , 8 ] .
these infections are mainly caused by bacterial strains insensitive to the antibiotics used or due to yeast colonization by candida species , which frequently reside in the vagina , or even by other normal vaginal flora , like lactobacillus .
as bacterial endotoxins dramatically disrupt granulosa cells growth and function in vitro in different species [ 1113 ] , a technique for the isolation and plating of human glcs that prevent microbial contamination would provide a powerful tool to guarantee the long - term management of functional cells in vitro .
the methods in common use today to prevent microbial contamination in ivf granulosa cells culture employ the supplementation of the culture media with antibiotics and/or antimycotics [ 1416 ] .
alternatively , the use of antibiotics and antimycotics during the initial isolation and cell - plating procedures has been also shown to reduce the potential contamination of various types of mammalian cells cultures ; however , the efficacy of this procedure to prevent microbial contamination of the human glcs culture remains to be determined .
accordingly , the purpose of this study was to determine the feasibility of using an isolation protocol with pbs containing antibiotic / antimycotic as washing solution during the recovery of granulosa cells from the follicular aspirate during oocyte retrieval for art in order to obtain germ - free long - term culture .
after 144 hours , the cultures of human gcs were examined for morphological and functional characteristics . the use of pbs containing antibiotic / antimycotic as washing solution improved cell culture purity and retained cell functionality , which is essential for characterization of granulosa cells function in vitro .
human glcs were obtained from five patients aged between 18 and 40 years , who presented ovulatory cycles and fsh below 12 miu / ml . all patients were indicated for assisted reproduction procedure because of male or tubal factor infertility and agreed to sign the informed consent .
patients were excluded if they had endometriosis or failed fertilization in previous cycles , presence of any endocrinopathies as congenital adrenal hyperplasia , hyperprolactinemia , or thyroid disorders , even if compensated .
patients using drugs known to affect reproductive or metabolic function , as treatment with glucocorticoids or antiandrogens , for at least 60 days before the beginning of the ovulation induction were also excluded .
all patients were submitted to follicular aspiration for ivf procedures at the human reproduction division - department of obstetrics and gynecology , faculty of medicine of ribeiro preto , university of so paulo .
all procedures were approved by the research ethics committee from this institution ( protocol hcrp no 7474/2008 ) .
follicular development was achieved by treatment for 10 days with 400 mcg / day of gnrh agonist nafarelin - synarel , pfizer ( before ovarian hyper stimulation ) , followed by daily dose of 100 to 375 ui of recombinant fsh , administered subcutaneously ( gonal f , serono canada , oakville , on , canada ) .
when the majority of the follicles reached 17 mm diameter or more , the patients were injected with 10,000 iu of hcg ( ovidrel , serono , brazil ) or 250 mcg of recombinant lh ( organon ) .
oocyte retrieval was performed 3436 hours after the drug administration and the follicular aspiration was guided by transvaginal ultrasound .
the follicular fluid was examined by stereomicroscope , and the oocytes were identified and used for art . for cell culture experiments the follicular fluid was collected in 50 ml sterile polypropylene tubes ( falcon ) containing pbs or pbs supplemented with 1000 u / ml penicillin , 1000 g / ml streptomycin , and 0.25 g / ml amphotericin b ( invitrogen - gibco / brl , grand island , ny ) . the follicular fluid was washed with pbs in sterile polystyrene petri dish .
the glcs were centrifuged at 300 g for 10 min at 4c and the pellet was resuspended in tcm-199 ( invitrogen , gibco laboratories life technologies inc . ,
glcs were separated from remaining red blood cells by gradient using histopaque-1077 ( sigma chemical co. , st .
after 20 min centrifugation at 500 g the glcs layer was collected with pasteur pipette from the interface between the histopaque and the medium .
the cells were then centrifuged at 500 g for 10 min at 4c with 2 ml pbs , to remove the histopaque .
aliquots from isolated cells with or without pbs containing antibiotic / antimycotic were counted in hemocytometer .
the cell viability was accessed with 0.2% trypan blue , and 1 10 viable cells were transferred into individual wells of 24-well plates containing 200 l tcm-199 medium supplemented with 10% fetal calf serum , 100 u / ml penicillin , 100 g / ml streptomycin , and 0.025 g / ml amphotericin b ( invitrogen - gibco / brl ) .
the cells were cultured at 37c in 5% ( v / v ) co2 in air atmosphere for 144 h , and70% of the culture media ( 140 l ) was collected and replaced every 48 h and stored at 20c .
cultures were evaluated by microscopy , and further investigation for bacterial or fungal contamination was done in the microbiology laboratory according to standard procedures .
samples were inoculated on blood agar plates and ( brain heart infusion ) bhi for detection of bacterial , yeast , or fungal contaminations .
plates were incubated aerobically at 37c and read within 24 h and 48 h. after culture the glcs were fixed in 2% glutaraldehyde , 2%formaldehyde , and 0.05%cacl2 in pbs withca / mg.thenthesampleswere postfixedin1%osmium tetroxide in distilled water(ph7.4),contrasted with0.5% uranyl acetate , dehydrated in ethanolpa ( merck ) , and embedded inepon 812 .
semithin sections ( 0.51 m thick ) were stained with toluidine blue and examine by light microscopy .
ultrathin sections ( 60 nm ) were mounted on copper grids , stained with 0.5% uranyl acetate and lead citrate , and examine in transmission electron microscope ( jem-100cxii , jeol ) .
estradiol ( e2 ) and progesterone ( p4 ) media levels were analyzed by chemiluminescence using a commercial kit ( dpc , immulite system , los angeles , ca , usa ) , in accordance with the manufacturer 's protocol .
all samples were analyzed in duplicate , to minimize intra - assay variability or variability in the same assay .
differences in e2 and p4 levels between bacteria - infected and - noninfected groups were analyzed by student 's t test .
human glcs collected with pbs containing antibiotic / antimycotic were free from bacterial contaminations after 144 h of culture .
noninfected glcs showed their typical elongated morphology of adherent cell that grows in monolayer ( figure 1 ) .
the ultrastructural analyses showed nucleoplasm contained finely dispersed chromatin and peripheral patches of heterochromatin ( figure 1(a ) ) as a dense cytoplasm contained several organelles and clear contacts between cells ( figure 1(b ) ) .
human glcs collected only with pbs showed bacterial contaminations after 144 h in culture ( figure 2 ) .
ultrastructural analyses showed disrupted glcs cytoplasm containing innumerous vacuoles and bacteria ( figures 2(a ) and 2(b ) ) as undefined nucleus ( figures 2(c ) and 2(d ) ) .
several bacteria were observed inside the cytoplasm and in the extracellular media next to the cells or the cell debris ( figure 2(c ) ) . before plating the cell viability
was assessed by trypan blue dye exclusion , and it was 90% ( data not shown ) .
estradiol production by glcs that were collected with pbs supplemented with antibiotic / antimycotic was higher than that produced by cells collected only with pbs ( figure 3(a ) ) .
in contrast , the progesterone production by glcs cells collected only with pbs was higher than that produced by cells that were previously washed in pbs supplemented with antibiotic / antimycotic ( figure 3(b ) ) .
in this report we described an optimized protocol for isolation of human granulosa - lutein cells where the cells were rinsed in pbs containing antibiotic / antimycotic prior to the culture .
although antibiotics are routinely added to media for long - term culture of cells and tissues , to avoid bacterial contamination , it also could lead to development of resistant bacteria with slow - growing property .
as the vaginal flora contains a large variety of bacterial species [ 10 , 18 ] it may contaminate the sample during oocyte retrieval with transvaginal ultrasound leading to further bacteria growth into the culture system .
our electron microscopy results revealed bacterial contamination in glcs culture that could not be seen by light microscopy .
the culture glcs with bacterial contamination showed several ultrastructural damages . in the present study using a mixture solution containing 10-fold of antibiotic / antimycotic in pbs to rinse the cells prior to the culture and
also in the culture media was possible to culture human glcs for 144 hours without bacterial contamination .
our results also showed that the use of antibiotic / antimycotic only in the culture media could not avoid the contamination .
indeed , infections in ivf culture dishes have been associated with bacterial strains insensitive to the antibiotics used or due to yeast colonization by candida species , which frequently reside in the vagina .
as suggested by vierck the use of antibiotics and antimycotics in primary cultures of muscle and fat stem cells during the initial isolation and cell plating procedures may greatly reduce the potential for contamination of the cultures .
penicillin ( 100 iu / ml ) and streptomycin ( 100 mg / ml ) are the most common antibiotics used to control microorganisms in culture media , effective against a variety of gram - positive and gram - negative bacteria .
amphotericin b ( 0.25 mg / ml ) is often added to control fungal contamination .
our finds demonstrate that it is important to rinse the cells with pbs containing antibiotic / antimycotic before placing the cells in culture .
moreover , these results indicated that the contamination was not acquired during the cell handily since all steps of the culture procedure such as , oocyte retrieval , cells platting , and media preparation and replacement were done with extremely care and in sterile conditions .
we also showed that human glcs steroidogenesis was markedly affected by bacteria contamination in the culture .
these crypts contaminants may persist indefinitely in cultures causing subtle biochemical changes into the culture medium disturbing cell growth and differentiation .
estradiol levels in the culture media were significantly reduced after bacterial contamination while progesterone levels increased .
similar results were shown using glcs cultured in the presence of escherichia coli , which leads to stimulation of progesterone and inhibition of estradiol production in vitro .
studies in different experimental models have suggested that the effects of bacterial contamination on granulosa cells function are likely mediated directly through the endotoxin , lipopolysaccharide ( lps ) , or indirectly through the inflammatory mediators associated with bacterial infection including cytokines such as tumor necrosis factor alpha ( tnf - alpha ) [ 1113 ] .
although suppression of estradiol granulosa cells secretion by bacterial infection has been associated with downregulation of transcripts for aromatase , the mechanism ( s ) by which bacteria exert its adverse effects upon progesterone secretion remains to be determined .
as granulosa cells function is pivotal during follicle development and these cells nurture the oocyte until ovulation , the maintenance of an adequate milieu for granulosa cells growth and differentiation in vitro is likely to be an important approach underlying ovarian follicular cells physiology . in conclusion ,
the cell isolation protocol presently used allowed the prevention of microbial contamination in long - term culture of human glcs and the maintenance of cells growth and function in vitro .
thus , taken together , our results suggest that the use of antibiotics and antimycotics in wash buffer and in the culture media is essential for long - term culture of human glcs .
future experiments will be directed to determine whether this protocol may help to develop healthy culture system for coculture of granulosa cells with immature oocytes or preantral follicles in order to obtain applicable results to fertility preservation programs and for infertility treatments . | purpose . to investigate whether the addition of antibiotic / antimycotic during human granulosa - lutein cells ( glcs ) isolation and cell - plating procedures prevents microbial contamination after 144 h of culture and
also evaluate the effects of contamination on glcs ultrastructure and steroid secretion .
methods .
glcs obtained from five women submitted to assisted reproductive techniques ( arts ) were isolated with pbs supplemented with antibiotic / antimycotic or pbs nonsupplemented and cultured for 144 h. glcs were evaluated by transmission electron microscopy ( tem ) , and estradiol ( e2 ) and progesterone ( p4 ) secretion was assayed by chemiluminescence . results .
although no contaminating microorganisms were identified by light microscopy , tem analyses revealed several bacterial colonies in culture dishes of glcs isolated with only pbs .
bacterial contamination disrupted the adherence of the glcs to the culture plate interfering with monolayer formation affecting the growth pattern of glcs .
various cellular debris and bacteria were observed , and no organelles were found in the cytoplasm of infected cells . while bacterial contamination decreased estradiol media levels , it increased progesterone , as compared with noncontaminated group .
conclusion . taken together
, our data showed that the addition of a high dose of antibiotic / antimycotic during the isolation and cell - plating procedures prevents microbial contamination of long - term glcs culture as its effects on cells growth and function in vitro . |
neutron stars represent the most dense form of matter known before black hole formation .
the equation of state of such material is not well understood but typical expected size scales of @xmath2 km for a @xmath3 object give @xmath4 similar to that of the last stable orbit around a schwarzschild black hole .
the gravitational potential seen by the accreting material is then very similar in neutron stars and black holes , but with the obvious difference that the material may then fall seamlessly and invisibly from the edge of the disc through the event horizon in the black holes ( but see e.g. krolik , hawley & hirose 2005 for an alternative view ) , but must impact onto the solid surface for the neutron stars .
this boundary layer emission should give a clear distinction between the two types of systems , yet in practice it can be quite hard to discriminate between the disc accreting , low magnetic field neutron stars and galactic black holes ( gbh ) . both show hard spectra at low mass accretion rates ( e.g. barret & vedrenne 1994 ; barret et al .
2000 ) while at higher mass accretion rates the black holes can show low temperature , optically thick comptonized emission from a corona which can look similar to an optically thick boundary layer in the neutron stars systems ( the black hole ` very high state ' , done & gierliski 2003 , hereafter dg03 ) .
nonetheless , dg03 showed that there are clear differences between the black hole and neutron star systems .
they used the huge database now available on these objects from the _ rossi x - ray timing explorer _ ( _ rxte _ ) to build a picture of the x - ray spectral evolution as a function of overall mass accretion rate ( as measured by luminosity , parameterized in units of the eddington rate , @xmath5 ) .
they used data from gbh and both subclasses of disc accreting , low magnetic field neutron stars namely atolls and z sources ( see e.g. hasinger & van der klis 1989 ) .
the atolls and gbh cover the same luminosity range in @xmath5 , from @xmath6 to @xmath7 , so their accretion flows should be directly comparable ( z sources are typically more luminous , and may have residual magnetic fields : hasinger & van der klis 1989 ) .
dg03 showed that the gbh as a class were all consistent with the same spectral evolution as a function of mass accretion rate , as were the atolls , but that this behaviour _ differed substantially _ between the two types of system even though they covered the same range in @xmath5 .
dg03 interpreted this in the light of the recent advances in accretion flow models , which suggest that at low mass accretion rates the optically thick , cool , inner disc can evaporate into an optically thin , hot flow ( e.g. an advection dominated accretion flow : narayan & yi 1996 or a jet dominated accretion flow : falcke , kording & markoff 2004 ) .
these models are currently controversial as they conflict with the occasional detection of extremely broad iron lines in gbh spectra in this state ( miller et al 2002 ; miniutti , fabian & miller 2004 ; miller et al 2006 ) , though these extreme widths could also be an artifact of complex absorption ( done & gierliski 2006 ) .
nonetheless , the truncated disc / hot inner flow models are very attractive as they can qualitatively explain a wide range of observed properties in x - ray binaries .
this includes the spectral evolution of the gbh , which can be broadly explained by the transition radius between the disc and hot flow progressively decreasing as the mass accretion rate increases , while the atolls are consistent with an identical accretion flow behaviour but with the addition of the expected boundary layer / surface emission ( dg03 )
. these observational differences between gbh and atolls are consistent with the existence of the event horizon , the most fundamental predicted property of a black hole ( see also mcclintock , narayan & rybicki 2004 ; narayan & heyl 2002 ; garcia et al .
2001 ; sunyaev & revnivtsev 2000 ) . however , the sample of atolls used by dg03 was fairly small , with only 4 objects ( 1 of which was an accreting millisecond pulsar ) .
this contrasts with their gbh selection , which included all available objects which were not heavily absorbed . here
we present a much wider study using all the available atolls in the _ rxte _ database which are not heavily absorbed to investigate their behaviour in more detail .
we find that while all the atolls ( and millisecond pulsars ) broadly show the same spectral evolution , there are some subtle differences . some of these can be connected to spin / inclination effects , but there are also some differences in transition behaviour which correlate with long term mass accretion rate .
we speculate that these may be linked through the jet being affected by any remnant polar magnetic field , which in turn depends on the accretion rate .
we searched the _ rxte _ database for low magnetic field , disc accreting neutron star systems .
we do not include z sources ( sco x-1 , gx349 + 2 , gx17 + 2 , cyg x-2 , gx51 , gx340 + 0 e.g. kuulkers et al 1996 , cir x-1 , lmc x-2 , hasinger & van der klis 1989 ) as we were interested in the range @xmath8 to compare with the galactic black holes from dg03 .
we also exclude all objects with heavy absorption , defined as @xmath9 @xmath10 , as above this the spectral decomposition becomes more uncertain .
given that most systems are in the galactic plane , this removes many objects ( 4u 162449 , gro j174428 , grs 1747312 , sax j1747.02853 ) .
the absorption criteria also excludes objects where there is substantial intrinsic absorption .
this can be continuous , completely blocking our view of the continuum source so that the only scattered flux is seen ( the accretion disc corona sources ) , or the absorption can be episodic , giving discrete dips in the lightcurve ( the dippers ) .
we exclude all accretion disc corona sources ( 2s 0921 - 630 , 4u 1624 - 49 , 4u 1822 - 371 , ms 1603 + 206 ) , and dippers where the absorption events are so frequent that most observations are affected by them ( exo 0748 - 676 ) , but we do include dippers where the absorption is limited to contaminating only a few observations ( which we remove , see next section ) .
details of all included sources are shown in table [ tab : sources ] . [ cols="^,^,^,^,^,^,^,^,^,^ " , ]
the standard products spectra ( and associated background and response files ) from the proportional counter array ( pca ) , available from the high energy astrophysics science archive research centre ( heasarc ) database were gathered for each source , giving a total of over 3000 spectra . following dg03 we fit these with a model of the disc emission and a comptonized continuum , described by diskbb ( mitsuda et al .
1984 ) and thcomp ( zdziarski et al . 1996 ) in xspec , together with a smeared edge and gaussian line to approximately mimic the reflected spectrum . the absorption was fixed at the galactic value for each object ( see table [ tab : sources ] ) .
this model gave a good fit to all the spectra ( @xmath11 ) .
following dg03 , the best - fitting model to each spectrum was integrated to form intrinsic soft and hard colours ( i.e. absorption corrected and independent of the instrument response ) , defined as flux ratios in the bandpasses 46.4/34 and 9.716/6.49.7 kev , respectively .
the unabsorbed model was also used to estimate the bolometric flux in the 0.011000 kev bandpass , and this converted into a luminosity using the distance estimate given in table [ tab : sources ] . as discussed by dg03 ,
the colours are fairly robust to changes in the model spectra as long as the source is not heavily absorbed and the advantage of using intrinsic colours ( as opposed to the more widely used instrument colours ) is that many objects can be directly compared on the same plot .
the bolometric fluxes are more uncertain , as the model is extrapolated outside of the observed energy bandpass .
nonetheless , this model corresponds to expected physical components , and we fix a lower limit to the disc temperature of @xmath12 kev and an upper limit to the comptonizing temperature of @xmath13 kev so the continuum components can not produce arbitrarily large luminosities in the unobserved energy ranges ( dg03 ) .
we identify and exclude data contaminated by dips and x - ray bursts by using the standard 1 lightcurves ( 0.125s time resolution ) corresponding to each standard 2 spectra .
we used the intrinsic r.m.s .
variability as a tracer of these .
all lightcurves with r.m.s above 50 percent were inspected for bursts , while the 16-s rebinned lightcurves were checked for dips if their r.m.s
. was above 20 percent .
observations were also excluded if they were contaminated by galactic ridge emission , seen as a softening of the spectra and large iron line contribution at the lowest luminosities in objects with low galactic latitude : see e.g. wardziski et al .
( 2002 ) for an example of this in the black hole gx339 - 4 .
[ fig : landr ] shows the resulting colour - colour and colour - luminosity diagram for all 34 atolls and 6 millisecond pulsars combined together .
one interesting thing to note is that several atoll sources approach or even exceed eddington luminosities ( 4u 1735 - 44 ; 4u 1744 - 26 ( gx 3 + 1 ) ; 4u 1758 - 20 ( gx 9 + 1 ) ; xte j1806 - 246 : gladstone 2006 ) , showing that the high luminosity sources are not necessarily z sources ( hasinger & van der klis 1989 )
[ fig : landr](a ) shows that while the atolls show the same overall behaviour as claimed by dg03 , they also show subtle but significant differences .
this is most evident in terms of the spectral evolution during the transition between the hard ( island ) and soft ( banana ) spectral states , which forms the middle branch of the total z - shaped track on the colour - colour diagram ( even though these are atolls , not z sources , see gierliski and done 2002 ; muno , remillard & chakrabarty 2002 ) .
we have highlighted this by picking out in red those objects where the transition makes an almost vertical track on the colour - colour diagram ( hereafter called verticals ) , while the blue symbols show those where the transition from island to banana starts much further to the right on the colour - colour diagram , but ends at approximately the same place , making a much more diagonal middle branch ( hereafter called diagonals ) .
this difference in spectral evolution is also picked out in the colour - luminosity diagram as a different luminosity for the hard - soft transition . while the distances are generally rather uncertain , this correlation between the behaviour on the colour - colour and colour - luminosity diagrams give some confidence in the reality of the luminosity difference .
we stress that this is not primarily due to hysteresis , the well known effect in both black holes and neutron stars where the luminosity at which the hard - soft transition occurs varies considerably in the same object ( e.g. nowak 1995 , maccarone & coppi 2003 ) . here ,
the transition luminosity is varying between different objects .
we show this difference in transition behaviour by plotting the colour - colour and colour - luminosity diagrams for each individual source which shows a clear state transition .
those making a vertical transition are shown in fig .
[ fig : verticals ] , while those making a diagonal transition are shown in fig .
[ fig : diagonals ] . not all objects have data covering a transition .
some , such as all the millisecond pulsars , are only seen in the hard ( island ) state ( see fig . [
fig : msps ] ) , others e.g. 4u 1758 - 20 are seen only in the soft ( banana ) branch .
of the ones which do make transitions , showing both hard and soft spectra , the effects of data windowing mean that not all have observations covering the transition period .
nonetheless , the size of the _ rxte _ database mean there are 12 sources which do have enough data to constrain the shape of the transition on the colour - colour diagrams .
the remaining sources , where there is insufficient transition data available at present are included in the background points plotted on each image , but not plotted individually here ( they can be seen in gladstone 2006 ) .
the majority of sources have well defined transition luminosities ( to within a factor 23 ) , irrespective of whether the transition is from hard to soft i.e. on the rising part of the light curve , or from soft to hard i.e. with a decreasing flux . however , there are two sources where the transitions have a much large scatter in their properties , namely 4u 160852 and 4u 1908 + 005 ( aql x-1 ) .
the colour - colour and colour - luminosity diagrams for these are plotted as the bottom two panels in fig .
[ fig : verticals ] ) , but it is not clear from the data that these sources should be classed as verticals , so here we examine them in more detail .
these two systems are also the only two ( apart from the millisecond pulsars ) which show large scale outbursts . in order to investigate their scatter in transition
behaviour we select simple outbursts from the light curve , where there is a clear fast rise followed by a monotonic decay . from this data
we build a new , simplified colour - luminosity diagram ( fig .
[ fig : hysteresis ] ) .
the black triangular points show the island state seen on the rise , which looks very similar to the msps ( fig .
[ fig : msps ] ) .
we then exclude all of the transition data on the rise / peak of each outburst , and plot the remaining banana branch and transition back to island state on the decay as the blue square points .
plainly the transition luminosity is much larger in the rise to outburst than during the decay .
this effect of hysteresis is also seen in most galactic black holes ( e.g. maccarone & coppi 2003 ) .
equally plainly , the decay shows a clear vertical track , confirming the identification of these as verticals .
hence we speculate that the msps are similar objects , and that if the msp outburst ever reached high enough luminosities to make a transition then this transition would display hysteresis and the colour - colour track during the outburst decay would be vertical .
none of the diagonals show marked hysteresis , though 4u 170544 and ks 173126 may show a small effect in that their top branch ( island state ) extends to higher luminosities than seen during the transition ( fig .
[ fig : diagonals ] ) .
a similar small hysteresis effect may also be present in the vertical 4u 091954 .
there are subtle differences in the spectral evolution of the atolls on the colour - colour and colour - luminosity diagrams : there is the distinction between the transition track ( verticals and diagonals ) , and then within the diagonals there is a difference in spectral hardness of the banana branch , and within the verticals there are objects which show large scale hysteresis . here
we examine possible explanations for these effects .
a range of inclinations is expected for these sources , and this could be important for the observed spectrum if the intrinsic emission is not isotropic .
some degree of anisotropy is certainly expected from the accretion disc due to its planar geometry , and as long as the boundary layer has a different angular dependence then the overall spectrum will change as a function of inclination . to estimate the effects of inclination we use the spectral model consisting of the disc emission ( diskbb ) and the optically thick boundary layer emission , which we model by thermal comptonization ( comptt ) .
dg03 showed that the banana branch could be roughly characterized by a disc varying in temperature in the range 1.01.5 kev together with an equal luminosity boundary layer with @xmath14 = 3 kev and @xmath15 = 5 ( see also revnivtsev & gilfanov ( 2006 ) ) .
we use these parameters to model the shape of the banana branch .
we first assume that the boundary layer is isotropic , while the disc normalization varies as @xmath16 but with angle averaged luminosity equal to that of the boundary layer .
thus the apparent ratio of disc to boundary layer flux will change as the inclination angle varies . in fig .
[ fig : inclination](a ) we show how the banana branch moves on the colour - colour diagram for inclinations of @xmath17 , @xmath18 and @xmath19 .
the change is mainly only in the soft colour , with a greater proportion of disc emission shifting the start of the banana branch to lower soft colours .
plainly this can not account for either of the two subtle spectral effects seen , but seems to have more potential to explain the different positions of the banana branch amongst the diagonals than the difference between verticals and diagonals .
examination of some of the individual banana branch spectra of the diagonals showed that the comptonization temperature of the boundary layer is also changing , and in a way which is correlated with @xmath20 .
this could indicate that the boundary layer emission is itself anisotropic , perhaps with a temperature gradient so that it is hotter close to the equatorial plane where the disc hits the neutron star .
[ fig : inclination](b ) shows the effect of changing the temperature of the boundary layer from 2.5 , 3.0 and 3.5 kev , for inclination angles of @xmath17 , @xmath18 and @xmath19 , respectively .
this matches very well with the range of banana branches seen in the diagonals .
testing this would require knowledge of the inclination , but very few sources have good enough orbital determinations to constrain this
. however , any source exhibiting dips must be at fairly high inclination ( @xmath21 ) , and hence would be expected to have a banana branch starting at fairly large hard and soft colours .
this can be seen in the case of 4u 1724307 ( see fig [ fig : diagonals ] ) , a dipping source whose banana branch ranges from 1.651.75 in soft colour and 0.7 to 0.8 in hard colour
. there are three other dipping sources , 4u 170430 , 4u 174637 and 4u 191505 ( not included in this work ) , that also support this idea , with each exhibiting large values of both hard and soft colours in the banana state ( for details , see gladstone 2006 ) .
burst oscillations and khz qpos have finally given observational constraints on lmxb neutron star spins ( e.g. the review by van der klis 2000 ) .
for our sample , the inferred range is from 330 to 619 hz .
however , this is unlikely to be the origin of the difference in transition track as the spins seem fairly evenly distributed between the two classes .
however , spin could also give a difference in the overall luminosity / temperature of the boundary layer .
lower spin gives a higher relative speed between the inner edge of the disc and the surface , leading to a lower @xmath20 ratio and a higher boundary layer temperature , as required for the different banana branch hard colours seen .
thus it seems likely that some combination of spin and inclination effects are responsible for the different banana branches seen in the diagonals , but neither is likely to explain the origin of the two different types of transition behaviour . of the subsample of systems with data covering the transition , the publically available asm and/or pca galactic bulge long term light curves
show large scale transient outbursts only in 4u 160852 , 4u 1908 + 005 and all the millisecond pulsars ( see table 1 ) .
this is very intriguing as 4u 160852 and 4u 1908 + 005 are both verticals .
however , examination of the long term lightcurves of the other verticals clearly shows that these objects do not undergo dramatic outbursts , so this can not be the origin of the vertical / diagonal distinction . however , 4u 160852 and 4u 1908 + 005 are also the only objects to show clear large - scale hysteresis .
thus it seems possible that hysteresis is linked to large amplitude outbursts .
there are no counterexamples i.e. no systems that show major disc outbursts ( which push the accretion rate high enough to make a spectral transition ) which do not show hysteresis .
all the millisecond pulsar outbursts remain in the hard state , and all other atoll sources with enough data to deliniate the transition and hence constrain hysteresis do not exhibit major outbursts .
this hypothesis can be tested on the black hole lmxb systems . unlike the atolls , none of these sources are persistant ( mcclintock & remillard 2006 ) .
this distinction in disc instability behaviour between black holes and neutron stars can be broadly explained in the context of the hydrogen ionization models .
neutron stars are lower in mass than black holes , so for the same companion star to overflow its roche lobe requires a smaller binary orbit for a neutron star compared to a black hole .
smaller orbital separation means a smaller disc due to tidal truncation .
the size of the disc , together with the mass loss rate from the companion star ( determined by its evolutionary state ) determines the temperature of the coolest part of the disc .
thus the smaller neutron star systems are less likely to have a disc which can drop below the hydrogen ionization temperature required to trigger the disc instability ( king & ritter 1998 ; king , kolb & szuszkiewicz 1997 ; dubus et al 1999 )
. it is well known that most black hole systems show large scale hysteresis ( e.g. maccarone & coppi 2003 ) .
thus they support the idea above that hysteresis is linked to large amplitude outbursts .
even more support comes from the one obvious exception , which is cyg x-1 .
this does not show hysteresis during its hard / soft transitions , and is of course a persistent ( hmxrb ) source ( e.g. maccarone & coppi 2003 ; dg03 ) .
maccarone & coppi ( 2003 ) also suggested that hysteresis could be linked to large scale outbursts , but with only cyg x-1 as an counterexample , the connection to outbursts is not quite so unambiguous .
cyg x-1 is also one of the few known galactic black holes with a high mass companion , so there is the possibility that its accretion structure is somewhat different due to lower angular momentum material from a stellar wind . by contrast , with the neutron stars being generally stable to the hydrogen ionization trigger for the disc outbursts , there are many counterexamples , all with low mass companions .
we can also rule out the alternative origin for hysteresis discussed by maccarone & coppi ( 2003 ) , namely that it is produced simply by a difference in behaviour in low mass x - ray binaries between a hard to soft transition on the rising part of the light curve , and a soft to hard transition as the flux decreases .
most of the sources shown in figs .
[ fig : diagonals ] and [ fig : verticals ] make the transition in both directions , and do not show large scale hysteresis ( though there are smaller scale effects , consistent with the difference in environment : meyer & meyer - hoffmeister 2005 ) . instead , hysteresis is seen where the mass accretion rate changes dramatically ( from @xmath22 to @xmath23 ) .
we speculate that the accretion flow is able to access non - equilibrium states during the rapid changes in accretion disc structure caused by the disc instability .
thus the neutron stars clearly show a one to one correlation between the dramatic large amplitude outbursts triggered by the disc instability and hysteresis , consistent this being the origin of hysteresis .
this predicts that the millisecond pulsar outbursts should also show hysteresis if their accretion rate at the outburst peak ever goes high enough to trigger a spectral transition ( in which case we would expect them also be verticals , along with 4u 160852 and 4u 1908 + 005 ) . however , there is no such one to
one correlation between outbursts and transition behaviour ( vertical / diagonal ) , so we explore further aspects of the systems below .
table [ tab : sources ] shows the binary parameters where these are known .
we first explore whether there is any correlation between transition behaviour and binary period ( which is a tracer of companion type , and also of superburst behaviour : cumming 2003 ) . for the verticals ,
the periods span a large range , from 1 hour for the persistent sources 4u 0614 + 091 and 4u 091954 through to 19 and 288 hours for the transients 4u 160852 and 4u 1908 + 005 .
this distinction is as expected from the disc instability model ( wide binary implies a much larger disc , so a cooler outer edge which is more likely to trigger the hydrogen instability ) .
if the millisecond pulsars are also verticals then these fill in the period distribution from 40 minutes to 4 hours.there is very little data to compare this to the diagonals , as only 2 have periods ( 11 minutes and 3.9 hours ) , but the broad span seen from the verticals encompasses most of the binary periods seen in atolls , so binary period alone is unlikely to be the origin of the transition track dichotomy .
the distinction between millisecond pulsars , which plainly retain a residual magnetic field channelling the flow , and other atolls which do not show pulsations is most probably due to the long timescale mass accretion rate ( cumming , zweibel & bildsten 2001 ) .
plausibly , high accretion rates can bury the magnetic field below the neutron star surface , but the very low average mass accretion rate in the millisecond pulsars is insufficient to bury the field ( cumming et al .
thus there is a potential physical mechanism for the long term mass accretion rate to change the properties of the accretion flow .
we estimate the long - term mass accretion rate , @xmath24 , ( or corresponding average luminosity , @xmath25 ) for all of the systems from the observed x - ray emission .
the pca data gives estimates for @xmath26 through spectral fitting , but the light curves are highly incomplete , so the data can not simply be used as an indicator of the long term average mass accretion rate . by contrast , the _ rxte _ all sky monitor ( asm ) gives an almost continuous light curve for every bright x - ray source in its field of view , but its lack of spectral resolution means that going from count rate to @xmath27 is highly uncertain . hence we combine the two approaches .
we use the pca light curve to define the average @xmath25 during these observations , then select the simultaneous asm points to find the average asm count rate during the pca observations .
the ratio of this to the full asm light curve gives the correction for the incompleteness of the pca observations .
this approach works well unless the source becomes very faint , in which case contamination of the asm by other nearby sources and/or galactic ridge emission can be a problem .
the only sources for which this is an issue are the transients i.e. the verticals 4u 160852 and 4u 1908 + 005 and all the millisecond pulsars .
the outbursts of 4u 160852 and 4u 1908 + 005 are so bright that they dominate the average of the asm lightcurves . however , this is not the case for the millisecond pulsars , so for these we use a different approach .
here we use the pca data alone , which have good outburst coverage , assuming that the source intensity is negligible in the periods outside the known outbursts .
the results of both the millisecond pulsars and atoll sources are shown in table [ tab : lbol ] .
ccc source name & source type & @xmath28 + + igr j00291 + 5934 & msp & 1.4 @xmath29 + xte j0929314 & msp & 1.4 @xmath30 + xte j1751305 & msp & 5.2 @xmath29 + xte j1807294 & msp & 2.7 @xmath30 + xte j1808369 & msp & 6.7 @xmath29 + xte j1814338 & msp & 1.6 @xmath30 + + 4u 0614 + 091 & v & 3.2 @xmath31 + 4u 091954 & v & 3.1 @xmath31 + 4u 160852 & v & 6.6 @xmath31 + 4u 1908 + 005 & v & 3.7 @xmath31 + slx 1735 - 269 & v & 1.6 @xmath31 + + 4u 163653 & d & 4.4 @xmath32 + 4u 170243 & d & 7.8 @xmath31 + 4u 170544 & d & 1.9 @xmath32 + 4u 1724307 & d & 7.3 @xmath31 + 4u 172834 & d & 1.9 @xmath32 + 4u 1820303 & d & 1.3 @xmath33 + ks 173126 & d & 3.4 @xmath32 + + it can be seen that there is a systematic difference between the three classes of sources .
the millisecond pulsars have the lowest @xmath28 , then the verticals , then the diagonals .
thus it seems possible that this is the origin of the difference in transition properties .
the millisecond pulsars low @xmath34 allows the field to diffuse out of the crust , and to be strong enough to collimate the flow and produce pulsations .
one possibility might be that while the high @xmath35 of the diagonals suppresses the field entirely , the medium @xmath34 in the verticals allows some field to diffuse out .
but the verticals show no trace of pulsation , so the magnetic field can not collimate any significant part of the flow .
one way around these pulsation limits is to separate the field and accretion flow .
any non - spherical accretion flow will predominantly bury the field in the region of the flow , leaving the field to escape in regions with little accretion .
even the hot accretion flow envisaged for the hard island states favours the equatorial plane , with a geometry which is more like a thick disc than a truly spherical flow ( e.g. narayan & yi 1995 ) .
this nicely circumvents the pulsation limits , but then there is no interaction between the magnetic field and the flow , and so no physical mechanism to change the behaviour of the transition . however , one aspect of the system that a polar magnetic field could affect is the jet .
the most recent numerical simulations of the accretion flow magnetohydrodynamics show a causal link between the jet and accretion flow ( hawley & krolik 2006 ; mckinney 2006 ) , so this might give an indirect link between the magnetic field and accretion flow properties . one way to test this is to look at the radio emission from these systems .
while theoretical models of jets are not well developed , we can use the observed gbh behaviour as a template .
these show a clear correlation between radio and x - ray luminosity in their low / hard state , showing that @xmath36 is important in determining the power of the jet ( gallo et al .
2006 ) . hence to see whether there are differences in the jet emission between the millisecond pulsars , verticals and diagonals we need to compare the radio emission at the same @xmath36 .
hysteresis gives potential problems , so ideally the comparison would be between persistent verticals and diagonals in the hard island state at the same @xmath37 .
however , there is very little data to make this comparison , with only 4u 0614 + 091 and 4u 172834 for the persistent verticals and diagonals , respectively , and these do not overlap in @xmath37 ( migliari & fender 2006 ) . thus we speculate that the origin of the difference in transition behaviour between the verticals and diagonals is due to the presence of some magnetic field at the pole in the verticals which affects the accretion flow indirectly through jet formation , by contrast to the diagonals which have higher mass accretion rates , sufficient to bury the field everywhere .
the atolls and millisecond pulsars are consistent with showing the same overall spectral evolution with changing mass accretion rate , but there are some subtle differences .
the spectral shape of the soft ( banana ) branch shows subtle variations from object to object , most probably due to combination of inclination and spin changing the ratio of the observed disc to boundary layer luminosity , and boundary layer temperature . however , there are also clear differences in behaviour during the hard / soft transition which point to a more fundamental distinction .
the data shows two types of sources , those where the transition makes a vertical track on the colour - colour diagram , and occurs at @xmath0 , and those which make a diagonal track on the colour - colour diagram with the transition at @xmath38 .
there are hysteresis effects in individual sources which introduce dispersion in the transition luminosity , but these are large _ only _ for the outbursting atolls ( which are both verticals ) . splitting these outbursts into the rapid rise and slow decay phases
show that the rapid rise looks like the millisecond pulsars ( so they are probably also verticals ) while the slow decay looks like the persistent verticals .
thus it seems likely that large scale hysteresis effects are only seen in sources where the disc structure changes rapidly due to the onset of the hydrogen ionization instability .
this is also consistent with the observed black hole behaviour .
the association of the millisecond pulsars with verticals suggests that the difference in transition is ultimately linked to the surface magnetic field , and indeed , all the verticals have long term mass accretion rates which are smaller than those of the diagonals , though not as small as those of the millisecond pulsars . thus the verticals could have some small b field which is able to affect the inner accretion flow , but this must be indirect as otherwise these systems also would show pulsations .
we speculate that the physical link between the magnetic field ( predominantly polar ) and accretion flow ( predominantly equatorial ) may be due to the changes in the jet , which would be testable with more radio data on these sources .
this research has made use of data obtained through the high energy astrophysics science archive research center online service , provided by the nasa / goddard space flight center . | we systematically analyze all the available x - ray spectra of disc accreting neutron stars ( atolls and millisecond pulsars ) from the _ rxte _ database .
we show that while these all have similar spectral evolution as a function of mass accretion rate , there are also subtle differences .
there are two different types of hard / soft transition , those where the spectrum softens at all energies , leading to a diagonal track on a colour - colour diagram , and those where only the higher energy spectrum softens , giving a vertical track .
the luminosity at which the transition occurs is _ correlated _ with this spectral behaviour , with the vertical transition at @xmath0 while the diagonal one is at @xmath1 .
superimposed on this is the well known hysteresis effect , but we show that classic , large scale hysteresis occurs only in the outbursting sources , indicating that its origin is in the dramatic rate of change of mass accretion rate during the disc instability . we show that the long term mass accretion rate correlates with the transition behaviour , and speculate that this is due to the magnetic field being able to emerge from the neutron star surface for low average mass accretion rates .
while this is not strong enough to collimate the flow except in the millisecond pulsars , its presence may affect the inner accretion flow by changing the properties of the jet .
= -0.5 cm [ firstpage ] accretion , accretion discs x - rays : binaries , atoll sources |
autism spectrum disorders ( asd ) have a significant genetic component , and they are a large heterogeneous group of different disorders which are difficult to distinguish clinically due to their similar phenotype .
autistic features have been associated with many syndromes of known genetic etiology and with de novo and inherited copy number and single nucleotide variants in a magnitude of genes.1 examples of known genetic disorders that have autism as one of their frequent symptoms include the fragile x syndrome , tuberous sclerosis , prader willi syndrome , and mecp2-associated disorders.2 the deciphering of genetic etiology in a patient with asd has important consequences for family planning and also for prognosis and management of the patient , including future targeted therapies .
myotonic dystrophy type 1 ( dm1 ) is also often listed among genetic disorders associated with asd.2,3 dm1 is an autosomal - dominant disorder with an estimated prevalence of 1/8,000 and a highly variable spectrum of manifestations progressively affecting muscles and many other systems , including the central and peripheral nervous system .
the length of the expansion influences the severity and age of onset of the disease.4 four clinical forms of dm1 can be distinguished:4 1 ) the minimal form with cataract and mild or no muscular manifestations at old age ; 2 ) adult forms mainly presenting with typical progressive muscular dystrophy , muscle weakness , and myotonia ; 3 ) childhood forms with onset between 1 and 20 years of age often manifesting learning disabilities while the neuromuscular symptoms are initially absent ; 4 ) congenital forms with prenatal and neonatal manifestation of severe generalized muscle weakness and hypotonia , hyperreflexia , facial weakness , arthrogryposis , and respiratory insufficiency .
especially the childhood forms of dm1 represent a diagnostic challenge as they initially show only an unspecific psychopathological phenotype with a variable extent of cognitive impairment .
most children with congenital and childhood dm1 show speech and language delay , attention deficit , hyperactivity , or mood and anxiety disorder ( reviewed in echenne and bassez5 and ho et al6 ) .
sleep disturbances , muscular weakness , typical facial appearance , cataracts , and heart and gastrointestinal tract problems are usually among the later developing symptoms .
several reports of asd in children later diagnosed with dm1 exist,710 and a large study has shown that up to 50% of children with congenital and childhood forms of dm1 have asd.11 we report dizygotic twin boys who were referred for laboratory genetic analysis due to autistic features .
karyotyping , fragile x syndrome testing , and single nucleotide polymorphism ( snp ) array analysis yielded negative results . at the time of referral and testing of the twins , their father lived separately from the family and his clinical data
were not available . in his early forties , he was diagnosed with dm1 and laboratory analysis showed dmpk gene expansions in his genome as well as in the genomes of both twins and their elder brother who also suffered from asd . this experience and literature reports of autistic features and developmental and speech delay as the first symptoms of dm1 prompted us to screen dmpk expansions in a sample of 330 patients with asd who were first seen by a geneticist before they reached the age of 10 when the muscular weakness , which may signal dm1 , usually becomes obvious .
the currently studied 9-year - old twin boys were born from a second pregnancy of nonconsanguineous czech parents ( at the birth of the twins , the mother and father were 32 and 35 years old , respectively ) .
the delivery was in the 35th week of gestation by cesarean section due to breech position of twin a. twin a had a birth weight of 2,150 g ( 25th percentile ) and a height of 44 cm ( 25th percentile ) . the adaptation after delivery was uncomplicated ( apgar score 10 - 10 - 10 ) , but the newborn had a weak sucking reflex and he failed to thrive .
his psychomotor development was delayed , and because of cerebellar signs and central hypotonic syndrome , he has undergone physiotherapy since infancy .
he could sit at 12 months and started to walk at 18 months of age .
his first words were noted at 3.5 years of age , but his speech was incomprehensible and improved only after intensive speech therapy at 5 years of age . a neurological examination at the age of 3 years suggested asd , which was then confirmed at 6 years of age .
a psychological examination at 5 years of age revealed a mild form of attention deficit hyperactivity disorder ( adhd ) , a lower degree of emotional maturity , affective lability , moderately increased anxiety , uncertainty , introversion , and specific behavioral features like excessive demand for order and rituals . at the age of 7 years , he was diagnosed with atypical autism with mild or borderline symptomatology using autism diagnostic interview - revised and the assessment was also supplemented by the childhood autism rating scale .
his behavior was characterized by affective lability , increased anxiety , clinginess , nervousness , lowered adaptability , solitary activities in a child group , impaired reciprocal communication , and reduced eye contact .
a combined type of adhd was observed with agitation , neurotic reactions , impulsivity , easy fatigability , and a short attention span .
twin b had a birth weight of 2,850 g ( 75th percentile ) and a height of 47 cm ( 50th percentile ) .
his food intake was normal , but the switch over to solid food was accompanied by persistent chewing difficulties .
his first words were noted at 14 months and stagnation in language development was observed between 1.5 and 2.5 years of age .
after intensive speech therapy , he could speak in simple sentences at 4 years of age .
neurological examination revealed expressive dysphasia , poor fine motor skills , psychomotor retardation , autism , and hypotonic syndrome .
a psychiatric examination at 3 years of age showed expressive language disorder , delayed speech development , subnormal cognitive development , borderline intellectual disability ( i d ) ( intelligence quotient 70 using the stanford binet intelligence scale , 4th edition ) , attention deficit , clinginess , and autistic features like rituals , hypersensitivity , social immaturity , and emotional lability . at the age of 4 years , he was diagnosed with moderate - functioning childhood autism with mild - to - moderate symptomatology using autism diagnostic interview - revised and childhood autism rating scale .
he had a disproportional profile of cognitive skills at the border of mild i d .
due to central sleep apnea and intolerance to physical stress , cardiological examinations were performed at 7 years of age , which confirmed the observations and showed palpitation and a first degree atrioventricular block .
a repeated psychological examination at the age of 7 years showed high - functioning autism with borderline normal intelligence , lowered adaptability , negativism , emotional instability , developmental expressive dysphasia , and verbal stereotypes .
a neurological examination showed prominent hypotonia , dyspraxia , problems with self - care , enuresis , and encopresis , but no signs of myotonia .
the brother of the twins , who is currently 21 years old , had accelerated early psychomotor and speech development ( he has been able to speak fluently since 2 years of age and write in capital letters and read since 3 years of age ) . in the preschool age , he was diagnosed with adhd with aggressiveness .
the hyperactivity lasted till 12 years of age when it changed to attenuation , fatigue , and hypersomnia .
asd was first considered between 13 and 15 years of age . at the age of 17 years , he started developing cramps in his hands and facial muscles , and at the same time , supraventricular tachycardia and chronic atrial flutter were diagnosed and treated by radiofrequency ablation . based on the diagnosis in his brothers ,
a psychological examination was performed at 19 years of age , which showed low - functioning asperger syndrome with above - average mental performance ( intelligence quotient 111 ) using the childhood asperger syndrome test , autism screening questionnaire , high - functioning autism spectrum screening questionnaire , and australian scale for asperger s syndrome .
currently , his phenotype is characterized with prominent asthenic habitus , poor posture , narrow chest , slight ptosis , and thinning hair with frontal baldness .
their clinical information was not available but it was known that the younger girl was diagnosed with adhd and her behavior was similar to that of twin b. the mother of the twins was healthy , but three maternal relatives suffered from schizophrenia , and a nephew of the maternal grandfather of the twins was diagnosed with childhood autism .
the clinical data of the twins father were missing at the time of asd testing of the children .
, he was referred by a neurologist for genetic testing of dm1 due to mixed polyneuropathy affecting his upper limbs and chronic neurogenic impairment with myotonic discharges detected on electromyography .
a retrospective analysis showed that the first signs , like occasional tongue spasms , prolonged muscle contraction , and inability to relax fingers after exertion , had manifested since the age of 40 years .
alcoholism and bipolar affective disorder ( but no muscular symptoms ) were reported also in his father , grandfather , and sister , but the clinical data available on these individuals were very sparse .
the study of the family was approved by the ethics committee of the charles university 2nd faculty of medicine and university hospital motol . written informed consent for participation in the study was obtained from all family members or their legal guardians .
the asd patient cohort included 330 consecutive patients ( 272 boys and 58 girls ) who were referred for laboratory genetic analysis of asd at < 10 years of age ( average age at the first visit was 5.8 years ) between december 2005 and march 2010 . only patients with a normal karyotype , no fmr1 gene expansion and no clinically recognizable syndrome
the study of the asd patient cohort was approved by the ethics committee of the charles university 2nd faculty of medicine and university hospital motol . written informed consent was obtained from all participants or their legal guardians .
both twins were examined using conventional cytogenetic analysis with standard g - banding and fragile x syndrome testing using the fmr1 tp - pcr kit ( abbott , abbott park , il , usa ) ( tp - pcr , triplet - repeat primed polymerase chain reaction ) .
subsequently snp array testing was performed using humancytosnp-12 beadchip ( ~300k resolution ; illumina , san diego , ca , usa ) . due to
numerous weakly supported and likely false positive findings in twin b , this analysis was repeated in this patient using a higher - resolution snp array ( humanomniexpress-24 beadchip ; ~700k resolution ; illumina ) .
analysis of the ctg repeat in the dmpk gene in the family was performed using triplet - primed pcr on both strands of the repeat according to published protocols.12,13 the triplet - primed pcr products were separated on an abi3130 genetic analyzer ( applied biosystems , foster city , ca , usa ) .
long - range pcr employed to assess the size of the expansions used the expand long template pcr system ( roche diagnostics , mannheim , germany ) as previously described,14 in buffer 2 with 2 m betaine .
screening of dmpk expansions in the asd patient cohort was performed on one strand using the specific primer located at the 5 side of the ctg repeat.13
the currently studied 9-year - old twin boys were born from a second pregnancy of nonconsanguineous czech parents ( at the birth of the twins , the mother and father were 32 and 35 years old , respectively ) .
the delivery was in the 35th week of gestation by cesarean section due to breech position of twin a. twin a had a birth weight of 2,150 g ( 25th percentile ) and a height of 44 cm ( 25th percentile ) . the adaptation after delivery was uncomplicated ( apgar score 10 - 10 - 10 ) , but the newborn had a weak sucking reflex and he failed to thrive .
his psychomotor development was delayed , and because of cerebellar signs and central hypotonic syndrome , he has undergone physiotherapy since infancy .
he could sit at 12 months and started to walk at 18 months of age .
his first words were noted at 3.5 years of age , but his speech was incomprehensible and improved only after intensive speech therapy at 5 years of age . a neurological examination at the age of 3 years suggested asd , which was then confirmed at 6 years of age .
a psychological examination at 5 years of age revealed a mild form of attention deficit hyperactivity disorder ( adhd ) , a lower degree of emotional maturity , affective lability , moderately increased anxiety , uncertainty , introversion , and specific behavioral features like excessive demand for order and rituals . at the age of 7 years , he was diagnosed with atypical autism with mild or borderline symptomatology using autism diagnostic interview - revised and the assessment was also supplemented by the childhood autism rating scale .
his behavior was characterized by affective lability , increased anxiety , clinginess , nervousness , lowered adaptability , solitary activities in a child group , impaired reciprocal communication , and reduced eye contact .
a combined type of adhd was observed with agitation , neurotic reactions , impulsivity , easy fatigability , and a short attention span .
twin b had a birth weight of 2,850 g ( 75th percentile ) and a height of 47 cm ( 50th percentile ) .
his food intake was normal , but the switch over to solid food was accompanied by persistent chewing difficulties .
his first words were noted at 14 months and stagnation in language development was observed between 1.5 and 2.5 years of age .
after intensive speech therapy , he could speak in simple sentences at 4 years of age .
neurological examination revealed expressive dysphasia , poor fine motor skills , psychomotor retardation , autism , and hypotonic syndrome .
a psychiatric examination at 3 years of age showed expressive language disorder , delayed speech development , subnormal cognitive development , borderline intellectual disability ( i d ) ( intelligence quotient 70 using the stanford binet intelligence scale , 4th edition ) , attention deficit , clinginess , and autistic features like rituals , hypersensitivity , social immaturity , and emotional lability . at the age of 4 years , he was diagnosed with moderate - functioning childhood autism with mild - to - moderate symptomatology using autism diagnostic interview - revised and childhood autism rating scale .
he had a disproportional profile of cognitive skills at the border of mild i d .
due to central sleep apnea and intolerance to physical stress , cardiological examinations were performed at 7 years of age , which confirmed the observations and showed palpitation and a first degree atrioventricular block .
a repeated psychological examination at the age of 7 years showed high - functioning autism with borderline normal intelligence , lowered adaptability , negativism , emotional instability , developmental expressive dysphasia , and verbal stereotypes .
a neurological examination showed prominent hypotonia , dyspraxia , problems with self - care , enuresis , and encopresis , but no signs of myotonia .
the brother of the twins , who is currently 21 years old , had accelerated early psychomotor and speech development ( he has been able to speak fluently since 2 years of age and write in capital letters and read since 3 years of age ) . in the preschool age , he was diagnosed with adhd with aggressiveness .
the hyperactivity lasted till 12 years of age when it changed to attenuation , fatigue , and hypersomnia .
asd was first considered between 13 and 15 years of age . at the age of 17 years , he started developing cramps in his hands and facial muscles , and at the same time , supraventricular tachycardia and chronic atrial flutter were diagnosed and treated by radiofrequency ablation . based on the diagnosis in his brothers ,
a psychological examination was performed at 19 years of age , which showed low - functioning asperger syndrome with above - average mental performance ( intelligence quotient 111 ) using the childhood asperger syndrome test , autism screening questionnaire , high - functioning autism spectrum screening questionnaire , and australian scale for asperger s syndrome .
currently , his phenotype is characterized with prominent asthenic habitus , poor posture , narrow chest , slight ptosis , and thinning hair with frontal baldness .
their clinical information was not available but it was known that the younger girl was diagnosed with adhd and her behavior was similar to that of twin b. the mother of the twins was healthy , but three maternal relatives suffered from schizophrenia , and a nephew of the maternal grandfather of the twins was diagnosed with childhood autism .
the clinical data of the twins father were missing at the time of asd testing of the children .
, he was referred by a neurologist for genetic testing of dm1 due to mixed polyneuropathy affecting his upper limbs and chronic neurogenic impairment with myotonic discharges detected on electromyography .
a retrospective analysis showed that the first signs , like occasional tongue spasms , prolonged muscle contraction , and inability to relax fingers after exertion , had manifested since the age of 40 years .
alcoholism and bipolar affective disorder ( but no muscular symptoms ) were reported also in his father , grandfather , and sister , but the clinical data available on these individuals were very sparse .
the study of the family was approved by the ethics committee of the charles university 2nd faculty of medicine and university hospital motol . written informed consent for participation in the study was obtained from all family members or their legal guardians .
the asd patient cohort included 330 consecutive patients ( 272 boys and 58 girls ) who were referred for laboratory genetic analysis of asd at < 10 years of age ( average age at the first visit was 5.8 years ) between december 2005 and march 2010 . only patients with a normal karyotype , no fmr1 gene expansion and no clinically recognizable syndrome
the study of the asd patient cohort was approved by the ethics committee of the charles university 2nd faculty of medicine and university hospital motol . written informed consent was obtained from all participants or their legal guardians .
both twins were examined using conventional cytogenetic analysis with standard g - banding and fragile x syndrome testing using the fmr1 tp - pcr kit ( abbott , abbott park , il , usa ) ( tp - pcr , triplet - repeat primed polymerase chain reaction ) .
subsequently snp array testing was performed using humancytosnp-12 beadchip ( ~300k resolution ; illumina , san diego , ca , usa ) . due to
numerous weakly supported and likely false positive findings in twin b , this analysis was repeated in this patient using a higher - resolution snp array ( humanomniexpress-24 beadchip ; ~700k resolution ; illumina ) .
analysis of the ctg repeat in the dmpk gene in the family was performed using triplet - primed pcr on both strands of the repeat according to published protocols.12,13 the triplet - primed pcr products were separated on an abi3130 genetic analyzer ( applied biosystems , foster city , ca , usa ) .
long - range pcr employed to assess the size of the expansions used the expand long template pcr system ( roche diagnostics , mannheim , germany ) as previously described,14 in buffer 2 with 2 m betaine .
screening of dmpk expansions in the asd patient cohort was performed on one strand using the specific primer located at the 5 side of the ctg repeat.13
routine laboratory testing of asd in the twins , including snp array analysis , did not show any significant findings .
after the clinical diagnosis of suspected dm1 was established in the father , dmpk expansions were revealed first in the father and subsequently also in both twins and their brother .
the dmpk genotypes identified in the father , elder brother , twin a , and twin b were 13/130 , 5/500 , 5/300 and 5/500 ctg repeats , respectively ( figure 1 ) .
dmpk expansion testing in the sample of 330 patients with asd yielded no positive result ( all alleles were in the normal range , < 35 ctg repeats ) .
we report a case of dizygotic twin boys who were referred for genetic testing of asd and in whom a routine panel of laboratory analyses yielded no findings .
the availability of the clinical data of the father and his diagnosis of suspected dm1 caused a key shift in the deciphering of the genetic basis of the disorder in the family .
a dmpk gene expansion and the diagnosis of dm1 were first confirmed in the father and subsequently the same genetic defect was revealed in both twins and their elder brother who also suffered from asd .
the length of the expansion in the father was 130 ctg repeats , which was in accord with the adult form of dm1 .
this is in agreement with the tendency of the repeat to elongate and cause earlier onset of the disorder and increase its severity in subsequent generations.4 the span of 300550 ctg repeats corresponds to a wide spectrum of clinical forms of dm1 , ranging from congenital to adult forms.15 the clinical signs in the twins and their elder brother are consistent with childhood dm1 .
characteristic muscular signs of dm1 , such as muscle weakness , atrophy , and myotonia ( which also lead to the typical facial appearance of dm1 ) , are just mildly expressed or absent in childhood and juvenile forms of dm1 , and can appear at any age , usually in the second decade of life.4,5 the twins showed prominent neuropsychiatric phenotypes characterized by hypotonia , developmental and language delays , sleep disturbances , fatigue , i d , asd , and attention deficits , which are often the childhood symptoms of dm1.5,6 however , these symptoms are also associated with many other genetic disorders .
concerning asd specifically , several reports described autism in children with dm1710,16 and a targeted study of 57 children with mainly congenital and childhood forms of dm1 showed that almost half of them had asd.11 conversely , the incidence of dm1 among asd patients was estimated to be < 0.2%,3 but focused studies are still missing in the literature .
our analysis of 330 children with asd , which revealed no dmpk gene expansions in this cohort , strongly supports the rather low rate of dm1 in asd .
as the incidence is so low , the determination of its exact figure would require a very large sample of young asd patients .
nevertheless , several studies reported a low occurrence or absence of asd in dm1 patients : autism was diagnosed in 1/16 patients with juvenile forms;10 in 0/24 patients with childhood and juvenile forms;17 in 0/79 patients with adult forms;18 in 1/17 and 0/15 patients with congenital and infantile / juvenile forms , respectively;16 and in 0/28 patients with childhood and early adult forms.19 when asd were identified in these studies , they were exclusively present only in congenital and infantile forms of dm1 .
the main difference between these reports and ekstrm et al s 2008 study,11 which showed a very high incidence of asd in dm1 patients , was the high proportion of congenital and early childhood forms of dm1 in the latter
. however , other factors , like the use of different tests and different historical asd classification schemes and criteria or random coincidence , can also contribute .
douniol et al s study in 201219 proposed that dm1 patients did not suffer from asd but just presented a combination of symptoms that may mimic autism . from the point of view of genetic testing , this has a limited practical impact as these patients are apparently referred for genetic testing due to suspected asd , notwithstanding the fact as to whether this diagnosis is formally correct or not .
the behavioral phenotypes observed in childhood dm1 patients included social phobia , anxiety , and language delay , while the stereotyped behavior might not be so pronounced.19 also the patients included in ekstrm et al s 2008 study11 had less severe impairment in the area of restricted repetitive and stereotyped patterns of behavior , interests , and activities .
language delay , anxiety , and introversion with social withdrawal were clearly present in the twins reported here , who , however , also showed remarkable ritual behaviors , stereotypes , and insistence on sameness .
in addition to one case of autism identified in echenne et al s 2008 study,16 almost a half of their patients with childhood and congenital dm1 showed psychiatric phenotypes , including attention deficit disorders , hyperactivity , conduct disorders , aggression , opposition , anxiety , and depression .
similar to the patients included in ekstrm et al s 2008 study,11 our twin b could also be described as calm , easily fatigued , passive , and with a low pace .
twin a was diagnosed with a mixed type of adhd , which contrasts with previous reports of prevailing inattention in these patients.19 our observations thus support the notion that young individuals with dmpk gene expansions show a characteristic wide spectrum of psychiatric phenotypes . in light of the current understanding of asd as an extremely heterogeneous large group of different conditions with different genetic etiology,1
it is not surprising that subtypes of asd with specific genetic determination can have individual asd symptoms differently pronounced , and that their spectra of symptoms can overlap the spectra of other psychiatric disorders and the continuum of normal population variability .
interestingly , the preponderance of asd among the congenital and early childhood forms of dm1 may point to a developmental window in which the deleterious role of dmpk expansions , if materialized , can specifically affect the behavioral and cognitive profile of the patient .
this may be reminiscent of other genes known to be associated with neurodevelopmental disorders , especially asd and i d , which affect basic cellular processes like regulation of gene expression ; however , the negative phenotypic effect of their defects is limited to early brain development , which is a highly orchestrated and sensitive process.20 studies in model organisms may suggest that the timing of toxic ribonucleic acid expression during development can affect dm1 severity , with different effects on individual symptoms.21 when considering the causal role of the dmpk expansions for asd , it has to be recognized that they could also represent only a disease modifier potentiating the expression of another factor , and that the genetic background , which is not fully understood , is likely to play an important role . in conclusion ,
the family reported here illustrates the association between dm1 and asd , and the description of the clinical picture of the patients contributes to the definition of the spectrum of asd symptoms associated specifically with the dmpk gene expansions . concurrently
, our analysis of the dmpk gene status in a sample of 330 patients with asd referred for genetic analysis at < 10 years of age indicates that dmpk expansions are rather rare among children with autism .
targeted dmpk testing can thus be recommended only in asd patients with specific symptoms suggestive of dm1 or in patients with a family history of symptoms reminiscent of dm1 .
the awareness of asd in children with dmpk expansions is important for the planning of early behavioral training and other supports and interventions , including pharmacotherapy of specific symptoms . | myotonic dystrophy type 1 ( dm1 ) belongs to the broad spectrum of genetic disorders associated with autism spectrum disorders ( asd ) .
asd were reported predominantly in congenital and early childhood forms of dm1 .
we describe dizygotic twin boys with asd who were referred for routine laboratory genetic testing and in whom karyotyping , fmr1 gene testing , and single nucleotide polymorphism array analysis yielded negative results .
the father of the boys was later diagnosed with suspected dm1 , and testing revealed characteristic dmpk gene expansions in his genome as well as in the genomes of both twins and their elder brother , who also suffered from asd . in accord with previous reports on childhood forms of dm1 , our patients showed prominent neuropsychiatric phenotypes characterized especially by hypotonia , developmental and language delay , emotional and affective lability , lowered adaptability , and social withdrawal .
the experience with this family and multiple literature reports of asd in dm1 on the one side but the lack of literature data on the frequency of dmpk gene expansions in asd patients on the other side prompted us to screen the dmpk gene in a sample of 330 patients with asd who were first seen by a geneticist before they were 10 years of age , before the muscular weakness , which may signal dm1 , usually becomes obvious .
the absence of any dmpk gene expansions in this cohort indicates that targeted dmpk gene testing can be recommended only in asd patients with specific symptoms or family history suggestive of dm1 . |
This undated handout photo provided by Mark Gurney shows a olinguito. Imagine a raccoon with a teddy bear face that is so cute it's hard to resist, let alone overlook. But somehow science did _ until... (Associated Press)
Imagine a raccoon with a teddy bear face that is so cute it's hard to resist, let alone overlook. But somehow science did _ until now.
Researchers announced Thursday a rare discovery of a new species of mammal called the olinguito. It belongs to a grouping of large creatures that include dogs, cats and bears.
The raccoon-sized critter leaps through the trees of mountainous forests of Ecuador and Colombia at night, according to a Smithsonian researcher who has spent the past decade tracking them.
But the adorable olinguito should not have been too hard to find. One of them lived in the Smithsonian-run National Zoo in the Washington for a year in a case of mistaken identity.
"It's been kind of hiding in plain sight for a long time" despite its extraordinary beauty, said Kristofer Helgen, the Smithsonian's curator of mammals.
The zoo's little critter, named Ringerl, was mistaken for a sister species, the olingo. Ringerl was shipped from zoo to zoo in the U.S. from 1967 to 1976 to try to get it to breed with other olingos.
It would not.
"It turns out she wasn't fussy," Helgen said. "She wasn't the right species."
The discovery is described in a study in the journal ZooKey.
Helgen first figured olinguitos were different from olingos when he was looking at pelts and skeletons in a museum. He later led a team to South America in 2006.
"When we went to the field we found it in the very first night," said study co-author Roland Kays of the North Carolina Museum of Natural Sciences. "It was almost like it was waiting for us."
It is hard to figure how olingos and onlinguitos were confused for each other.
"How is it different? In almost every way that you can look at it," Helgen said.
Olinguitos are smaller, have shorter tails, a rounder face, tinier ears and darker bushier fur, he said.
"It looks kind of like a fuzzball ... kind of like a cross between a teddy bear and a house cat," Helgen said.
It eats fruit, weighs about 2 pounds (1 kilogram) and has one baby at a time. Helgen figures there are thousands of olinguitos in the mountainous forest, traveling through the trees at night so they are hard to see.
While new species are found regularly, usually they are tiny and not mammals, the warm-blooded advanced class of animals that have hair, live births and mammary glands in females.
Outside experts said this is not merely renaming something, but a genuine new species and a significant find, the type that has not happened for about 35 years.
"Most people believe there are no new species to discover, particularly of relatively large charismatic animals," said Case Western Reserve University anatomy professor Darin Croft. "This study demonstrates that this is clearly not the case."
___
Follow Seth Borenstein on Twitter at http://twitter.com/borenbears ||||| Story highlights The olinguito weighs about 2 pounds and is 2.5 feet long
This creature lives in cloud forests in Ecuador and Colombia
Previously it was mistaken for its sister species, the olingo
A small mammal with fluffy red-orange fur, a short bushy tail, and an adorable rounded face has leapt onto the raccoon family tree.
Scientists at the Smithsonian in Washington announced Thursday the discovery of a new species of mammal called the olinguito (pronounced oh-lin-GHEE-toe). If you're a fan of long technical names, this one is Bassaricyon neblina.
Such a discovery is rare. The olinguito is the first mammalian carnivore species to be newly identified in the Americas in 35 years, according to Kristofer Helgen, curator of mammals at the Smithsonian's National Museum of Natural History. His research group's study on the creature is being published in the journal ZooKeys
Researchers argue that the olinguito should be considered the smallest living member of the raccoon family, which includes other animals that make us go "awww" such as coatis and kinkajous . The Smithsonian describes the olinguito's appearance as a cross between a house cat and a teddy bear. Cats, bears, and olinguitos belong to the Carnivora order
JUST WATCHED Hiding in plain sight Replay More Videos ... MUST WATCH Hiding in plain sight 03:14
This animal had been seen before by humans, Helgen said, but it had been "a case of mistaken identity."
"It was in museums, it's been in zoos, and its DNA had even been sequenced, but no one had connected the pieces and looked close enough to realize, basically, the significance of this remarkable and this beautiful animal," Helgen said.
Previously, scientists had assumed that olinguitos were members of their sister species, the olingos, Helgen said. Olingos are larger, less furry and have longer faces than the newly discovered species.
Tracking the olinguito
Helgen began his detective work in pursuit of the new species when he set out about a decade ago to comprehensive study of olingos.
Behind the scenes at the Chicago Field Museum in 2003, he remembers pulling out a drawer of skins and skulls that didn't look like any animal he had ever seen before, or that had been reported by zoologists. The teeth and skull were smaller and shaped differently than olingos, and the coat was denser.
Records indicated to Helgen that such specimens came from the northern Andes about 5,000 to 9,000 feet above sea level, which is much higher than olingo habitats.
Helgen and colleagues worked with Miguel Pinto, a zoologist in Ecuador, who had shot a few seconds of video that appeared to depict the animal.
They teamed up in Ecuador in 2006, using Pinto's knowledge of cloud forest habitats to pick the best spots to investigate. Cloud forests are "cloaked in fog," Helgen said.
On their very first night on the pursuit, the team found a real, living olinguito.
Seeing the fluffy tree-dweller for the first time, Helgen felt "sheer elation, just incredible excitement but at the same time almost disbelief. This animal had been missed by everyone."
Even people who live in the Andes had the same confusion about olinguitos being olingos, because humans don't hunt them and the creatures stay in the trees, Helgen said.
How it lives
The researchers found out that the olinguito primarily eats fruits, but also insects and nectar, and its activity is mostly at night. The animal lives in the trees and can jump from one to another. Mothers raise a single baby at a time.
At about 2.5 feet long from nose tip to tail tip, the olinguito weighs about 2 pounds and is a little smaller than a house cat.
DNA analysis confirmed that while olinguitos and olingos both belong to the raccoon family, they are "sister groups," in the same way that humans are closely related to chimpanzees.
The olinguito's misty high-elevation habitats in Colombia and Ecuador, and the tendency for the animal to stay in the trees, have helped keep the species relatively obscure to scientists until now, Helgen said.
It turns out, according to Helgen, there are four subspecies of olinguitos, differing in color -- shades of reds, orange and browns -- and size and living in various sections of the Andes.
New species of mice, bats and shrews are more commonly discovered, but these animals are tiny and hard to tell apart, Helgen said.
Prior to the olinguito, the most recent mammal to be discovered in the Americas was a small weasel from the Andes -- the same area and habitat where the olinguitos live, he said.
"It shows us that there's a long way to go to exploring the whole world, but especially maybe these cloud forests," Helgen said. More olinguitos may be found in other South American countries with cloud forests in the future, according to the Smithsonian.
The olinguito is not yet considered an endangered species, but there are threats to its home environment, Helgen said. Many have such forests been chopped down.
"We also kind of hope that in telling this story to the world about the olinguito, that this beautiful new animal serves as something of an ambassador for those embattled cloud forest habitats."
The zoo olinguito
Helgen's group has "discovered" the olinguito, but it been evolving as an independent species for about 3 to 4 million years, he said.
One olinguito whose history Helgen's group studied was exhibited in the United States during its lifetime as if it were an olingo. The creature came from the mountains of Colombia to the Louisville Zoo in 1967, courtesy of a German couple with a love of raccoon family members, Helgen said. It was also in the Smithsonian National Zoo in Washington and the Bronx Zoo, where it passed away.
DNA from this olinguito shows that it is clearly not an olingo, Helgen said.
The wife of the animal's keeper told Helgen, "We always thought there was something strange about that olingo," he said.
She told Helgen this particular animal moved from zoo to zoo because she wouldn't breed with the olingos around her.
"It wasn't because she was fussy, it was because she was not at all even the same species," Helgen said.
With the olinguito research announcement, the oddball animal's aloofness has been vindicated. | – Scientists have discovered the first new mammalian carnivore species in the Americas in 35 years, and it's being met with a resounding "Awww!" (CNN's headline includes the word "cute," while the AP goes with "adorable.") The olinguito "looks kind of like a fuzzball," says the Smithsonian's curator of mammals. "Kind of like a cross between a teddy bear and a house cat." Here's the weird part: Decades ago, an olinguito lived in the Smithsonian-run National Zoo for an entire year, but at the time it was thought to be a member of sister species olingo. Smithsonian scientists announced the discovery today. The curator first noticed the difference between olingos and olinguitos while studying pelts and skeletons about 10 years ago; in 2006, he led a team to South America and found the new species "the very first night," a study co-author says. Even natives thought olingos and olinguitos were the same animal, since they remain in the trees of Colombia and Ecuador. But olinguitos (technical name: Bassaricyon neblina) are smaller than olingos, with rounder faces, shorter tails, smaller ears, and bushier fur; DNA analysis confirmed the two are not the same species. Olinguitos are the smallest members of the raccoon family at about 2.5 feet long from nose to tail and 2 pounds. (Another, not nearly as cute new species discovery: naked bone-eating worms in Antarctica.) |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``American Pension Investments
Modernization Act of 2014''.
SEC. 2. CONSIDERATION OF FIRM-SPECIFIC RISKS AND INCLUSION OF DIVERSE
ASSET MANAGERS IN ERISA PLANS.
(a) In General.--Section 404(a) of the Employee Retirement Income
Security Act of 1974 (29 U.S.C. 1104(a)) is amended--
(1) in paragraph (1)--
(A) in subparagraph (C), by striking ``and'' at the
end;
(B) by designating subparagraph (D) as subparagraph
(E); and
(C) by inserting after subparagraph (C) the
following:
``(D) in any case in which the fiduciary appoints an
investment manager or managers to manage any assets of a plan
under section 402(c)(3), or business enterprise or enterprises
for brokerage and investment banking services, by establishing
policies under which the fiduciary will consider--
``(i) the concentration level of the plan's
exposure to firm-specific risks, including operational,
compliance, and fraud risks;
``(ii) the inclusion, to the greatest extent
feasible, of minority business enterprises for
brokerage and investment banking services; and
``(iii) the utilization of diverse asset managers,
taking into consideration the investment opportunities
they offer in sectors, strategies, geographies, and
demographics not meaningfully available to the
plans.''; and
(2) by inserting at the end the following:
``(3)(A) For purposes of this subsection, the term `minority
business enterprise' means any business entity--
``(i) not less than 51 percent of which is owned by one or
more individuals described in subparagraph (C) or, in the case
of any publicly owned business, not less than 51 percent of the
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case of any publicly owned business, not less than 35 percent
of the stock of which is owned by such individuals; and
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which are controlled by one or more individuals described in
subparagraph (C).
``(B) For purposes of this subsection, the term `diverse asset
manager' means a minority business enterprise that manages an
investment portfolio of at least $100,000,000 and not more than
$25,000,000,000.
``(C) An individual described in this subparagraph is--
``(i) an African-American, Hispanic-American, Asian Pacific
American, Subcontinent Asian American, or Native American;
``(ii) a woman; or
``(iii) a veteran (as defined in section 101(2) of title
38, United States Code).''.
(b) Issuance of Guidance by Secretary of Labor.--Not later than 1
year after the date of the enactment of this Act, the Secretary of
Labor shall issue guidance relating to the requirement imposed by
section 404(a)(1)(D) of such Act (as amended by subsection (a)). In
issuing guidance under this subsection, the Secretary of Labor shall
consider successful practices from State, local, and private-sector
retirement systems' utilization of diverse and emerging asset managers
and of minority business enterprises for brokerage and investment
banking services, including established efforts, programs, plans, and
goals designed to increase their participation in financial services,
and providing pension plans with greater access to investment
opportunities that may otherwise be overlooked.
SEC. 3. CONSIDERATION OF FIRM-SPECIFIC RISKS AND INCLUSION OF DIVERSE
ASSET MANAGERS IN THE THRIFT SAVINGS PLAN.
(a) In General.--Section 8472 of title 5, United States Code, is
amended by adding at the end the following:
``(k) In establishing policies under subsection (f)(1)(A), the
Board shall take into account the guidance issued by the Secretary of
Labor pursuant to section 404(a)(1)(D) of the Employee Retirement
Income Security Act of 1974 (29 U.S.C. 1104(a)).''.
(b) Conforming Amendment.--Section 8477(b)(1)(C) of such title is
amended by inserting after ``of this title,'' the following: ``and
consistent with the policies developed under section 8472(k),''.
SEC. 4. ACTIVE MANAGEMENT OPTION UNDER THE THRIFT SAVINGS PLAN.
(a) In General.--Subchapter III of chapter 84 of title 5, United
States Code, is amended by inserting at the end the following:
``Sec. 8440g. Active management option
``(a) The Board shall provide employees and Members and former
employees or Members the option to participate in actively managed
funds within such employee or Member's Thrift Savings Fund account.
Such option or options shall allow not more than 20 percent of an
employee or Member's (or former employee or Member's) funds to be
actively managed.
``(b) Notwithstanding the requirement of subsection (a), the Board
may not subject more than 20 percent of the total assets under
management of the Thrift Savings Fund to active management.
``(c) The Board shall promulgate guidelines regarding the active
management of funds under this section. In promulgating such
guidelines, the Board shall consider modern and successful practices
from State, local, and private-sector retirement systems' utilization
of active management strategies in order to--
``(1) reduce market downside risks to the best extent
possible, including dramatic swings in major market indexes;
``(2) take advantage of research and investment
opportunities offered by small-, minority-, women- and veteran-
owned firms that specialize in less traditional asset classes,
or less efficient market segments with high-growth potentials,
including investments in sectors, strategies, geographies and
demographics that are not meaningfully available to large
passively invested funds; and
``(3) take advantage of more effective portfolio designs
that diversify across active and passive investment strategies
and managers.''.
(b) Clerical Amendment.--The table of sections for such subchapter
is amended by adding after the item relating to section 8440f the
following new item:
``8440g. Active management option.''.
SEC. 5. REPORTS.
Not later than 1 year after the issuance of guidance under section
2(b) and annually thereafter, the Secretary of Labor and the Chairman
of the Federal Retirement Thrift Investment Board shall submit a report
to Congress on the progress achieved and efforts being made to
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report shall include such recommendations as the Secretary and the
Chairman, respectively, deem necessary or appropriate. In addition,
each report shall include--
(1) an assessment of the extent to which compliance with
the requirements contained in such amendments is being
achieved;
(2) a summary of the enforcement actions taken by each of
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IV of the Employee Retirement Income Security Act of 1974--
(A) a list of all asset management firms (minority-
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and the amount allocated to each asset management firm;
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(C) the list of all firms (minority-owned and
others) used for brokerage and investment banking
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SEC. 6. EFFECTIVE DATE.
The amendments made by sections 2 and 3 shall apply with respect to
plan years beginning at least 9 months after the issuance of guidance
under section 2(b). | American Pension Investments Modernization Act of 2014 - Amends the Employee Retirement Income Security Act of 1974 (ERISA) to require the fiduciary of an employee benefit plan to establish policies for appointment of an investment manager or managers to manage any plan assets or business enterprise or enterprises for brokerage and investment banking services. Requires the fiduciary, under these policies, to consider: the concentration level of the plan's exposure to firm-specific risks, including operational, compliance, and fraud risks; the inclusion, to the greatest extent feasible, of minority business enterprises for brokerage and investment banking services (including enterprises owned or controlled by specified percentages of African-Americans, Hispanic-Americans, Asian Pacific Americans, Subcontinent Asian Americans, Native Americans, women, or veterans); and the utilization of diverse asset managers, taking into consideration the investment opportunities they offer in sectors, strategies, geographies, and demographics not meaningfully available to the plans. Defines "diverse asset manager" as a minority business enterprise that manages an investment portfolio of between $100 million and $25 billion. Directs the Secretary of Labor to issue related guidance and requires the Federal Retirement Thrift Investment Board (FRTIB) under the Federal Employees Retirement System (FERS) to take this guidance into account. Directs the FRTIB to give current and former federal employees and Members of Congress in FERS the option to participate in actively managed funds within the employee's or Member's Thrift Savings Fund account (but no more than 20% of a current or former employee's or Member's funds). Prohibits the FRTIB from subjecting more than 20% of the total assets under management of the Thrift Savings Fund to active management. |
black holes present us with a very deep paradox . the path to resolving this paradox
may well be the path to a consistent unified theory of matter and quantized gravity . in classical gravity ,
a black hole is a classical solution of the equations of motion such that there is a region of spacetime that is causally disconnected from asymptotic infinity ( see e.g. reference @xcite ) .
the boundary of such a region is called the event horizon .
consider a large collection of low - density matter , in an asymptotically flat spacetime . for simplicity , we take the starting configuration to be spherically symmetric and nonrotating ( these restrictions do not affect the nature of the paradox that emerges )
. this ball of matter will collapse toward smaller radii under its self - gravitation . at some point
, the matter will pass through a critical radius , the schwarzschild radius @xmath0 , after which its further collapse can not be halted , whatever the equation of state .
the final result , in classical general relativity , is that the matter ends up in an infinite - density singular point , while the metric settles down to the schwarzschild form @xmath1 here @xmath2 is newton s constant of gravity , and @xmath3 is the speed of light .
the horizon radius of this hole is @xmath4 where the last expression arises after we set @xmath5 , @xmath6 .
( in what follows , we adopt these units unless otherwise explicitly indicated ; we also set @xmath7 . )
classically , nothing can emerge from inside the horizon to the outside .
a test mass @xmath8 has effective energy zero if it is placed at the horizon ; it has rest energy @xmath9 , but a negative gravitational potential energy exactly balances this positive contribution . for a rough estimate of the horizon size , we may put this negative energy to be the newtonian value @xmath10 , for which @xmath11 .
it may appear from the above that the gravitational fields at the horizon of a black hole are very large .
this is not true . for a neutral black hole of mass @xmath12 ,
the magnitude of the curvature invariants , which are the measure of local gravitational forces , is given by | r| ~g_n m r^3 .
thus , at the horizon @xmath13 , the curvature scales as @xmath14 . as a result , for black holes with masses @xmath15 ,
the curvatures are very small and the spacetime is locally rather close to flat spacetime .
in fact , an object falling into a black hole will not experience any strong force as it crosses the horizon
. however , an asymptotic observer watching this object will see that it takes an infinite time to reach the horizon .
this is because there is an infinite gravitational red - shift between the horizon and the asymptotic region .
an important point about black hole formation is that one does not need to crush matter to high densities to form a black hole .
in fact , if the hole has mass @xmath12 , the order of magnitude of the density required of the matter is @xmath16 thus , a black hole of the kind believed to exist at the center of our galaxy ( @xmath17 solar masses ) could form from a ball with the density of water .
in fact , given any density we choose , we can make a black hole if we take a sufficient total mass with that density .
this fact makes it very hard to imagine a theory in which black holes do not form at all because of some feature of the interaction between the matter particles . as a consequence , if black holes lead to a paradox , it is hard to bypass the paradox by doing away with black holes in the theory .
it is now fairly widely believed that black holes exist in nature .
solar - mass black holes can be endpoints of stellar evolution , and supermassive black holes ( @xmath18 solar masses ) probably exist at the centers of galaxies . in some situations , these holes accrete matter from their surroundings , and the collisions among these infalling particles create very powerful sources of radiation that are believed to be the source of the high - energy output of quasars . in this article , however , we are not concerned with any of these astrophysical issues .
we concentrate instead on the quantum properties of isolated black holes , with a view toward understanding the problems that arise as issues of principle when quantum mechanical ideas are put in the context of black holes .
for example , the hawking radiation process discussed below is a quantum process that is much weaker than the radiation from the infalling matter mentioned above , and it would be almost impossible to measure even by itself .
( the one possible exception is the hawking radiation at the last stage of quantum evaporation .
this radiation emerges in a sharp burst with a universal profile , and there are experiments under way to look for such radiation from very small primordial black holes . ) already , at this stage , one finds what may be called the entropy problem .
one of the most time - honored laws in physics has been the second law of thermodynamics , which states that the entropy of matter in the universe can not decrease .
but with a black hole present in the universe , one can imagine the following process .
a box containing some gas , which has a certain entropy , is dropped into a large black hole .
the metric of the black hole then soon settles down to the schwarzschild form above , though with a larger value for @xmath12 , the black hole mass .
the entropy of the gas has vanished from view , so that if we only count the entropy that we can explicitly see , then the second law of thermodynamics has been violated !
this violation of the second law can be avoided if one associates an entropy to the black hole itself . starting with the work of bekenstein @xcite , we now know that if we associate an entropy @xmath19 with the black hole of horizon area @xmath20 , then in any gedanken experiment in which we try to lose entropy down the hole , the increase in the black hole s attributed entropy is such that @xmath21 ( for an analysis of such gedanken experiments , see e.g. @xcite ) . furthermore , an `` area theorem '' in general relativity states that in any classical process , the total area of all black holes can not decrease .
this statement is rather reminiscent of the statement of the second law of thermodynamics the entropy of the entire universe can never decrease . thus the proposal ( equation [ eq : two ] )
would appear to be a nice one , but now we encounter the following problem .
we would also like to believe on general grounds that thermodynamics can be understood in terms of statistical mechanics ; in particular , the entropy @xmath22 of any system is given by s = log , [ eq : none ] where @xmath23 denotes the number of states of the system for a given value of the macroscopic parameters .
for a black hole of one solar mass , this implies that there should be @xmath24 states !
but the metric ( equation [ eq : one ] ) of the hole suggests a unique state for the geometry of the configuration .
if one tries to consider small fluctuations around this metric , or adds in , say , a scalar field in the vicinity of the horizon , then the extra fields soon flow off to infinity or fall into the hole , and the metric again settles down to the form of equation [ eq : one ] .
if the black hole has a unique state , then the entropy should be @xmath25 , which is not what we expected from equation [ eq : two ] .
the idea that the black hole configuration is uniquely determined by its mass ( and any other conserved charges ) arose from studies of many simple examples of the matter fields .
this idea of uniqueness was encoded in the statement `` black holes have no hair . ''
( this statement is not strictly true when more general matter fields are considered . )
it is a very interesting and precise requirement on the theory of quantum gravity plus matter that there be indeed just the number ( equation [ eq : two ] ) of microstates corresponding to a given classical geometry of a black hole .
if black holes have an entropy @xmath26 and an energy equal to the mass @xmath12 , then if thermodynamics were to be valid , we would expect them to have a temperature given by @xmath27 for a neutral black hole in four spacetime dimensions , @xmath28 , which gives t=(dsdm)^-1=18g_n m. [ eq : ntwo ] again assuming thermodynamical behavior , the above statement implies that if the hole can absorb photons at a given wave number @xmath29 with absorption cross section @xmath30 , then it must also radiate at the same wave number at the rate @xmath31 in other words , the emission rate is given by the absorption cross section multiplied by a standard thermal factor ( this factor would have a plus sign in place of the minus sign if we were considering fermion emission ) and a phase space factor that counts the number of states in the wave number range @xmath32 and @xmath33 .
( @xmath34 denotes the number of spatial dimensions . )
classically , nothing can come out of the black hole horizon , so it is tempting to say that no such radiation is possible .
however , in 1974 , hawking @xcite found that if the quantum behavior of matter fields is considered , such radiation is possible .
the vacuum for the matter fields has fluctuations , so that pairs of particles and antiparticles are produced and annihilated continuously . in normal spacetimes ,
the pair annihilates quickly in a time set by the uncertainty principle .
however , in a black hole background , one member of this pair can fall into the hole , where it has a net negative energy , while the other member of the pair can escape to infinity as real positive energy radiation @xcite .
the profile of this radiation is found to be thermal , with a temperature given by equation [ eq : ntwo ] .
although we have so far discussed the simplest black holes , there are black hole solutions that carry charge and angular momentum .
we can also consider generalizations of general relativity to arbitrary numbers of spacetime dimensions ( as will be required below ) and further consider other matter fields in the theory .
it is remarkable that the above discussed thermodynamic properties of black holes seem to be universal .
the leading term in the entropy is in fact given by equation [ eq : two ] for all black holes of all kinds in any number of dimensions .
furthermore , the temperature is given in terms of another geometric quantity called the surface gravity at the horizon , @xmath35 , which is the acceleration felt by a static object at the horizon as measured from the asymptotic region .
the precise relation also universal is t = 2 .
[ eq : nthree ] `` hawking radiation '' is produced from the quantum fluctuations of the matter vacuum , in the presence of the gravitational field of the hole .
for black holes of masses much larger than the scale set by newton s constant , the gravitational field near the horizon , where the particle pairs are produced in this simple picture , is given quite accurately by the classical metric of equation [ eq : one ] .
the curvature invariants at the horizon are all very small compared with the planck scale , so quantum gravity seems not to be required .
further , the calculation is insensitive to the precise details of the matter that went to make up the hole . thus , if the hole completely evaporates away , the final radiation state can not have any significant information about the initial matter state .
this circumstance would contradict the assumption in usual quantum mechanics that the final state of any time evolution is related in a one - to - one and onto fashion to the initial state , through a unitary evolution operator .
worse , the final state is in fact not even a normal quantum state .
the outgoing member of a pair of particles created by the quantum fluctuation is in a mixed state with the member that falls into the hole , so that the outgoing radiation is highly `` entangled '' with whatever is left behind at the hole .
if the hole completely evaporates away , then this final state is entangled with `` nothing , '' and we find that the resulting system is described not by a pure quantum state but by a mixed state . if the above reasoning and computations are correct , one confronts a set of alternatives , none of which are very palatable ( for a survey see e.g. reference @xcite ) .
the semiclassical reasoning used in the derivation of hawking radiation can not say whether the hole continues to evaporate after it reaches planck size , since at this point quantum gravity would presumably have to be important . the hole may not completely evaporate away but leave a `` remnant '' of planck size .
the radiation sent off to infinity will remain entangled with this remnant . but this entanglement entropy is somewhat larger @xcite than the black hole entropy @xmath26 , which is a very large number ( as we have seen above ) .
thus , the remnant will have to have a very large number of possible states , and this number will grow to infinity as the mass of the initial hole is taken to infinity . it is uncomfortable to have a theory in which a particle of bounded mass ( planck mass ) can have an infinite number of configurations .
one might worry that in any quantum process , one can have loops of this remnant particle , and this contribution will diverge , since the number of states of the remnant is infinite .
but it has been argued that remnants from holes of increasingly large mass might couple to any given process with correspondingly smaller strength , and then such a divergence can be avoided .
another possibility , advocated most strongly by hawking , is that the hole does evaporate away to nothing , and the passage from an intial pure state to a final mixed state is a natural process in any theory of quantum gravity . in this view
, the natural description of states is in fact in terms of density matrices , and the pure states of quantum mechanics that we are used to thinking about are only a special case of this more general kind of state .
some investigations of this possibility have suggested , however , that giving up the purity of quantum states causes difficulties with maintaining energy conservation in virtual processes ( @xcite ; for a counterargument , see reference @xcite ) .
the possibility that would best fit our experience of physics in general would be that the hawking radiation does manage to carry out the information of the collapsing matter @xcite .
the hole could then completely evaporate away , and yet the process would be in line with the unitarity of quantum mechanics .
the hawking radiation from the black hole would not fundamentally differ from the radiation from a lump of burning coal the information of the atomic structure of the coal is contained , though it is difficult to decipher , in the radiation and other products that emerge when the coal burns away .
let us review briefly the difficulties with having the radiation carry out the information .
to study the evolution , we choose a foliation of the spacetime by smooth spacelike hypersurfaces .
this requires that the spatial slices be smooth and that the embedding of neighboring slices changes in a way that is not too sharp .
as we evolve along this foliation , we see the matter fall in toward the center of the hole , while we see the radiation collect at spatial infinity .
it is important to realize that the information in the collapsing matter can not also be copied into the radiation in other words , there can be no quantum `` xeroxing . ''
the reason is as follows .
suppose the evolution process makes two copies of a state @xmath36 where the @xmath37 are a set of basis states .
then , as long as the linearity of quantum mechanics holds , we will find @xmath38 thus , a general state can not be `` duplicated '' by any quantum process .
figure 1 shows the spacetime in a symbolic way .
we use a foliation of spacetime by the following kind of spacelike hypersurfaces . away from the black hole ,
say for @xmath39 , we let the hypersurface be a @xmath40 surface ( this description uses the schwarzschild coordinates of equation [ eq : one ] ) . inside the black hole , an @xmath41constant surface is spacelike ; let us choose @xmath42 so that this part of the surface is neither close to the horizon ( @xmath43 nor close to the singularity ( @xmath44 ) .
this part of the hypersurface will extend from some time @xmath45 near the formation of the hole to the value @xmath40 .
finally , we can connect these two parts of the hypersurface by a smooth interpolating region that is spacelike as well .
each of the spacelike hypersurfaces shown in figure 1 is assumed to be of this form .
the lower one has @xmath45 , whereas the upper one corresponds to a time @xmath46 , where a mass @xmath47 has been evaporated away as radiation .
we assume , however , that at @xmath48 the black hole is nowhere near its endpoint of evaporation , either by assuming that a slow dose of matter was continually fed into the black hole to maintain its size ( the simplest assumption ) or by considering a time @xmath48 where say a quarter of the hole has evaporated ( and modifying the metric to reflect the slow decrease of black hole mass ) . on the lower hypersurface
, we have on the left the matter that fell in to make the hole .
there is no radiation yet , so there is nothing else on this hypersurface .
let us call this matter `` a. '' on the upper hypersurface , we expect the following sources of stress energy , in a semiclassical analysis of the hawking process . on the left , we will still have the matter that fell in to make the hole , since this part of the surface is common to both hypersurfaces . on the extreme right
, we will have the hawking radiation that has emerged in the evaporation process ; let us call this `` c. '' in the middle are the infalling members of the particle - antiparticle pairs .
these contribute a negative value to the total mass of the system because of the way the hypersurface is oriented with respect to the coordinate @xmath49this maintains overall energy conservation in the process .
let us call this part of the state `` b. '' the semiclassical process gives a state for the light matter fields , which is entangled between components b and c. on the other hand , components a and b are expected to somehow vanish together ( or leave a planck mass remnant ) , since their energies cancel each other . at the end of the process
, the radiation c will have the energy initially present in a. but since c will be entangled with b , the final state will not be a pure state of radiation .
we can now see explicitly the difficulties with obtaining in any theory a unitary description of the process of black hole formation and evaporation . in a general curved spacetime
, we should be able to evolve our hypersurfaces by different amounts at different points this is the `` many - fingered time '' evolution of general relativity extended to include the quantum matter on the spacetime . by using an appropriate choice of this evolution ,
we have captured both the infalling matter a and the outgoing radiation c on the same spacelike hypersurface .
if we want the radiation c to carry the information of the matter a , then we will need `` quantum xeroxing , '' which , as mentioned above , can not happen if we accept the principle of superposition of quantum mechanics .
it would have been very satisfactory if we just could not draw a smooth hypersurface like the upper one in figure 1 , a hypersurface that includes both the infalling matter and the outgoing radiation .
for example , we could have hoped that any such surface would need to be non - spacelike at some point , or that it would need a sharp kink in one or more places .
but it is easy to see from the construction of surfaces described above that all the hypersurfaces in the evolution are smooth .
in fact , the later one is in some sense just a time translate of the earlier one the part @xmath50 in each surface has the same intrinsic ( and extrinsic ) geometry for each hypersurface , and the segment that connects this part to the @xmath51 part can be taken to be the same as well .
the only difference between the hypersurfaces is that the later one has a larger @xmath51 part .
one can further check that the infalling matter has finite energy along each hypersurface and that scalar quantities such as @xmath52 are bounded and smooth along each surface ( @xmath53 is the proper length along the surface ) . in the above calculations ,
spacetime was treated classically , but the conclusions do not change even if we let the evolution of spacelike surfaces be described by the wheeler de witt equation , which gives a naive quantization of gravity ; quantum fluctuations of the spacetime may appear large in certain coordinates @xcite , but such effects cancel out in the computation of hawking radiation @xcite .
it thus appears that in order to have unitarity one needs a nonlocal mechanism ( which operates over macroscopic distances @xmath47 ) that moves the information from a to c. even though the spacetime appears to have no regions of planck - scale curvature , we must alter our understanding of how information in one set of low - energy modes ( a ) moves into another set of low energy modes ( c ) .
a key point appears to be that , in the semiclassical calculation , the radiation c emerges from modes of the quantum field that in the past had a frequency much higher than planck frequency .
a naive model of the quantum field would have these modes at all frequencies , but if the complete theory of matter and gravity has an inbuilt cutoff at the planck scale , then the radiation c must have had its origins somewhere else possibly in some nonlocal combination of modes with sub - planckian energy .
if some such possibility is true , we would obtain unitarity , while also obtaining some nontrivial insight into the high - energy structure of the quantum vacuum .
basic to such an approach would be some way of understanding a black hole as a complicated version of usual matter states , and not as an esoteric new object that must be added to a theory of `` regular '' matter .
it would still be true that the final state of a system changes character significantly when its density changes from that of a star , for instance , to the density at which it collapses to form a black hole , but the resulting hole should still be described by the same essential principles of quantum mechanics , density of states , statistical mechanics , etc , as any other matter system . as we show below
, string theory provides not only a consistent theory of quantized gravity and matter , but also a way of thinking about black holes as quantum states of the matter variables in the theory .
in a certain regime of parameters , string theory is best thought of as a theory of interacting elementary strings ( for expositions of superstring theory , see reference @xcite ) .
the basic scale is set by the string tension @xmath54 or , equivalently , the `` string length '' l_s = 1 .
[ eq : szero ] the quantized harmonics of a string represent particles of various masses and spins , and the masses are typically integral multiples of @xmath55 .
thus , at energies much smaller than @xmath55 , only the lowest harmonics are relevant . the interaction between strings
is controlled by a dimensionless string coupling @xmath56 , and the above description of the theory in terms of propagating and interacting strings is a good description when @xmath57 . even in weak coupling perturbation theory
, quantization imposes rather severe restrictions on possible string theories .
in particular , all consistent string theories ( @xmath58 ) live in ten spacetime dimensions and ( @xmath59 ) respect supersymmetry . at the perturbative level , there are five such string theories , although recent developments in nonperturbative string theory show that these five theories are in fact perturbations around different vacua of a single theory , whose structure is only incompletely understood at this point ( for a review of string dualities , see reference @xcite ) .
remarkably , in all these theories there is a set of exactly massless modes that describe the very - low - energy behavior of the theory .
string theories have the potential to provide a unified theory of all interactions and matter .
the most common scenario for this is to choose @xmath60 to be of the order of the planck scale , although there have been recent suggestions that this length scale can be considerably longer without contradicting known experimental facts @xcite .
the massless modes then describe the observed low - energy world .
of course , to describe the real world , most of these modes must acquire a mass , typically much smaller than @xmath55 .
it turns out that the massless modes of open strings are gauge fields .
the lowest state of an open string carries one quantum of the lowest vibration mode of the string with a polarization @xmath61 ; this gives the gauge boson @xmath62 .
the effective low - energy field theory is a supersymmetric yang - mills theory .
the closed string can carry traveling waves both clockwise and counterclockwise along its length .
in closed string theories , the state with one quantum of the lowest harmonic in each direction is a massless spin-2 particle , which is in fact the graviton : if the transverse directions of the vibrations are @xmath61 and @xmath63 , then we get the graviton @xmath64
. the low - energy limits of closed string theories thus contain gravity and are supersymmetric extensions of general relativity
. however , unlike these local theories of gravity , which are not renormalizable , string theory yields a _
finite _ theory of gravity essentially due to the extended nature of the string .
how can such theories in ten dimensions describe our 4-dimensional world ?
the point is that all of the dimensions need not be infinitely extended some of them can be compact .
consider , for example , the simplest situation , in which the 10-dimensional spacetime is flat and the `` internal '' 6-dimensional space is a 6-torus @xmath65 with ( periodic ) coordinates @xmath66 , which we choose to be all of the same period : @xmath67 .
if @xmath68 denotes the coordinates of the noncompact 4-dimensional spacetime , we can write a scalar field @xmath69 as ( x , y ) = _ n_i _ n_i ( x ) , [ eq : sone ] where @xmath70 denotes the six components of integer - valued momenta @xmath71 along the internal directions .
when , for example , @xmath72 is a massless field satisfying the standard klein - gordon equation @xmath73 , it is clear from equation [ eq : sone ] that the field @xmath74 has ( in four dimensions ) a mass @xmath75 given by @xmath76 .
thus , a single field in higher dimensions becomes an infinite number of fields in the noncompact world . for energies
much lower than @xmath77 , only the @xmath78 mode can be excited . for other kinds of internal manifolds ,
the essential physics is the same .
now , however , we have more complicated wavefunctions on the internal space .
what is rather nontrivial is that when one applies the same mechanism to the spacetime metric , the effective lower - dimensional world contains a metric field as well as vector gauge fields and scalar matter fields . before the advent of strings as a theory of quantum gravity
, there was an attempt to control loop divergences in gravity by making the theory supersymmetric .
the greater the number of supersymmetries , the better was the control of divergences .
but in four dimensions , the maximal number of supersymmetries is eight ; more supersymmetries would force the theory to have fields of spin higher than 2 in the graviton supermultiplet , which leads to inconsistencies at the level of interactions .
such @xmath79 supersymmetric theories appear complicated but can be obtained in a simple way from a @xmath80 theory or a @xmath81 theory via the process of dimensional reduction explained above .
the gravity multiplet in the higher - dimensional theory gives gravity as well as matter fields after dimensional reduction to lower dimensions , with specific interactions between all the fields .
the bosonic part of 11-dimensional supergravity consists of the metric @xmath82 and a 3-form gauge field @xmath83 with an action s_11 = 1 ( 2)^8 l_p^9[d^11x [ r - 148 f_mnpq f^mnpq ] + 16d^11x a f f ] ] , [ eq : hone ] where @xmath84 is the ricci scalar and @xmath85 is the field strength of @xmath83 .
@xmath86 denotes the 11-dimensional planck length so that the 11-dimensional newton s constant is @xmath87 .
this theory has no free dimensionless parameter .
there is only one scale , @xmath86 .
now consider compactifying one of the directions , say @xmath88 .
the line interval may be written as ds^2 = e^-6g_dx^dx^+ e^43(dx^11 - a_dx^)^2 .
[ eq : htwo ] in equation [ eq : htwo ] , the indices @xmath89 run over the values @xmath90 .
the various components of the 11-dimensional metric have been written in terms of a 10-dimensional metric , a field @xmath91 and a field @xmath92 .
clearly , from the point of view of the 10-dimensional spacetime , @xmath93 is a vector and @xmath94 is a scalar . in a similar way ,
the 3-form gauge field splits into a rank-2 gauge field and a rank-3 gauge field in ten dimensions , @xmath95 and @xmath96 .
the field @xmath91 behaves as a @xmath97 gauge field .
the bosonic massless fields are thus 1 . the metric @xmath98 ; + 2 . a real scalar , the dilaton @xmath92 ; + 3 .
a vector gauge field @xmath91 with field strength @xmath99 ; + 4 .
a rank-2 antisymmetric tensor gauge field @xmath100 with field strength @xmath101 ; + 5 . a rank-3 antisymmetric tensor gauge field @xmath102 with field strength @xmath103 . at low energies , all the fields in the action ( equation [ eq : hone ] ) are independent of @xmath88 and
the 10-dimensional action is & s = 1 ( 2)^7 g^2 l_s^8d^10 x ( r - & 12()^2 - 112e^- f_f^ - 14 e^32 f_f^ + & & + 148e^/2f _ f^ ) + [ eq : hsix ] where the ellipsis denotes the terms that come from the dimensional reduction of the last term in equation [ eq : hone ] .
@xmath104 denotes the field strength of the appropriate gauge field .
the action ( equation [ eq : hsix ] ) is precisely the bosonic part of the action of type iia supergravity in ten dimensions .
the scalar field @xmath92 is called a dilaton and plays a special role in this theory .
its expectation value is related to the string coupling g_s = exp ( ) .
[ eq : hseven ] the overall factor in equation [ eq : hsix ] follows from the fact that the 11-dimensional measure in equation [ eq : hone ] is related to the 10-dimensional measure by a factor of the radius of @xmath88 ( which is @xmath84 ) , giving = 1 ( 2)^7 g^2 l_s^8 , [ eq : height ] which defines the string length @xmath60 .
@xmath105from the 11-dimensional metric , it is clear that @xmath106 , so that equation [ eq : height ] gives @xmath107 .
the 10-dimensional metric @xmath98 used in equations [ eq : htwo ] and [ eq : hsix ] is called the `` einstein frame '' metric because the einstein - hilbert term in equation [ eq : hsix ] is canonical .
other metrics used in string theory , most notably the `` string frame '' metric , differ from this by conformal transformations . in this article
we always use the einstein frame metric .
although we have given the explicit formulae for dimensional reduction of the bosonic sector of the theory , the fermionic sector can be treated similarly .
there are two types of gravitinos
fermionic partners of the graviton .
one of them has positive 10-dimensional chirality whereas the other has negative chirality .
the resulting theory is thus nonchiral .
there is another supergravity in ten dimensions , type iib supergravity .
this can not be obtained from d=11 supergravity by dimensional reduction .
the bosonic fields of this theory are + 1 . the metric @xmath98 + 2 .
two real scalars : the dilaton @xmath92 and the axion @xmath108 + 3 .
two sets of rank-2 antisymmetric tensor gauge fields : @xmath100 and @xmath109 with field strengths @xmath110 and @xmath111 + 4 . a rank-4 gauge field @xmath112 with a self - dual field strength @xmath113 . both the gravitinos of this theory have the same chirality .
because of the self - duality constraint on the 5-form field strength , it is not possible to write down the action for type iib supergravity , although the equations of motion make perfect sense . if , however , we put the 5-form field strength to zero , we have a local action given by & s = 1 ( 2)^7 g^2 l_s^8d^10 x [ ( r - & 12()^2 -112e^- h_h^ + & & - 112e^ ( h_- h_)(h^ - h^ ) ] . + [ eq : hsixa ] of course , these supergravities can not be consistently quantized , since they are not renormalizable
. however , they are the low - energy limits of string theories , called the type iia and type iib string .
although string theory removes ultraviolet divergences leading to a finite theory of gravity , such features as the necessity of ten dimensions and the presence of an infinite tower of modes above the massless graviton made it unpalatable to many physicists .
furthermore , some find the change from a pointlike particle to a string somewhat arbitrary
if we accept strings , then why not extended objects of other dimensionalities ? over the past few years ,
as nonperturbative string theory has developed , it has been realized that the features of string theory are actually very natural and also perhaps essential to any correct theory of quantum gravity .
a crucial ingredient in this new insight is the fact that higher - dimensional extended objects branes are present in the spectrum of string theory
. a closer look at even supergravity theories leads to the observation that the existence of extended objects is natural within those theories ( and in fact turns out to be essential to completing them to unitary theories at the quantum level ) .
consider the case of 11-dimensional supergravity .
the supercharge @xmath114 is a spinor , with @xmath115 .
the anticommutator of two supercharge components should lead to a translation , so we write @xmath116 where @xmath117 is the charge conjugation matrix . because the anticommutator is symmetric in @xmath118 , we find that there are @xmath119 objects on the left - hand side of this equation , but only @xmath120 objects ( the @xmath121 ) on the right - hand side .
if we write down all the possible terms on the right that are allowed by lorentz symmetry , then we find @xcite \{q _ , q_}=(^a c)_p_a+(^a ^b c)_z_ab+(^a ^b^c ^d^e c)_z_abcde , [ eq : stwo ] where the @xmath122 are totally antisymmetric .
the number of @xmath123 is @xmath124 , whereas the number of @xmath125 is @xmath126 , and now we have a total of @xmath127 objects on the right , in agreement with the number on the left .
although , for example , @xmath128 implies that the configuration has momentum in direction @xmath129 , what is the interpretation of @xmath130 ?
it turns out that this can be interpreted as the presence of a `` sheetlike '' charged object stretched along the directions @xmath131 .
it is then logical to postulate that there exists in the theory a 2-dimensional fundamental object ( the 2-brane ) .
similarly , the charge @xmath125 corresponds to a 5-brane in the theory .
the 2-brane has a @xmath132-dimensional world volume and couples naturally to the 3-form gauge field present in 11-dimensional supergravity , just as a particle with 1-dimensional world line couples to a 1-form gauge field as @xmath133 .
the 5-brane is easily seen to be the magnetic dual to the 2-brane , and it couples to the 6-form that is dual to the 3-form gauge field in 11 dimensions .
thus , it is natural to include some specific extended objects in the quantization of 11-dimensional supergravity . but how does this relate to string theory , which lives in ten dimensions ? let us compactify the 11-dimensional spacetime on a small circle , thus obtaining 10-dimensional noncompact spacetime .
then , if we let the 2-brane wrap this small circle , we get what looks like a string in ten dimensions .
this is exactly the type iia string that had been quantized by the string theorists !
the size of the small compact circle turns out to be the coupling constant of the string .
we can also choose not to wrap the 2-brane on the small circle , in which case there should be a two - dimensional extended object in type iia string theory .
such an object is indeed present
it is one of the d - branes shown to exist in string theory by polchinski @xcite .
similarly , we may wrap the 5-brane on the small circle , getting a 4-dimensional d - brane in string theory , or leave it unwrapped , getting a solitonic 5-brane , which is also known to exist in the theory .
thus , one is forced to a unique set of extended objects in the theory , with specified interactions between them in fact , there is no freedom to add or remove any object , nor to change any couplings .
a very important property of such branes is that when they are in an unexcited state , they preserve some of the supersymmetries of the system , and are thus bogomolny - prasad - sommerfield saturated ( bps ) states .
let us see in a simple context what a bps state is .
consider first a theory with a single supercharge @xmath134 : @xmath135 where @xmath136 is the hamiltonian .
these relations show that the energy of any state can not be negative . if @xmath137 then @xmath138 where the equality holds in the last step if and only if @xmath139 that is , the state is supersymmetric .
nonsupersymmetric states occur in a `` multiplet '' containing a bosonic state @xmath140 and a fermionic state @xmath141 of the same energy : @xmath142 supersymmetric states have @xmath143 and need not be so paired .
now suppose there are two such supersymmetries : @xmath144 where @xmath122 is a `` charge '' ; it will take a @xmath3 number value on the states that we consider below . in a spirit similar to the calculations above
, we can now conclude @xmath145 this implies that @xmath146 with equality holding if and only if @xmath147 now we have three kinds of states : 1 . states with @xmath148 .
these have @xmath143 and do not fall into a multiplet . by equation [ eq : twoseven ]
, they also have @xmath149 , so they carry no charge .
states not in category 1 , but satisfying equation [ eq : twonine ] . for concreteness ,
take the case @xmath150 .
these states fall into a `` short multiplet '' described by , say , the basis @xmath151 .
note that @xmath152 so that we have no more linearly independent states in the multiplet .
such states satisfy @xmath153 and are called bps states .
note that by equation [ eq : twoseven ] , the state with @xmath154 satisfies @xmath150 while the state with @xmath155 satisfies @xmath156 .
states that are not annihilated by any linear combination of @xmath157 .
these form a `` long multiplet '' @xmath158 .
they must have @xmath159 . in the above discussion
, we have regarded the bps states as states of a quantum system , but a similar analysis applies to classical solutions . in 10-dimensional supergravity , the branes mentioned above appear as classical solutions of the equations of motion , typically with sources .
they are massive solitonlike objects and therefore produce gravitational fields . apart from that
, they produce the p - form gauge fields to which they couple and , in general , a nontrivial dilaton .
a brane in a general configuration would break all the supersymmetries of the theory . however , for special configurations corresponding to `` unexcited branes''there are solutions which retain some of the supersymmetries .
these are bps saturated solutions , and since they have the maximal charge for a given mass , they are stable objects .
we use such branes below in constructing black holes . instead of using the 11-dimensional algebra ,
we could have used the 10-dimensional algebra and arrived at the same conclusions . in a similar fashion
, the existence of bps branes in type iib supergravity follows from the corresponding algebra . for each antisymmetric tensor field present in the spectrum , there is a corresponding bps brane .
thus we have 1 .
d(@xmath160)-brane , or d - instantons , carrying charge under the axion field @xmath108 ; 2 .
ns1-brane , or elementary string , carrying electric charge under @xmath100 ; 3 .
d1-brane , carrying electric charge under @xmath109 ; 4 .
3-brane , carrying charge under @xmath161 ; 5 .
ns5-brane , carrying magnetic charge under @xmath100 ; 6 .
d5-brane , carrying magnetic charge under @xmath109 ; 7 .
d7-brane , the dual of the d(@xmath160 ) brane .
we have denoted some of the branes as d - branes .
these play a special role in string theory , as explained below .
consider the low - energy action of the supergravity theories .
we have remarked above that the equations of motion for the massless fields admit solitonic solutions , where the solitons are not in general pointlike but could be @xmath162-dimensional sheets in space [ thus having @xmath163-dimensional world volumes in spacetime ] . in each of these cases ,
the soliton involves the gravitational field and some other @xmath163-form field in the supergravity multiplet so that the final solution carries a charge under this @xmath163-form gauge field .
in fact , in appropriate units , this soliton is seen to have a mass equal to its charge and is thus an object satisfying the bps bound of supersymmetric theories .
this fact implies that the soliton is a stable construct in the theory .
the possible values of @xmath162 are determined entirely by the properties of fermions in the type ii theory .
it turns out that for type iia , @xmath162 must be even ( @xmath164 ) , whereas for type iib @xmath162 must be odd ( @xmath165 ) . recalling the massless spectrum of these theories , we find that for each antisymmetric tensor field there is a brane that couples to it .
because the brane is not pointlike but is an extended object , we can easily see that there will be low - energy excitations of this soliton in which its world sheet suffers small transverse displacements that vary along the brane ( in other words , the brane carries waves corresponding to transverse vibrations ) .
the low - energy action is thus expected to be the tension of the brane times its area . for a single 1-brane , for instance
, the action for long - wavelength deformations is s = t_1 2d^2^ , [ eq : sseven ] where @xmath166 , with @xmath167 , denotes an arbitrary coordinate sytem on the d1-brane world sheet and @xmath168 denotes the induced metric on the brane , g _ = _
x^_x^_. [ eq : seight ] the @xmath169 with @xmath170 , denotes the coordinates of a point on the brane .
this action is invariant under arbitrary transformations of the coordinates @xmath166 on the brane . to make contact with to the picture discussed above , it is best to work in a static gauge by choosing @xmath171 and @xmath172 .
the induced metric ( equation [ eq : seight ] ) then becomes g _
_ ij , where @xmath173 with @xmath174 , are the remaining fields .
the determinant in equation [ eq : sseven ] may be then expanded in powers of @xmath175 .
the lowest - order term is just the free kinetic energy term for the eight scalar fields @xmath176 .
it is now straightforward to extend the above discussion for higher - dimensional branes .
now we can have both transverse and longitudinal oscillations of the brane .
for a @xmath162-brane we have @xmath177 transverse coordinates , labeled by @xmath178 , and hence as many scalar fields on the @xmath163-dimensional brane world volume , @xmath176 .
it turns out that the longitudinal waves are carried by a @xmath97 _ gauge _ field @xmath179 with the index @xmath180 ranging over the world volume directions .
the generalization of equation [ eq : sseven ] [ called the dirac - born - infeld ( dbi ) action ] is s = t_p 2d^p+1 , where @xmath181 is the gauge field strength .
once again , one can choose a static gauge and relate the fields directly to a string theory description .
the low - energy expansion of the action then leads to electrodynamics in @xmath163 dimensions with some neutral scalars and fermions . in the above description
, we had obtained the branes as classical solutions of the supergravity fields ; this is the analog of describing a point charge by its classical electromagnetic potential .
such a description should apply to a collection of a large number of fundamental branes all placed at the same location .
but we would like to obtain also the microscopic quantum physics of a single brane .
how do we see such an object in string theory ?
the mass per unit volume of a d - brane in string units is @xmath182 , where @xmath183 is the string coupling .
so the brane would not be seen as a perturbative object at weak coupling .
but the excitations of the brane will still be low - energy modes , and these should be seen in weakly coupled string theory .
in fact , when we quantize a free string we have two choices : to consider open strings or closed strings .
if we have an open string then we need boundary conditions at the ends of the string that do not allow the energy of vibration of the string to flow off the end .
there are two possibilities : to let the ends move at the speed of light , which corresponds to neumann ( n ) boundary conditions , or to fix the end , which corresponds to dirichlet ( d ) boundary conditions .
of course we can choose different types of conditions for different directions of motion in spacetime .
if the ends of the open strings are free to move along the directions @xmath166 but are fixed in the other directions @xmath184 , then the ends are constrained to lie along a @xmath162-dimensional surface that we may identify with a @xmath162-brane , and such open strings describe the excitations of the @xmath162-brane @xcite . because these branes were discovered through their excitations , which were in turn a consequence of d - type boundary conditions on the open strings , the branes are themselves called d - branes .
( for a review of properties of d - branes , see reference @xcite . )
an interesting effect occurs when two such branes are brought close to each other .
the open strings that begin and end on the first brane will describe excitations of the first brane , and those that begin and end on the second brane will describe excitations of the second brane .
but , as shown in figure 2 , an open string can also begin on the first brane and end on the second , or begin on the second and end on the first , and this gives two additional possibilities for the excitation of the system .
these four possibilities can in fact be encoded into a @xmath185 matrix , with the @xmath186 element of the matrix given by open strings that begin on the @xmath61th brane and end on the @xmath63th brane .
this structure immediately extends to the case where @xmath187 branes approach each other .
the low - energy limits of open string theories are generally gauge theories .
indeed the low - energy worldbrane theory of a collection of @xmath187 parallel d@xmath162-branes turns out to be described by a _
non - abelian _
@xmath188 gauge theory in @xmath163 dimensions @xcite .
the @xmath189 gauge fields are best written as an @xmath190 matrix @xmath191 where @xmath192 .
similarly , there are @xmath189 scalar fields @xmath193 , which transform according to the adjoint representation of @xmath188 .
the coupling constant of the theory is g_ym^2 ~g_s ( l_s)^p-3 .
each of these fields has its corresponding fermionic partner .
since bps states break half the supersymmetries of the original theory , we have a supersymmetric yang - mills theory with 16 supercharges .
the potential for such a theory turns out to be @xmath194)^2 $ ] , so that in the ground state one can always choose a gauge so that all the @xmath176s are diagonal .
in fact , the diagonal entries in the matrix @xmath193 denote the locations of the branes .
thus @xmath195 denotes the center - of - mass transverse coordinate of the pair of branes labeled by @xmath58 and @xmath59 , while @xmath196 denotes the separation along direction @xmath61 .
a nonzero expectation value for @xmath197 means that the gauge symmetry is spontaneously broken .
generically , the gauge group is broken to @xmath198^n$]this is the situation when all the branes are separated from each other , i.e. all the @xmath197 are nonzero . however , when some number , say @xmath12 , of the branes are coincident , the corresponding @xmath197 are zero for @xmath199 , resulting in an enhanced unbroken symmetry , @xmath200^{n - m}$ ] .
the analog of the dbi action for a collection of @xmath187 branes is not completely known at present , although there are some proposals ( for discussion see reference @xcite and references therein ) . however , the low - energy action is that of a standard supersymmetric yang - mills theory in @xmath201 dimensions .
in fact , this is the dimensional reduction of the 10-dimensional supersymmetric yang - mills theory to @xmath201 dimensions .
the latter has no scalar fields but has @xmath202 components of the gauge field , @xmath203 where @xmath204 , each of which is a @xmath205 matrix . under dimensional reduction ,
the components parallel to the brane , i.e. @xmath206 , remain gauge fields , whereas the components transverse to the brane with @xmath207 are scalars on the world volume and are renamed as @xmath176 .
the ground states of the above d - branes are bps states states , which means that they are stable .
recently , other kinds of non - bps and unstable d - branes have been constructed in string theory @xcite . in this article , however , we restrict ourselves to bps branes and their excitations
. not all the branes that were listed for type iia and type iib theory are d - branes .
consider the type iia theory .
it arises from a dimensional reduction of 11-dimensional supergravity on a circle .
the 11-dimensional theory has 5-branes and 2-branes , and the 2-brane can end on the 5-brane .
if we wrap on the compact circle both the 5-brane and the 2-brane that ends on it , then in the type iia theory we get a d4-brane and an open string ending on the d4-brane .
but if we do not wrap the 5-brane on the circle , and thus get a 5-brane in the type iia theory , then the open string can not end on this brane , since there is no corresponding picture of such an endpoint in 11 dimensions .
the physics of the 5-brane in type iia theory is an interesting one , but we will not discuss it further .
much more is known about the physics of d - branes in type iia and iib theories , since they can be studied through perturbative open string theory .
branes of different kinds can also form bound states , and for specific instances these can be threshold bound states .
a useful example is a bound state of @xmath208 d1-branes and @xmath209 d5-branes . when these branes are not excited , they are in a threshold bound state . the open strings that describe this system are ( @xmath58 ) @xmath210 strings with both endpoints on any of the d1-branes ; ( @xmath59 ) @xmath211 strings with both endpoints on d5-branes ; and ( @xmath3 ) @xmath212 and @xmath213 strings with one endpoint on any of the d1-branes and the other endpoint on one of the d5-branes .
a remarkable feature of string theory is the large group of symmetries called dualities ( see reference @xcite for review ) .
consider type iia theory compactified on a circle of radius @xmath84 .
we can take a graviton propagating along this compact direction ; its energy spectrum would have the form @xmath214 .
but we can also wind an elementary string on this circle ; the spectrum here would be @xmath215 , where @xmath216 is the winding number of the string and @xmath54 its tension .
we note that if we replace @xmath217 , then the energies of the above two sets of states are simply interchanged .
in fact this map , called t - duality , is an exact symmetry of string theory ; it interchanges winding and momentum modes , and because of an effect on fermions , it also turns a type iia theory into type iib and vice versa .
the type iib theory also has another symmetry called s - duality , there the string coupling @xmath56 goes to @xmath218 . at the same time , the role of the elementary string is interchanged with the d1-brane .
such a duality , which relates weak coupling to strong coupling while interchanging fundamental quanta with solitonic objects , is a realization of the duality suggested for field theory by montonen & olive @xcite .
the combination of s- and t - dualities generates a larger group , the u - duality group .
there are other dualities , such as those that relate type iia theory to heterotic string theory , and those that relate these theories to the theory of unoriented strings . in this article
, we do not use the idea of dualities directly , but we note that any black hole that we construct by using branes is related by duality maps to a large class of similar holes that have the same physics , so the physics obtained is much more universal than it may at first appear .
string theory is a quantum theory of gravity .
thus , black holes should appear in this theory as excited quantum states .
an idea of susskind @xcite has proved very useful in the study of black holes . because the coupling in the theory is not a constant but a variable field
, we can study a state of the theory at weak coupling , where we can use our knowledge of string theory .
thus we may compute the `` entropy '' of the state , which would be the logarithm of the number of states with the same mass and charges .
now imagine the coupling to be tuned to strong values .
then the gravitational coupling also increases , and the object must become a black hole with a large radius . for this black hole we can compute the bekenstein entropy from ( equation [ eq : two ] ) , and ask if the microscopic computation agrees with the bekenstein entropy .
for such a calculation to make sense , we must have some assurance that the density of states would not shift when we change the coupling .
this is where bps states come in .
we have shown above that the masses of bps saturated states are indeed determined once we know their charges , which are simply their winding numbers on cycles of the compact space .
thus , for such states , we may calculate the degeneracy of states at weak coupling and , since the degeneracy can be predicted also at strong coupling , compare the result with the bekenstein - hawking entropy of the corresponding black hole .
such states give , at strong coupling , black holes that are `` extremal''they have the minimal mass for their charge if we require that the metric does not have a naked singularity .
the extended objects discussed in the previous section have played an important role in understanding black holes in string theory .
an example of such an object is a fundamental string in type iia or iib string theory .
let some of the directions of the 10-dimensional spacetime be compactified on small circles . take a fundamental string and
wrap it @xmath219 times around one of these circles , say along the @xmath220 direction , which has a radius @xmath84 .
this will produce a rank-2 ns field @xmath221 with a charge @xmath219 , which is a `` winding charge . ''
the energy of the state is @xmath222 , which saturates the bps bound . from the point of view of the noncompact directions ,
this looks like a massive point object carrying electric charge under the gauge field that results from the dimensional reduction of the rank-2 field . from the microscopic viewpoint ,
the state of such a string is unique ( it does have a 256-fold degeneracy due to supersymmetry , but we can ignore this it is not a number that grows with @xmath219 ) .
thus , the microscopic entropy is zero .
if we increase the coupling , we expect a charged black hole .
furthermore , this is an extremal black hole , since for a given charge @xmath219 this has the lowest allowed mass given by the energy given above .
however , this black hole turns out to have a vanishing horizon area .
one way to understand this is to note that the tension of the string `` pinches '' the circle where the string was wrapped .
thus , entropy is zero from both the microscopic and the black hole viewpoints , which is consistent but not really interesting . to prevent this pinching
, we can put some momentum along the string , which amounts to having traveling waves move along the string .
the momentum modes have an energy that goes as @xmath77 , so now this circle attains a finite size .
if we put waves that are moving only in one of the directions , we still have a bps saturated state , but with a further half of the supersymmetries broken .
the total energy of the state is now given by @xmath223 , where the second term is now the contribution from the momentum waves .
because of the winding , the effective length of the string is @xmath224 , so that the momentum may be written as @xmath225 .
thus , for given values of @xmath219 and @xmath226 , a large number of states have the same energy .
these correspond to the various ways one can get the oscillator level @xmath227 . in addition , it is necessary to consider the fact that there are eight possible polarizations , and there are fermionic oscillators as well .
the resulting degeneracy of states has been known since the early days of string theory . for large @xmath219 and @xmath226 ,
the number of states asymptotes to n(n_1,n_2 ) ~exp[2 ] .
[ eq : bhone ] from the viewpoint of the noncompact directions , we have an object with two quantized charges @xmath219 and @xmath226 .
the charge @xmath219 is due to the winding of the string , as mentioned above .
the second charge is due to the presence of momentum , which results in a term in the 10-dimensional metric proportional to @xmath228 .
then , by the kaluza - klein mechanism explained in the previous section , this is equivalent to a gauge field @xmath229 from the viewpoint of the noncompact world .
the corresponding charge is @xmath226 and is an integer since the momentum in the compact direction is quantized . at strong coupling , this object
is described by an extremal black hole solution with two charges .
the identification of such fundamental string states with the corresponding classical solution was proposed by dabholkar & harvey @xcite .
the horizon area is still zero and the curvatures are large near the horizon . in an important paper , sen @xcite argued that the semiclassical entropy ( for similar black holes in heterotic string theory ) is given not by the area of the event horizon but by the area of a `` stretched horizon . ''
this is defined as the location where the curvature and local temperature reach the string scale .
it is indeed inconsistent to trust a classical gravity solution beyond this surface , since the curvatures are much larger than the string scale and stringy corrections to supergravity become relevant . there is a great deal of ambiguity in defining the stretched horizon precisely .
however , sen found that the area of the stretched horizon in units of the gravitational constant is proportional to @xmath230 , which is precisely the logarithm of the degeneracy of states given by equation [ eq : bhone ] .
this was the first indication that degeneracy of states in string theory may account for bekenstein - hawking entropy .
however , in this example , the precise coefficient can not be determined , since the definition of the stretched horizon is itself ambiguous .
it is clear that what we need is a black hole solution that ( @xmath58 ) is bps and ( @xmath59 ) has a nonzero large horizon area .
the bps nature of the solution would ensure that degeneracies of the corresponding string states are the same at strong and weak couplings , thus allowing an accurate computation of the density of states .
a large horizon would ensure that the curvatures are weak and we can therefore trust semiclassical answers . in that situation , a microscopic count of the states could be compared with the bekenstein - hawking entropy in a regime where both calculations are trustworthy .
it turns out that this requires three kinds of charges for a 5-dimensional black hole and four kinds of charges for a 4-dimensional black hole .
the simplest black holes of this type are in fact 5-dimensional charged black holes .
extremal limits of such black holes provided the first example where the degeneracy of the corresponding bps states exactly accounted for the bekenstein - hawking entropy @xcite .
there are several such black holes in type iia and iib theory , all related to each other by string dualities .
we describe below one such solution in type iib supergravity .
we start with 10-dimensional spacetime and compactify on a @xmath231 along @xmath232 @xmath233 .
the noncompact directions are then @xmath234 . there is a solution of type iib supergravity that represents ( @xmath58 ) d5-branes wrapped around the @xmath231 , ( @xmath59 ) d1-branes wrapped around @xmath235 , and ( @xmath3 ) some momentum along @xmath235 .
finally , we perform a kaluza - klein reduction to the five noncompact dimensions .
the resulting metric is ds^2 = - [ f(r)]^-2/3 ( 1-r_0 ^ 2 r^2 ) dt^2 + [ f(r)]^1/3 , [ eq : fdone ] where f(r ) ( 1 + r_0 ^ 2 ^ 2_1 r^2 ) ( 1 + r_0 ^ 2 ^2 _
5r^2 ) ( 1 + r_0 ^ 2 ^2 r^2 ) .
[ eq : fdtwo ] here @xmath236 is the radial coordinate in the transverse space , @xmath237 , and @xmath238 is the line element on a unit 3-sphere @xmath239 .
the solution represents a black hole with an outer horizon at @xmath240 and an inner horizon at @xmath241 .
the background also has nontrivial values of the dilaton @xmath92 , and there are three kinds of gauge fields : 1
. a gauge field @xmath242 , which comes from the dimensional reduction of the rank-2 antisymmetric tensor gauge field @xmath243 in 10 dimensions .
this is nonzero , since we have d1-branes along @xmath235 .
a gauge field @xmath244 , which comes from the dimensional reduction of an off - diagonal component of the 10-dimensional metric @xmath245 .
this is nonzero , since there is momentum along @xmath235 .
3 . a rank-2 gauge field @xmath246 with @xmath61 and @xmath63 lying along the 3-sphere @xmath239 .
this is the dimensional reduction of a corresponding @xmath246 in ten dimensions , since there are 5-branes along @xmath247 .
the presence of these gauge fields follows in a way exactly analogous to the dimensional reduction from 11-dimensional supergravity discussed in equations [ eq : hone ] and [ eq : htwo ] .
the corresponding charges @xmath248 are given by q_1 = v r_0 ^ 2 2_1 32 ^4 g l_s^6 q_5 = r_0 ^ 2 2_5 2 g l_s^2 n = v r^2 32 ^4 l_s^8 g^2 r_0 ^ 2 2 , [ eq : fdfive ] where @xmath249 is the volume of the @xmath250 in the @xmath251 directions , @xmath84 is the radius of the @xmath235 circle , and @xmath183 is the string coupling .
the charge @xmath187 comes from momentum in the @xmath235 direction . if we look at the higher - dimensional metric before dimensional reduction , it is straightforward to identify the arnowitt - deser - misner ( adm ) momentum as p_adm = n r [ eq : fdfivea ] the adm mass of the black hole is given by m = rv r_0 ^ 2 32 ^ 4 g^2 l_s^8[2_1 + 2_5 + 2 ] .
[ eq : fdsix ] the semiclassical thermodynamic properties of the black hole may be easily obtained from the classical solution using equations [ eq : two ] and [ eq : nthree ] and the relationship g_5 = 4 ^ 5 g^2 l_s^8 rv [ eq : fdseven ] between the 5-dimensional newton s constant @xmath252 and @xmath253 .
the expressions are s_bh & = & a_h g_5 = rv r_0 ^ 3 8 ^3 l_s^8 g^2 _ 1 _ 5 + and + t_h & = & 1 2r_0 _ 1 _ 5 .
[ eq : fdnine ] the solution given above represents a general 5-dimensional black hole .
the extremal limit is defined by & r_0 ^ 2 0&_1,_5 , + & q_1,q_5,n = fixed .
[ eq : fdten ] in this limit , the inner and outer horizons coincide .
however , it is clear from the above expressions that adm mass and entropy remain finite while the hawking temperature vanishes .
of particular interest is the extremal limit of the entropy , s_extremal = 2 .
[ eq : fdeleven ] this is a function of the charges alone and is independent of other parameters , such as the string coupling , volume of the compact directions , and string length . in the following , we are interested in a special kind of departure from extremality
this is the regime in which @xmath254 , but @xmath255 and @xmath256 are finite . in this case
, the total adm mass may be written in the suggestive form e = r q_1 g l_s^2 + 16 ^4 rv q_5 l_s^6 + e_l + e_r .
[ eq : fdtwelve ] here we have defined e_l = n r + vr r_0 ^ 2 e^-2 64 ^4 g^2 l_s^8 and e_r = vr r_0 ^ 2 e^-2 64 ^4 g^2 l_s^8 , [ eq : fdthirteen ] and used the approximations r_1 ^ 2 & & r_0 ^ 2 ^2 _ 1 ~r_0 ^ 2 2 2_1 = 16
^4 g l_s^6 q_1 v , + r_5 ^ 2 & & r_0 ^ 2 ^2 _ 5 ~r_0 ^ 2 2 2_5 = g l_s^2 q_5 , [ eq : fdfourteen ] and the expressions for the charges ( equation [ eq : fdfive ] ) . the meaning of the subscripts @xmath257 and @xmath84 will be clear soon . in a similar fashion , the thermodynamic quantities
may be written as s = s_l + s_r 1 t_h = 12(1t_l + 1t_r ) , [ eq : fdfifteen ] where s_l , r = r v r_1 r_5 r_0 e^ 16 ^3 g^2 l_s^8 t_l , r = r_0 e^ 2r_1 r_5 .
[ eq : fdsixteen ] the above relations are highly suggestive . the contribution to the adm mass from momentum along @xmath235 is @xmath258 . in the extremal limit @xmath259
, it then follows from equations [ eq : fdthirteen ] and [ eq : fdfivea ] that @xmath260 , which implies that the waves are moving purely in one direction .
this is the origin of the subscripts @xmath257 and @xmath84we have denoted the direction of momentum in the extremal limit as left , @xmath257 . for finite @xmath256
we have both right- and left - moving waves , but the total momentum is still @xmath261 .
the splitting of various quantities into left- and right - moving parts is typical of waves moving at the speed of light in one space dimension .
in fact , using equations [ eq : fdfifteen ] , [ eq : fdsixteen ] , and [ eq : fdfive ] , we can easily see that the following relations hold : t_i = 1 = s_i 2 ^ 2 rq_1q_5 , i = l , r .
[ eq : fdseventeen ] finally , we write the expressions that relate the temperature @xmath262 and the entropy @xmath22 to the excitation energy over extremality @xmath263 : e & = & ^2 2(rq_1q_5 ) t^2 + and s & = & s_extremal [ 1 + ( r e 2n)^12 ] .
[ eq : fdeighteen ] this solution and the semiclassical properties described above are valid in regions where the string frame curvatures are small compared with @xmath264 .
if we require this to be true for the entire region outside the horizon , we can study the regime of validity of the classical solution in terms of the various parameters .
a short calculation using equations [ eq : fdone ] , [ eq : fdtwo ] , and [ eq : fdfive ] shows that this is given by ( gq_1 ) , ( gq_5 ) , ( g^2 n ) 1 . in this regime ,
the classical solution is a good description of an intersecting set of d - branes in string theory .
however , in string theory , the way to obtain a state with large d - brane charge @xmath265 is to have a collection of @xmath265 individual d - branes .
thus , the charges @xmath208 and @xmath209 are integers , and we have a system of @xmath208 d1-branes and @xmath209 d5-branes . the third charge is from a momentum in the @xmath235 direction equal to @xmath261 .
thus , @xmath187 is quantized in the microscopic picture to ensure a single valued wave function . in the extremal limit ( equation [ eq : fdten ] ) , these branes are in a threshold bound state , i.e. a bound state with zero binding energy .
this is readily apparent from the classical solution .
the total energy ( equation [ eq : fdtwelve ] ) is then seen to be the sum of the masses of @xmath208 d1-branes , @xmath209 d5-branes and the total momentum equal to @xmath261 .
the low - energy theory of a collection of @xmath265 d@xmath162-branes is a ( @xmath201)-dimensional supersymmetric gauge theory with gauge group @xmath266 .
however , now we have a rather complicated bound state of intersecting branes .
the low - energy theory is still a gauge theory but has additional matter fields ( called hypermultiplets ) . instead of starting from the gauge theory itself ,
we first present a physical picture of the low - energy excitations .
the low - energy excitations of the system become particularly transparent in the regime where the radius of the @xmath235 circle , @xmath84 , is much larger than the size of the other four compact directions @xmath267 .
then the effective theory is a @xmath268-dimensional theory living on @xmath235 .
the modes are essentially those of the oscillations of the d1-branes .
these , however , have four rather than eight polarizations .
this is because it costs energy to pull a d1-brane away from the d5-brane , whereas the motions of the d1-branes along the four directions parallel to the d5-branes , but transverse to the d1-branes themselves ( i.e. along @xmath269 ) , are gapless excitations .
even though a system of static d1- and d5-branes is marginally bound , there is a nonzero binding energy whenever the d1-branes try to move transverse to the d5-branes .
if we had a single d1-brane and a single d5-brane , the quantized waves would be massless particles with four flavors .
since we have a supersymmetric theory , we have four bosons and four fermions .
when we have many d1-branes and d5-branes , it would appear at first sight that there should be @xmath270 such flavors : each of the d1-branes can oscillate along each of the d5-branes , and there are four polarizations for each such oscillation .
this is indeed the case if the d1-branes are all separate .
however , there are other possible configurations .
these correspond to several of the d1-branes joining up to form a longer 1-brane , which is now multiply wound along the compact circle . in fact , if we only have some number @xmath216 of d1-branes without anything else wrapping a compact circle , they would also prefer to join into a long string , which is of length @xmath271 .
this was discovered in an analysis of the nonextremal excitations of such d1-branes @xcite .
s - duality relates d1-branes to fundamental wrapped strings .
if one requires that the nonextremal excitations of the d1 brane are in one - to - one correspondence with the known near - extremal excitations of the fundamental string and therefore yield the same degeneracy of states , one concludes that the energies of the individual quanta of oscillations of the d1 string must have fractional momenta @xmath272 , which simply means that the effective length of the string is @xmath271 .
for the situation we are discussing , i.e.d1-branes bound to d5-branes , the entropically favorable configuration turns out to be that of a single long string formed by the d1-branes joining up to wind around the @xmath235 direction @xmath273 , i.e. an effective length of @xmath274 @xcite .
we thus arrive at a gas of four flavors of bosons and four flavors of fermions living on a circle of size @xmath275 . since the string is relativistic , these particles are massless .
the problem is to count the number of states with a given energy @xmath276 and given total momentum @xmath277 and see if the results agree with semiclassical thermodynamics of black holes .
this approach to the derivation of black hole thermodynamics comes from callan & maldacena @xcite and horowitz & strominger @xcite , with the important modification of the multiply wound d - string proposed by maldacena & susskind @xcite .
our treatment below follows reference @xcite . at weak coupling
these bosons and fermions form an ideal gas , which we assume thermalizes .
consider the general case of such an ideal gas with @xmath279 flavors of massless bosons and fermions ( each polarization counted once ) living on a circle of size @xmath257 .
for large @xmath257 , we should be able to treat the system in a canonical ensemble characterized by an inverse temperature @xmath280 conjugate to the energy and a chemical potential @xmath281 conjugate to the momentum . if @xmath282 denotes the number of particles with energy @xmath283 and momentum @xmath284 , the partition function @xmath285 is = e^h = _ states exp .
[ eq : therone ] then @xmath281 and @xmath280 are determined by requiring e = -h and p = -h .
[ eq : thertwo ] the average number of particles @xmath282 in state @xmath286 is then given by ( e_r , p_r ) = 1 e^e_r + p_r 1 , [ eq : therthree ] where as usual the plus sign is for fermions and the minus sign is for bosons .
finally , the entropy @xmath22 is given by the standard thermodynamic relation s = h + p + e. [ eq : therfour ] the above quantities may be easily evaluated : p & = & fl8 , + e & = & fl8 , + and s & = & fl4[1 + + 1 - ] . [ eq : therfive ] since we have massless particles in one spatial dimension , they can be either right - moving , with @xmath287 , or left - moving , with @xmath288 .
the corresponding distribution functions then become _
r = 1 e^(+ ) e_r1 and _
l = 1 e^(- ) e_r 1 .
[ eq : thersix ] thus , the combinations @xmath289 and @xmath290 act as effective temperatures for the right- and left - moving modes , respectively , resulting in = 12 ( 1t_l + 1t_r ) .
[ eq : thersixa ] in fact , all the thermodynamic quantities can be split into left- and a right - moving pieces : @xmath291 .
the various quantities @xmath292 may be read off from equation [ eq : therfive ] , t_r = = 4 s_r f l t_l = = 4 s_l f l. [ eq : therseven ] it is now clear that the statistical mechanics of this free gas in fact reproduces the thermodynamics of the near - extremal black hole .
the relationships of equation [ eq : therseven ] become the relations equation [ eq : fdseventeen ] if fl = 8rq_1q_5 .
[ eq : thereight ] given this agreement , it is obvious that the thermodynamic relations of equation [ eq : fdeighteen ] are also exactly reproduced . in particular , the physical temperature @xmath262 agrees with the hawking temperature , as is clear from equations [ eq : thersixa ] and [ eq : fdfifteen ] .
recall that the size of the @xmath235 circle is @xmath293 .
thus , one way to satisfy the relation in equation [ eq : thereight ] is to consider @xmath294 and @xmath295 .
this would be the situation if we had @xmath208 d1-branes individually wrapping the @xmath235 direction . another way to satsify equation
[ eq : thereight ] is to take @xmath296 and @xmath297 .
this is the content for the long string , where all the d1-branes join up to form a single multiply wound string .
it might appear that thermodynamics does not distinguish between these two configurations .
however , the above thermodynamic relations assume that the system is extensive @xcite .
one condition for that is that @xmath298 .
it follows from equation [ eq : therseven ] that this would require s_l , s_r f. [ eq : thereighta ] there is an important difference between the two cases . when multiple branes are each singly wound , the energy of a single particle is @xmath299 for some integer @xmath300 .
thus , a near - extremal configuration may be obtained from an extremal configuration by adding @xmath300 pairs of left- and right - handed quanta , leading to an excitation energy @xmath301 . for the long string , similarly , we would have @xmath302 , since the length is now @xmath303 . from this
it is apparent that for the multiple singly wound branes , s_l = 2 and s_r = 2 , [ eq : thernine ] whereas for the multiply wound long string s_l = 2 and s_r = 2 .
[ eq : therninea ] it is then clear that the extensivity condition ( equation [ eq : thereighta ] ) is always satisfied for the long string , whereas it is violated by the singly wound branes when @xmath304 and @xmath187 are all comparable and large .
the multiply wound string has much lower energy excitations , with a minimum gap of @xmath305 .
this is consistent with the conditions for the validity of statistical mechanics for black holes @xcite .
the point is that for statistical mechanics to hold , the temperature of a system must be such that the specific heat is larger than one .
it follows from the relations in equation [ eq : fdeighteen ] that this requires ( up to numerical factors of order one ) e > 1rq_1q_5 , which indicates that the system should have an energy gap @xmath305 .
this is exactly what the long string provides . in the above discussion we adopted a simple model of the d1-d5 bound state and used it to compute the entropy of momentum excitations .
we now discuss more rigorous results on the count of states that can be obtained by using the fact that we are counting supersymmetric states when we compute the entropy of an extremal black hole .
in fact , such a chain of arguments was used in the first exact calculation of the microscopic entropy of a black hole by strominger & vafa @xcite .
we outline the main ideas of such a treatment here .
( this subsection assumes some familiarity with dualities in string theory . ) ( a ) : we count not the actual states of the system but an `` index . ''
the simplest example of an index is the witten index of a supersymmetric system @xmath306 $ ] ( @xmath104 is the fermion number and @xmath136 is the hamiltonian ) .
this index counts the number of bosonic ground states minus the number of fermionic ground states .
the ground states are maximally supersymmetric states , so if one were interested in states preserving maximal supersymmetry , then the witten index would provide useful information .
note , however , that the index can only give a lower bound on the number of supersymmetric states , since some states are counted with a negative sign .
as we change the parameters of the theory , states can appear and disappear in bose - fermi pairs , but the index is a robust quantity . in the black hole context , we are interested not in the ground states of the system but in states preserving some fraction of the supersymmetry .
( in fact , the states we want carry momentum and thus a nonzero total energy . )
we need a generalization of the witten index that will carry nontrivial information about the count of excited states of the system . of course
, we will again obtain a lower bound to the state count for the given quantum numbers ; we then hope that the bound will approximate the actual state count well enough to permit a meaningful comparison to the bekenstein entropy .
( b):let us consider the black hole discussed by strominger & vafa @xcite .
take type iib theory but let the complete 10-dimensional spacetime be @xmath307 , where @xmath308 are the noncompact directions , @xmath309 is a special kind of compact 4-dimensional surface , and @xmath309 along with the circle @xmath310 makes up the five compact directions .
since one compact direction is @xmath310 , there is really no difference between type iia and type iib theories here ; we can go from one to the other by a t - duality .
what kind of charges can we place on the compact directions to make the black hole ?
in analogy to the discussion above of the black hole in @xmath311 , we can wrap various branes around the cycles of the compact directions , making sure that they all stretch along the @xmath310 .
then we can put a momentum charge along the @xmath310 direction and obtain a black hole carrying a momentum charge @xmath312 along with the charges arising from the wrapped branes .
we need some way to describe the charges carried by the branes .
type iib theory has 1- , 3- , and 5-dimensional branes . on the other hand ,
@xmath309 has 0- , 2- , and 4-dimensional cycles on which something can be wrapped , so we can wrap all these branes on the @xmath313 space as desired . as mentioned above , we can view the theory as type iia on @xmath313 , and then we note that there is a duality map that relates type iia compactified on @xmath309 to heterotic string theory compactified on @xmath250 .
type iia compactified on @xmath314 maps to heterotic string theory compactified on @xmath231 , and here the charges are easy to understand .
the charges that are dual to the wrapped branes in type iia now arise in the heterotic theory from momentum and winding of the elementary heterotic string on the compact directions of the theory .
the possible charge states are characterized by points on a lattice @xmath315 , which means a lattice with 21 positive signature directions and 5 negative signature directions .
the only relevant property of these charges is that a bilinear invariant , which we may call @xmath316 , gives the invariant length squared of a charge vector in this space .
this invariant is a generalization of @xmath317 , the product of winding and momentum charges in any one direction ; such a product is invariant under t - duality , since the two kinds of charges get interchanged .
( c):since we will be looking for a quantity that will not vary with the continuous parameters of the system , we can take the size of the @xmath310 to be much larger than the size of the @xmath309 .
then the physics of the wrapped branes looks like a @xmath268-dimensional sigma model , with the space direction being the @xmath310 cycle .
it is possible to count the degeneracy of the ground states of the wrapped branes and infer that the target space of this sigma model must be essentially the symmetric product of @xmath318 copies of @xmath309 ( @xmath316 as defined is an even number ) . here
the term `` essentially '' means that this target space may be a deformation of the stated one , but the topological properties of the space would remain unchanged , and the space would remain hyper - khler , which means that the number of supersymmetries would also remain the same .
the @xmath318 copies of @xmath309 are analogous to the @xmath273 strands of the string that we took as the vibrating elements in the heuristic treatment of section 5.5 above ; each point on each strand could move on @xmath250 in that case , and the @xmath250 is now replaced by @xmath309 .
the fact that we take a symmetric product amounts to saying that the strands are identical and must be so treated in any quantum mechanical count .
we now consider @xmath319 units of momentum along the @xmath310 direction of this sigma model , just as we did in the case of @xmath250 compactification .
if we hold @xmath319 fixed and take the size of @xmath310 to infinity , then we will be looking at modes of very long wavelength , longer than any length scale that existed in the sigma model .
the physics of such modes must be a conformal field theory ( cft ) in @xmath278 dimensions , and in particular we can separate the excitations into left- and right - moving modes .
if we do not excite the right movers and let the left movers carry the given momentum , then we will have states with half the maximal supersymmetry : the right supercharges will annihilate the state and the left ones will not .
if we have such a conformal theory with @xmath320 or larger supersymmetry , then it can be shown that the elliptic genus @xmath321\ ] ] is also a robust quantity that does not change when the moduli are varied . here
@xmath322 and @xmath323 are integer - valued @xmath97 charges for the left and right sectors ; these are the @xmath97 symmetries that rotate the two supercharges of @xmath320 supersymmetry into each other .
we want only the count of states when the charges are large , since only then can we compare the count with the bekenstein entropy computed from the classical gravity solution . in a cft , the degeneracy of states at an excitation level @xmath300 above the ground state ( in , say , the left sector ) is given in terms of the central charge of the cft by the formula @xmath324 the central charge for a supersymmetric sigma model with a hyper - khler space is easy to calculate .
the dimension of the target space must be of the form 4@xmath29 .
each bosonic direction contributes 1 to the central charge , and its corresponding fermion gives an extra 1/2 .
thus @xmath325 . putting in the values of @xmath29 and @xmath326
, we get @xmath327 which agrees with the bekenstein entropy for the classical geometry with the same charges .
( d):although the above expression was derived for large @xmath319 , it is also possible to compute the elliptic genus for the symmetric product of copies of @xmath309 without making any approximation .
one can relate the elliptic genus when the target space is a symmetric product of @xmath29 copies of the space @xmath328 to the elliptic genus when there is only one copy of the space @xcite .
the derivation of this relation is combinatorial ; one symmetrizes over bosonic states and antisymmetrizes over fermionic states .
but the case where the target space is only one copy of @xmath328 is the theory of a single string on @xmath328 , which is a simple cft to handle , and the elliptic genus can be explicitly written .
if we apply the above method to the case where the compact space is @xmath250 instead of @xmath309 , we find that the elliptic genus is zero .
this happens because there are fermion zero modes on the torus , which relate a set of bosonic states to an identical spectrum of fermionic states , and there is a cancellation in the elliptic genus and we get no useful information about the state count .
maldecena et al showed @xcite that one can use the fact that we have @xmath329 supersymmetry in the cft to argue that the quantity @xmath330\ ] ] is a topological invariant in this case .
this quantity is nonzero , and it turns out to give for large charges a state count that reproduces the bekenstein entropy .
we now show how the above picture of a nonlinear sigma model follows from gauge theory considerations . as explained above , we are interested in the long - distance limit of the theory of the d1-d5 system .
this system has @xmath210 , @xmath211 , and @xmath212 strings and has @xmath331 supersymmetry when viewed as a 1-dimensional theory living along @xmath235 .
there is a global r symmetry which rotates the various supercharges : @xmath332 .
in fact , this r symmetry is nothing but the rotation symmetry in the four transverse directions .
the lowest oscillator modes of the open strings lead to a @xmath333 gauge theory with the following supersymmetry multiplets : 1 .
the states of the @xmath210 and @xmath211 strings along the transverse directions @xmath334 form a `` vector multiplet . ''
there are thus four scalars transforming as @xmath335 of the r symmetry group and four fermions .
the left - handed fermions transform as @xmath336 of r symmetry , and the right - handed fermions transform as @xmath337 .
the states of the @xmath210 and @xmath211 strings with polarizations along the @xmath250 directions form a `` hypermultiplet . ''
this also has four scalars transforming trivially under the r - symmetry group and has four fermions .
the left - moving fermions now transform as @xmath337 and the right - moving fermions as @xmath336 .
3 . the states of the @xmath212 and @xmath213 strings lead to hypermultiplets whose transformation properties under r symmetry are the same as those of the previous hypermultiplets .
we want the branes to be on top of each other .
this requires the vector multiplet scalars to have vanishing expectation values , since these represent the relative distances between individual branes in the transverse space .
on the other hand , the scalars in the hypermultiplet will have expectation values .
this is known as the higgs branch of the theory . as a result
, the vector multiplets typically acquire a mass .
component of the vector multiplet remains massless , representing the overall motion of the branes in transverse space .
however , the @xmath97 parts of the fields are decoupled from the @xmath338 part and can be ignored in this discussion . ]
the hypermultiplet scalars are massless .
however , they are not all independent of each other but are related by a set of conditions .
it is necessary to solve for the independent set of fields and find the low - energy theory of these fields . even at the classical level , this is a complicated affair .
it has been pursued elsewhere @xcite , although a detailed low - energy theory has not yet been rigorously derived .
nevertheless , it is possible to obtain an important universal quantity of the low - energy conformally invariant theory the central charge .
this is because the central charge is related , by superconformal symmetry , to the anomaly of the r - symmetry current .
the r - symmetry current is anomalous because the left- and right - moving fermions behave differently under r - symmetry transformations . at high energies where the theory does not have superconformal invariance but
does have @xmath331 supersymmetry , the anomaly coefficient @xmath29 may be easily computed in terms of the number of hypermultiplets and vector multiplets , and it turns out to be @xmath339 . because of the well - known t hooft anomaly matching conditions , this coefficient is the same at low energies , where the theory flows to a superconformal theory .
superconformal symmetry then determines the central charge of the superconformal algebra in terms of the anomaly coefficient @xmath340
. the asymptotic density of states in a conformal field theory can be now determined in terms of the central charge , and for bps states this leads to the expression for entropy given above .
there is a slightly different but equivalent approach to the problem .
d1-branes in the d5-branes can be considered as `` instanton strings '' of the 6-dimensional @xmath341 gauge theory on the d5-brane @xcite .
actually these are not really instantons but rather solitonic objects .
consider configurations of the gauge theory that are independent of @xmath235 and time @xmath342 .
such configurations may be regarded as configurations of a euclidean 4-dimensional gauge theory living in the @xmath251 directions .
instantons are such configurations , which are self - dual in this 4-dimensional sense . from the point of view of the 6-dimensional theory ,
they are thus solitonic strings .
the number of d1-branes is equal to the instanton number @xmath208 .
these instantons form a continuous family of solutions with the same energy
the corresponding parameters form the `` instanton moduli space . ''
the low - energy excitations of the system are described by the collective excitations or dynamics on this moduli space .
because of translation invariance of the original configurations along @xmath235 and @xmath342 , the collective coordinates are functions of @xmath235 and @xmath342their dynamics is thus given by a @xmath268-dimensional field theory that is essentially a sigma model with the target space as the moduli space of these instantons .
this is the sigma model discussed in the previous section .
in fact , the independent moduli are obtained by solving a set of equations identical to the equations that determine the independent set of hypermultiplet scalars .
it turns out that in the orbifold limit , the theory of these instanton strings may be interpreted in terms of a gas of strings @xcite that are wound around the @xmath235 and move along the @xmath250 with a total winding number @xmath343 .
these strings can be singly wound or multiply wound .
the `` long string '' used in the previous sections is nothing but the maximally wound sector .
as we have argued , this is the entropically favored configuration . in the orbifold limit , however , the supergravity approximation is not valid , which is why one has to turn on some of the supergravity moduli fields to go to the correct regime .
in fact , by turning on a ns - ns two - form field , one can get rid of the coulomb branch altogether , forcing the branes to lie on top of each other , thus ensuring that we are dealing with the higgs branch of the theory @xcite . the behavior of the system with such moduli turned on has been further analyzed elsewhere @xcite .
there is a wide variety of black hole solutions in string theory ( for reviews and references see e.g. reference @xcite ) , and numerous studies have related them to states in string theory .
one notable example is a 4-dimensional black hole with four kinds of charges @xcite , where once again there is an exact agreement of the extremal entropy .
near - extremal limits of these black holes have also been studied ; there is , in fact , a natural analog of the long string approximation in which these black holes are regarded as intersecting branes in 11-dimensional supergravity @xcite .
rotating versions of such 5- and 4-dimensional black holes also provide exact microscopic derivations of the extremal entropy @xcite .
in classical gravity , black holes absorb matter via standard wave scattering by an effective potential arising from the gravitational field .
consider the absorption of some field .
an incident wave is partly scattered back and partly absorbed , and the absorption cross section can be calculated by solving the relevant wave equation in the black hole background . hawking radiation is a quantum process .
however , the radiation rate can be obtained by considering a black hole in equilibrium with its environment of radiated quanta .
the principle of detailed balance then relates the radiation rate to the absorption cross section by the relation in equation [ eq : four ] .
we are interested in the decay of a slightly nonextremal black hole by hawking radiation .
the dominant decay mode is the emission of massless neutral particles .
it is clear that the black hole will evaporate until the excess mass over extremality has been radiated away , leaving an extremal black hole that is stable .
note that for such black holes , the specific heat is positive ( in contrast to neutral black holes , which have negative specific heat ) , so that this evaporation is a well - defined process .
furthermore , as long as the extremal limit corresponds to a large black hole , one would expect that at all stages of the decay process , semiclassical approximations are valid for these large black holes . in the microscopic models described above
, the processes of absorption and radiation appear to be rather different .
consider a closed string incident on the intersecting d - brane configurations representing black holes .
when the closed string hits the d - brane , it can either reflect back or split up into open strings whose ends are attached to the brane .
the open strings then do not leave the brane and hence do not re - emerge in the asymptotic region .
thus , there is a finite probability that the closed string quantum will be absorbed by the black hole , which should be calculated using standard rules of quantum mechanics .
radiation is the reverse of this process : open strings can join up to form closed strings , which can then escape from the brane system . at low energies , the closed string that is propagating in the bulk of spacetime
may be replaced by the quantum of some supergravity field , whereas the open strings may be replaced by quanta of the low - energy gauge theory living on the brane .
we are interested in this low - energy limit . to compare the absorption or radiation rates of semiclassical black holes and d - brane configurations
, we must compute the classical absorption cross sections of the relevant fields in the black hole background .
we are interested in the low - energy behavior of these absorption cross sections .
let @xmath344 denote all the supergravity fields collectively .
then the wave equation satisfied by a test field in the classical background @xmath345 can be obtained by substituting the perturbed field @xmath346 in the supergravity equations of motion and retaining the part linear in @xmath347 .
the equations of motion would generically couple the various perturbations , leading to a complicated set of equations .
however , various symmetries of the background classical solution allow us to isolate special perturbations that satisfy simple decoupled equations . for the 5-dimensional black hole we are discussing , there are 20 such bosonic perturbations , called minimal scalars , that satisfy decoupled massless
minimally coupled klein - gordon equations .
as we shall see , these have the largest absorption rate and hence dominate the hawking radiation .
examples of such fields are traceless parts of the components of the 10-dimensional metric , which have polarizations along the @xmath250 in the @xmath348 direction .
scattering of massless particles by 4-dimensional black holes was studied in the 1970s @xcite , and the low - energy limit of the s - wave absorption cross section for massless minimally coupled scalars was found to be exactly equal to the horizon area for schwarzschild and charged reissner - nordstrom black holes . a similar calculation for
the near - extremal 5-dimensional black hole described above also showed that the leading term of the absorption cross section is again the horizon area @xcite .
it was soon realized , however , that this is in fact a universal result : for all spherically symmetric black holes in any number of dimensions , the s - wave cross section of minimally coupled massless scalars is always the area of the horizon @xcite .
the actual calculation of the cross section involves solving the wave equation analytically in various regimes and then matching solutions in the overlapping regions .
as an example , we describe the essential steps that led to the result obtained in @xcite . consider a metric of the form ds^2 = -f(r ) dt^2 + h(r ) , [ eq : absone ] where @xmath349 denotes the line element on a unit @xmath162-sphere .
let the horizon be at @xmath350 so that @xmath351 .
we want to solve the minimally coupled massless equation @xmath352 for a spherically symmetric scalar field @xmath353 .
using time translation invariance , we decompose the field into fields of definite frequency , @xmath354 , through @xmath355 .
the frequency component @xmath354 satisfies _ ( r ) = 0 , [ eq : abstwo ] where f(r ) = \{f(r ) [ h(r)]^p-1}^1/2 r(r ) = r [ h(r)]^1/2 .
[ eq : absthree ] let @xmath356 denote the largest length scale in the classical solution .
we then solve the equation to lowest order in @xmath357 .
then there are two regions in which the equation can be easily solved . in the outer region @xmath358
, the equation becomes that of a scalar field in flat background and may be solved in terms of bessel functions . in the near - horizon region
@xmath359 , the function @xmath360 may be replaced and the equation may be solved after a simple change of variables .
we must then match the two solutions in the overlapping region .
the physical input is a boundary condition .
it is necessary to impose a boundary condition so that there is no outgoing wave at the horizon . in the asymptotic region
, there is both an incoming and an outgoing wave , and matching the solution to the near - horizon solution yields the ratio of the outgoing and incoming components and hence the absorption probability .
this can be converted into an absorption cross section @xmath361 for a plane wave of momentum @xmath32 using standard techniques .
the result is , as advertised , _ 0(k ) = 2 ^(p+1)/2(p+1 2 ) r_h^p = a_h , [ eq : absthreea ] where @xmath20 is the horizon area and the last equality follows from the form of the metric ( equation [ eq : absone ] ) . for the 5-dimensional black hole , the absorption cross section for such minimally coupled scalars may be calculated in the so - called dilute gas regime defined by r_0 , r_n r_1 , r_5 r_1 r_5 ~r_0 r_n ~o(1 ) [ eq : absfour ] when the energy @xmath362 is in the regime r_5 1 t_l ~o(1 ) t_r ~o(1 ) .
[ eq : absfive ] the various parameters of the classical solution have been defined in previous sections .
the final result is @xcite ( ) = 2 ^ 2 r_1 ^ 2 r_5 ^ 2 2 ( e^/t_h - 1 ) ( e^/2t_l - 1)(e^/2t_r - 1 ) .
[ eq : abssix ] remarkably , the cross section appears as a combination of thermal factors , even though it is a result of a solution of the klein - gordon equation .
when @xmath363 and @xmath364 , one has @xmath365 and the cross section becomes exactly equal to the area of the horizon . the expression ( equation [ eq : abssix ] )
is called a grey - body factor because of the nontrivial energy dependence .
finally , let us briefly discuss the absorption of higher angular momentum modes and higher spin fields .
writing the relevant wave equations , we find for such modes an additional `` centrifugal '' potential near the horizon that suppresses absorption of these modes by the black hole at low energies @xcite .
the exceptions are modes of spin-1/2 fields that are supersymmetric partners of the minimal scalars . when these modes have their orbital angular momentum , the absorption cross section is twice the area of the horizon , in agreement with expectations from supersymmetry .
a first - principles calculation of the decay of a slightly nonextremal 5-dimensional black hole would involve a strongly coupled gauge theory of the d1-d5 gauge theory coupled to the bulk supergravity fields . as discussed above , the gauge theory is difficult to analyze even in weak coupling .
however , we have a fairly good effective theory the long string model and weak coupling calculations in the model give exact strong coupling answers .
one might wonder whether the model may be used to compute decay rates .
once again one may hope that weak coupling calculations could give reasonable answers for the same reasons that they succeeded in predicting the right thermodynamics . in this subsection , we show that this is indeed unambiguously possible for a certain set of modes , and indeed weak coupling calculations for these modes agree exactly with the semiclassical results described in the previous subsection .
the theory of the long string is a @xmath268-dimensional massless supersymmetric field theory with four flavors of bosons @xmath366 , the index @xmath367 referring to the four directions of the @xmath250 along @xmath251 and their corresponding fermionic partners .
we want to figure out how these degrees of freedom couple to the supergravity modes in the bulk .
in fact , we are mostly interested in supergravity modes that are minimal scalars in the dimensionally reduced theory . out of these 20 scalars , it is particularly easy to write down the interaction of the long string with the transverse traceless components of the 10-dimensional graviton @xmath368 , with indices @xmath369 lying along the @xmath250 . at low energy , the relevant action is d^2_^i ^^j g_ij , [ eq : absseven ] where the @xmath166 denote the coordinates on the long string world sheet and @xmath370 is the metric on the @xmath250 .
@xmath371 is a constant .
this form of the action follows from the principle of equivalence . when there is no supergravity background , the action should be a free action given by equation [ eq : absseven ] with @xmath370 replaced by @xmath372 . the fields @xmath366 transform as vectors under the local @xmath373 transformations of the tangent space of the @xmath250 .
this requires that at low energies the action in the presence of a background is given by equation [ eq : absseven ] .
if we expand the metric as g_ij = _ ij + 2_10 h_ij(,^i , x^1x^4 ) [ eq : absnine ] we immediately get the coupling of @xmath368 with the long string degrees of freedom . in equation [ eq : absnine ] , we have made explicit the dependence of the supergravity field on the coordinates on the long string world sheet @xmath374 , the @xmath250 coordinates @xmath366 ( which are the fields of the long string theory ) , and the coordinates transverse to the black hole @xmath375 . the 10-dimensional gravitational coupling , @xmath376 , is related to the string coupling and string length by _ 10 ^ 2 = 64 ^7 g^2 l_s^8 .
[ eq : absninea ] the factor @xmath377 in equation [ eq : absnine ] is determined by requiring that the field @xmath368 be canonically coupled and follows from the bulk supergravity action ( equation [ eq : hsixa ] ) .
there will be other terms in the action , but these would contain more derivatives and are suppressed at low energies .
it is clear from equation [ eq : absseven ] that the decay of a nonextremal state into the mode @xmath368 is dominated by the process of annihilation of a pair of modes of vibration from the long string , one of which is left - moving and the other right - moving ( see figure 3 ) . because we are working in the limit where the radius @xmath84 of the @xmath235 circle is much larger than the size of the @xmath250 , we can ignore the dependence of @xmath368 on @xmath366 . furthermore , we are interested in computing s - wave absorption / decay , which depends on the transverse coordinates only through the radial variable .
the constant @xmath371 is an effective tension of the long string and depends on the details of the rather complicated d1-d5 bound state .
it appears that the action we have written has little predictive power unless we figure out these details .
however , it has been recognized @xcite that the cross section in question does not depend on such details .
this is because the free kinetic term of the fields @xmath366 has to be canonically normalized . because the interaction is also quadratic in @xmath366 , normalization thus completely removes the constant @xmath371 from the action .
the amplitudes that result from this action are therefore universal . in the following ,
we give the basic steps for calculation of the decay rate when the mode @xmath368 carries no momentum along @xmath235 and is in an s - wave in the transverse space .
this corresponds to the decay into neutral scalars from the noncompact 5-dimensional point of view .
consider the annihilation of two long string modes : ( @xmath58 ) one with polarization @xmath367 and momenta @xmath378 [ along the @xmath379 direction ] and ( @xmath59 ) one with polarization @xmath380 and momenta @xmath381 into an @xmath368 bulk mode with momenta @xmath382 along the @xmath383 directions .
using equations [ eq : absseven ] and [ eq : absnine ] , we find that the decay rate for this process is ( p , q;k ) = ( 2)^2 l ( p_0+q_0-k_0 ) ( p_5 + q_5 - k_5 ) 2 ^2 ( p q)^2 ( 2p_0 l)(2q_0 l)(2 k_0 v l v_4 ) v_4d^4 k ( 2)^4 . [ eq : absten ] the delta functions impose energy conservation and momentum conservation along the @xmath235 direction ( momentum is not conserved in the other directions because of dirichlet conditions ) .
the denominators come from normalization of the modes : the open string modes are normalized on the circle along @xmath235 of circumference @xmath384 whereas the closed string field is normalized in the entire space with volume @xmath385 , where @xmath386 is the volume of the noncompact four spatial dimensions @xmath334 . to obtain the total cross section for production of a scalar
, one must now average over all initial states . because these states are drawn from a thermal ensemble , the decay rate is ( k ) = ( l 2)^2_-^dp_5 _ -^dq_5 ( p_0,p_5 ) ( q_0,q_5 ) ( p , q;k ) , [ eq : abseleven ] where @xmath387 denotes the bose distribution functions discussed in the previous section .
the integral may be evaluated easily and the answer is ( k ) = 2 ^2 r_1 ^ 2 r_5 ^ 2 2 1 ( e^2 t_l - 1)(e^2 t_r - 1 ) . [
eq : abstwelve ] finally , the decay rate is converted into an absorption cross section by multiplication by an inverse bose distribution of the supergravity mode : ( ) ^d - brane = 2 ^2 r_1 ^ 2 r_5 ^ 2 2 e^t - 1 ( e^t_l - 1)(e^t_r - 1 ) .
[ eq : absfourteen ] we have expressed the answer in terms of the parameters in the classical solution by using the length of the effective string , l = 2q_1 q_5 r = 8 ^ 4 r_1 ^ 2 r_5 ^ 2 v r ^2 . [
eq : absthirteen ] the physical temperature @xmath262 is related to @xmath388 and @xmath389 by equation [ eq : thersixa ] .
thus , when @xmath363 , we have @xmath390 .
however , we know that the quantities @xmath388 and @xmath389 above are in fact exactly the same as the semiclassical quantities and @xmath391 .
for very low energies @xmath364 , one of the thermal factors above can be simplified . using equations [ eq : fdfourteen ] through [ eq : fdsixteen ]
, we see that in this limit ( ) = 2 ^ 2 ( r_1r_5)^2 t_l = ( r_1r_5)^2 s_l rq_1q_5 = a_h .
[ eq : absfifteen ] we have used equation [ eq : fdseventeen ] and the fact that in the regime @xmath363 we have @xmath392 , where @xmath393 and @xmath394 is given by equation [ eq : absninea ] .
we have also used equation [ eq : fdfourteen ] to express @xmath395 in terms of @xmath396 .
this is exactly the low - energy classical result .
the fact that the cross section turns out to be proportional to the horizon area was already known @xcite .
the precise calculation outlined above was performed in reference @xcite . even before taking this low - energy limit ,
the entire result ( equation [ eq : absfourteen ] ) is in exact agreement with the semiclassical grey - body factor @xcite .
it is clear from equation [ eq : abstwelve ] that the thermal factor in the decay rate comes from the thermal factors of the long string modes . in the strict classical limit
, we can have absorption but no hawking radiation ; this comes about because the temperature in this limit is zero , so the corresponding thermal factor suppresses emission completely while absorption is still nonzero @xcite . the supergravity mode can also split into a pair of fermions .
however , then the thermal factors that appear in equation [ eq : abstwelve ] are fermi - dirac distributions and these go to a constant at low energies , rather than diverging as bose factors do . as a result , the corresponding cross section is suppressed at low energies . in a similar way
, we may consider emission / absorption of a fermionic supergravity mode .
this would require one left - moving bosonic mode of the long string with a right - moving fermionic mode .
following the above calculations , it is apparent that the thermal factor of the left - moving long string mode gives the right powers of energy to lead to a nonzero low - energy cross section , and the thermal factor for the right - moving mode provides the thermal factor of the emitted supergravity fermion and this is a fermi - dirac factor as expected @xcite .
classical emission of higher angular momentum modes is suppressed by centrifugal barriers provided by the gravitational field . in the microscopic model , such emission
is again suppressed , but for a different reason .
note that the bosonic degrees of freedom of the long string are all vectors under the internal @xmath373 of the @xmath250 but are scalars under the tangent space @xmath373 of the transverse space .
therefore , these can never collide to give rise to modes with nonzero angular momentum in transverse space .
fermions on the long string , however , carry transverse tangent space indices ( typically as a r - symmetry index ) since they are dimensional reductions of 10-dimensional fermions .
thus , multifermion processes are responsible for emission of higher angular momentum modes .
however , these can be seen to be necessarily suppressed , since they involve more than two fermion fields and therefore correspond to higher - dimension operators on the long string world sheet .
angular - momentum
mode emission is not completely understood in the long string picture although the qualitative aspects have been understood @xcite .
similar calculations have been performed for several other situations , e.g. for absorption / emission of charged scalars from both 5- and 4-dimensional black holes @xcite .
the low - energy effective action used above follows from a dirac - born - infeld ( dbi ) action of the long string in the presence of supergravity backgrounds .
one might wonder whether this dbi action can be used to predict absorption rates for other supergravity modes .
it turns out that this can be done for several other minimal scalars , namely the dilaton and the components of the ns @xmath397 field along the @xmath250 .
there are four other minimal scalars in this background , the couplings of which can not be obtained from the dbi action .
perhaps more significantly , there is a set of other scalar fields that do not obey minimal klein - gordon equations e.g .
the fluctuations of the volume of the @xmath250 . if we trust the dbi action to obtain the couplings of these fields , we get answers that do not agree with supergravity calculations @xcite .
these cross sections are suppressed at low energies and it is probably not surprising that the simplest low - energy effective theory does not work .
the agreement of the low - energy limit of the absorption cross section or , equivalently , decay rate is strong evidence for the contention that hawking radiation is an ordinary , unitary quantum decay process .
this is , however , surprising like the agreement of near - extremal thermodynamics since our weak coupling calculation agreed with a strong coupling expectation .
the agreement of nontrivial grey - body factors is even more surprising because now not just a single number but an entire function of energy is correctly predicted by a weak coupling calculation .
weak coupling calculations also gave the correct answer for the extremal entropy , but that case involves bps states and supersymmetry guarantees the agreement . in nonextremal situations , supersymmetry is broken .
however , for small amounts of nonextremality , we have small excitations over a supersymmetric background and we may still expect nonrenormalization theorems to ensure that higher - loop effects vanish at low energies . a complete understanding of this is still lacking .
explicit one - loop calculations @xcite seem to support this scenario .
there is also some evidence for nonrenormalization theorems of the type required @xcite .
the above discussion has addressed extremal solutions with large horizon areas and their excitations .
extremal solutions with vanishing horizon areas generally have singular horizons , for which semiclassical results can not be trusted .
there are , however , several exceptions to this rule . in this section
we consider one of them the 3-brane in type iib supergravity .
the classical solution for @xmath187 parallel extremal 3-branes along @xmath398 is given by the ( einstein - frame ) metric ds^2 = [ f(r)]^-1/2[-dt^2 + dx^2 ] + [ f(r)]^1/2[dr^2 + r^2 d_5 ^ 2 ] , [ eq : tbone ] where @xmath399 is the radial coordinate in the transverse space , @xmath400 are the coordinates on the brane , and @xmath401 is the measure on a unit 5-sphere . the harmonic function @xmath402 is given by f(r ) = 1 + ( r r ) ^4 r^4 = 4g_s n l_s^4 .
[ eq : tbtwo ] the dilaton is a constant and the only other nontrivial field is the 4-form gauge field with a field strength f_0789r = 4 r^4 g_s r^5[f(r)]^-2 .
[ eq : tbthree ] the horizon is at @xmath241 and the horizon area is indeed zero .
however , the spacetime is completely nonsingular . in the near - horizon or near - brane region @xmath403 ,
the metric ( equation [ eq : tbthree ] ) becomes , in terms of coordinates @xmath404 , ds^2 = ( r z ) ^2[-dt^2 + dx^2 + dz^2 ] + r^2 d_5 ^ 2 .
[ eq : tbthreea ] this is the metric of the space ads@xmath405 , the first factor being composed of @xmath406 while the sphere @xmath407 has a constant radius @xmath84 . the ads@xmath408 has a constant negative curvature @xmath409 , whereas the sphere @xmath407 has a constant positive curvature .
thus , near the horizon the spacetime approaches a `` throat geometry , '' where the length of the throat is along the ads@xmath408 coordinates and the cross sections are 5-spheres of constant radii @xmath84 . from equation [ eq : tbtwo ]
it follows that this curvature is much smaller than the string scale when @xmath410 .
this is thus the regime where semiclassical supergravity is valid .
it is possible to calculate the classical absorption cross section of various supergravity modes by the extremal 3-brane . for s - wave absorption of minimally coupled scalars , the leading - order result is @xcite = 18 ^ 4 r^8 ^3 = 132 ( n)^2 ^3 , [ eq : tbfour ] where we have used equation [ eq : tbtwo ] .
the cross section of course vanishes at @xmath411 , since the horizon area vanishes .
also note that we are dealing with an extremal solution that has zero temperature , so we have absorption but no hawking radiation .
it turns out that in this case one can also analytically calculate the low - energy absorption cross section of such scalars for arbitrary angular momentum @xcite .
the microscopic theory of @xmath187 3-branes is a @xmath188 gauge theory in @xmath412 dimensions with 16 supersymmetries , or @xmath329 supersymmetry .
this is a well - studied theory and is known to be conformally invariant with zero beta function .
it is the dimensional reduction of @xmath413 supersymmetric yang - mills in ten dimensions .
as we will see below , a natural symmetry argument determines the coupling of some of the supergravity modes to the brane degrees of freedom .
however , if we consider modes like the dilaton and longitudinal traceless parts of the 10-dimensional graviton , the coupling can be once again read off from the equivalence principle .
for example , the longitudinal graviton has to couple to the energy - momentum tensor of the yang - mills theory .
thus , one can perturbatively calculate the absorption cross section of such modes ( which are minimal scalars from the 7-dimensional point of view ) along the lines of the calculation in the 5-dimensional black hole .
again , an exact agreement was found for s - waves @xcite , and the agreement was found to extend to all angular momenta @xcite . in this case , the reason for the agreement of the weak coupling calculation with supergravity answers is much better understood . in particular , it is known that the two - point function of the energy - momentum tensor of @xmath329 yang - mills theory is not renormalized , so that the lowest - order result is exact @xcite .
the imaginary part of the two - point function in euclidean space is in turn related to the absorption cross section , which is thus also protected from higher - order corrections .
there are similar nonrenormalization theorems known for operators coupling to other modes as well .
the extremal 3-brane of supergravity described above is of course a limit of a general nonextremal solution with finite horizon area and finite temperature .
it is thus natural to expect that the microscopic description of this is in terms of a yang - mills theory at finite temperature .
the thermodynamics of this yang - mills theory was calculated @xcite at lowest order in the coupling constant ( i.e. a free gas ) , and it was found that although the dependence of the thermodynamic quantities on the energy , volume , and @xmath187 is the same as in semiclassical thermodynamics of the corresponding black brane , the precise coefficient differs by a factor of @xmath414 . we know of no reason why the thermodynamic quantities are not renormalized as we go from weak to strong coupling , so the discrepancy is not unexpected .
however , it is significant that the dependences agree although the dependence on the energy and the volume is dictated by scaling arguments ( this is a conformally invariant theory ) , the dependence on @xmath187 is not . at weak coupling ,
we know that there are @xmath189 degrees of freedom ; there is no known argument why this should continue at strong coupling .
we have presented a unitary description of black hole evaporation in terms of the emission of closed strings from the branes .
this description was at weak coupling ; in order to describe absorption by the black hole of quanta with arbitrary energies , one must imagine that it is continued to strong coupling .
let us see what form this continuation to higher energies might take .
in the lowest - order calculation , there was only one string interaction , where two open strings joined up to the emitted closed string . at higher orders in the coupling , we expect the emitted string to interact several times with the branes before escaping to infinity as radiation .
let us consider for simplicity the case of the d3-branes described above .
each such interaction gives one `` hole '' on the string world sheet , with the boundary of the hole being constrained to the branes . from the viewpoint of the dynamics of open strings on the 3-branes , each hole looks like an open string loop .
thus , as we increase the coupling , we encounter higher loop processes among the open strings , in the process of emitting a closed string . on the other hand , a loop of open strings can be interpreted as a propagation of a closed string at tree level ( see figure 4 ) .
thus , these open string multiloop processes might be reinterpreted as closed string exchanges between the departing quantum and the branes . but among such closed string exchange must be the effect of the gravitational effect of the branes , which , crudely speaking , would attempt to retard the outgoing quantum , redshifting it to lower energies .
such a redshift is easily seen if we consider the propagation of the outgoing quantum in the metric produced by the branes .
but now we ask : as we increase the coupling in the microscopic calculation , should we take into account the complicated loop processes of the gauge theory ( which are significant when the open string @xmath415 coupling is not small ) , as well as the fact that the metric around the branes will cease to be flat ?
( this curvature is significant when the closed string coupling @xmath416 ceases to be small . )
the discussion above indicates that taking both of these effects into account might amount to overcounting .
the effect of open string loops might well be counted in the propagation of closed string modes ( which include gravitons that can be said to condense to generate the curvature ) .
it is hard to answer this question from a direct consideration of loop expansions , since in the domain of large coupling we are unlikely to have any good expansion in the number of loops .
thus , the above considerations are somewhat heuristic .
the situation is reminiscent , though , of the appearance of duality in tree - level string scattering .
the @xmath49-channel exchange has a sequence of poles , as does the @xmath53-channel scattering , and we confront the issue of whether these are two different effects to be added together in some way or just dual manifestations of a common underlying dynamics . in the case of this string scattering , of course , it is now well understood that the @xmath53-channel poles result from an infinite sum over @xmath49-channel poles and are not to be considered as additional contributions to the @xmath22-matrix . in the much more complicated case of the black hole evaporation process , maldacena s bold postulate addressed the relation between microscopic theory of the branes and the effects of gravity in 10-dimensional spacetime .
maldacena considered the following limit .
place together a large number @xmath417 of d3-branes .
let the string coupling be weak ( @xmath418 ) , but take the limits of large @xmath187 and small @xmath183 in such a way that @xmath419 tends to a finite value .
now consider energies of excitation that are low , so that on the d3-branes we get open strings but only in their lowest states .
the dynamics of these open strings is , as we saw above , given by a ( @xmath420 ) supersymmetric yang - mills theory .
the quantity @xmath421 is the t hooft coupling of the gauge theory . at small t hooft coupling
, we can study the large-@xmath187 gauge theory perturbatively ; at large t hooft coupling @xmath422 such a perturbative analysis is not possible .
but for @xmath423 we are in a regime where the d3-branes produce an appreciable gravitational field around themselves , and in fact distort the spacetime into the form of equation [ eq : tbone ] .
in particular , as shown above , as we approach the horizon the geometry becomes the throat geometry ads@xmath405 given by equation [ eq : tbthreea ] .
maldacena postulated that we can consider either ( @xmath58 ) the gauge theory on the branes ( which is given by the open string interactions at a perturbative level ) or ( @xmath59 ) no branes , but the space ads@xmath424 and closed string theory ( which has gravity as a low - energy limit ) on this curved manifold .
these two theories were dual descriptions of exactly the same underlying theory .
if the gauge theory of the branes and gravity on the 10-dimensional spacetime are indeed exactly dual descriptions of the same theory , then we must have a way of computing the same quantity in two dual ways , and thus to see manifestly the consequences of this duality . to do this , we need an operational definition of the dual map , which was provided by gubser et al @xcite and witten @xcite .
let us rotate the signature of the spacetime to a euclidean one .
in this case , the space spanned by @xmath425 , which is now euclidean ads@xmath408 , has @xmath44 as a regular point in the interior of the space .
thus , there is no singularity that might represent the place where the d3-branes were placed in a gauge theory description . but this space has a boundary at @xmath426 , which has the topology of @xmath427 .
the conjecture now states that string theory on this smooth ads@xmath424 is dual to @xmath420 supersymmetric @xmath428 yang - mills on the 4-dimensional boundary of the ads space .
note that in this formulation of the conjecture , all reference to d3-branes has disappeared .
in fact , a geometry that is ads@xmath429 everywhere ( and not just at small @xmath236 ) is an exact solution of string theory without any branes present .
we take the 5-form field strength @xmath104 present in type iib string theory to have a constant value with integral @xmath187 on the @xmath407 ; since this field must be self - dual , it also has a constant value on the ads@xmath408 .
the energy density of this field yields the equal and opposite curvatures of the @xmath407 and the ads@xmath408 spaces ; the radius of curvature in each case is @xmath430 ( @xmath60 is the string length ) .
if we had taken a collection of d3-branes as above , then the flux of @xmath104 on the sphere surrounding the branes would have been @xmath187 , but only the near - brane geometry would have resembled ads@xmath431at large @xmath236 the space becomes flat .
thus , it seems better to formulate the duality without reference to any d - branes , although , as we discuss below , this makes the issues related to black hole information loss somewhat more difficult to access . an important fact that led maldacena to the duality conjecture was the agreement of global symmetries between the gravity theory and the gauge theory .
ads@xmath408 is a maximally symmetric space with a 15-parameter isometry group .
the gauge theory is in four dimensions , so one may expect a 10-dimensional set of symmetries , which are the translations and rotations on @xmath427 .
but the @xmath420 supersymmetric @xmath428 yang - mills theory is a conformal theory , and the conformal group in four dimensions is indeed isomorphic to the 15-parameter group of isometries of ads@xmath408 space .
further , the @xmath420 gauge theory has four supercharges forming , having an @xmath432 symmetry of rotations among themselves .
the gravity theory has an internal space that is @xmath407 .
thus , when we decompose fields in harmonics on this space in the process of kaluza - klein reduction , the multiplets obtained fall into representations of @xmath433 .
but @xmath434 , so both the theories have the same r - symmetry group .
further , because of conformal invariance , the gauge theory has 16 conformal supercharges in addition to its 16 regular supercharges ; this agrees with the 32 supercharges of the gravity theory on ads@xmath424 .
let us return to the issue of how to compare quantities in the two dual theories .
let @xmath23 be the ads space , and @xmath435 its boundary .
let us consider for simplicity a scalar field , the dilaton @xmath92 , present in the string theory .
if we specify the value @xmath436 of @xmath92 on the boundary @xmath435 , then we can solve for @xmath92 in the interior of @xmath23 and compute the action @xmath437 of supergravity on this solution .
the field @xmath92 , on the other hand , will be dual to an operator in the yang - mills theory , and in this case symmetries fix this operator to be @xmath438 .
the duality relation is e^-s^_sugra[_b ] = _ da e^-s_ym+d_b()tr f^2 ( ) _ da e^-s_ym .
[ eq : adsmain ] here @xmath439 represents the path integral over the gauge theory variables . the action on the left - hand side is a string action in general , but at the leading order it can be replaced by the supergravity action . using the above relation
, it is possible in principle to compute @xmath300-point correlation functions from supergravity and compare the results to calculations in the gauge theory .
the gravity theory is simple ( perturbative classical supergravity to lowest order ) when @xmath187 is large ( loops of gravity are suppressed by @xmath440 ) and @xmath419 is large ( because then the ads space has a large radius , and stringy corrections , which depend on @xmath441 , can be ignored to leading order ) .
thus it is difficult to compare results on the gravity side with explicit computations in the yang - mills theory , which has a well - known treatment of the large-@xmath187 limit but no simple way to handle a regime with @xmath442 .
however , supersymmetry protects the values of some quantities from changing when the coupling is varied , and here agreement is indeed found .
thus , anomalous dimensions of chiral operators @xcite and three - point functions of chiral operators @xcite are found to have the same value when computed from the gauge theory or from the gravity dual using equation [ eq : adsmain ] . for quantities that are not protected in this fashion ,
the gravity calculation gives a prediction for the strongly coupled gauge theory .
examples of such predictions are the potential between external quarks placed in the gauge theory @xcite , four - point correlation functions , and anomalous dimensions of composite operators ( which can be deduced from the four - point functions ) @xcite .
if one considers the gauge theory at a finite temperature by compactifying the `` time '' direction , then one obtains a nonsupersymmetric theory with a discrete spectrum of glueball states @xcite . in this case
, the strong coupling calculation has no direct physical meaning , and only a weak coupling calculation would give the true glueball masses ( the coupling flows with scale after supersymmetry is broken ; with supersymmetry intact , it does not , and each value of the coupling gives a different well - defined theory ) .
nevertheless , there is a surprising agreement of the qualitative features of the glueball spectrum between the gravity calculation and lattice simulations @xcite .
the ads / cft correspondence has been studied extensively over the past two years [ see @xcite for review ] . this section explains how this correspondence illustrates another important property of holography that is in fact its very essence : the bekenstein bound @xcite .
a general argument states that in any theory of gravity , the total entropy @xmath22 of anything in a large box of volume @xmath249 and surface area @xmath443 is bounded by s , [ eq : holone ] where @xmath444 is newton s constant .
numerical constants are ignored in this relation .
the form of this bound appears surprising , since in the absence of gravity we know that entropy is an extensive quantity and should scale as @xmath249 .
however , the result follows from the existence of black holes .
suppose we start with a state whose entropy is bigger than this bound , but whose energy is smaller than the mass of a black hole that fills the entire box .
then we slowly add matter , increasing the energy . at some stage
, gravitational collapse takes over and a black hole is formed , which then continues to grow until it fills up the box .
we know that the entropy of a black hole is proportional to the area of the horizon measured in units of newton s constant
. however , for this black hole , the area of the horizon is the same as the area of the box @xmath443 , i.e. the right - hand side of equation [ eq : holone ] .
thus , we have managed to decrease the entropy in this process and hence have violated the second law .
t hooft @xcite and susskind @xcite have proposed a radical interpretation of the holographic bound ( equation [ eq : holone ] ) , namely , a @xmath445-dimensional theory of gravity should be equivalent to a @xmath34-dimensional theory that lives on the boundary of space , and this @xmath34-dimensional theory must have one degree of freedom per planck area . if this is true , the bekenstein bound naturally follows .
we have seen that supergravity in ads@xmath405 is dual to a strongly coupled large-@xmath187 yang - mills theory in @xmath412 dimensions .
is it then true that the latter has one degree of freedom per planck area ?
this is indeed true @xcite . in the ads@xmath405 metric ( equation [ eq : tbthreea ] ) the boundary is at @xmath446 and continuum yang - mills theory living on this boundary
is dual to supergravity in the whole space .
but suppose we impose an infrared cutoff at @xmath447 .
then it turns out that supergravity in the region @xmath448 is dual to a yang - mills theory with a position space ultraviolet cutoff @xmath449 .
in fact , renormalization group flows of the gauge theory become motion in the fifth dimension .
consider a large patch of this boundary of coordinate size @xmath257 ( in terms of the @xmath450 coordinates ) .
it follows from equation [ eq : tbthreea ] that the physical area of this boundary is a ~r^3 z_0 ^ 3 l^3 .
[ eq : holothree ] using the expression for @xmath84 in equation [ eq : tbtwo ] and the fact that the 5-dimensional newton s constant @xmath252 is given by @xmath451 , we see that ~n^2 l^3 z_0 ^ 3 .
[ eq : holofour ] now the yang - mills theory has @xmath189 degrees of freedom per unit cell .
this is manifest at weak coupling , but the result for the entropy of near - extremal 3-branes shows that this must also be true in strong coupling .
furthermore , the cutoff of this theory is precisely @xmath452 .
thus , the right - hand side of equation [ eq : holofour ] is indeed the number of degrees of freedom in this cutoff yang - mills theory .
this shows that the gauge theory
supergravity duality provides a concrete demonstration of the bekenstein bound .
another example of the holographic connection is provided by the near - horizon geometry of the d1-d5 system .
this spacetime is ads@xmath453 @xcite , where @xmath454 is either @xmath250 or @xmath455 on which the five branes are wrapped .
the ads@xmath456 is made up of time , the transverse radial coordinate @xmath236 , and @xmath235 .
the boundary theory is once again a superconformal field theory .
however , this is no longer a gauge theory but rather the low - energy theory of the d1-d5 system discussed in the previous sections .
once again , the symmetries of the bulk agree with the symmetries of the conformal field theory . furthermore , 5d black holes obtained by putting in some momentum now become the banados - teitelboim - zanelli ( btz ) black holes of 3-dimensional gravity .
in fact , recently the holographic connection has been used to understand the properties of the d1-d5 system . details of this development are supplied elsewhere @xcite . unfortunately , despite these agreements between the two dual descriptions , we do not yet understand the explicit map that relates the gauge theory variables to the gravity variables
. there is , in fact , an earlier example of holography : @xmath268-dimensional string theory .
this theory has a nonperturbative definition in terms of quantum mechanics of @xmath190 matrices .
one starts with the action @xmath457 $ ] , noting that when the matrix is large , there is a critical form for the potential in which successive terms in the loop expansion are comparable .
the theory can be written in terms of @xmath458 , the density of eigenvalues of the matrix @xcite . at the critical point ,
the extra dimension @xmath459 ( which is the space of eigenvalues ) becomes continuous and the collective field @xmath458 becomes a smooth field in @xmath278 dimensions .
remarkably , in terms of appropriate variables , these two dimensions ( which emerged in totally different ways ) exhibit a local lorentz invariance @xcite , though in the presence of a background that breaks the full symmetry . in fact , at the critical point the loop diagrams of the matrix model generate discretizations of an oriented world sheet with dynamical world sheet metric and one scalar field .
the usual quantization of noncritical string theory then converts the scale on the world sheet to an extra dimension in target space @xcite , resulting in a @xmath268-dimensional field theory .
furthermore , renormalization group flow on the world sheet is related to motion in this extra target space direction @xcite
. it would be interesting if the gauge theory in @xmath412 dimensions acquired extra dimensions in a similar manner to map onto string theory in 10 dimensions .
so far , such an approach has not succeeded , despite several attempts .
the progress of string theory over the past few years has been truly remarkable .
consistent quantization of the string forced us to consider a 10-dimensional supersymmetric theory .
within such a theory , one discovers branes as solitonic states .
regarding such solitons as elementary quanta turns out to be a duality transformation , and such duality maps unify all the five perturbative quantizations of the string , as well as 11-dimensional supergravity .
there is no room for any free parameters in the theory , although many solutions of the field equations appear equally acceptable at first sight , and we do not yet know which to choose to describe the low - energy physics of the world that we see around us .
the results on black holes have provided a striking validation of this entire structure .
the entropy of black holes can be deduced from robust thermodynamic arguments , using just the classical properties of the black hole metric and gedanken experiments with low - density quantum matter .
a correct quantum theory of gravity should reproduce this entropy by a count of allowed microstates , and string theory yields the correct microscopic entropy of extremal and near - extremal holes ( the only cases in which we know how to compute with some confidence ) .
further , interaction with these microscopic degrees of freedom yields a unitary description of black hole absorption and hawking emission for low - energy quanta from near - extremal holes ( again this is the case in which we may compute with some confidence ) , thus suggesting that black holes can be unified into physics without having to modify basic principles of quantum mechanics or statistical physics . in no other route that has been attempted for quantizing gravity
has it been possible to arrive at a value for black hole entropy ; the power of supersymmetry and our understanding of the nonperturbative features of string theory have allowed us to extract more than just the perturbative physics of graviton scattering . what about the information issue in black hole evaporation ?
the derivation of unitary low - energy hawking radiation from microstates certainly gives a strong indication on the information _ question , _
i.e. that information in the matter falling into the hole is not lost but is recovered in the radiation that emerges .
but it is fair to say that we do not yet have a good understanding of the information _ paradox . _
the paradox presents us with one way of computing hawking radiation , via the foliation of spacetime depicted in figure 1 , and this radiation process appears to be nonunitary .
the paradox then challenges us to point out which of the assumptions that went into the calculations were wrong .
it now appears reasonable that there are nonlocalities in quantum gravity that can extend beyond planck scale .
indeed holography , and in particular the maldacena conjecture , requires that the degrees of freedom in a volume be encoded by degrees of freedom at the surface of that volume , so we must give up naive ways of thinking about locality .
but we do not yet understand in detail the mechanism of this nonlocality , and in particular we lack an explicit description in string theory of the foliation in figure 1 .
these gaps in our understanding are probably linked to our lack of an adequate language to understand the variables of string theory in a way that is not based on perturbation around a given background . in recent years
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d _ 55:5112 ( 1997 ) | we review recent progress in our understanding of the physics of black holes .
in particular , we discuss the ideas from string theory that explain the entropy of black holes from a counting of microstates of the hole , and the related derivation of unitary hawking radiation from such holes . epsf black holes , information loss , string theory , d - branes , holography |
ESPN, the sports network where male announcers have repeatedly faced disciplinary action in high-profile episodes of sexist behavior, has benched yet another host for his remarks to a female colleague.
The network acknowledged Monday that it yanked one of its announcers, Ron Franklin, from covering the Fiesta Bowl college football game Saturday, reportedly after Franklin made belittling comments to sideline reporter Jeannine Edwards.
Franklin, 68, allegedly called Edwards an insulting seven-letter word after she objected to being called "sweet baby" by Franklin during a conversation that took place at a pregame production meeting Friday, hours before the pair were to cover another football game for ESPN.
The incident is the latest in a long string of episodes in which ESPN hosts have demeaned or engaged in sexual-harassing behavior toward the Disney-owned network's female employees.
Baseball analyst Harold Reynolds was fired in 2006 after being accused of harassment by a female employee. Steve Phillips, another baseball analyst, lost his job in 2009 as a result of an affair with a much-younger production assistant who disclosed the relationship to Phillips's wife after he sought to break it off. In 2007, a makeup artist working on the since-canceled show "Cold Pizza" sued the program's co-hosts, alleging they groped and harassed her. (The suit was thrown out.)
Last year, former Washington Post sports columnist Tony Kornheiser, co-star of the popular ESPN show "Pardon the Interruption," was suspended for critical comments he made on his local radio program about "SportsCenter" host Hannah Storm's clothes.
Franklin, a veteran ESPN announcer, reportedly addressed another sideline reporter, Holly Rowe, as "sweetheart" during a 2005 broadcast. He later apologized to Rowe.
The run-in prompted ESPN ombudsman George Solomon to observe at the time: "Play-by-play commentators need to take sideline reporters - many of whom are women - more seriously. So does ESPN, which needs to give these reporters more airtime and more serious issues to address."
ESPN declined to comment in detail on the latest episode. It issued a statement saying, "We're not going to get into specifics other than to say adhering to our personal-conduct policies and showing respect for colleagues are of the utmost importance to our company and we take them extremely seriously."
The network also issued a statement from Franklin saying: "I said some things I shouldn't have and am sorry. I deserved to be taken off the Fiesta Bowl."
ESPN dealt with dozens of sexual harassment incidents in the two decades after its founding in 1979, according to "ESPN: The Uncensored History," a book by New York Times sportswriter Mike Freeman that was published in 2000. Among those disciplined, according to the book, was "Monday Night Football" announcer Mike Tirico, who in 1992 was suspended for unwelcome advances toward another employee.
Despite its track record, ESPN is no more hospitable to harassing behavior than other male-dominated workplaces, said Dan Lebowitz, executive director of the Sport in Society program at Northeastern University. ||||| ESPN announced Tuesday afternoon that veteran announcer Ron Franklin has been terminated by the company.
ESPN released the following short statement on Franklin’s firing: “Based on what occurred last Friday, we have ended our relationship with him.”
As reported here on Sunday, Franklin made insulting comments to ESPN sideline reporter Jeannine Edwards last Friday that included calling her an “a–hole” and, as later clarified by Edwards, “sweet baby.”
After Franklin’s comments to Edwards were reported by a third party to ESPN management, Franklin was subsequently taken off the ESPN Saturday Fiesta Bowl radio broadcast.
Franklin signed a two-year contract with ESPN last July. He had been scheduled to work Big 12 basketball games twice per week this season.
After the firing, an ESPN source told me that Franklin’s termination was not only related to the incident with Edwards, but also an inappropriate on-air comment the veteran announcer made to ESPN sideline reporter Holly Rowe in 2005.
Another ESPN source indicated to me after the termination that ESPN Programming Executive Norby Williamson was dissatisfied with Franklin’s level of contrition following the incident with Edwards. That lack of remorse included Franklin failing to apologize to Edwards personally.
Follow Brooks on Twitter for real-time updates. | – Ron Franklin's 23-year career at ESPN is over because of sexist remarks he made to a colleague. "Listen to me, sweet baby, let me tell you something," Franklin said to sideline reporter Jeannine Edwards ahead of last week's Chick Fil-A-Bowl in the middle of an interview. When she told him not to address her like that, the sportscaster responded: "OK, then listen to me a-hole," reports the Washington Post. Franklin was pulled from the Fiesta Bowl broadcast over the incident and ESPN yesterday confirmed that he has been canned. "Based on what occurred, we have ended our relationship with him," an ESPN spokesman said. Franklin apologized for his remarks in a statement earlier this week, but sources say he was fired anyway because he refused to apologize to Edwards personally. The incident is the latest in a long string of similar episodes at the Disney-owned network. |
the radiation environment in deep space or on the moon can be very harsh ( macfarlane et al . , 1991 ) . without the earth
s atmosphere and magnetic field to protect them , astronauts will be directly exposed to high - energy galactic cosmic rays ( gcr ) , to intense fluxes of protons and other particles from solar flares , and to radiation from on - board power plants or nuclear propulsion systems .
such radiation is also very dangerous to computers and electronics on spacecraft , as it may cause enough single - event upsets to lead to device failure .
the economic penalties of additional mass to provide shielding may be huge . to minimize this expense ,
we need to be able to reliably calculate the amount of shielding required . performing this task
requires nuclear data for reactions induced by different projectiles , on different targets , for a large range of incident energies .
similarly , addressing different astrophysical problems , such as investigation the origin and propagation of cosmic rays ( cr ) and the nuclide abundances in the solar system and in cr , again requires a large amount of different nuclear reaction data .
experiments to obtain such data are costly , there is a limited number of facilities available to make such measurements , and some reactions of interest can not yet be measured at current accelerators . therefore reliable models and codes are required to provide the necessary estimates . during recent years at the los alamos national laboratory
, we have developed an improved version of the cascade - exciton model ( cem ) , contained in the code cem2k , to describe nucleon - induced reactions at incident energies up to 5 gev ( mashnik and sierk , 2001 and 2002 ) and the los alamos version of the quark - gluon string model , realized in the high - energy code laqgsm ( gudima et al . , 2001 ) , able to describe both particle- and nucleus - induced reactions at energies up to 1000 gev / nucleon .
both codes have been tested against most of the available data and compared with predictions of other modern codes ( mashnik and sierk , 2001 and 2002 ; mashnik et al .
, 2002a-2002d ; titarenko et al . , 2002 ) .
our comparisons have shown that both codes describe a large variety of spallation , fission , and fragmentation reactions quite reliably and have one of the best predictive powers compared with other available monte - carlo codes . in the present paper ,
we outline our models and show several typical results that testify that both cem2k and laqgsm are reliable event - generators which can be used in many different applications . as an illustration of application of our evaluated cross sections in astrophysics ,
we show an estimate of the size of the cr halo obtained using the cr propagation code galprop ( strong and moskalenko , 1998 ; moskalenko et al . , 2002 ) .
a detailed description of the initial version of the cem may be found in gudima et al .
( 1983 ) , therefore we outline here only its basic assumptions .
the cem assumes that reactions occur in three stages .
the first stage is the intranuclear cascade ( inc ) in which primary particles can be re - scattered and produce secondary particles several times prior to absorption by or escape from the nucleus .
the excited residual nucleus remaining after the cascade determines the particle - hole configuration that is the starting point for the preequilibrium stage of the reaction .
the subsequent relaxation of the nuclear excitation is treated in terms of an improved modified exciton model ( mem ) of preequilibrium decay followed by the equilibrium evaporative final stage of the reaction .
generally , all three stages contribute to experimentally measured outcomes .
the improved cascade - exciton model in the code cem2k differs from the older cem95 version by incorporating new approximations for the elementary cross sections used in the cascade , using more precise values for nuclear masses and pairing energies , employing a corrected systematics for the level - density parameters , improving the approximation for the pion binding energy " , @xmath0 , adjusting the cross sections for pion absorption on quasi - deuteron pairs inside a nucleus , considering the effects of refractions and reflections from the nuclear potential on cascade particles , allowing for nuclear transparency of pions , including the pauli principle in the preequilibrium calculation , and improving the calculation of the fission widths .
implementation of significant refinements and improvements in the algorithms of many subroutines led to a decrease of the computing time by up to a factor of 6 for heavy nuclei , which is very important when performing simulations with transport codes .
essentially , cem2k has a longer cascade stage , less preequilibrium emission , and a longer evaporation stage with a higher excitation energy , as compared to its precursors cem97 and cem95 . besides the changes to cem97 and cem95 mentioned above
, we also made a number of other improvements and refinements , such as : ( i ) imposing momentum - energy conservation for each simulated event ( the monte carlo algorithm previously used in cem provides momentum - energy conservation only statistically , on the average , but not exactly for the cascade stage of each event ) , ( ii ) using real binding energies for nucleons at the cascade stage instead of the approximation of a constant separation energy of 7 mev used in previous versions of the cem , ( iii ) using reduced masses of particles in the calculation of their emission widths instead of using the approximation of no recoil used previously , and ( iv ) a better approximation of the total reaction cross sections . on the whole , this set of improvements led to a much better description of particle spectra and yields of residual nuclei and a better agreement with available data for a variety of reactions .
details , examples , and further references may be found in mashnik and sierk ( 2001 and 2002 ) and in titarenko et al .
( 2002 ) .
the los alamos version of the quark - gluon string model ( laqgsm ) by gudima et al . , ( 2001 ) is a next - generation of the quark - gluon string model ( qgsm ) by amelin et al .
( 1990 , and references therein ) and is intended to describe both particle- and nucleus - induced reactions at energies up to about 1 tev / nucleon .
the core of the qgsm is built on a time - dependent version of the intranuclear cascade model developed at dubna , often referred in the literature simply as the dubna intranuclear cascade model ( dcm ) ( see toneev and gudima , 1983 and references therein ) .
the dcm models interactions of fast cascade particles ( participants " ) with nucleon spectators of both the target and projectile nuclei and includes interactions of two participants ( cascade particles ) as well .
it uses experimental cross sections ( or those calculated by the quark - gluon string model for energies above 4.5 gev / nucleon ) for these elementary interactions to simulate angular and energy distributions of cascade particles , also considering the pauli exclusion principle .
when the cascade stage of a reaction is completed , qgsm uses the coalescence model described in toneev and gudima ( 1983 ) to create " high - energy d , t , @xmath1he , and @xmath2he by final state interactions among emitted cascade nucleons , already outside of the colliding nuclei . after calculating the coalescence stage of a reaction , qgsm moves to the description of the last slow stages of the interaction , namely to preequilibrium decay and evaporation , with a possible competition of fission using the standard version of the cem by gudima et al . , ( 1983 ) .
but if the residual nuclei have atomic numbers with @xmath3 , qgsm uses the fermi break - up model to calculate their further disintegration instead of using the preequilibrium and evaporation models .
laqgsm differs from qgsm by replacing the preequilibrium and evaporation parts of qgsm described according to the standard cem ( gudima et al . , 1983 ) with the new physics from cem2k ( mashnik and sierk , 2001 and 2002 ) and
has a number of improvements and refinements in the cascade and fermi break - up models ( in the current version of laqgsm , we use the fermi break - up model only for @xmath4 ) . a detailed description of laqgsm and further references may be found in gudima et al .
( 2001 ) . originally , both cem2k and laqgsm were not able to describe fission reactions and production of light fragments heavier than @xmath2he , as they had neither a high - energy - fission nor a fragmentation model .
recently , we addressed these problems ( mashnik et al
. , 2002a and 2002c ) by further improving our codes and by merging them with the generalized evaporation model code gem2 developed by furihata ( 2000 and 2001 ) .
we have benchmarked our codes on all reactions measured recently at gsi ( darmstadt , germany ) and on many other different reactions at lower and higher energies measured earlier at other laboratories .
we found that cem2k and laqgsm allow us to describe quite well a large variety of spallation , fission and fragmentation reactions at energies from 10 mev to 800 gev , without any free fitting parameters , though we still have to solve a number of problems for a better description of nuclides produced near the intersection of the spallation and fission regions .
our current versions of cem2k and laqgsm were incorporated recently into the mars ( mokhov , 1995 ) and lahet ( prael and lichtenstein , 1989 ) transport codes and are currently being incorporated into mcnpx ( waters , 1999 )
. this will allow others to use our codes as event - generators in these transport codes to simulate reactions with targets of practically arbitrary geometry and nuclide composition .
figure 1 shows examples of calculated by cem2k and laqgsm neutron spectra from interactions of protons with @xmath5pb at 0.8 gev , while figure 2 gives examples of p , d , t , @xmath1he , and @xmath2he spectra from p ( 61 mev ) + fe compared with experimental data by ishibashi et al .
( 1997 ) and bertrand and peelle ( 1973 ) .
we note that all reactions shown in figures 1 and 2 , and in all the following figures of this paper , were calculated within a single approach , without fitting any parameters of cem2k or laqgsm .
we see that both cem2k and laqgsm describe well spectra of secondary neutrons and protons .
similar results are obtained for other targets and energies of incident protons , as well as for reactions induced by neutrons , pions , and photons .
spectra of @xmath2he are also described by our codes quite well , while spectra of d , t , and @xmath1he are reproduced reasonably , but not as well as those of nucleons and @xmath2he .
this is partially due to the fact that we do not fit here the probability @xmath6 for @xmath7 excited nucleons ( excitons ) to condense into a complex particle which can be emitted during the preequilibrium stage of a reaction to get the best agreement with the data , as is often done in the literature by other authors ( see details in gudima et al . , 1983 and mashnik et al . , 2002c
) . in the present version of our models
we do not take into account direct production of complex particles like pick - up and knock - out , and this leads to some underestimation of emission of high - energy complex particles , and to under - prediction of the high - energy tails of their spectra seen in figure 2 .
we note that some of the evaporation models used often in the literature , like the gsi evaporation model by schmidt ( gaimard and schmidt , 1991 ; junghans et al . , 1998 ) , which is used in conjunction with the liege inc by cugnon ( boudard et al . ,
2002 ) in the code incl , do not consider preequilibrium particle emission ; they only evaporate n , p , and @xmath2he , and do not produce d , t , and @xmath1he at all .
recently , nakamura s group measured neutron double - differential cross sections from many reactions induced by light and medium nuclei on targets from @xmath8c to @xmath5pb , at several incident energies from 95 to 600 mev / nucleon ( iwata et al . , 2001 and references therein ) .
we have calculated all these cross sections using laqgsm . as an example ,
our results for interactions of 600 mev / nucleon @xmath9ne with cu are compared in figure 3 with experimental data and calculations with the qmd ( aichelin , 1991 ) and hic ( bertini et al . , 1974 ) models kindly provided to us by nakamura s group .
we see that laqgsm describes these data quite well and agrees with the measurements much better than do qmd and hic .
similar results are obtained for all the other reactions measured by this group .
recently , for the proton radiography ( prad ) project , we have performed ( mashnik et al . , 2002b ) a benchmark of qgsm ( and laqgsm ) , mars , and lahet3 ( prael , 2001 ) against all measured double - differential cross sections of proton - nucleus reactions at energies around 50 gev for all targets for which we were able to find experimental data .
we calculated , compared with experimental data , and analyzed more than 500 spectra of p , d , t , @xmath1he , @xmath2he , @xmath10 , @xmath11 , @xmath12 , @xmath13 , and @xmath14 emitted from targets from @xmath15be to @xmath5pb at angles from 0 to 159 deg at incident proton energies from 30 to 70 gev .
this study has shown that laqgsm describes well most of the measured spectra .
a detailed and comprehensive report on this work is now in preparation , while figure 4 shows just one example , namely spectra of deuterons emitted at 9.17 deg from p ( 70 gev ) + @xmath5pb .
we see that deuterons with momentum of up to about 15 gev / c are emitted and measured in this particular reaction .
utilizing the coalescence mechanism for complex particle emission , laqgsm is able to describe high - energy deuteron production , and agrees well with the measurement .
lahet3 does not consider the coalescence of complex particles and therefore describes emission of only evaporative and preequilibrium deuterons with momenta not higher than 1 gev / c .
even though the cross section for emission of deuterons with momentum of @xmath16 gev / c is more than six orders of magnitude lower than for evaporation of low energy deuterons , such high energy deuterons and other complex particles may be extremely dangerous to people and equipment in space .
therefore , we need to be able to calculate such reactions as well as possible , to accurately estimate the necessary shielding . recently at gsi in darmstadt , germany , a large amount of measurements have been performed using inverse kinematics for interactions of @xmath17fe , @xmath5pb and @xmath18u at 1 gev / nucleon and @xmath19au at 800 mev / nucleon with liquid @xmath20h .
these measurements provide a very rich set of cross sections for production of practically all possible isotopes from such reactions in a pure " form , _
i.e. _ , individual cross sections from a specific given bombarding isotope ( or target isotope , when considering reactions in the usual kinematics , p + a )
. such cross sections are much easier to compare to models than the camouflaged " data from @xmath21-spectrometry measurements .
these are often obtained only for a natural composition of isotopes in a target and are mainly for cumulative production , where measured cross sections contain contributions not only from the direct production of a given isotope , but also from all its decay - chain precursors . in addition , many reactions where a beam of light , medium , or heavy ions with energy near to or below 1 gev / nucleon interact with different nuclei , from the lightest , d , to the heaviest , @xmath5pb were measured recently at gsi .
references on these measurements and many tabulated experimental cross sections may be found on the web page of prof .
schmidt ( 2002 ) . we have analyzed with cem2k and laqgsm all measurements done at gsi
we are acquainted of , both for proton - nucleus and nucleus - nucleus interactions .
some examples of our cem2k results compared with the gsi data and calculations by other current models for proton - nucleus reactions may be found in mashnik and sierk ( 2001 and 2002 ) , mashnik et al .
( 2002a , 2002c , and 2002d ) , and titarenko et al .
figure 5 shows an example of laqgsm results for the reaction p(1 gev ) + @xmath5pb compared with gsi data and calculations by a version of lahet using the incl event - generator incorporated recently into lahet .
we have described incl above ; it is well known and often used in europe .
one can see that laqgsm merged with gem2 ( laqgsm+gem2 ) describes quite well the gsi data and agrees better with the measurement than incl does .
similar results are obtained for all other reactions measured at gsi for which we found data . figure 6 shows an example of the highest energy we calculated so far with laqgsm , namely results by laqgsm+gem2 for the reaction p(800 gev ) + a compared with experimental data ( sihver et al . , 1992 ) and calculations with the phenomenological code yieldx ( silberberg et al . , 1998 )
for the sake of brevity , we present in this figure only every third yield measured and tabulated in sihver et al .
( 1992 ) , though we calculated all possible products from this reaction and get similar results for nuclides not shown here .
one can see that laqgsm agrees reasonably with most of the measured yields and describes the data better than yieldx .
more than a half of the measured products are described by laqgsm+gem2 with an accuracy of a factor of two or better , though we find some large discrepances for several nuclides like @xmath22hf and @xmath23rh .
at last , figure 7 shows a heavy - ion induced reaction measured at gsi ( junghans , 1997 ; junghans et al . , 1998 ) , namely the yields of measured products ( black circles ) from the interaction of a 950 mev / nucleon @xmath18u beam with copper compared with our laqgsm+gem2 results ( open circles ) .
one can see that laqgsm+gem2 describes most of these data with an accuracy of a factor of two or better .
this section shows an example of using cross sections calculated by cem2k and laqgsm ( together with available data ) to put constraints on the galactic cr halo size . for this calculation
we use a state - of - the - art cr propagation code galprop .
the galprop models have been described in full detail elsewhere ( strong and moskalenko , 1998 ; moskalenko et al . , 2002 and references therein ) ; here we summarize their basic features .
the code solves a transport equation on a full 3d spacial grid @xmath24 or 2d grid .
the 2d models have cylindrical symmetry in the galaxy , and the basic coordinates are @xmath25 , where @xmath26 is galactocentric radius , @xmath27 is the distance from the galactic plane and @xmath28 is the total particle momentum .
the propagation region is bounded by @xmath29 ( taken @xmath30 kpc ) , @xmath31 beyond which free escape is assumed . for a given @xmath32 the diffusion coefficient as a function of momentum and the reacceleration parameters
is determined by the energy - dependence of the b / c ratio .
the spatial diffusion coefficient is taken as @xmath33 , assuming independence of position , where @xmath34 is rigidity .
for the case of reacceleration the momentum - space diffusion coefficient @xmath35 is related to the spatial coefficient .
the reacceleration is parameterized by @xmath36 where @xmath37 is the alfvn speed and @xmath38 the ratio of wave energy density to magnetic field energy density .
the source spectrum of nuclei is assumed to be a power law in momentum , @xmath39 for the injected particle density , if necessary with a break .
the interstellar hydrogen distribution uses h i and co surveys and information on the ionized component ; the helium fraction of the gas is taken as 0.11 by number .
energy losses of nuclei by ionization and coulomb interactions are included .
the distribution of cr sources is chosen to reproduce the cr distribution determined by analysis of egret gamma - ray data .
the primary source abundances are adjusted to give as good agreement as possible with the observed abundances after propagation , for a given set of cross - sections .
the heliospheric modulation is taken into account using the force - field approximation .
the nuclear reaction network is built using the nuclear data sheets .
the isotopic cross section database now includes the lanl t-16 compilation by mashnik et al .
( 1999 ) consisting of several tens of thousands of experimental points .
this includes a critical re - evaluation of some data and cross checks .
the isotopic cross sections are calculated in galprop using the authors fits to major beryllium and boron production cross sections c , n , o @xmath40 be , b , and to other major reactions ; all other cross sections at present are calculated using the webber et al .
( 1990 ) and/or silberberg et al .
( 1998 ) phenomenological approximations renormalized to the data where it exists .
the reaction network is solved starting at the heaviest nuclei ( i.e. @xmath41ni ) , solving the propagation equation , computing all the resulting secondary source functions , and proceeding to the nuclei with @xmath42 .
the procedure is repeated down to @xmath43 . in this way
all secondary , tertiary etc .
reactions are automatically accounted for . to be completely accurate for all isotopes , e.g. for some rare cases of @xmath44-decay
, the whole loop is repeated twice . for some astrophysically important reactions we produced our own evaluations of excitation functions ( e.g. , moskalenko et al . , 2001 ) instead of using only scarce experimental data or calculations by stand - alone phenomenological systematics or nuclear reaction models .
such evaluated data files ( mashnik et al . 1999 ) proved to be useful , e.g. , to study production of radioisotopes for medical and industrial applications using high power accelerators ( van riper et al . , 2001 ) . at present ,
neither available experimental data nor any of the current models or phenomenological systematics can be used alone to produce a reliable evaluated activation cross section library covering a wide range of target nuclides and incident energies .
instead , such an evaluated library should be created by constructing excitation functions using all available experimental data along with calculations employing some of the most reliable codes in the regions of targets and incident energies where they are most applicable .
when there are reliable experimental data , they , rather than model results , should be taken as the highest priority for the evaluation .
for this purpose we used all available to us experimental data from the lanl t-16 compilation ( mashnik et al .
, 1999 ) together with calculations by cem2k , and for several reactions , by laqgsm and the older versions of the cem code , cem97 and cem95 .
one example of such an evaluated excitation function , for the reaction @xmath45si(p , x)@xmath46al , is shown in figure 8 together with available data , cem2k results , and calculations using phenomenological systematics by webber et al .
( 1990 ) and silberberg et al . (
it is seen that cem2k has some problems in a correct description of this particular cross section near the threshold ; therefore we used abundant experimental data available for this reaction to produce our evaluated excitation function at these energies .
it is clear that neither the webber et al .
( 1990 ) systematics nor the silberberg et al .
( 1998 ) approximation describe correctly this excitation function ; using their results as an input to cr propagation codes may lead to errors in results and interpretation . the results of the calculation of galactic propagation of radioactive isotopes @xmath46al , @xmath47cl , and @xmath48mn are shown in figure 9 , where the evaluated excitation functions used were produced as described above .
the radioactive isotopes of these elements are the main astrophysical `` time clocks '' which together with stable secondary isotopes allow us to probe global galactic properties , such as the diffusion coefficient and the halo size . based on the cr data from spacecraft ( ace , ulysses , and voyager , for details
see moskalenko et al . , 2001 ) we were able to restrict the halo size as @xmath49 kpc . using the semiempirical systematics yields less consistent results ( see , e.g. , strong and moskalenko , 2001 ) rizing questions about the interpretation .
this result supports the conclusion that large uncertainties for the halo size obtained in previous works were mostly due to cross - section inaccuracies . in future
, we plan to develop evaluated data libraries for other astrophysical reactions of interest and to use them in future studies of galactic cr propagation .
from the results presented here and in the cited references , we conclude that cem2k and laqgsm describe well ( and without any fitting parameters ) a large variety of medium- and high - energy nuclear reactions and are suitable for evaluations of nuclear data for science and applications .
we continue our work on further improvements and development of both cem2k and laqgsm , but even in their present versions they are quite reliable and may be used as event - generators for astrophysical applications .
we thank prof . nakamura , drs .
iwata , and iwase for sending us numerical values of their measured neutron spectra and results of calculations with qmd and hic .
this study was supported by the u. s. department of energy and by the moldovan - u .
s. bilateral grants program , crdf project mp2 - 3025 .
s.g.m . and i.v.m
. acknowledge partial support from a nasa astrophysics theory program grant .
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151 - 162 , oak ridge , 1999 ; ( nucl - th/9812071 ) ; our compilation ( lanl t-16 lib ) is permanently updated as new experimental data become available to us .
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_ , * c41 * , 566 - 571 , 1990 . | the cem2k and laqgsm codes have been recently developed at los alamos national laboratory to simulate nuclear reactions for a number of applications .
we have benchmarked our codes against most available data measured at incident particle energies from 10 mev to 800 gev and have compared our results with predictions of other current models used by the nuclear community . here , we present a brief description of our codes and show some illustrative results that testify that cem2k and laqgsm can be used as reliable event generators for space - radiation - shielding , cosmic - ray propagation , and other astrophysical applications . finally , we show an example of combining of our calculated cross sections with experimental data from our lanl t-16 compilation to produce evaluated files .
such evaluated files were successfully used in the model of particle propagation in the galaxy galprop to better constrain the size of the cosmic - ray halo . |
one of the most intriguing theoretical results in quantum field theory ( qft henceforth ) has been the realization that fermions can emerge out of purely bosonic lagrangians as solitonic excitations ( for a detailed review see @xcite ) . the clearest demonstration that the importance of this result goes far beyond pure theoretical physics
is given by the skyrme theory @xcite which is one of the most important models of nuclear and particle physics .
the skyrme term @xcite allows the existence of static soliton solutions with finite energy , called
_ skyrmions _ ( see @xcite ) describing fermionic degrees of freedom ( see @xcite and references therein ) .
the wide range of applications of the theory in other areas ( such as astrophysics , bose - einstein condensates , nematic liquids , multi - ferric materials , chiral magnets and condensed matter physics in general @xcite ) is well recognized by now .
it is also worth to emphasize that the skyrme model appears in a very natural way in the context of the ads / cft correspondence @xcite . from the point of view of nuclear physics , it is very important to have analytic tools allowing to analyse the skyrme model when interacting skyrmions are present within bounded regions .
this case is relevant whenever one wants to take into account the effects of the finite size on the topological properties of the skyrmions themselves .
it is commonly believed that many - nucleons systems ( such as the ones occurring in nuclear pasta @xcite ; for a review see @xcite ) are completely out of reach of the analytical techniques provided by soliton theory already in the @xmath4 case ( while , at a first glance , the @xmath5 case is even worse ) . in particular ,
the task to compute physical parameters of such multi - nucleon systems with analytic multi - skyrmionic configurations is believed to be completely hopeless .
recently , the generalized hedgehog ansatz in the @xmath4 case , introduced in @xcite , allowed the construction of the first multi - skyrmions at finite volume : namely , the first exact solutions of the skyrme model representing interacting elementary skyrmions with a non - trivial winding number , in which finite - volume effects can be explicitly taken into account ( arriving at a good prediction for the compression modulus ) , was obtained @xcite . the way to do
this is to write the system in a modified cylinder - like " metric whose curvature is parametrized by a length @xmath6 .
then multi - skyrmionic configurations look like necklaces of elementary skyrmions interacting in bounded tube - shaped regions .
the ground state of such multi - skyrmions has the remarkable property that , although the bps bound in terms of the winding can not be saturated , a new topological charge exists which leads to a different bps bound , which can instead be saturated . in this paper , we consider the @xmath5 case . a very powerful technique to construct multi - skyrmionic configurations in unbounded regions is given by an ansatz for @xmath5 skyrmions introduced in @xcite and @xcite , based on harmonic maps of @xmath0 into @xmath1 , which allowed the construction of many interesting numerical multi - skyrmionic configurations .
here we will exploit the fact that the metric we use is spherically symmetric , just like flat space , so the harmonic map ansatz can be used also in the present case without modifications .
we shall see that in the new metric the equations simplify with respect to those studied in @xcite and @xcite ; in particular they become autonomous , thus techniques from dynamical systems theory become available . thanks to the choice of the background geometry , a novel type of large @xmath2 limit becomes possible in which @xmath2 is large and the curvature is small in such a way that their product is constant . in this way
one can see that both the effects of the curvature become negligible and the field equations remain autonomous ( so that , in such a limit , one can kill the curvature of the metric but keeping all the advantages of the technique of @xcite ) .
it is also worth to emphasize that it is precisely the large @xmath2 limit which discloses in the clearest possible way the role of the skyrme model as low energy limit of qcd . a non constructive proof of the existence of such nontrivial solutions is also provided and a few numerical solutions are exhibited as well .
this paper is organized as follows : in the second section , the @xmath4 case treated in @xcite will be briefly reviewed in order to set the stage . in the third section
, the ansatz for the skyrmions will be described . in the fourth section ,
the general equations of motion are written down and the flat - large @xmath2 limit is discussed .
in the fifth section , we study the system using techniques from the theory of dynamical systems ; in particular , the stability of the fixed points in the @xmath7 case is analyzed , and their dependence on the geometric t hooft parameter is discussed . in the sixth section , some nontrivial numerical solution of the equations of motion in the @xmath8 case will be studied . in the seventh section , some conclusions will be drawn . in the appendix ,
it is proved on general grounds that the equations of motion do have nontrivial solutions which can be interpreted as genuine @xmath5 skyrmions .
in this section , the construction of analytic multi - skyrmionic configurations in the @xmath4 case @xcite will be shortly reviewed .
the action of the four dimensional skyrme model is given by @xmath9 \ , \nonumber\end{aligned}\ ] ] where the planck constant and the speed of light have been set to @xmath10 , and @xmath11 and @xmath12 are the coupling constants .
the @xmath13 s are the generators of the flavor group , which in this section is @xmath4 .
notice that we allowed for curved metrics .
the coupling constants @xmath11 and @xmath12 are related to the couplings @xmath14 and @xmath15 used in @xcite . ] by @xmath16 the non - linear sigma model term of the skyrme action is necessary to take into account pions .
the second term is the only covariant term leading to a well - defined hamiltonian formalism in time which supports the existence of skyrmions .
the field equations following from the above action are @xmath17=0 . \label{nonlinearsigma1}\ ] ] the following standard parametrization of the @xmath4-valued scalar @xmath18 will be adopted@xmath19 where @xmath20 is the @xmath21 identity matrix ; to describe a spherically symmetric field configuration we use the hedgehog ansatz @xcite:@xmath22@xmath23 in order to mimic finite - volume effects without loosing the nice properties of the hedgehog ansatz we will consider the following curved background , but this has already been considered in @xcite . the geometry in eq .
( [ metric ] ) was considered in @xcite but with a motivation different from the analysis of finite - volume effects .
consequently , the main results obtained in @xcite ( the derivation of both a novel bps bound which can be saturated and analytic multi - skyrmions at finite volume and an explicit formula for the compression modulus in good agreement with experiments ) are indeed novel . ]
@xmath24@xmath25 where @xmath26 is the length of the @xmath27interval .
the total volume of space is @xmath28 .
this geometry describes three - dimensional cylinders whose sections are @xmath0 spheres , so that parameter @xmath6 plays the role of the ( finite ) diameter of the transverse sections of the tube .
the fact that this parameter replaces the radial variable @xmath29 in the metric also leads , as we will see , to considerable simplification of the equations of motion , even allowing to find exact solutions in the @xmath4 case .
moreover , the curvature of this metric is proportional to @xmath30 . as it will be explained in the next sections , the explicit presence of this parameter in eq .
( [ metric ] ) together with the @xmath2 of @xmath5 allows to define a smooth flat limit in which @xmath31 and so all the effects of the curvature disappear ( however , the global topology of space remains cylindrical even in the flat limit and so it differs from the trivial @xmath32 topology of flat static _ unbounded _
skyrmions ) .
thus , in a sense , the above metric is introduced just as a regulator " whose local effects can be removed at the end . in the present context ,
flat limit " really means @xmath33 so that , from the practical point of view , already when @xmath6 is around @xmath34 @xmath35 all the effects of the curvature are negligible and , consequently , even in the flat limit in eq .
( [ flatl2 ] ) finite volume effects will not disappear .
it is also worth to emphasize that the well known result that elementary skyrmions should be quantized as fermions ( which originally was derived on flat spaces ) has been extended to space - times with compact orientable three - dimensional spatial sections in @xcite ( and the metric in eq .
( [ metric ] ) belongs to this class ) . since , at the end , we will be interested in the flat limit in eq .
( [ flatl2 ] ) , one may wonder whether it would be possible to start from the very beginning with a flat metric .
in fact , as it has been shown in @xcite , the background metric in eq .
( [ metric ] ) is a very suitable tool to take into account finite volume effects ( since the total spatial volume is finite ) without breaking relevant symmetries of the hedgehog ansatz , with the additional advantage of simplifying the field equations .
a further relevant advantage of the above background metric is that , unlike what happens in the usual unbounded case , it allows to define in a very transparent way a smooth large @xmath2 limit of the @xmath5 skyrmions .
therefore , it is much more convenient to analyze the skyrme theory first within the background metric in eq .
( [ metric ] ) , and take the flat limit only later .
the effectiveness of such a choice for the metric is also shown by the results in @xcite and @xcite in which it has been shown that , unlike what happens in flat space , the equations for the yang - mills - higgs system ( in the sector with non - vanishing non - abelian electric and magnetic charges ) possess analytic solutions even in the case in which the higgs coupling is non - zero . with the above ansatz the skyrme field equations reduce in the static case to the following scalar differential equation for the skyrmion profile @xmath36 @xcite : @xmath37 \right ) = 0\ ] ] the winding number @xmath38 for such a configuration reads:@xmath39 in the present case
, the natural boundary conditions correspond to the choice:@xmath40 and with these boundary conditions the winding number takes the integer value @xmath41 .
these boundary conditions are unique in that they ensure @xmath42 , which correspond to bosonic and fermionic states for even and odd @xmath41 , respectively .
smooth solutions exist for any @xmath41 satisfying the above boundary conditions for a finite range @xmath43 .
in particular multi - soliton solutions exist , which represent skyrmions with winding number @xmath41 living in a finite spatial volume @xmath28 .
it is worth to remark that the large @xmath41 limit in the present context is quite natural in order to consider thermodynamical properties of the multi - skyrmions system and @xmath41 is the baryon number : obviously , a thermodynamical analysis only makes sense in the cases in which the number of particles is very large .
now we switch to the @xmath5 case with generic @xmath2 .
our analysis will be based on the techniques introduced in @xcite , which we shall now briefly describe .
the hedgehog ansatz for @xmath5 spherically symmetric skyrmions living in flat minkowski metric @xmath44 is based on a suitable family of projectors from @xmath0 into @xmath1 ( see @xcite ) . such projectors @xmath45 can be written as @xmath46 where @xmath47 is an @xmath2-component complex vector of two complex variables @xmath48 and @xmath49 which locally parametrize @xmath0 , where @xmath50 , and @xmath51 . the first @xmath52 is constructed with a holomorphic @xmath53 while the gram - schmidt procedure gives rise to the others . indeed , @xmath54 can be found by its action on any vector @xmath55 @xcite as @xmath56 consequently , the other vectors @xmath57 are determined inductively : @xmath58 .
thus the operator @xmath59 corresponding to the family of vectors @xmath60 ( for @xmath61 ) reads @xmath62 where , due to the orthogonality of the projectors , we have @xmath63 . due to the holomorphy of @xmath64 , the following identities of the above defined vectors can be proved @xcite : @xmath65 & \partial_{\bar{\xi}}|v_{k}\rangle= -|v_{k-1}\rangle\frac{|v_{k}|^{2}}{|v_{k-1}|^{2}},\hspace{5mm}\hspace{5mm}\partial_{\xi}\left ( \frac { |v_{k-1}\rangle}{|v_{k-1}|^{2}}\right ) = \frac{|v_{k}\rangle}{|v_{k-1}|^{2}}. \label{aaa}\ ] ] for @xmath5 the components of @xmath66 , up to an irrelevant overall factor which cancels in the projector , are functions of only @xmath49 . the @xmath5 hedgehog ansatz defined in @xcite reads then@xmath67 where we defined @xmath68 .
such an ansatz involves the introduction of @xmath69 projectors and of @xmath69 profile functions @xmath70 , @xmath71 ; .
note that the projector @xmath72 is not included in the above formula since it is a linear combination of the others .
one of the main results in @xcite and @xcite has been to show that the above ansatz in eq .
( [ ansatzsu(n ) ] ) , when inserted into the full skyrme field equations in the case in which the background metric is the standard flat metric in spherical coordinates in eq . ( [ flat ] ) , gives rise to a consistent set of @xmath69 coupled non - linear differential equations for the @xmath69 profiles @xmath73 .
moreover , such field equations can also be derived as stationary equations for the energy functional with respect to variations of the profiles .
a close inspection of the computations in @xcite shows that the main requirement in order for the ansatz to work is the @xmath74 invariance of the background metric .
this then suggests that the above ansatz may also work in the finite - volume metric in eq .
( [ metric ] ) adopted in @xcite .
this is what we show in the next section .
in this section we switch back to the finite - volume @xmath74-invariant metric in eq .
( [ metric ] ) .
a direct computation shows that the ansatz in eq .
( [ ansatzsu(n ) ] ) , when inserted into the full skyrme field equations in this metric gives rise to a consistent system of @xmath69 coupled _ autonomous _ non - linear differential equations for the @xmath69 profiles @xmath73 which is simpler than the flat _ non - autonomous _ system analyzed in @xcite as it will be now discussed .
furthermore , also in the present case the field equations can be derived as stationary equations for the energy functional with respect to variations of the @xmath75 s .
it is worth emphasizing here that the explicit presence of the parameters @xmath2 and @xmath76 allows to consider a flat large @xmath2 limit in which the curvature is negligible and the product @xmath77 remains constant .
hence , the present formalism is also relevant for people only interested in the skyrme model on flat space - times .
it is important to notice that in such a flat limit , while the effects of the curvature of the metric in eq.([metric ] ) disappear , _ the effects of the cylindrical topology do not_. from now on we shall use the following energy @xmath78 $ ] and length @xmath79 $ ] units:@xmath80 & = \frac{f_{\pi}}{4e}\approx1\ gev\ ,
\label{conv1}\\ \left [ l\right ] & = \frac{2}{ef_{\pi}}\approx0.6\ fm\ \rightarrow \label{conv2}\]]@xmath81 following the same steps of @xcite in the new metric , one arrives at the following expressions for the winding number , the total energy of the @xmath5 hedgehog and the field equations respectively : @xmath82 \right\vert _ { x =- l/2}^{x = l/2}\ , \label{winding(n)}\]]@xmath83 \ , \label{enersu(n)}\]]@xmath84 \ \ \mathbf { , } \label{equ(n)}\ ] ] where we introduced the quantities @xmath85 @xmath86 , and we defined @xmath87 notice that the winding number gets _ two _ different contributions ( while in the minkowski case it just gets one ) , as a consequence of the different topology of the cylinder - like metric we are using .
another important point is that when the parameter @xmath6 is very large the field equations ( [ equ(n ) ] ) tend to linear equations , on the other hand when @xmath6 is small the nonlinear terms become very important .
thus , this parameter ( more precisely , the quantity @xmath88 ) controls the nonlinearity of the theory , and thus it plays the rle of an additional coupling constant .
all the analyses we shall perform in the following will confirm the fact that the physics of the model crucially depends on it . more precisely ,
both the numerical analysis of sect .
[ numsol ] and the existence theorem of the appendix tell us that the global properties of the solutions of the system depend on the dimensionless parameter @xmath89 , which controls the shape of the cylinder . by comparing the present total energy in eq .
( [ enersu(n ) ] ) and the field equations in eq . ( [ equ(n ) ] ) with the corresponding expressions in @xcite , the first of the advantages mentioned above in working within the metric in eq . ( [ metric ] )
is apparent .
namely , the field equations become an autonomous system which can , as such , be analyzed with the powerful tools of dynamical systems theory . in the special case in which all the profiles are equal ,
i.e. @xmath90 all the equations of the above system become proportional and equivalent to : @xmath91 = 0\ ] ] upon setting @xmath92 , this is precisely eq .
, valid in the @xmath4 case .
this is to be expected since setting all the profiles to be equal corresponds to looking for solutions which are embeddings of the @xmath4 ones in @xmath5 . in the next sections we shall see numerically in some cases that the above system of equations does admit nontrivial solutions , i.e. solutions whose profiles are not equal nor proportional , while in the appendix we shall prove analytically the existence of such solutions .
such solutions have winding numbers which in general are nonvanishing , therefore can be interpreted as genuine @xmath5 multi - skyrmion configurations .
as said , the formalism developed so far strongly relies on the usage of a spacetime whose spatial sections have a finite radius @xmath93 , and whose curvature goes to zero as @xmath94 . in this section
we will show that there is a natural way to accommodate this flat limit , which requires to take the large @xmath2 limit as well .
the latter is a common tool in quantum field theory , see e.g. @xcite for a review . the field equations in eq .
( [ equ(n ) ] ) can be rewritten as follows@xmath95 \
\ \mathbf { , } \label{largen1}\ ] ] where we introduced the effective radius @xmath96 the nonlinear part of the field equations ( [ largen1 ] ) behaves smoothly in the large @xmath2 limit provided also @xmath6 is large , so that @xmath97 is kept constant .
more precisely : @xmath98 hence , the proper way to consider the large @xmath2 limit is to simultaneously consider the _ flat _
limit @xmath99 in such a way that the parameter @xmath100 in eq .
( [ largen2 ] ) remains finite .
since in the large @xmath2 limit in eq .
( [ largen4 ] ) the nonlinear part of the field equations eq .
( [ largen1 ] ) does not depend on @xmath2 and @xmath6 separately but only on the effective radius @xmath97 defined in eq .
( [ largen2 ] ) , the quantity @xmath101 plays the rle of a _ geometric _ ( it defines a length scale ) t hooft coupling .
physically , the parameter @xmath100 in eq .
( [ largen2 ] ) represents the effective area " available for each skyrmion within each section of the tube . in conclusion
, one can see the metric defined in eq .
( [ metric ] ) just as a technical device in order to analyze multi - skyrmionic configurations since , at the end , one can turn off all the effects of the curvature ( keeping the cylindrical topology ) . in this limit ,
the solutions of the field equations represent multi - skyrmionic configuration living in a _
flat _ tube - shaped region whose sections have a radius much bigger than the scale @xmath97 .
when n is large the equations read : @xmath102 \ \ \mathbf { , } \label{largen10}\ ] ] the first two terms in the above equation ( involving summations ) describe the free part of the theory , while the rest ( involving @xmath97 ) is responsible for interactions , therefore defines nontrivial dynamics .
therefore we find our prescription a reasonable way to implement flat ( large volume ) limit within our formalism . in the next section
we will demonstrate ( for @xmath103 ) , that the dynamics _ does _ depend on @xmath97 .
one of the strongest advantages of our formalism lies in the fact that we have an _ autonomous _ system of differential equations .
the latter can be qualitatively described by its phase portrait , an important characteristic of which is the set of critical points . in particular
if under some change of parameters the set of critical points remains the same ( their number and their character ) , then one does not expect that dynamics of the system changes dramatically under the same change . on the contrary , if the number and/or character of the critical points changes , one may definitely say that the dynamics of the system is qualitatively different . in this section
we are going to study our system by using the tools of dynamical system theory ( we will follow @xcite ) . in particular , we will analyze how changing the value of @xmath100 the number of the critical points of the dynamical system , as well as their linear stability properties , change . for simplicity , we shall perform the analysis in the @xmath7 case . in this case
we have two profiles , @xmath104 and @xmath105 , and the equations of motion are given by : @xmath106 & = 0\ , \nonumber \\
\overset{{\cdot\cdot}}{f_{1}}\left ( \frac{2}{3}+\frac{1}{2r^{2}}\left ( 1-\text{cos}f_{1}\right ) \right ) + \frac{1}{3}\overset{{\cdot\cdot}}{f_{0}}+\frac{\text{sin}f_{1}}{4r^{2}}\left [ \overset{{\cdot}}{f_{1}}^{2}-4-\frac{2\left ( 1-\text{cos}f_{1}\right ) } { r^{2}}+\frac{\left ( 1-\text{cos}f_{0}\right ) } { r^{2}}\right ] & = 0\ .
\label{eqmn3}\end{aligned}\ ] ] notice that the two equations go one into the other by exchanging @xmath104 and @xmath105 .
we are going to exploit this symmetry . in order to study critical points of the system ( [ eqmn3 ] ) , first of all we rewrite it as a system of first order equations as follows : @xmath107 where @xmath108 , \quad \vec{g}\left(\vec{z}\right ) = \left[\begin{array}{c } -\hat a^{-1}\left[\begin{array}{c } q(f_0,f_1,\delta ) \\
q(f_1,f_0,e ) \end{array}\right ] \\
\delta \\e \end{array}\right],\ ] ] and we introduced the following notations for brevity @xmath109 , \quad q(\xi , \eta,\theta ) \equiv \frac{\text{sin } \xi } { 4r^{2}}\left [ \theta^2 -4-\frac{2\left ( 1-\text{cos } \xi \right ) } { r^{2}}+\frac{\left ( 1-\text{cos}\eta\right ) } { r^{2}}\right].\ ] ] stationary points @xmath110 are defined by vanishing of the vector field @xmath111 , which defines the flow of the autonomous equation in phase space : @xmath112 one can easily check that @xmath113 , therefore @xmath110 can be written as follows : @xmath114\ ] ] where @xmath115 and @xmath116 are solutions of the following algebraic equations @xmath117
equations imply one of the three possibilities ( the fourth possibility does not have real solutions ) : 1 .
@xmath118 ; @xmath119 ; 2 .
@xmath119 ; @xmath120 ; 3 .
@xmath118 ; @xmath121 .
linearizing in the vicinity of the critical point @xmath110 we obtain @xmath122 where @xmath123 is the jacobian matrix of the diffeomorphism @xmath124 taken at the point @xmath110 @xmath125 in order to analyze stability of the critical point @xmath110 i.e. in order to understand whether phase trajectories starting near this point run away " exponentially or not , one has to check whether eigenvalues of @xmath123 have real part or they are purely imaginary .
below we present a complete analysis of the critical points . since in the algebraic equations the unknowns @xmath126 and @xmath127 enter via sine and cosine , it is sufficient to consider critical points modulo @xmath128 .
we identify the following four independent subcases : @xmath129 @xmath130 ; @xmath129 @xmath131 ; @xmath129 @xmath132 ; @xmath129 @xmath133 . in the ( equal profile ) case
@xmath134 jacobian matrix is @xmath135\ ] ] whose four eigenvalues are : @xmath136 therefore this fixed point is unstable ; this property does not depend on @xmath97 .
also in this case we have equal profiles @xmath137 . in this case the jacobian matrix is @xmath138\ ] ] and the eigenvalues @xmath139 are purely imaginary , therefore this point is stable for all @xmath97 .
now we consider @xmath140 , @xmath141 . in this case
the jacobian matrix @xmath142\ ] ] has the eigenvalues @xmath143 unlike the previous cases , now the properties of this critical point change at a critical value of the parameter @xmath97 . indeed , while the eigenvalues @xmath144 and @xmath145 are always purely imaginary , @xmath146 and @xmath147 are purely imaginary only when @xmath148 .
in this regime this critical point is stable . for @xmath149 instead
the first two eigenvalues become real , therefore the fixed point becomes unstable .
this is a nice example of how the stability properties change at a critical value of the parameter .
interestingly , the value of @xmath97 at which the transition happens is the same below which new fixed points appear ( i.e. those occurring in cases 2 and 3 described above ) . in this case
the equations are exactly the same of case 3 , only with @xmath152 and @xmath153 exchanged .
the eigenvalues are therefore exactly the same so that the same discussion applies .
we now consider cases 2 and 3 in the above list .
since they are related by the exchange @xmath154 , they will have the same eigenvalues and hence the same stability properties .
let us then consider case 2 : @xmath155 one may immediately check that a real solution only exists for @xmath156 , and it is given by @xmath157 modulo @xmath128 . for @xmath158
this critical point disappears .
the jacobian matrix reads @xmath159\ ] ] and its eigenvalues are : @xmath160 in the whole range @xmath161 , the first two eigenvalues are purely imaginary , while @xmath144 and @xmath145 are real , therefore this critical point is unstable . at @xmath162 , @xmath144 and @xmath145
vanish .
the analysis we just performed discloses the crucial dependence of the dynamics of our system on the parameter @xmath97 .
in fact we saw that there is a critical value @xmath162 at which the nature and the number itself of the critical points change . for @xmath163 and for @xmath158 we have two _ qualitatively _ different phase portraits , thereby different dynamics .
these are genuine finite volume effects ( since the parameter @xmath97 represents the available surface per baryon within the tube - shaped region ) which can be disclosed only within the present framework . in fig.[f1 ] we present location of critical points for @xmath164 and @xmath158 .
as one can easily see , the two plots are qualitatively different : while the latter grid is invariant under the discrete group of reflections @xmath165 about the axes @xmath126 and @xmath127 , the former is not , that is the symmetry is broken .
moreover the former is sensitive to the particular value of @xmath97 , while the latter is always the same for all @xmath158 .
finally , the concentration of different critical points changes as well , since some of them changed color ( i.e. type ) when @xmath97 passed through the critical value , while new ( green ) fixed points appeared . these metamorphoses of the phase portrait hint at the presence of some sort of phase transition occurring at strong coupling ( recall that @xmath166 plays the rle of a coupling constant ) .
it is interesting to notice that , in our units , this critical value is of the order of the @xmath35 , so although irrelevant from a flat limit perspective , it may have important consequences in view of applications to nuclear physics , where the dimensions of the tube - shaped region should be precisely of that order of magnitude in order to model an atomic nucleus @xcite . on the left and for @xmath167 on the right .
in the latter case the grid is independent on a particular choice of @xmath97 , while for the former case we chose @xmath168 .
blue points represent stable fixed points , red points represent absolutely " unstable fixed points ( i.e. all eigenvalues of the corresponding jacobi matrix are real ) , while green points represent softer " unstable fixed points ( i.e two eigenvalues values are real and two imaginary ) .
[ f1 ] , title="fig : " ] on the left and for @xmath167 on the right . in the latter case
the grid is independent on a particular choice of @xmath97 , while for the former case we chose @xmath168 .
blue points represent stable fixed points , red points represent absolutely " unstable fixed points ( i.e. all eigenvalues of the corresponding jacobi matrix are real ) , while green points represent softer " unstable fixed points ( i.e two eigenvalues values are real and two imaginary ) .
[ f1 ] , title="fig : " ]
in this section we perform a numerical study of the system in the @xmath169 case . in this case
we have three profiles , @xmath170 , and the equations of motion reduce to : @xmath171 = 0,\\ & \overset{{\cdot\cdot}}{f_{1}}\left ( 1+\frac{2}{r_{0}^{2}}\left ( 1-\text{cos}f_{1}\right ) \right ) + \frac{\overset{{\cdot\cdot}}{f_{0}}+\overset{{\cdot\cdot}}{f_{2}}}{2 } + \\ & + \frac{\text{sin}f_{1}}{r_{0}^{2}}\left [ \overset{{\cdot}}{f_{1}}^{2}-4- \frac{8\left ( 1-\text{cos}f_{1}\right ) } { r_{0}^{2}}+ \frac{3\left ( 1-\text{cos}f_{0}\right ) } { r_{0}^{2}}+ \frac{3\left ( 1-\text{cos}f_{2}\right ) } { r_{0}^{2}}\right ] = 0,\\ & \overset{{\cdot\cdot}}{f_{2}}\left ( 1+\frac{2}{r_{0}^{2}}\left ( 1-\text{cos}f_{2}\right ) \right ) + \frac{\overset{{\cdot\cdot}}{f_{0}}+2\overset{{\cdot\cdot}}{f_{1}}}{3 } + \frac{\text{sin}f_{2}}{r_{0}^{2}}\left [ \overset{{\cdot}}{f_{2}}^{2}-4- \frac{6\left ( 1-\text{cos}f_{2}\right ) } { r_{0}^{2}}+ \frac{4\left ( 1-\text{cos}f_{1}\right ) } { r_{0}^{2}}\right ] = 0.\end{aligned}\ ] ] the first and the second go one onto the other upon exchanging @xmath172 .
we can exploit this symmetry to look for solutions which have @xmath173 ( another possibility allowed by the symmetry is to set @xmath174 and at the same time @xmath175 , however this would give vanishing winding number , so we do not consider it ) .
let us also call @xmath176 .
in this case we get the two independent equations : @xmath177 = 0,\\ \overset{{\cdot\cdot}}{g}\left ( 1+\frac{2}{r_{0}^{2}}\left ( 1-\text{cos}g\right ) \right ) + \overset{{\cdot\cdot}}{f}+ \frac{\text{sin}g}{r_{0}^{2}}\left [ \overset{{\cdot}}{g}^{2}-4- \frac{8\left ( 1-\text{cos}g\right ) } { r_{0}^{2}}+ \frac{6\left ( 1-\text{cos}f\right ) } { r_{0}^{2}}\right ] = 0,\end{aligned}\ ] ] and the energy density ( which is defined by @xmath178 ) is given by : @xmath179 + \nonumber\\ & + \frac{1}{r_{0}^{4}}\left [ 9\left ( 1-\text{cos}f\right ) ^{2 } -12 \left ( 1-\text{cos}f\right ) \left ( 1-\text{cos}g\right ) + 8\left ( 1-\text{cos}g\right ) ^{2}\right ] .\end{aligned}\ ] ] before solving the system we must choose a set of boundary conditions to impose on @xmath180 and @xmath181 in such a way to get solutions with a nontrivial winding number . recall that we have to impose ( anti-)periodic boundary conditions on the field @xmath182 : @xmath183 for simplicity
we shall limit ourselves to the periodic case . according to the ansatz we are using the field
can be written as : @xmath184 it is convenient to use the second form .
we notice that the matrix @xmath182 is diagonal in the basis @xmath185 , therefore the above boundary condition is equivalent to its diagonal matrix elements .
the diagonal matrix elements of @xmath182 are @xmath186 thus the boundary conditions are satisfied if @xmath187 with these conditions the winding number is given by @xmath188 we also need to impose conditions on the first derivative of @xmath182 , i.e. of @xmath180 and @xmath181 .
we choose the simplest possibility which is compatible with the periodicity of the first derivative of @xmath182 , i.e. @xmath189 we have solved numerically the system ( [ su(4)eqs ] ) with the boundary conditions ( [ su(4)bcs1 ] ) and ( [ su(4)bcs2 ] ) , for some values of the integers @xmath190 and @xmath41 , taking @xmath191 , and we computed the energies of the solutions . the results are summarized in the tables below and in the one in sect .
[ eqprofsubsect ] . we have allowed @xmath190 and @xmath41 to vary in a small range , beyond which our numerical procedure is not very accurate .
[ c]p1cmp1cmp1cmp1cm|p1cmp1cmp1cmp1cm|p1cmp1cmp1cmp1cm@xmath190 & @xmath41 & @xmath38 & @xmath193 & @xmath190 & @xmath41 & @xmath38 & @xmath193 & @xmath190 & @xmath41 & @xmath38 & @xmath193 + -1 & 1 & 2 & 26.68 & 1 & 0 & 6 & 11.43 & 1 & 1 & 14 & 43.87 + -2 & 2 & 4 & 100.65 & 2 & 0 & 12 & 42.41 & 2 & 2 & 28 & 168.31 + -3 & 3 & 6 & 228.42 & 3 & 0 & 18 & 92.08 & 3 & 3 & 42 & 376.07 + & & & & 4 & 0 & 24 & 161.61 & & & & + the energies are exactly the same if we change sign simultaneously to @xmath190 and @xmath41 .
there are sectors in which , to a very good approximation , the energy grows like the square of the modulus of the winding number , with different coefficients in different sectors .
however , this is not true in all sectors , for example : [ c]p1cmp1cmp1cmp1cm@xmath190 & @xmath41 & @xmath38 & @xmath193 + 0 & 1 & 8 & 24.48 + 0 & 2 & 16 & 93.20 + we notice that the solutions with the smallest winding numbers are not energetically favored , since to achieve small winding numbers both profiles must grow going along @xmath194 in opposite directions , while the smallest energy solutions are those where only one of the profile grows while the other oscillates and stays small , i.e. _ either _ @xmath190 _ or _ @xmath41 are different from zero , but not both .
notice also that increasing @xmath41 costs much more than increasing @xmath190 , despite their contributions to the winding number being not so different . in figs.1 - 6 the plots of some solutions are reported .
[ m-1n1 ] [ m-2n2 ] [ m1n0 ] [ m2n0 ] [ m1n1 ] [ m2n2 ] if we impose that the profiles are equal , i.e @xmath195 , the equations of motion reduce of course to ( [ eqprofeq ] ) . in this case
the same procedure followed above tells us that the boundary conditions to achieve a periodic @xmath182 are @xmath196 in which case the winding number is simply @xmath197 in order to compare the equal profile situation with the non equal profile one we have to consider cases with the same winding number .
this is achieved if in the latter case we have @xmath198 .
we did the computation in the two simplest cases , with @xmath191 , and the results are : [ c]p1cmp1cmp1cm|p1cmp1cmp1cmp1@xmath199 & @xmath200 & @xmath201 & @xmath190 & @xmath41 & @xmath38 & @xmath193 + 1 & 20 & 82.67 & 2 & 1 & 20 & 82.67 + 2 & 40 & 325.70 & 4 & 2 & 40 & 325.57 + we see that the energies are the same ( in the second case the discrepancy is due to small numerical inaccuracies : the numerical computation for the @xmath202 , @xmath203 case gave the winding number of the solutions to be 40.13 , thus signalling such inaccuracies ) .
therefore , in topological sectors whose winding number is compatible with equal profile configurations , with the chosen values of the parameters , equal - profile solutions and non - equal profile ones are energetically equivalent .
besides the above analysis , which was performed at fixed @xmath6 , we also studied what happens when this parameter is varied , considering for definiteness the lowest winding number case , i.e @xmath204 . we checked that when @xmath6 is increased the solutions tend to linear functions , in agreement with triviality of the dynamics for large radius .
instead , for values of @xmath6 ( or @xmath89 if we allow also @xmath26 to vary ) substantially smaller than @xmath10 the numerical procedure becomes unstable and the results unreliable .
this is of course to be expected since lowering @xmath6 the non - linearity of the problem increases .
this is in agreement with the bounds ( [ ban10.5]-[ban11.7 ] ) , which are more difficult to satisfy when @xmath6 is small , and trivial when @xmath6 is large . in the small @xmath6 case a more sophisticated numerical analysis would therefore be needed .
in particular it would be interesting to see whether at strong coupling non - equal profile solutions are energetically favored with respect to equal profile ones with the same winding number , as suggested by the fixed point analysis of section [ fpoints ] .
another interesting issue requiring a more accurate numerical work is the identification of a range of the parameters in which the dependence of the energy on the winding number is linear rather than quadratic .
we hope to come back on these interesting issues in a future investigation .
in this paper the @xmath5 skyrme model is studied in a tube - shaped geometry which allows to consider finite volume situations .
the use of such a geometry allows to introduce a parameter which regulates the dynamics as a new ( inverse ) coupling constant .
these simplifications , which make the system autonomous , allow us to perform a detailed study of the system using several techniques , i.e. dynamical systems , numerical solutions and rigorous existence theorems .
all these analyses confirm the relevance of the parameter @xmath6 introduced by the metric on the dynamics of the system . as a further bonus ,
when combined with @xmath2 as @xmath205 , this parameter defines an effective t hooft coupling . in the large @xmath2 limit in which such coupling is kept fixed , flat space - time
is recovered .
this effective t hooft parameter determines the discrete symmetries of the skyrmions configurations .
these results clearly show that the present framework is a very promising tool to study interacting skyrmions systems .
a very interesting problem which we hope to analyse in a future publication is to extend the present analysis at finite temperature and/or chemical potential .
the authors would like to thank j. zanelli for enlightening discussions and comments .
this work has been funded by the fondecyt grant 1120352 .
the centro de estudios cientficos ( cecs ) is funded by the chilean government through the centers of excellence base financing program of conicyt .
m. k. acknowledges partial support from unina and compagnia di san paolo in the framework of the program star 2013 .
in this appendix we prove analytically that non - trivial solutions which are not trivial embeddings of @xmath4 into @xmath5 ( in which the profiles are not proportional ) do indeed exist .
we will focus for simplicity on the @xmath7 case but the same argument can be easily extended to the general case .
the basic mathematical tool of this section is a well - known result of nonlinear functional analysis , the _ schauder theorem _ ( see for a detailed pedagogical review on mathematical tools to deal with non - linear partial differential equations @xcite ) .
the statement of the schauder theorem ( @xcite ) is the following .
let @xmath206 be a banach space between any pair of elements of the space is defined , and it is called complete if ( with respect to the chosen metric ) from every cauchy sequence one can extract a convergent subsequence ( see , for instance , @xcite ) . ] .
let @xmath207 a bounded closed convex set in @xmath206 , and let @xmath208 be a compact operator from a banach space @xmath206 into itself ( see , for a detailed discussion , @xcite ) is called _ compact _ if and only if , for any bounded sequence @xmath209 , the sequence @xmath210 has a convergent subsequence .
] from the banach space @xmath206 into itself such that @xmath208 maps @xmath207 into itself:@xmath211 : c\rightarrow c\ . \label{ban2}\
] ] then the map @xmath212 $ ] has ( at least ) one fixed point in @xmath207 . in other words , under the above hypotheses , there exists a solution to the equation @xmath213 = x\ . \label{ban3}\ ] ] let us recall the equations of motion for the @xmath7 case : @xmath106 & = 0\ , \label{su(3)eq1}\\ \overset{{\cdot\cdot}}{f_{1}}\left ( \frac{2}{3}+\frac{1}{2r^{2}}\left ( 1-\text{cos}f_{1}\right ) \right ) + \frac{1}{3}\overset{{\cdot\cdot}}{f_{0}}+\frac{\text{sin}f_{1}}{4r^{2}}\left [ \overset{{\cdot}}{f_{1}}^{2}-4-\frac{2\left ( 1-\text{cos}f_{1}\right ) } { r^{2}}+\frac{\left ( 1-\text{cos}f_{0}\right ) } { r^{2}}\right ] & = 0\ . \label{su(3)eq2}\ ] ] we want to prove that the system in eqs .
( [ su(3)eq1 ] ) and ( [ su(3)eq2 ] ) admits non - trivial solutions in which the profiles @xmath104 and @xmath105 are not proportional . in order to achieve this goal ,
let us rewrite it as coupled integral equations ( for notational simplicity in this section we shall consider @xmath214 $ ] instead of @xmath215 $ ] , since everything just depends on the length @xmath26 of the tube ) : where @xmath218 \ , \ \label{int1.35}\\ h_{1}\left ( \rho\right ) & = \left [ \overset{{\cdot}}{f_{1}}^{2}-4-\frac{2\left ( 1-\text{cos}f_{1}\left ( \rho\right ) \right ) } { r^{2}}+\frac{\left ( 1-\text{cos}f_{0}\left ( \rho\right ) \right ) } { r^{2}}\right ] , \label{int2.35}\\ a_{i } & = \left ( \frac{2}{3 } + \frac{1}{2\,r^{2}}\left ( 1-\cos\,f_{i}\right ) \right ) ^{-1 } , \quad i=0,1\end{aligned}\ ] ] where @xmath219 , @xmath220 , and @xmath221 and @xmath222 represent the initial data for the two profiles @xmath104 and @xmath105 and their derivatives at @xmath223 .
it is a trivial computation to show that the above system of integral equation is equivalent to the system in eqs .
( [ su(3)eq1 ] ) and ( [ su(3)eq2 ] ) .
the system in eqs .
( [ int1 ] ) and ( [ int2 ] ) can be written as a fixed point condition for the following vectorial operator @xmath224 acting component - wise on pairs of @xmath225 functions
@xmath226:@xmath227 \times c^{2}\left [ 0,l\right ] \rightarrow c^{2}\left [ 0,l\right ] \times c^{2}\left [ 0,l\right ] \ , \\ \overrightarrow{f}\left ( x\right ) & = \left ( f_{0}\left ( x\right ) , f_{1}\left ( x\right ) \right ) \in c^{2}\left [ 0,l\right ] \times c^{2}\left [ 0,l\right ] \ , \end{aligned}\]]@xmath228 = \overrightarrow{t}\left [ \ \overrightarrow{f}\left ( x\right ) \right ] = \left ( t_{0}\left ( x\right ) , t_{1}\left ( x\right ) \right ) \ , \label{int2.5}\ ] ] with @xmath229 where the functions @xmath230 are defined in eqs .
( [ int1.25 ] ) , ( [ int2.25 ] ) , ( [ int1.35 ] ) and ( [ int2.35 ] ) .
it is then obvious that the system in eqs .
( [ int1 ] ) and ( [ int2 ] ) can be written as the following fixed - point condition@xmath231 \ , \label{fixedpoint}\ ] ] where the operator @xmath224 has been defined in eqs .
( [ int2.5 ] ) , ( [ int3 ] ) and ( [ int4 ] ) .
hence , now the task is to define @xmath224 as a compact operator from a bounded closed convex sub - set of a banach space into itself . in order to achieve this goal ,
first of all let us define the following metric into the space @xmath232 \times c^{2}\left [ 0,l\right ] $ ] : @xmath233 } { \sup}\left\vert f_{0}(x)-g_{0}(x)\right\vert + \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert \frac{df_{0}}{dx}-\frac{dg_{0}}{dx}\right\vert + \underset{x\in\left [ 0,l\right ] } { \sup } \left\vert \frac{d^{2}f_{0}}{dx^{2}}-\frac{d^{2}g_{0}}{dx^{2}}\right\vert + \nonumber\\ & + \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert f_{1}(x)-g_{1}(x)\right\vert + \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert \frac{df_{1}}{dx}-\frac{dg_{1}}{dx}\right\vert + \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert \frac{d^{2}f_{1}}{dx^{2}}-\frac{d^{2}g_{1}}{dx^{2}}\right\vert \ , \label{ban4.01}\\ \overrightarrow{f}\left ( x\right ) & = \left ( f_{0}\left ( x\right ) , f_{1}\left ( x\right ) \right ) \ , \ \overrightarrow{g}\left ( x\right ) = \left ( g_{0}\left ( x\right ) , g_{1}\left ( x\right ) \right ) \ \in c^{2}\left [ 0,l\right ] \times c^{2}\left [ 0,l\right ] \ .\nonumber\end{aligned}\ ] ] with respect to this metric , which is induced by a norm , the space @xmath232 \times c^{2}\left [ 0,l\right ] $ ] is a banach space which we will call @xmath206 .
_ the next task _ to apply the schauder theorem is to define a bounded closed convex sub - set @xmath207 of the banach space defined above ( using the metric in eq .
( [ ban4.01 ] ) ) such that @xmath224 maps @xmath207 into itself .
let us define @xmath207 as@xmath234 \ \right . \
\left\vert f_{0}(x)-a_{0}\right\vert \leq b\ , \
\left\vert f_{1}(x)-a_{1}\right\vert \leq b\ \ , \label{ban5}\\ & \left . \
\left\vert \frac{df_{0}}{dx}\right\vert \leq b\ , \ \
\left\vert \frac{d^{2}f_{0}}{dx^{2}}\right\vert \leq b\ , \ \
\left\vert \frac{df_{1}}{dx}\right\vert \leq b\ , \
\left\vert \frac{d^{2}f_{1}}{dx^{2}}\right\vert \leq b\right\ } \ , \quad\ \ \
b\in\mathbb{r } _ { + } \ , \nonumber\end{aligned}\ ] ] where @xmath221 are the initial data appearing in eqs .
( [ int1 ] ) and ( [ int2 ] ) so that @xmath207 is closed by definition .
it is easy to see that @xmath207 is bounded as well , since from the definition of @xmath207 it follows that@xmath235 which clearly implies that there exists @xmath236 such that @xmath237 , given any two functions @xmath238 .
it remains to prove that @xmath207 is convex , i.e. to check that if @xmath239 and @xmath240 both belong to @xmath207 then also @xmath241 belongs to @xmath207 , @xmath242 $ ] .
this can be seen as follows:@xmath243 while the conditions on the derivatives are trivially satisfied . from the definition of @xmath207 in eq .
( [ ban5 ] ) we deduce the inequalities @xmath245 } { \sup}\left\vert h_{0}\left ( x\right ) \right\vert & \leq l\left\ { \frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] \right\ } \ , \label{useful1}\\ \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert h_{1}\left ( x\right ) \right\vert & \leq l\left\ { \frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] \right\ } \ , \label{useful2}\ ] ] @xmath245 } { \sup}\left\vert \frac{dh_{0}}{dx}\right\vert & \leq\frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac { 6}{r^{2}}\right ] \ , \label{useful3}\\ \underset{x\in\left [ 0,l\right ] } { \sup}\left\vert \frac{dh_{1}}{dx}\right\vert & \leq\frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac { 6}{r^{2}}\right ] \ , \label{useful4}\ ] ] ( where we used the fact that @xmath246 ) , which will be needed later . _ the next task _ to apply the schauder theorem is to prove that @xmath224 is a compact operator . to do this we advocate the _ ascoli - arzel theorem _ , which states that
if a sequence of functions ( defined on a compact metric space ) @xmath247 is uniformly bounded and equicontinuous , then a convergent subsequence can be extracted from it is uniformly bounded if @xmath248 , where @xmath236 does not depend on @xmath41 ; @xmath249 is said to be equicontinuous if , given @xmath250 , @xmath251 such that @xmath252 whenever @xmath253 _ and , moreover , _
@xmath152 _ does not depend on _ @xmath41 ( otherwise the sequence would be continuous but not equicontinuous : see @xcite ) . ] .
thus compactness of @xmath224 is equivalent to the statement that if @xmath254 is a sequence in @xmath207 , then the sequence @xmath255
= \left ( t_{0}\left ( n;x\right ) , t_{1}\left ( n;x\right ) \right ) $ ] is uniformly bounded and equicontinuous .
uniform boundedness can be proved as follows:@xmath256a_0+b_0l+lh_0 ( n;x ) . and
therefore , from eq .
( [ useful1 ] ) , one gets:@xmath257 \right\ } \ , \label{ban10}\ ] ] and , similarly , for @xmath258 : @xmath259 \right\ } \ . \label{ban11}\ ] ] now , the sequence of images @xmath260 $ ] has to belong to @xmath207 as well .
as it always happens ( see @xcite and @xcite ) this will give some constraints on the range of the initial data as well as on the parameters @xmath261 , @xmath26 and @xmath97 since , from the definition of @xmath207 , one has to require that for any @xmath41 @xmath262 consequently , as it can be easily seen comparing eqs .
( [ cons1 ] ) , ( [ cons2 ] ) , ( [ ban5 ] ) , ( [ ban6 ] ) and ( [ ban7 ] ) with eqs . ( [ useful1 ] ) , ( [ useful2 ] ) , ( [ useful3 ] ) , ( [ useful4 ] ) , ( [ ban10 ] ) and ( [ ban11 ] ) , the following constraints arise:@xmath263 \right\ } & \leq b\ , \label{ban10.5}\\ \left\vert
b_{1}l\right\vert + l^{2}\left\ { \frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] \right\ } & \leq b\ , \label{ban11.5}\]]@xmath264 \right\ } & \leq b\ , \label{ban10.6}\\ \left\vert b_{1}\right\vert + l\left\ { \frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] \right\ } & \leq b\ , \label{ban11.6}\]]@xmath265 & \leq b\ \ , \label{ban10.7}\\ \frac{b}{2 } + \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] & \leq b\ . \label{ban11.7}\ ] ] therefore , in order for this theorem to work , the length @xmath26 of the tube - shaped region in which these multi - skyrmions are living can not exceed the bounds defined in eqs .
( [ ban10.5 ] ) and ( [ ban11.5 ] ) ( indeed , if @xmath26 is too large , the bounds will be violated at a certain point can not be arbitrarily big for the theorem to hold can be also seen by observing that in the limit @xmath266 the domain of definition of the functions would not be compact any more , thus invalidating the ascoli - arzel theorem ] . ) .
it is also to be noticed that one can not obtain a very large value for the allowed @xmath26 by increasing @xmath261 since the left hand sides of eqs .
( [ ban10.5 ] ) and ( [ ban11.5 ] ) increase faster than the right hand sides .
moreover , the situation gets worse if @xmath100 is very small ( as all the above inequalities are violated at a certain point ) .
however , if @xmath97 is large ( namely , in the flat limit ) , eqs .
( [ ban10.7 ] ) and ( [ ban11.7 ] ) are always satisfied and eqs .
( [ ban10.6 ] ) and ( [ ban11.6 ] ) become mild constraints on the initial data . on the other hand ,
it is trivial to see that it is always possible to choose the initial data and @xmath261 , @xmath26 and @xmath97 in such a way that all the above inequalities are fulfilled .
_ the second step _ to prove that @xmath208 is compact is to show that if @xmath267 is a sequence in @xmath207 then the sequence @xmath268 $ ] is _
equicontinuous_. to show this , we must evaluate , _ for a generic _ @xmath41 , the absolute values of following differences:@xmath269 where @xmath270 .
after trivial manipulations ( which use the fact that all the functions @xmath271 belong to @xmath207 and consequently eqs.([ban6 ] ) and ( [ ban7 ] ) are satisfied ) one arrives at @xmath272 \right\ } \right ] \ , \label{ban14}\\ \left\vert t_{1}\left ( n;x\right ) -t_{1}\left ( n;y\right ) \right\vert & \leq\left\vert x - y\right\vert \left [ \left\vert b_{1}\right\vert + l\left\ { \frac{1}{2}b+ \frac{3}{8r^{2}}\left [ b^{2}+4+\frac{6}{r^{2}}\right ] \right\ } \right ] \ , \label{ban15}\ ] ] in summary , eqs .
( [ ban10 ] ) , ( [ ban11 ] ) , ( [ ban10.5 ] ) , ( [ ban11.5 ] ) , ( [ ban10.6 ] ) , ( [ ban11.6 ] ) , ( [ ban10.7 ] ) and ( [ ban11.7 ] ) show that , if @xmath275 is any sequence in @xmath207 , then the sequence @xmath276 $ ] is uniformly bounded in @xmath207 . secondly , eqs .
( [ ban14 ] ) , ( [ ban15 ] ) , ( [ ban16 ] ) and ( [ ban18 ] ) show that , if @xmath267 is any sequence in @xmath207 , then the sequence @xmath277 $ ] is _
equicontinuous_. consequently , by virtue of the ascoli - arzel theorem , from any sequence @xmath278 $ ] one can extract a convergent subsequence : this , together with the bounds ( [ ban10.5])-([ban11.7 ] ) , implies that the operator @xmath224 is a compact operator from a bounded closed convex set into itself .
thus , it is possible to apply the schauder theorem , which ensures that eq .
( [ fixedpoint ] ) ( which is equivalent to our original system ) has at least one solution .
moreover , it is always possible to choose appropriately the inital data @xmath221 and @xmath222 in such a way that the two profiles are not proportional .
the conclusion is that not only one can construct numerical solutions ( which are very interesting by themselves ) , as we do in the main text , but also one can prove analytically that non - trivial multi - skyrmions in which the profiles are not proportional do indeed exist . besides the intrinsic mathematical elegance of the fixed - point schauder - type argument , the present procedure also discloses the presence of the bounds in eqs.([ban10.5])-([ban11.7 ] ) on the radius @xmath97 and on the length @xmath26 of the tube - shaped region in which these multi - skyrmions are living ( which constrain its shape ) , as well as on the other parameters of the model . at the present stage of the analysis ,
it is not possible yet to say whether such a bound is just a limitation of the method or it signals some deeper physical limitation on the volume of the regions in which one constrains these skyrmions to live .
however , to understand whether or not @xmath5 multi - skyrmions can fit into very large tube - shaped regions is certainly a very interesting and deep question on which we hope to come back in a future investigation .
f. jonietz , s. mhlbauer , c. pfleiderer , a. neubauer , w. mnzer , a. bauer , t. adams , r. georgii , p. bni , r. a. duine , k. everschor , m. garst , a. rosch , _ science _ * 330 * ( 2010 ) , 1648 - 1651 s. seki , x. z. yu , s. ishiwata , y. tokura , _ science _ * 336 * ( 2012 ) , 198 - 201 . | we study multi - soliton solutions of the four - dimensional su(n ) skyrme model by combining the hedgehog ansatz for su(n ) based on the harmonic maps of @xmath0 into @xmath1 and a geometrical trick which allows to analyze explicitly finite - volume effects without breaking the relevant symmetries of the ansatz .
the geometric set - up allows to introduce a parameter which is related to the t hooft coupling of a suitable large @xmath2 limit , in which @xmath3 and the curvature of the background metric approaches zero , in such a way that their product is constant .
the relevance of such a parameter to the physics of the system is pointed out . in particular , we discuss how the discrete symmetries of the configurations depend on it . |
entanglement @xcite is one of the most intriguing feature of quantum mechanics , having myriads of potential applications in quantum information and communication @xcite . so far ,
preparation and manipulation of entanglement has been successfully demonstrated in microscopic systems , such as atoms , photons , ions @xcite etc . however , the validity of entanglement in the macroscopic realm is still a debatable fact . in this
regard , optomechanical system @xcite where a macroscopic mechanical motion interacts with an optical field has emerged as a promising platform to realize entanglement at a macroscopic level .
several studies have been reported to generate entanglement between optical and mechanical mode or two optical modes or two mechanical modes @xcite .
these studies mostly explore entanglement in the steady - state regime of the system where the strength of the entanglement is strictly limited by the stability conditions .
in particular , in this regime entanglement becomes maximum only when the system is driven close to the stability threshold , which demands a strong multi - photon optomechanical coupling or high external laser driving @xcite .
recently , it has been proposed @xcite and experimentally demonstrated @xcite that a two - level system or a nonlinear inductive element ( single - cooper pair transistor ) coupled to an optomechanical system , can significantly enhance the single - photon radiation - pressure coupling .
more importantly , it induces an additional cross - kerr type coupling between the optical and mechanical mode . in nonlinear optics ,
cross - kerr effect describes the change in refractive index of one electromagnetic mode by the intensity of another .
it has been extensively studied in the context of quantum information processing , such as non - demolition photon number detection @xcite , c - not gate @xcite and continuous - variable entanglement concentration @xcite .
concerning optomechanical system , the cross - kerr coupling between the optical and mechanical mode , involves the change in the refractive index of the optical mode depending on the resonators phonon number @xcite .
recently , ref .
@xcite has showed that this cross - kerr coupling gives rise to a frequency shift in mechanical and optical mode , with the shift depending on the cavity photon number and mechanical phonon number .
furthermore , ref .
@xcite studied the effect of cross - kerr nonlinearity on the stability of the optomechanical system .
along this line , ref .
@xcite showed that in presence of an additional cross - kerr coupling , the steady - state response of the mechanical resonator becomes a nonmonotonous function of cavity photon number and the bistable behavior of the mean cavity photon can be turned into a tristable behavior .
motivated by these works , we study the combined effect of radiation pressure and cross - kerr coupling on the steady - state optomechanical entanglement .
first , we analyze the effect of cross - kerr coupling on the steady - state behavior and the stability conditions of the optomechanical system .
then , we focus on the optomechanical entanglement and find the influence of cross - kerr coupling on it . finally , we discuss the robustness of our scheme with respect to system parameters and environmental temperature .
as depicted in fig . [ fig1 ] , we consider an optomechanical system which consists of an optical and a mechanical mode , respectively , with frequency @xmath0 and @xmath1 . as usual , these two modes are coupled via the generic radiation pressure coupling @xmath2 . in addition , here we consider an extra cross - kerr type coupling @xmath3 between the optical and mechanical mode , generated by a two - level system or a superconducting charge qubit @xcite .
also , the whole system is driven by an external laser of frequency @xmath4 . with this consideration ,
the complete hamiltonian of the optomechanical system in a rotating frame of the laser reads ( @xmath5 ) @xmath6 here , @xmath7 ( @xmath8 ) and @xmath9 ( @xmath10 ) are , respectively , the annihilation ( creation ) operators of the optical and mechanical mode , @xmath11 is the optical detuning and @xmath12 is the driving amplitude , related to driving power @xmath13 and optical decay rate @xmath14 by @xmath15 .
in addition , the system dynamics also includes fluctuation - dissipation processes affecting both the optical and mechanical mode .
starting from hamiltonian , the time evolution of the optomechanical system is given by the following nonlinear quantum langevin equations : [ eq:2 ] @xmath16 where @xmath17 is the mechanical damping rate , and @xmath18 and @xmath19 are the corresponding zero - mean input gaussian noises , with nonzero correlation functions @xcite , given by : [ eq:3 ] @xmath20 here , @xmath21 is the mean thermal phonon number , related to boltzmann constant @xmath22 and environmental temperature @xmath23 by : @xmath24^{-1}$ ] . under intense laser driving
, we now expand each heisenberg operators as a sum of its semi - classical steady - state value plus an additional small fluctuation operator with zero - mean value : @xmath25 and @xmath26 .
the steady - state values are given by the following nonlinear equations : @xmath27 where @xmath28 is the effective optical detuning , modified owing to the both radiation pressure and cross - kerr coupling , and , @xmath29 is the effective mechanical frequency , modified owing to the cross - kerr interaction . as for the fluctuations , their dynamics
is given by the linearized quantum langevin equations @xcite : [ eq:5 ] @xmath30 where @xmath31 is the effective optomechanical coupling strength with modified @xmath32 .
note that , in the above calculation we have chosen the phase reference of the optical field , such that @xmath33 is real .
next , we introduce the dimensionless quadrature operators , respectively , for the optical and mechanical mode : @xmath34 , @xmath35 and @xmath36 , @xmath37 , and , similarly for the corresponding hermitian input noise operators : @xmath38 , @xmath39 and @xmath40 , @xmath41 . with the above definitions , we express eq . in a more compact form : @xmath42 where @xmath43 is the vector of continuous variable ( cv ) fluctuation operators , @xmath44 is the drift matrix : @xmath45 -\tilde{\omega_b } & -\gamma & g & 0 \\[4 pt ] 0 & 0 & -\kappa & \tilde{\delta } \\[4 pt ] g & 0 & -\tilde{\delta } & -\kappa \\[4 pt ] \end{array } \right),\end{aligned}\ ] ] and @xmath46 is the vector of corresponding noises . a formal solution of eq . is given by : @xmath47 where @xmath48 .
the system is stable and reaches its steady - state when all the eigenvalues of the drift matrix @xmath44 have negative real parts .
these stability conditions are derived by applying the routh - hurwitz criteria @xcite , which is given in terms of the system parameters by the following two nontrivial equations : [ eq:9 ] @xmath49 + 4g^2\tilde{\delta}\tilde{\omega_b}(\gamma+\kappa)^2>0,\\ ( { \tilde{\delta}}^2+\kappa^2)({\tilde{\omega_b}}^2+\gamma^2)-g^2\tilde{\delta}\tilde{\omega_b}>0.\end{gathered}\ ] ] note that , in the following work we will strictly restrict to red - detuned driving ( @xmath50 ) , for which the first condition is always satisfied , only the second condition is relevant .
since dynamics is linearized and the initial state of the system is gaussian in nature , the steady - state for the quantum fluctuations is simply a zero - mean gaussian bipartite state , which is fully characterized by its @xmath51 correlation matrix ( cm ) : @xmath52 here , @xmath53 is the vector of cv fluctuation operators in the steady - state @xmath54 . when the system is stable , performing a substitution of eq . in the defination of cm
, we get @xmath55 where @xmath56 is the matrix of stationary noise correlations . using eq .
, @xmath57 further simplifies to @xmath58 , where @xmath59 is a diagonal matrix , given by : @xmath60.\end{aligned}\ ] ] therefore , eq .
becomes @xmath61 , which , when the stability conditions are satisfied ( @xmath62 ) is equivalent to the following lyapunov equation for @xmath63 : @xmath64 note that eq . is a linear equation in @xmath63 which can be straightforwardly solved .
however , an exact analytical expression is too cumbersome and will not be reported here .
indeed , we resort to a numerical solution of @xmath63 . finally , to study the entanglement between the optical and mechanical mode , we use logarithmic negativity @xmath65 as a computable measure of entanglement @xcite . for a continuous - variable system ,
@xmath65 is defined as @xmath66,\end{aligned}\ ] ] where @xmath67^{1/2}$ ] is the lowest symplectic eigenvalue of the partial transpose of @xmath63 with @xmath68 , and , we have used @xmath69 block form of the cm : @xmath70 where @xmath71 , @xmath72 and @xmath73 , respectively corresponds to the mechanical mode , the optical mode and the optomechanical correlation between them . therefore ,
the gaussian state is entangled ( @xmath74 ) if and only if @xmath75 which is equivalent to simon s necessary and sufficient nonpositive partial transpose criteria @xcite .
we start our discussion by considering the effect of cross - kerr coupling on the steady - state behavior of the optomechanical system . to numerically illustrate our result we consider a set of experimentally accessible parameters : @xmath76 thz , @xmath77 mhz , @xmath78 khz , @xmath79 hz , @xmath80 mw and @xmath81 . in fig .
2(a ) , we plot the steady - state amplitudes of the optical and mechanical mode along with the stability range of the system ( with @xmath82 ) , as a function of the driving power .
it is clear that for the chosen value of the parameters , both these amplitudes satisfy @xmath83 which ensures the validity of our linearization assumption .
we also note that unlike pure radiation - pressure coupling , now @xmath84 changes drastically with increasing power , as can be explained from eq .
@xcite . in fig . ( 2b ) we plot @xmath85 and @xmath86 against the driving power .
we can see that with increasing power @xmath85 decreases and @xmath86 increases . in particular , at a driving power @xmath87 ( just before the instability ) , we get @xmath88 and @xmath89 . therefore , in presence of cross - kerr coupling , owing to this significant change in the effective mechanical frequency and ( single photon ) coupling strength , the system becomes unstable at a considerably lower driving power .
next , we focus on the steady - state optomechanical entanglement and the influence of cross - kerr coupling on it . in fig .
[ fig3 ] , we plot @xmath65 as a function of the normalized cross - kerr coupling strength @xmath90 , for a fixed driving power and optical detuning .
we can see that with increasing cross - kerr coupling the degree of entanglement increases and becomes maximum just before the instability .
in particular , for the pure radiation - pressure coupling case ( @xmath91 ) we have @xmath92 . on the other hand ,
in presence of a cross - kerr coupling with coupling strength @xmath82 we obtain @xmath93 .
therefore , by invoking cross - kerr coupling on a generic optomechanical system , we can significantly enhance the degree of steady - state optomechanical entanglement . to further probe into entanglement properties and its dependence on the system parameters , we plot in fig .
[ fig4 ] , @xmath65 as a function of the normalized detuning @xmath94 and normalized driving power @xmath95 , for @xmath91 ( a ) ( no cross - kerr coupling ) , @xmath96 ( b ) , and @xmath97 ( c ) .
we observe that with increasing cross - kerr coupling , the degree of entanglement increases , however , the parameter region in which the steady - state is entangled significantly narrows .
in fact , with increasing cross - kerr coupling the system becomes unstable at a lower driving power , which leads to the significant enhancement of steady - state optomechanical entanglement near the stability threshold .
[ fig5 ] , depicts the same @xmath65 as a function of the normalized optical decay rate @xmath98 and normalized driving power @xmath95 , for @xmath91 ( a ) ( no cross - kerr coupling ) , @xmath96 ( b ) , and @xmath97 ( c ) . here also , we find the enhancement of the steady - state optomechanical with increasing cross - kerr coupling .
however , now the maximum entanglement only occurs for @xmath99 ( fig .
5(c ) ) at higher driving power and lower optical decay rate .
it is also important to note that even in the presence of cross - kerr coupling , we find significant entanglement only in the resolved sideband region , i.e. for @xmath100 . finally , in fig .
[ fig6 ] , we plot @xmath65 as a function of the mean thermal phonon number @xmath21 .
we observe that the degree of entanglement monotonically decreases with increasing thermal phonon number .
however , the maximum number of thermal phonons up to which entanglement persists increases with increasing cross - kerr coupling .
for example , for the pure radiation - pressure coupling case the entanglement persists up to @xmath101 .
in contrast , in presence of a cross - kerr coupling with coupling strength @xmath82 , we have entanglement up to @xmath102 .
this shows that with the introduction of cross - kerr coupling the bipartite entanglement becomes more robust against the thermal phonon fluctuations .
in conclusion , we have studied in detail the steady - state optomechanical entanglement in presence of an additional cross - kerr coupling between the optical and mechanical mode . within the standard linearized description
, we have shown that in presence of an additional cross - kerr coupling the system becomes unstable at a considerably lower driving power , which leads to significant enhancement of steady - state optomechanical entanglement near the stability threshold .
we have further shown that with increasing cross - kerr coupling , this bipartite entanglement becomes more robust against the variation of system parameters and thermal phonon fluctuation .
these results make our proposed scheme a promising way to improve optomechanical entanglement in the steady - state regime .
s. chakraborty would like to acknowledge the financial support from mhrd , government of india .
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lett . * 84 * , 2726 ( 2000 ) . | in this work , we study steady - state optomechanical entanglement in presence of an additional cross - kerr coupling between the optical and mechanical mode .
we find that a significant enhancement of the steady - state entanglement can be achieved at a considerably lower driving power , which is also extremely robust with respect to system parameters and environmental temperature .
pacs numbers : : ` 42.50.wk , 03.65.ud , 07.10.cm , 42.50.lc ` |
the study of free shear layers and their instabilities is one of the oldest problems in fluid dynamics , dating back to the pioneering work of kelvin @xcite and helmholtz @xcite . in this work
we will consider two types of shear layer , the magnetically induced shercliffe layer and the rotationally induced stewartson layer , that can easily be set up in a differentially rotating spherical shell .
previous work has studied each of these layers and its corresponding instabilities in isolation @xcite .
the basic shear layers are similar in many ways , but their instabilities may be very different .
here we compare and contrast the two problems , and then consider the mixed case , when both magnetic and rotational effects are present .
previous studies on magnetohydrodynamic spherical couette flow have included analytic @xcite , numerical @xcite and experimental @xcite work , with a variety of imposed magnetic fields .
nonmagnetic stewartson layers have also been widely studied , in both cylindrical @xcite and spherical @xcite geometries .
we start with two concentric spheres , of radii @xmath0 and @xmath1 , rotating about a common axis ( the @xmath2 axis ) with angular velocities @xmath3 and @xmath4 . the fluid filling the shell is taken to be electrically conducting , and a magnetic field @xmath5 is externally imposed .
the question then is , what sort of flow states will result as the parameters @xmath6 , @xmath3 and @xmath4 are varied , and can the solutions be classified in some systematic way , for example according to whether they are magnetically or rotationally dominated ? in the reference frame rotating with the outer sphere , the governing equations are @xmath7 @xmath8 @xmath9 where the hartmann number @xmath10 measures the strength of the imposed magnetic field , the taylor number @xmath11 measures the overall rotation of the whole system , and the reynolds number @xmath12 measures the differential rotation of the inner sphere .
the density @xmath13 , viscosity @xmath14 , diffusitivy @xmath15 , and permeability @xmath16 are ( constant ) material properties of the fluid . in these equations ,
length has been scaled by @xmath0 , time by @xmath17 , and @xmath18 by @xmath19 .
finally , the induced magnetic field @xmath20 has been scaled by @xmath21 , where @xmath22 is the magnetic reynolds number , and eqs .
( 1 ) and ( 2 ) have been formulated in the @xmath23 limit , in which @xmath24 no longer appears in the equations at all , but only in the interpretation associated with @xmath20 .
see also @xcite ; the problem considered here is precisely the extension of @xcite to include the overall rotation given by @xmath25 .
the boundary conditions associated with ( 1 ) are the usual spherical couette flow conditions @xmath26 where the radii will be fixed at @xmath27 and @xmath28 . for
the boundary conditions associated with ( 2 ) we take the exterior regions @xmath29 and @xmath30 to be insulating .
as shown in @xcite , taking these regions to be conducting instead can have dramatic consequences , yielding a counter - rotating jet rather than a shear layer .
however , precisely because we want to focus on shear layers here , we consider only the insulating case .
these equations and associated boundary conditions are solved numerically , using the spherical harmonics code @xcite .
we begin by considering the axisymmetric basic states , then we linearize about these solutions , and compute the linear onset of non - axisymmetric instabilities . resolutions as high as 300 legendre functions in @xmath31 and 180 chebyshev polynomials in @xmath32 were used , and results were tested to ensure that all aspects of the solutions were fully resolved .
figure 1 shows the solutions at @xmath33 , and @xmath34 , @xmath35 , @xmath36 , corresponding to an infinitesimal differential rotation , no overall rotation , and an increasingly strong magnetic field .
we see the emergence of an increasingly thin shear layer , the shercliffe layer , located on the so - called tangent cylinder @xmath37 , the cylinder just touching the inner sphere and parallel to the magnetic field .
the origin of this layer is easy to understand , in terms of the magnetic tension along the field lines .
fluid columns outside @xmath37 are coupled at both endpoints to the outer boundary only , so they remain at rest . in contrast ,
fluid columns inside @xmath37 are coupled to both boundaries , which are rotating at different angular velocities , 0 at the outer boundary , and 1 at the inner boundary , as imposed by ( 6 ) .
these columns then rotate at a rate intermediate between 0 and 1 .
the result is a jump in angular velocity across @xmath37 , which is precisely the shercliffe layer observed in figure 1 .
( inside @xmath37 there are also hartmann layers at the outer and inner boundaries , accomodating the jump from @xmath38 in the interior to 0 and 1 at the boundaries
. we will not be interested in these boundary layers though . )
figure 2 shows the solutions at @xmath39 , and @xmath40 , @xmath41 , @xmath42 .
we again see the emergence of an increasingly thin shear layer , the stewartson layer , on the same tangent cylinder @xmath37 as before .
the origin of this layer is also very similar to that of the shercliffe layer , the only difference being that now it is the taylor - proudman theorem that couples fluid columns along the @xmath2 axis , and not magnetic tension , which is of course entirely absent for @xmath43 . despite their similarities , there are also important differences between shercliffe and stewartson layers .
note for example how the contour lines in the stewartson layer are almost perfectly parallel , whereas in the shercliffe layer they spread out somewhat away from the inner sphere .
related to this is the fact that the asymptotics of these two shear layers are also slightly different ; the shercliffe layer consists of a single layer of thickness @xmath44 @xcite , whereas the stewartson layer consists of a primary layer of thickness @xmath45 across which the shear is resolved , but also contains secondary layers of thicknesses @xmath46 just inside @xmath37 and @xmath47 just outside @xmath37 @xcite . , @xmath35 , @xmath36 , and @xmath48 for all three .
] , @xmath41 , @xmath42 , and @xmath49 for all three . ]
the results in figs .
1 and 2 are all for the case of infinitesimally small differential rotation , @xmath50 .
now suppose the differential rotation is gradually increased .
as the shear across the layers is increased , one might expect the layers to become unstable eventually , to something like a kelvin - helmholtz instability .
that is , one might expect the initially circular , axisymmetric basic state to adopt a wavy , non - axisymmetric structure .
the instabilities of the pure shercliffe layer were considered by @xcite ; the left panel in fig .
3 shows their results ( fig .
4a in @xcite ) , over the range of hartmann numbers shown in fig . 1
. the instabilities of the pure stewartson layer were considered by @xcite ; the right panel in fig
. 3 shows these results ( fig . 4 in @xcite ) , again over the range of taylor numbers shown in fig . 2 .
( note though that the equations here are scaled differently from those in @xcite , to allow for the possibility of @xmath51 here .
the ekman and rossby numbers in @xcite are related to the taylor and reynolds numbers used here by @xmath52 and @xmath53 . ) as a function of @xmath54 for the pure shercliffe layer ; ( b ) shows @xmath55 as a function of @xmath56 for the pure stewartson layer .
the numbers beside individual curves indicate the azimuthal wavenumbers @xmath57 , showing only the most unstable modes . in ( b ) , the solid curves @xmath58 to @xmath59 are for @xmath60 , whereas the dashed curve @xmath61 is for @xmath62 . ] comparing the two panels in fig . 3 , there are clearly similarities between the two cases . most obviously , for comparable thicknesses of the underlying shear layers ( as indicated in figs . 1 and 2 ) the critical reynolds numbers for the onset of instabilities are also comparable , with @xmath63 for the @xmath64 and @xmath25 ranges shown . beyond that ,
in both cases the critical reynolds numbers increase as the thickness of the shear layers decreases . however , there is also one crucial difference between the instabilities of these two types of shear layer , more fundamental than any difference between the shear layers themselves .
specifically , for the pure shercliffe layer , the results are invariant to the sign of @xmath65 , that is , the direction in which the inner sphere rotates . the easiest way to see this is to note that reversing the rotation of the inner sphere is equivalent to turning the entire system upside down .
this merely reverses the sign of the imposed magnetic field though , which clearly has no effect . in sharp contrast , the results for the stewartson layer are not invariant to the sign of @xmath65 .
one can of course still imagine turning the system upside down , but instead of reversing the magnetic field , this now reverses the sense of the overall rotation . and unlike the magnetic field ,
whose sign does nt matter , the sign of the overall rotation does matter . that is , instead of reversing the sign of @xmath65 one could just as well reverse the sign of @xmath25 , but the result is still not equivalent to the original configuration . having @xmath65 and @xmath25 of the same sign
is fundamentally different from having them of the opposite sign .
returning to the right panel in fig . 3 then , we note that @xmath60 and @xmath62 do indeed yield strikingly different instabilities .
positive @xmath65 has increasingly large azimuthal wavenumbers @xmath57 for increasingly large @xmath25 , exactly as one would expect for a kelvin - helmholtz type instability , whereas negative @xmath65 has @xmath61 over the entire range of @xmath25 shown here .
comparing with the @xmath66 invariant shercliffe results in the left panel , we see that these are more like the @xmath60 stewartson results , in that they also show a progression to higher @xmath57 .
one reason for considering the mixed shercliffe - stewartson problem then is simply to see how this @xmath66 asymmetry manifests itself in this case , and at what point the results are more like the symmetric shercliffe problem or more like the asymmetric stewartson problem .
, @xmath67 , and @xmath51 .
the left panel shows the angular velocity , with a contour interval of 1/9 ; the middle panel shows the meridional circulation , with a contour interval of @xmath68 ; the right panel shows the azimuthally integrated kinetic energy of the instability , having wavenumber @xmath58 , as indicated in the left panel of fig . 3 .
] , @xmath69 , and @xmath43 .
the left panel shows the angular velocity , with a contour interval of 1/9 ; the middle panel shows the meridional circulation , with a contour interval of @xmath70 ; the right panel shows the azimuthally integrated kinetic energy of the instability , having wavenumber @xmath71 , as indicated in the right panel of fig .
first though we consider a few more aspects of the two pure problems , namely the spatial location of the instabilities .
4 shows the shercliffe case , fig . 5 the @xmath60 stewartson case .
the first panels in each figure show the angular velocity , as before in figs . 1 and 2 .
one point to note here is how similar these solutions at non - zero @xmath65 are to the @xmath50 solutions in figs . 1 and 2 .
the inertial term @xmath72 is crucially important in driving the instabilities , but in the basic states themselves it is almost completely balanced by the pressure - gradient term .
the second panels show the associated meridional circulation .
this is very weak though in comparison with the shear layers , and does not appear to play an important role in the instabilities . finally , the grey - shading in the third panels shows the azimuthally integrated kinetic energy of the instabilities , that is , the quantity @xmath73 . as expected , both instabilities are concentrated on the tangent cylinder @xmath37 , although it is interesting to note that the concentration is far greater in the shercliffe case than in the stewartson case .
figure 6 shows the corresponding results for the @xmath62 stewartson case , the anomalous @xmath61 mode .
the instability now appears to have curious gaps in cylindrical radius , resulting in a striped appearance .
furthermore , the instability reaches its maximum concentration not on @xmath37 , but instead just inside , where the stewartson layer intersects the ekman layer on the inner sphere .
this would suggest that this anomalous mode is perhaps not a stewartson layer instability at all , but instead an ekman layer instability , for which it is well known that the @xmath60 case ( von krmn flow ) and the @xmath62 case ( bdewadt flow ) are indeed very different @xcite . , and @xmath61 .
] , and @xmath61 . ]
the numerical tests conducted by @xcite considered exactly this possibility , and suggest that however plausible this idea may be , it is incorrect : this @xmath62 mode is not a bdewadt instability , but a stewartson layer instability , just like the @xmath60 modes .
however , these numerical tests @xcite , in which the meridional circulation and the ekman layers were simply deleted from the basic state before computing the instabilities , can be and indeed have been criticized as being unphysical , not corresponding to anything that one could actually set up in a lab , for example
. we would therefore like to repeat something like this deletion of the meridional circulation and the ekman layers , but in a way that is physical , and could be set up in an experiment .
fortunately , this can be accomplished rather easily : we simply replace the outer boundary condition @xmath74 by @xmath75 at @xmath76 , where @xmath77 is 1 inside @xmath37 , and 0 outside ( for numerical reasons the transition is actually smoothed out over a degree or so ) .
physically this would correspond to having the outer sphere split into differentially rotating segments , with the regions inside the tangent cylinder now co - rotating with the inner sphere , which is precisely how many stewartson layer experiments are indeed done @xcite .
figure 7 shows these results . if we begin by comparing the basic states in figs . 6 and 7
, we see that this new boundary condition has roughly doubled the jump in angular velocity across the shear , because everything inside @xmath37 is now co - rotating with the inner sphere , whereas before the fluid inside @xmath37 was rotating at a rate intermediate between 1 at the inner boundary and 0 at the outer . turning next to the ekman layers ,
these have been largely eliminated ; if everything inside @xmath37 is co - rotating , there is simply no need for ekman layers at the boundaries . and correspondingly , the meridional circulation , which is driven by ekman pumping in the boundary layers , is also dramatically reduced .
this new boundary condition has thus accomplished exactly what we wanted , but in a way that is physically realizable , unlike the numerical tests presented in @xcite . and if we compare the instabilities in the two cases then , the original boundary condition ( fig . 6 ) has @xmath61 and @xmath78 , and the new boundary condition ( fig .
7 ) has @xmath61 and @xmath79 .
that is , doubling the shear across the layer roughly halves the critical reynolds number , exactly as one would expect if it is indeed the shear layer that is triggering the instability .
this new boundary condition therefore confirms the claim made by @xcite that this anomalous @xmath61 mode is also a stewartson layer instability ( although beyond that there are unfortunately still many aspects of this mode that are not entirely clear ) .
figure 8 shows stability results for the mixed case , when neither @xmath64 nor @xmath25 are zero . starting with hartmann numbers @xmath80 and @xmath81 , @xmath25
is increased from @xmath82 to @xmath81 , for both positive and negative @xmath65 . for @xmath83 , @xmath66
are not surprisingly almost the same .
as rotational effects become comparable with magnetic effects though , the rotationally induced asymmetry becomes more and more pronounced . for positive / negative @xmath65 the wavenumber increases / decreases , until for @xmath84 we are almost back to the pure stewartson regime , with large @xmath57 for positive @xmath65 , and small @xmath57 for negative @xmath65 .
it is unfortunately not entirely clear why the wavenumbers behave in this way , but the fact that there is this smooth transition from the symmetric shercliffe case to the asymmetric stewartson cases , for both positive and negative @xmath65 , further reinforces the view that even these ` anomalous ' @xmath61 modes above are not so anomalous after all , but are merely the limiting case in this family of shear layer instabilities .
one other interesting , and completely unexpected result in fig .
8 is this initial decrease in the @xmath60 curves , reaching a minimum when @xmath85 .
@xmath86 is of course precisely the regime where rotational and magnetic effects are comparable , so it is not surprising that any interaction between the two would manifest itself most strongly there .
that rotational and magnetic effects can destabilize one another even though each separately has a stabilizing influence is also familiar in other contexts , such as rayleigh - bnard convection @xcite .
it is not clear though why this mutual destabilization in this case does not occur for @xmath62 as well . , with @xmath87 almost the pure shercliffe regime , and @xmath84 almost the pure stewartson regime .
( a ) is for @xmath80 ; ( b ) is for @xmath88 . within each panel
the upper set of curves , with decreasing wavenumbers , is for @xmath62 ; the lower set of curves , with increasing wavenumbers , is for @xmath60 . ] finally , we wish to consider the spatial structures of both the basic states and the instabilities in this case @xmath89 where rotational and magnetic effects are interacting most strongly , and see whether they are more like the pure shercliffe case , or more like the pure stewartson case .
figure 9 shows the results for @xmath60 ; comparing with figs . 4 and 5
, we see that they look more like the pure shercliffe case .
figure 10 shows the results for @xmath62 ; comparing with figs . 4 and 6
, we see that the basic state again looks more like the pure shercliffe case .
the instabilities though have aspects in common with both the stewartson case , namely this striped appearance , as well as the shercliffe case , namely the concentration more outside @xmath37 , rather than in the equatorial region as in the stewartson case . , @xmath90 , @xmath91 and @xmath92 , the bottom row at @xmath93 , @xmath94 , @xmath95 and @xmath96 ; that is , at the minima of the @xmath60 curves in fig .
the left panels show the angular velocity , with a contour interval of 1/9 ; the middle panels show the meridional circulation , with a contour interval of @xmath70 ( top ) and @xmath97 ( bottom ) ; the right panels show the azimuthally integrated kinetic energy of the instabilities . ] , with @xmath80 , @xmath98 , @xmath99 and @xmath100 for the top row , and @xmath88 , @xmath94 , @xmath101 and @xmath58 for the bottom row . ]
in this work we have explored the stability of two types of free shear layers that may be set up by magnetic and rotational effects .
although the shear layers themselves are very similar for the two effects , the instabilities are quite different in one important aspect , namely that in the magnetic shercliffe case they are invariant to the sign of the differential rotation that induces them , whereas in the rotational stewartson case they are not . however , as different as the @xmath66 pure stewartson cases may at first sight appear to be , by considering the mixed case , we showed that there is in fact a smooth progression from the invariant shercliffe limit to both of the @xmath66 stewartson cases , suggesting that these cases are not so different after all .
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the fluid is also taken to be electrically conducting ( in the low magnetic reynolds number limit ) , and a magnetic field is imposed parallel to the axis of rotation .
if the outer sphere is stationary , the magnetic field induces a shercliffe layer on the tangent cylinder , the cylinder just touching the inner sphere and parallel to the field .
if the magnetic field is absent , but a strong overall rotation is present , coriolis effects induce a stewartson layer on the tangent cylinder .
the non - axisymmetric instabilities of both types of layer separately have been studied before ; here we consider the two cases side by side , as well as the mixed case , and investigate how magnetic and rotational effects interact .
we find that if the differential rotation and the overall rotation are in the same direction , the overall rotation may have a destabilizing influence , whereas if the differential rotation and the overall rotation are in the opposite direction , the overall rotation always has a stabilizing influence . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Infant Crib Safety Act''.
SEC. 2. FINDINGS AND PURPOSE.
(a) Findings.--Congress finds the following:
(1) The disability and death of infants resulting from
injuries sustained in crib incidents are a serious threat to
the public health, welfare, and safety of people of this
country.
(2) The design and construction of a baby crib must ensure
that it is safe to leave an infant unattended for extended
periods of time. A parent or caregiver has a right to believe
that the crib in use is a safe place to leave an infant.
(3) Each year about 12,400 children are injured in cribs
seriously enough to require emergency room treatment.
(4) Each year at least 43 children under the age of 4 die
from injuries sustained in cribs.
(5) The Consumer Product Safety Commission estimates that
the cost to society resulting from deaths due to cribs is at
least $150,000,000 per year.
(6) Secondhand, hand-me-down, and heirloom cribs pose a
special problem. There are nearly 4 million infants born in
this country each year, but only an estimated one million to
two million new cribs sold. Many infants are placed in
secondhand, hand-me-down, or heirloom cribs.
(7) Most crib deaths occur in secondhand, hand-me-down, or
heirloom cribs.
(8) Existing State and Federal legislation is inadequate to
deal with the hazard presented by secondhand, hand-me-down, or
heirloom cribs.
(9) Prohibiting the contracting to sell, resell, lease,
sublease of unsafe cribs that are not new, or otherwise place
in the stream of commerce unsafe secondhand, hand-me-down, or
heirloom cribs, will prevent injuries and deaths caused by
cribs.
(b) Purpose.--The purpose of this Act is to prevent the occurrence
of injuries and deaths to infants as a result of unsafe cribs by making
it unlawful--
(1) to manufacture, sell, or contract to sell any crib that
is unsafe for any infant using it; or
(2) to resell, lease, sublet, or otherwise place in the
stream of commerce, after the effective date of this Act, any
unsafe crib, particularly any unsafe secondhand, hand-me-down,
or heirloom crib.
SEC. 3. REQUIREMENTS FOR CRIBS.
(a) Manufacture and Sale of Cribs.--It shall be unlawful for any
commercial user to manufacture, sell, resell, lease, or otherwise place
in the stream of commerce, any full-size or nonfull-size crib that--
(1) was manufactured before 1999;
(2) does not conform to the safety standards described in
subsection (c); or
(3) has any missing, loose, or broken components.
(b) Provision of Cribs by Lodging Facilities.--It shall be unlawful
for any hotel, motel, or similar transient lodging facility to offer or
provide for use or otherwise place in the stream of commerce, on or
after the effective date of this Act, any full-size crib or nonfull-
size crib that--
(1) was manufactured before 1999;
(2) does not conform to the safety standards described in
subsection (c); or
(3) has any missing, loose, or broken components.
(c) Crib Safety Standards.--A full-size or nonfull-size crib that
is not in compliance with the following safety standards shall be
considered to be a banned hazardous product under section 8 of the
Consumer Product Safety Act (15 U.S.C. 2057):
(1) Part 1508 of title 16 of the Code of Federal
Regulations (requirements for full-size baby cribs).
(2) Part 1509 of title 16 of the Code of Federal
Regulations (requirements for nonfull-size baby cribs).
(3) American Society for Testing Materials F406-07 Standard
Consumer Safety Specification for Non-Full Size Baby Cribs/Play
Yards.
(4) American Society for Testing Materials F1169 Standard
Specification for Full-Size Baby Crib.
(5) American Society for Testing and Materials F966-00
Consumer Safety Specification for Full-Size and Non-Full Size
Baby Crib Corner Post Extensions.
(6) Part 1303 of title 16 of the Code of Federal
Regulations.
(7) Any amendments to the above regulations or standards or
any other regulations or standards that are adopted in order to
amend or supplement the regulations or standards described in
paragraphs (1) through (6).
The Consumer Product Safety Commission shall have the power to enforce
the provisions of this section in the same manner that the Commission
enforces rules declaring products to be banned hazardous products.
(d) Exception.--These requirements shall not apply to a full-size
crib or nonfull-size crib that is not intended for use by an infant,
including a toy or display item, if at the time it is manufactured,
made subject to a contract to sell or resell, leased, or otherwise
placed in the stream of commerce, as applicable, it is accompanied by a
notice to be furnished by each commercial user declaring that the crib
is not intended to be used for an infant and is dangerous to use for an
infant.
SEC. 4. DURABILITY TEST REQUIREMENTS FOR CRIBS.
Not later than 90 days after the date of enactment of this Act, the
Consumer Product Safety Commission shall begin a rulemaking to revise
parts 1508 and 1509 of title 16, Code of Federal Regulations, to--
(1) include the safety requirements specified in paragraphs
(3) through (5) of section 3(c), or any successor standards
thereto; and
(2) address any potential hazards due to durability
exhibited by cribs and play yards, taking into consideration--
(A) the Underwriters Laboratories standard UL-2275
for full-size baby cribs; and
(B) the standards set forth in the Cribs and Cradle
Regulations established by the Department of Justice of
Canada, issued September 11, 1986 (SOR/86-962).
SEC. 5. SOFT BEDDING WARNING LABELS.
Not later than 1 year after the date of enactment of this Act, the
Consumer Product Safety Commission shall promulgate a consumer product
safety rule pursuant to section 7 of the Consumer Product Safety Act
(15 U.S.C. 2056) to require that all cribs manufactured and introduced
into interstate commerce contain a warning label affixed to the crib in
a conspicuous location warning consumers against the use of soft
bedding for infants placed in the crib, including bumper pads, quilts,
blankets, pillows, and sleep positioners.
SEC. 6. DEFINITIONS.
As used in this Act, the following definitions apply:
(1) Commercial user.--
(A) The term ``commercial user'' means--
(i) any person who manufactures, sells, or
contracts to sell full-size cribs or nonfull-
size cribs; or
(ii) any person who--
(I) deals in full-size or nonfull-
size cribs that are not new or who
otherwise by one's occupation holds
oneself out as having knowledge or
skill peculiar to full-size cribs or
nonfull-size cribs, including child
care facilities and family child care
homes; or
(II) is in the business of
contracting to sell or resell, lease,
sublet, or otherwise placing in the
stream of commerce full-size cribs or
nonfull-size cribs that are not new.
(B) The term ``commercial user'' does not mean an
individual who sells a used crib at a one-time private
sale.
(2) Crib.--The term ``crib'' means a full-size crib or
nonfull-size crib.
(3) Full-size crib.--The term ``full-size crib'' means a
full-size baby crib as defined in section 1508.1 of title 16 of
the Code of Federal Regulations.
(4) Infant.--The term ``infant'' means any person less than
35 inches tall or less than 2 years of age.
(5) Nonfull-size crib.--The term ``nonfull-size crib''
means a nonfull-size baby crib as defined in section 1509.2(b)
of title 16 of the Code of Federal Regulations (including a
portable crib and a crib-pen described in paragraph (2) of
subsection (b) of that section).
(6) Sleep positioner.--The term ``sleep positioner'' means
any wedge, roll, prop, or pillow designed to encourage one
position during sleep.
SEC. 7. EFFECTIVE DATE.
The requirements of section 3 of this Act shall be effective 1 year
after the date of enactment of this Act | Infant Crib Safety Act - Amends the Federal Hazardous Substances Act to make it unlawful for any commercial user to manufacture, sell, or otherwise place in the stream of commerce any full-size or nonfull-size crib which was made before 1999, does not conform to the standards of this Act, or has any missing, loose, or broken components.
Makes it unlawful for any hotel, motel, or similar lodging facility to offer or provide such a crib.
Considers to be a banned hazardous product under the Consumer Product Safety Act any crib which does not conform to specified regulations in the Code of Federal Regulations and standards of the American Society for Testing Materials, unless labeled as not intended to be used for, and dangerous to, an infant.
Requires the Consumer Product Safety Commission (CPSC) to begin a rulemaking to include the requirements of the American Society for Testing Materials standards and to address any hazards due to crib and play yard durability.
Requires the CPSC to promulgate a consumer product safety rule to require that cribs manufactured and introduced into interstate commerce contain a label warning consumers against the use of soft bedding.
Includes in the definition of commercial user any person who manufactures or sells cribs or, by his or her occupation holds himself or herself out as having knowledge or skill peculiar to cribs, including child care facilities and family child care homes. Excludes from that definition an individual who sells a used crib at a one-time private sale. |
MIAMI (AP) — Five men who have been held for more than 13 years at the U.S. base at Guantanamo Bay, Cuba, have been released and sent to the United Arab Emirates, the Pentagon said Sunday.
FILE – In this March 30, 2010, file photo, reviewed by the U.S. military, a U.S. trooper stands in the turret of a vehicle with a machine gun, left, as a guard looks out from a tower at the detention... (Associated Press)
The five Yemeni men were accepted for resettlement in the Persian Gulf nation after U.S. authorities determined they no longer posed a threat, the Defense Department said in a statement. Their release brings the Guantanamo prison population to 107.
The released men, who arrived in the UAE on Saturday, were identified as Ali Ahmad Muhammad al-Razihi, Khalid Abd-al-Jabbar Muhammad Uthman al-Qadasi, Adil Said al-Hajj Ubayd al-Busays, Sulayman Awad Bin Uqayl al-Nahdi, and Fahmi Salem Said al-Asani.
None of the men had been charged with a crime but had been detained as enemy combatants. They could not be sent to their homeland because the U.S. considers Yemen too unstable to accept prisoners from Guantanamo. These are the first prisoners accepted by the UAE for resettlement.
President Barack Obama has reduced the number of prisoners by more than half since he took office. He had sought to close the detention center but faced opposition to Congress. The administration is now seeking to move detainees to the United States amid intense opposition. ||||| The Pentagon transferred five Yemeni detainees who had been held for more than a decade at the prison at Guantanamo Bay, Cuba, to the United Arab Emirates, U.S. officials announced Sunday.
The men, all of whom were once suspected of having ties to al-Qaeda, arrived in the UAE on Saturday, officials said.
Adil Said al-Busayss, 42, Khalid Abd al-Qadasi, 46, Ali Ahmad Muhammad al-Rahizi, 36, Sulaiman al-Nahdi, 40, and Fahmi al-Sani, 38, were captured in 2001 by Pakistani and Afghan forces and eventually turned over to the United States.
Because of the conflict in Yemen and congressional prohibitions on sending Yemenis back to their native country, the Obama administration has cemented agreements with other governments to accept the detainees.
[Issue of where to move Guantanamo detainees threatens closure plan]
Earlier this year, the United States transferred four Yemeni detainees at Guantanamo Bay to Oman and a fifth to Estonia. Late last year, the administration moved three Yemeni prisoners to Kazakhstan.
The Yemenis make up the single largest national group at the military detention facility. Sixty-four Yemenis remain at the prison, with 39 of them approved for release.
A total of 107 detainees remain at the facility, including 48 cleared for repatriation or resettlement in a third country.
President Obama has made closing the prison a priority, saying that militants use it as a recruiting tool and that it has harmed the image of the United States.
After receiving criticism for not moving quickly enough to resettle detainees, Defense Secretary Ashton B. Carter has signed off on 15 transfers since taking the top job at the Pentagon. Nine of those have taken place since September.
[Once deemed too dangerous to release, Saudi detainee is repatriated]
“The administration is showing that if it wants to close Guantanamo, it can, and it can do it the right way by releasing people and stop holding them without charge,” said Andrea Prasow, who follows detainee issues for Human Rights Watch. “I assume the message came down pretty clearly from the president to the secretary of defense that the time is now.”
The administration hopes to reduce the Guantanamo inmate population to below 100 by the end of the year as it races to complete a plan to close the prison and win the backing of Congress.
However, administration officials and Democrats in Congress have hinted recently that the president could unilaterally close the prison, believing it to be detrimental to national security.
Read more:
Does Guantanamo Bay have a cancer problem? Three military lawyers are dead.
Moroccan detained at Guantanamo Bay for more than 13 years is repatriated
Why the U.S. base at Guantanamo Bay is probably doomed | – Five Guantanamo Bay inmates who had been held without charge for almost 14 years have been transferred to the United Arab Emirates, the Defense Department announced Sunday, marking the first time that the Gulf nation has accepted Guantanamo inmates from other countries. The men, who had been designated as enemy combatants, were lower-level detainees who were captured after the battle of Tora Bora in Afghanistan in 2001, the New York Times reports. Like dozens of other Gitmo inmates, the men are Yemeni nationals who were still in US custody because their homeland was considered too unstable to release them to, reports the AP. There are now 107 detainees remaining at the facility, and sources tell the Times that up to 17 more transfers of lower-level detainees are in the works. The release of detainees has accelerated over the last few months as the Obama administration looks into ways of closing the facility permanently. "The administration is showing that if it wants to close Guantanamo, it can, and it can do it the right way by releasing people and stop holding them without charge," a Human Rights Watch spokeswoman tells the Washington Post. "I assume the message came down pretty clearly from the president to the secretary of defense that the time is now." (The Pentagon has been eyeing a facility in Colorado as a possible future home for Guantanamo inmates.) |
* 1 . goal of the paper . * in this paper , we consider applications of coherent risk measures to optimization ; optimality pricing ; equilibrium . the optimization problem is considered in three forms .
first we study what we call the _ agent - independent optimization_. it is in fact the markowitz - type optimization problem with variance replaced by a coherent risk measure , instead of variance .
the function @xmath0 with @xmath1 is , in fact , an example of a coherent risk measure ( see @xcite ) .
thus , in essence , semivariance is a particular case of the coherent risk . ]
i.e. a problem of the form @xmath2 where @xmath3 means the discounted p&l earned by a portfolio and @xmath4 is a coherent risk measure ( p&l means the profit&loss , i.e. the difference between the terminal wealth and the initial wealth ) .
let us remark that this problem was considered in @xcite , @xcite , @xcite .
is defined by a finite number of probabilistic scenarios , then the corresponding optimization problem becomes the one considered in the generalized neyman
pearson lemma ( see ( * ? ? ?
as opposed to these papers , we have at our disposal the notion of a _ generator _ introduced in @xcite . in terms of generators
, we are able to give a geometric solution of ( see figures 1 , 2 ) .
the model we are considering takes into account such market imperfections as cone portfolio constraints , transaction costs , and the ambiguity of the historic probability measure .
problem is the optimization problem for an investor whose capital evolves in a risk - free way .
however , an investor might have a risky endowment with a random terminal wealth @xmath5 ( @xmath5 might have a financial or a non - financial structure ; for example , it might be the terminal wealth of a firm producing some goods ) .
the investor trying to minimize his / her risk by trading in the market faces the problem @xmath6 note that this coincides with the superreplication problem for the ngd pricing ( see ( * ? ? ?
* subsect . 3.6 ) ) .
we study in two forms , which we call the _ global _ and the _ local single - agent optimization _ , respectively . on the financial side ,
the former pertains to a `` small '' investor , while the latter pertains to a `` big '' investor . for both of them
, we provide a geometric solution ( see figures 4 , 6 ) .
also , in ( * ? ? ?
* sect . 5 )
, we provide sufficient conditions for the uniqueness of a solution of various optimization problems .
after considering the optimization problem , we return to the pricing problem and apply the obtained results to the optimality pricing of contingent claims ( in the finance literature , this is typically referred to as reservation pricing ) .
again , we propose three forms of this technique .
they differ by the inputs they require and the assumptions behind them ( thus , of course , they produce different outputs ) . the first technique , which we call the _ agent - independent optimality pricing _
, might be considered as the limit case of the raroc - based ngd pricing technique introduced in @xcite .
a rather surprising outcome of this technique is that it provides ( typically ) a single fair price of a contingent claim for all agents ( under the strong assumption that all the agents are using the same historic measure @xmath7 and the same risk measure @xmath4 and all the agents are trying to maximize raroc defined through @xmath7 and @xmath4 ) .
another technique is called the _ single - agent optimality pricing_. it is , in fact , the coherent version of the classical utility - indifference pricing with the expected utility replaced by the coherent one . as an outcome
, this technique typically provides a single number , which means the price of a contingent claim that is fair for a particular agent ( it depends on the risk measure he / she is using and on his / her endowment ) .
then we consider one more technique called the _ multi - agent optimality pricing_. the idea is as follows .
we have a contingent claim and several agents , each employing his / her own coherent risk measure .
a price is said to be fair if it provides no trading opportunity , which would allow each agent to decrease his / her risk ( this is a modified form of the idea proposed in @xcite ) . as an outcome , this technique typically provides a whole interval of prices , which are fair for this group of agents ( in fact , this interval is the convex hull of fair prices for these agents produced by the previous technique ) . finally , we turn to the equilibrium problem .
one of the basic results of the classical economic theory is the equivalence between the pareto optimum ( known also as the `` soviet - type optimum '' ) and the competitive optimum ( known also as the `` western - type optimum '' ) ; see @xcite .
this result is established within the framework of the expected utility . in the present paper , we establish the analog of this result within the coherent utility framework .
this is done for two types of equilibrium : for the unconstrained one ( theorem [ ec7 ] ) and for the constrained one ( theorem [ ei5 ] ) .
a very important feature of coherent utility ( which is not shared by the expected utility ) is that it admits a rich duality theory .
thus , we not only establish the equivalence between different types of equilibrium , but also provide its dual description .
moreover , for the constrained equilibrium problem , we are able to provide an explicit geometric solution based on generators ( see figure 11 ) .
it yields the equilibrium price as well as the equilibrium portfolios of the agents . *
2 . structure of the paper . * section [ o ] deals with the optimization problem . in subsections [ og ] , [ gog ] , and [ log ] , we consider the three techniques described above . in subsection [ os ] , the obtained results are applied to the problem of finding the optimal structure of a firm consisting of several units .
the provided theorem states that a structure is optimal if and only if the _ raroc contributions _ of different units are the same . in subsection
[ upl ] , we apply the obtained results to the study of the liquidity effects in the framework of the ngd pricing considered in @xcite . section [ op ] is related to the optimality pricing .
subsections [ aiop ] , [ saop ] , and [ maop ] correspond to the three techniques described above . section [ e ] deals with equilibrium
. subsections [ ec ] and [ ei ] are , in fact , duals of each other : they consider the unconstrained and the constrained equilibria , respectively .
altogether , there are seven pricing techniques proposed in @xcite and in the present paper .
they are compared in the final section [ c ] .
we consider the model of ( * ? ? ?
* subsect . 3.2 ) .
thus , we are given a probability space @xmath8 , a convex weakly compact set @xmath9 , an @xmath10-closed convex set @xmath11 , and a convex set @xmath12 .
let us introduce the notation @xmath13{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{pd}}}{\mathsf{e}}_{\mathsf{q}}x$ ] , @xmath14{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}x$ ] , @xmath15 ( we understand @xmath16 according to the convention of ( * ? ? ?
2.3 ) ) .
* problem ( agent - independent optimization ) : * the problem is @xmath17 where @xmath18 . clearly , if @xmath19 is a cone , then this problem is obviously equivalent to the problem of finding @xmath20 and @xmath21 where @xmath22 { \displaystyle}\frac{{\mathsf{e}}_{\mathcal{pd}}x}{\rho(x ) } & \text{otherwise } \end{cases}\ ] ] with the convention @xmath23 , @xmath24 .
the only statement we can make at this level of generality is that @xmath25{0mm}{1mm}}}\biggl\{r>0:\bigl(\frac{1}{1+r}\,{\mathcal{pd}}+\frac{r}{1+r}\,{\mathcal{rd}}\bigr)\cap{\mathcal{r}}\ne{\emptyset}\biggr\},\ ] ] which follows from ( * ? ? ?
* th . 3.10 ) .
of course , in general @xmath26 need not exist .
we will now study the problem for a static model with a finite number of assets .
let @xmath27 , where @xmath28 , @xmath29 , and @xmath30 is a closed convex cone ( here we impose no conditions on @xmath31 ) .
let us introduce the notation ( see figure 1 ) @xmath32 where `` @xmath33 '' denotes the closure , and let @xmath34 denote the relative interior of @xmath35 .
( the set @xmath36 is the generator for @xmath37 and @xmath38 . )
the sets @xmath39 and @xmath36 are convex compacts , while @xmath35 is convex and closed . note that , for @xmath40 , @xmath41{0mm}{1mm}}}_{x\in e}{\langle}h , x - s_0{\rangle},\\ \label{of3 } u({\langle}h , s_1-s_0{\rangle } ) & = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in g}{\langle}h , x - s_0{\rangle}={\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in d}{\langle}h , x - s_0{\rangle}.\end{aligned}\ ] ] we will assume that @xmath42 .
this assumption is justified economically . indeed , if @xmath43 , then , in view of , @xmath44 for any @xmath45 ; if @xmath46 , then , in view of , there exists @xmath45 with @xmath47 ( provided that @xmath39 belongs to the relative interior of @xmath48 ) . for @xmath49 ,
we denote @xmath50 and set @xmath51 , @xmath52 note that @xmath53 is nonempty provided that @xmath54 . in the case , where @xmath55 , we set @xmath56 .
( 150,62)(-31,-19.5 ) ( 0,0 ) ( 74,12.5)@xmath39 ( 71,24)@xmath36 ( 70.5,34)@xmath35 ( 43.5,20.7 ) ( 28,24.5)@xmath57 ( 58,13.5)@xmath58 ( 62.5,23.5)@xmath59 ( 17.5,6)@xmath60 ( 10,16)@xmath61 ( 15,-15 ) [ of1 ] we have @xmath62 and @xmath63 .
` proof ` .
we will prove the statement for the case @xmath54 .
the proof for the case @xmath55 is similar .
take @xmath64 and set @xmath65 . if @xmath66 , then @xmath67{0mm}{1mm}}}_{x\in e}{\langle}h , x - s_0{\rangle}}{-{\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in d}{\langle}h , x - s_0{\rangle } } = \frac{{\langle}h , u - s_0{\rangle}}{-{\langle}h , t - s_0{\rangle } } = { \lambda}_*^{-1}.\ ] ] if @xmath68 , then there are three possibilities : @xmath69 is orthogonal to the smallest affine subspace containing @xmath35 ; @xmath70 ; @xmath71{0mm}{1mm}}}_{x\in d}{\langle}h , x{\rangle}<{\langle}h , t{\rangle}$ ] .
in the first case , @xmath72 . in the second case , @xmath73{0mm}{1mm}}}_{x\in e}{\langle}h , x - s_0{\rangle}<{\langle}h , u - s_0{\rangle},\qquad { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in d}{\langle}h , x - s_0{\rangle}\le{\langle}h , t - s_0{\rangle},\ ] ]
so that @xmath74 .
the third case is analyzed in a similar way .
@xmath75 as a corollary , in the case , where @xmath76 and @xmath77 , the solution to the optimization problem is found as follows .
let @xmath78 be the intersection of the ray @xmath79 ( in this case @xmath80 ) with the border of @xmath36 .
then @xmath81 and @xmath82 is @xmath83 in the case , where @xmath36 has a nonempty interior , @xmath84 is the set of inner normals to @xmath36 at the point @xmath78 .
( 150,52.5)(-80,-35 ) ( -28.5,-16 ) ( -22,-14)@xmath78 ( -3,-5)@xmath58 ( 4,-1.5)@xmath39 ( -14,0)@xmath59 ( 14,-1)@xmath36 ( -38,-30 ) ` important remark ` .
in order to find the solution of the optimization problem for the case @xmath76 , @xmath77 , one needs to know the generating set @xmath36 and the vector @xmath85 .
the empirical estimation of @xmath36 is a problem similar to the empirical estimation of volatility , and hence , it can be successfully accomplished .
however , the empirical estimation of the mean vector @xmath85 is known to be a very unpleasant problem because it is very close to 0 ( see the discussion in @xcite and the 20 s example in @xcite ) .
but it turns out that the well - known security market line relationship of sharpe @xcite helps to overcome this problem .
this relation states that @xmath86 where @xmath87 is the risk - free interest rate , @xmath88 are true ( not discounted ) prices , and @xmath89 is the price of the market portfolio at time @xmath90 .
hence , @xmath91 the constant here contains as a factor the expected excess return on the market portfolio , which is again hard to estimate . but note that for our purposes this unknown constant is not needed !
indeed , the geometric solution of the optimization problem presented above requires only the direction of the vector @xmath92 , and this depends only on @xmath93 .
the following example shows that in natural situations the set of optimal strategies @xmath59 might not be unique ( of course , the uniqueness of @xmath59 should be understood up to multiplication by a positive constant ) .
[ of2 ] let @xmath94 have a continuous distribution with @xmath95 and take @xmath96 ( so that the second asset is a call option on the first one ) .
let @xmath76 , @xmath97 be the determining set of @xmath98 of order @xmath99 ( see ( * ? ? ?
* ex . 2.5 ) ) and @xmath100 .
assume that @xmath101 .
it is easy to see that @xmath102 consists of a unique element @xmath103 , where @xmath104 is the @xmath99-quantile of @xmath94 .
the border of @xmath36 has an angle @xmath105 at the point @xmath106 ( see figure 3 ) .
. then @xmath108 .
@xmath75 ( 150,55)(-45,-17.5 ) ( -0.5,-7.3 ) ( 0,0)(1,0)70 ( 0,0)(0,1)35 ( 45.3,16.5)@xmath36 ( 0,1.5 ) ( 13,-4)@xmath78 ( 26.5,3)@xmath58 ( 39,10)@xmath39 ( 33,-4)@xmath109 ( -6.5,-15)*figure 3 . *
nonuniqueness of an optimal strategy let us now find the solution of the optimization problem in the gaussian case .
[ of3 ] let @xmath37 have gaussian distribution with mean @xmath110 and covariance matrix @xmath48 .
let @xmath76 , @xmath77 , and @xmath97 be the determining set of a law invariant coherent utility function @xmath38 that is finite on gaussian random variables .
assume that @xmath58 belongs to the relative interior of @xmath36 and @xmath111 .
there exists @xmath112 such that , for a gaussian random variable @xmath113 with mean @xmath114 and variance @xmath115 , we have @xmath116 .
let @xmath117 denote the image of @xmath118 under the map @xmath119 .
it is easy to see that @xmath120 we have @xmath121 with some @xmath122 .
it is easy to see that @xmath123 if and only if @xmath124 and , for any @xmath125 such that @xmath126 we have @xmath127 .
this means that @xmath128 with some constant @xmath129 .
thus , @xmath130 note that this set does not depend on @xmath38 !
it is easy to see that @xmath131 this equality can also be deduced from ( * ? ? ?
@xmath75 let @xmath8 be a probability space , @xmath132 be a convex set ( we assume that @xmath133 ) and let @xmath134 be the discounted p&ls produced by different components of some firm .
we will consider the problem @xmath135 where @xmath136 is a positive constant meaning the capital available to the whole firm . from the financial point of view , is the problem of the central management of the firm deciding which components should grow and which should shrink .
this is a particular case of the optimization problem of the previous subsection ( with @xmath76 , @xmath137 , and @xmath138 ) , so that we already have a geometric recipe to find the optimal solution . here
we will present an economic characterization of optimality .
we will consider an arbitrary convex cone constraint @xmath60 ( not only @xmath139 as in ) .
we assume that @xmath140 and that the generator @xmath36 given by is strictly convex , i.e. its interior is nonempty and its border contains no interval .
[ os1 ] we define the _ raroc contribution of @xmath3 to @xmath141 _ as @xmath142 where @xmath143 is the risk contribution ( see ( * ? ? ?
* subsect . 2.5 ) ) .
the raroc contribution is well defined provided that @xmath144 is well defined and @xmath145 .
` remarks ` . `
( i ) ` the raroc contribution may take on negative values . `
( ii ) ` we have @xmath146 . [ os2 ] if @xmath147 and @xmath148 then @xmath149 and all the elements of this equality are equal to @xmath150 .
conversely , if @xmath69 is an inner point of @xmath60 and @xmath149 , then is satisfied .
` proof ` .
denote @xmath151 by @xmath141 .
it is seen from ( * ? ? ?
2.16 ) that @xmath152 . repeating the arguments of the proof of ( * ? ?
* th . 2.12 ) , we get @xmath153 , where @xmath154 ( this point is unique due to the convexity of @xmath36 ) .
thus , is equivalent to : @xmath155 , where @xmath156 .
it is seen from the results of the previous subsection that this condition implies that @xmath157 . as @xmath158 , we get @xmath159 , so that @xmath160 .
conversely , if @xmath69 is an inner point of @xmath60 , then @xmath161 ( @xmath35 is given by ) .
recalling the results of the previous subsection , we get the second statement .
@xmath75 ` remark ` .
the additional assumption that @xmath69 is in the interior of @xmath60 is essential for the converse statement of theorem [ os2 ] . as an example , take @xmath162 , where @xmath163 is a fixed vector .
then clearly @xmath164 , but of course might be violated .
let @xmath8 be a probability space , @xmath38 be a coherent utility function with the weakly compact determining set @xmath31 , @xmath165 be a @xmath31-consistent convex cone , and @xmath166 . from the financial point of view , @xmath5 is the terminal endowment of some agent , while @xmath19 is the set of discounted p&ls the agent can obtain by trading .
* problem ( single - agent global optimization ) : * find @xmath167 and @xmath168 [ gog1 ] we have @xmath169{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}w,\ ] ] where @xmath71{0mm}{1mm}}}{\emptyset}:=\infty$ ] .
` proof ` . by (
3.4 ) , for any @xmath170 , @xmath171 ( the notation @xmath172 was introduced in ( * ? ? ?
* def . 3.1 ) ) .
fix @xmath173 . as @xmath19 is a cone
, we have @xmath174 for any @xmath45 . as @xmath19 contains zero , @xmath175 .
thus , @xmath176 and @xmath175 .
conversely , if @xmath177 and these two conditions are satisfied , then @xmath173 . we get @xmath178 and the result follows .
@xmath75 we will now study the problem for a static model with a finite number of assets .
let @xmath179 , where @xmath180 and @xmath30 is a closed convex cone ( here we impose no conditions on @xmath31 ) . for the case
@xmath181 , we provided a geometric solution of this problem in ( * ? ? ? * subsect .
3.6 ) . for an arbitrary @xmath182 ,
it is more complicated and is given below .
let us introduce the notation ( see figure 4 ) @xmath183{0mm}{1mm}}}\{{\lambda}\in{\mathbb{r}}:({\lambda}e+{\widetilde}{h}^*)\cap g\ne{\emptyset}\},\\ { \widetilde}n&=\{h\in{\mathbb{r}}^{d+1}:h^{d+1}=1\text { and } \exists a\in{\mathbb{r}}:\\ & \hspace*{7mm}\forall x\in{\lambda}_*e+{\widetilde}{h}^*,\:\forall y\in g,\ ; { \langle}h , x{\rangle}\le a\le{\langle}h , y{\rangle}\},\\ n&=\{h\in{\mathbb{r}}^d:(h,1)\in{\widetilde}n\}.\end{aligned}\ ] ] if @xmath55 , we set @xmath184 .
( 150,90)(-67,-37.5 ) ( -20.4,-16.2 ) ( 0,0)(1,0)45 ( 0,0)(0,1)50 ( 9,0.5)(0,2)20(0,1)1 ( 0,40)(2,0)5(1,0)1 ( -3,34 ) ( -4.5,34 ) ( 43,-4)@xmath118 ( -4,48)@xmath185 ( -3,8)@xmath186 ( 7,-4)@xmath59 ( 9,38.5)@xmath187 ( 15.5,34.8)@xmath36 ( 11,11)@xmath188 ( -3,-13.6)@xmath189 ( 0,16 ) ( -21,-30 ) [ gof1 ] we have @xmath190 and @xmath191 . `
fix @xmath192 . as @xmath36 is a convex compact and @xmath189 is convex and closed , there exist @xmath193 and @xmath194 such that , for any @xmath195 and any @xmath196 , we have @xmath197 .
as @xmath36 is compact , @xmath198 can be chosen in such a way that @xmath199 . since @xmath200
, we have @xmath201 . without loss of generality , @xmath202 .
then , for any @xmath203 , we have @xmath204 . as @xmath189 is a cone , for any @xmath203 , we have @xmath205 and @xmath206 .
let @xmath69 be the @xmath207-dimensional vector that consists of the first @xmath207 components of @xmath198 .
assume that @xmath208 .
then in the @xmath207-dimensional plane @xmath209 we can select a @xmath210-dimensional plane @xmath117 that separates @xmath198 from @xmath211 . consider the @xmath207-dimensional plane generated by the origin of @xmath118 and @xmath117 , and let @xmath212 be its normal .
then @xmath213 , while @xmath214 .
consequently , @xmath215 , but then we get a contradiction with the choice of @xmath198 . as a result ,
furthermore , @xmath216{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}}{\mathsf{e}}_{\mathsf{q}}(w+{\langle}h , x{\rangle } ) = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in g}{\langle}{\widetilde}h , x{\rangle}>{\lambda}.\ ] ] as @xmath192 has been chosen arbitrarily , we conclude that @xmath217 .
let us prove the reverse inequality .
we can assume that @xmath54 .
let @xmath218 .
fix @xmath40 and set @xmath219 .
then @xmath216{0mm}{1mm}}}_{x\in g}{\langle}{\widetilde}h , x{\rangle}\le{\langle}{\widetilde}h , x_0{\rangle}.\ ] ] we can write @xmath220 with @xmath221 . then @xmath222 .
thus , @xmath223 . as a result , @xmath190 .
let us prove the equality @xmath191 . in the case
@xmath55 , its left - hand side and its right - hand side are empty , so it is trivially satisfied
. assume now that @xmath54 .
let @xmath66 .
using the same arguments as above , we show that @xmath40 . for @xmath219
, there exists @xmath224 such that , for any @xmath225 and any @xmath196 , we have @xmath226 .
the same arguments as above show that @xmath227 .
consequently , @xmath216{0mm}{1mm}}}_{x\in g}{\langle}{\widetilde}h , x{\rangle}\ge a \ge{\lambda}_*.\ ] ] let @xmath40 be such that @xmath228 .
this means that , for @xmath219 , we have @xmath71{0mm}{1mm}}}_{x\in g}{\langle}{\widetilde}h , x{\rangle}\ge{\lambda}_*$ ] .
furthermore , for any @xmath229 , we have @xmath230 .
thus , @xmath231 , which means that @xmath66 .
@xmath75 [ gof2 ] * ( i ) * let @xmath77
. then @xmath232 , @xmath233 , and @xmath234{0mm}{1mm}}}\{x^{d+1}:x\in g_0\}$ ] , where @xmath235 .
the condition that there exists no @xmath45 with @xmath236 is equivalent to : @xmath237 . if @xmath238 , where @xmath239 denotes the relative interior of @xmath36 , then @xmath240 . if @xmath241 , then both cases @xmath240 and @xmath242 are possible ( see figure 5 ) . *
( ii ) * let @xmath138 .
then @xmath243 , @xmath244 , and @xmath234{0mm}{1mm}}}\{x^{d+1}:x\in g_-\}$ ] , where @xmath245 . @xmath75 ( 150,62.5)(-33,-25 ) ( -0.7,-10 ) ( 0,0)(1,0)35 ( 0,0)(0,1)35 ( 60,0)(1,0)35 ( 60,0)(0,1)35 ( 72,0.5)(0,1.95)15(0,1)1 ( 60,29.3)(2,0)6(1,0)1 ( 57.2,23.8 ) ( 56,23.7)@xmath246 ( 0,0 ) ( 60,0 ) ( 33,-4)@xmath118 ( 93,-4)@xmath118 ( -4,33)@xmath185 ( 56,33)@xmath185 ( 13,19)@xmath36 ( 73,19)@xmath36 ( -3,8)@xmath186 ( 57,8)@xmath186 ( 72.5,30)@xmath187 ( 71,-4)@xmath59 ( 0.5,-9)@xmath189 ( 60.5,-9)@xmath189 ( 7,-22.5 ) let @xmath8 be a probability space , @xmath38 be a coherent utility function with the weakly compact determining set @xmath31 , @xmath12 be a @xmath31-consistent convex set containing zero , and @xmath166 .
the financial interpretation is the same as above .
as opposed to subsection [ gog ] , we assume that @xmath247 and @xmath248 . from the financial point of view
, we have a `` big '' investor possessing a capital with the terminal wealth @xmath5 and considering several trading opportunities , each of which is small as compared to @xmath5 .
mathematically , we consider the following problem .
* problem ( single - agent local optimization ) : * find @xmath249\ ] ] and an element @xmath250 , for which @xmath251=u_*.\ ] ] the statement below shows that the problem posed above is equivalent to the problem of maximizing @xmath252{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_{\mathcal{d}}(y)}{\mathsf{e}}_{\mathsf{q}}x$ ] over @xmath19 .
[ log1 ] we have @xmath253 .
furthermore , @xmath26 solves if and only if @xmath254 .
` proof ` .
the inequality @xmath255{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_{\mathcal{d}}(w)}{\mathsf{e}}_{\mathsf{q}}(w+{\varepsilon}x)-u(w)\biggr)\biggr)\\ & = \limsup_{{\varepsilon}{\downarrow}0}{\varepsilon}^{-1}\sup_{x\in a}{\varepsilon}{\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_{\mathcal{d}}(w)}{\mathsf{e}}_{\mathsf{q}}x\\ & = \sup_{x\in a } u^c(x;w),\end{aligned}\ ] ] combined with ( * ? ? ?
* th . 2.16 ) , shows that @xmath256 .
the reverse inequality and the second statement follow immediately from ( * ? ? ?
* th . 2.16 ) .
@xmath75 thus , the problem of single - agent local optimization is equivalent to maximizing another coherent utility over @xmath19 ( namely , @xmath257 ) . we will now consider a problem of maximizing a coherent utility , which we still denote by @xmath38 , over @xmath19 for a static model with a finite number of assets .
let @xmath179 , where @xmath180 and @xmath258 is a convex compact ( here we impose no conditions on the determining set @xmath31 of @xmath38 ) .
let us introduce the notation ( see figure 6 ) @xmath259{0mm}{1mm}}}\{{\lambda}\ge0:{\lambda}{h}^*\cap g\ne{\emptyset}\},\\ n&=\begin{cases } \{h:\forall x\in{\lambda}_*{h}^*,\:\forall y\in g,\ ; { \langle}h , x{\rangle}\le{\lambda}_*\le{\langle}h , y{\rangle}\}&\text{if}\;\;{\lambda}_*>0,\\ { \emptyset}&\text{if}\;\;{\lambda}_*=0 .
\end{cases}\end{aligned}\ ] ] note that @xmath54 , @xmath240 , and @xmath260 .
( 150,65)(-61.5,-40 ) ( -21,-21 ) ( 0,0 ) ( -1,-4)@xmath261 ( 35.8,9.5)@xmath36 ( 3,9)@xmath60 ( -12.5,-11)@xmath61 ( -15,19)@xmath262 ( 13.5,7)@xmath59 ( -15,-35 ) [ lof1 ] we have @xmath263 and @xmath264 . ` proof ` .
let @xmath265 .
for @xmath66 , we have @xmath266{0mm}{1mm}}}_{x\in g}{\langle}h , x{\rangle}={\lambda}_*.\ ] ] for @xmath68 , we have @xmath267 , and consequently , @xmath268{0mm}{1mm}}}_{x\in g}{\langle}h , x{\rangle}<{\lambda}_*.\ ] ] the case @xmath269 is analyzed trivially .
@xmath75 let @xmath8 be a probability space , @xmath38 be a coherent utility function with the weakly compact determining set @xmath31 , and @xmath12 be a convex set containing zero .
we assume that there exists no @xmath45 with @xmath236 .
[ upl1 ] we define the _ upper _ and _ lower utility - based ngd price functions _ of a contingent claim @xmath270 as @xmath271{0mm}{1mm}}}\{x:\text{the model } ( \omega,{\mathcal{f}},{\mathsf{p}},{\mathcal{d}},a+v(f - x ) ) \text { satisfies the ngd}\},\quad v>0.\end{aligned}\ ] ] from the financial point of view , @xmath272 means the volume of a trade .
` remark ` .
if @xmath19 is a cone , then @xmath273{0mm}{1mm}}}\{x:\exists x\in a : u(x - f+x)\ge0\},\\ \underline{v}(f,\,\cdot\,)&\equiv\sup\{x:\exists x\in a : u(x+f - x)\ge0\}.\end{aligned}\ ] ] these are the upper and the lower prices , which were studied in ( * ? ?
* subsect .
thus , the investigation of @xmath274 and @xmath275 is meaningful only if @xmath19 does not have a cone structure .
this corresponds to the liquidity effects . in view of the equality @xmath276 , it is sufficient to study only the properties of @xmath277 .
[ upl2 ] let @xmath278 . *
( i ) * the function @xmath277 is increasing and continuous . *
( ii ) * we have @xmath279 * ( iii ) * we have @xmath280 if @xmath247 , then @xmath281 ` proof ` . *
( i ) * it follows from the equality @xmath282 that @xmath283 , where @xmath284 .
note that @xmath285 is finite due to the ngd and the condition @xmath278 .
fix @xmath286 , @xmath287 , @xmath288 $ ] and find @xmath289 such that @xmath290 , @xmath291 .
then @xmath292 consequently , @xmath285 is concave . as @xmath19 contains zero and
the ngd is satisfied , we have @xmath293 .
this leads to the desired statement . *
( ii ) * by proposition [ gog1 ] , @xmath294{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}(-v f ) = -v\sup_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}f,\ ] ] where `` @xmath295 '' denotes the cone hull .
take @xmath287 and find @xmath296 , @xmath297 such that @xmath298 as the function @xmath299 is concave and vanishes at zero , we have @xmath300 as @xmath287 has been chosen arbitrarily , we get @xmath301 combining this with the inequality @xmath302{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}(-vf+x ) = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}(-vf ) = -v\sup_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}{\mathsf{e}}_{\mathsf{q}}f,\ ] ] we get the desired statement . *
( iii ) * the first statement follows from the inequality @xmath303 the second statement is an obvious consequence of the equality @xmath304 .
@xmath75 ` remarks ` . `
( i ) ` if @xmath19 is a cone , then clearly @xmath305 . `
( ii ) ` if @xmath247 , then @xmath306{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}}f,\ ] ] which is the length of the ngd price interval in the absence of a market .
the difference @xmath307{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}}f\ ] ] is the length of the ngd price interval in the presence of a market .
thus , the ratio @xmath308 measures the `` closeness '' of a new instrument @xmath270 to those already existing in the market .
( 150,57.5)(-62,-20 ) ( -2,4.7 ) ( 0,0)(1,0)45 ( 0,0)(0,1)35 ( -0.5,5)(2,0)9(1,0)1 ( -0.5,29)(2,0)9(1,0)1 ( -0.5,11.3)(1,0)1 ( -0.5,22.7)(1,0)1 ( 43,-4)@xmath118 ( -4,33)@xmath185 ( 16.2,15.7)@xmath36 ( -13.5,4 ) ( -12,10 ) ( -12,22 ) ( -13.5,28 ) ( -9.5,-15 ) [ upl3 ] consider a static model with a finite number of assets , i.e. @xmath179 , where @xmath180 and @xmath258 is a convex bounded set .
assume that @xmath60 contains a neighborhood of zero .
consider the generator @xmath309 .
then @xmath310 note that these values do not depend on @xmath60 !
consider the model of ( * ? ? ?
* subsect .
thus , we are given a probability space @xmath8 , a convex weakly compact set @xmath9 , an @xmath10-closed convex set @xmath11 , and a convex set @xmath12 .
assume that @xmath311 , where @xmath312 .
it follows from ( * ? ? ?
* th . 3.10 )
that @xmath25{0mm}{1mm}}}\biggl\{r\ge0:\bigl(\frac{1}{1+r}\,{\mathcal{pd}}+\frac{r}{1+r}\,{\mathcal{rd}}\bigr)\cap{\mathcal{r}}\ne{\emptyset}\biggr\}\ ] ] and @xmath313 , where @xmath314 ( 150,62.5)(-45,-10 ) ( 0,0 ) ( 27,24)@xmath315 ( 28,32)@xmath316 ( 27,40)@xmath97 ( 63.5,34)@xmath317 ( 48.5,24.5)@xmath318 ( 5,-7.5)*figure 8 . *
the structure of @xmath319 [ aiop1 ] an _ agent - independent nbc price _ of a contingent claim @xmath270 is a real number @xmath212 such that @xmath320 where @xmath321 .
the set of the nbc prices will be denoted by @xmath322 .
this pricing technique corresponds to the agent - independent optimization .
a price @xmath212 is fair if adding to the market a new instrument with the initial price @xmath212 and the terminal price @xmath270 does not increase the optimal value in the optimization problem .
[ aiop2 ] for @xmath323 , @xmath324 ` proof ` .
if @xmath325 , then , by ( * ? ?
* th . 3.10 ) , there exists @xmath326 .
this means that @xmath327 and @xmath328 .
conversely , if @xmath329 with some @xmath327 , then , for any @xmath330 , we have @xmath174 , so that @xmath331 . due to ( * ? ? ?
* th . 3.10 ) ,
@xmath332 .
@xmath75 the following statement yields a more definite representation of @xmath319 .
[ aiop3 ] if @xmath333 , then @xmath334 ` proof ` .
take @xmath335 we have @xmath73{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{pd}}}{\mathsf{e}}_{\mathsf{q}}x_*+r_*{\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}x _ * \le{\mathsf{e}}_{{\mathsf{q}}_1}x_*+r_*{\mathsf{e}}_{{\mathsf{q}}_2}x _ * \le0\ ] ] ( the second inequality follows from the inclusion @xmath176 ) . combining this with the equality @xmath336{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{pd}}}{\mathsf{e}}_{\mathsf{q}}x_*}{-{\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}x _ * }
= r_*,\ ] ] we get @xmath73{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{pd}}}{\mathsf{e}}_{\mathsf{q}}x_*+r_*{\mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}x _ * \le{\mathsf{e}}_{{\mathsf{q}}_1}x_*+r_*{\mathsf{e}}_{{\mathsf{q}}_2}x_*.\ ] ] this means that @xmath337 and @xmath338 .
@xmath75 as a corollary , if @xmath339 and @xmath340 are singletons ( this is true , for instance , if @xmath76 , @xmath97 is the determining set of weighted v@r , and @xmath26 has a continuous distribution ; see @xcite ) , then @xmath317 can be removed from , i.e. @xmath341 but in general this equality might be violated as shown by the example below .
[ aiop4 ] let @xmath76 , @xmath97 be the determining set of tail v@r with @xmath342 , and @xmath343 , @xmath344 be independent random variables with @xmath345 , @xmath346 .
let @xmath347 . for any @xmath348 with @xmath349 ,
we have @xmath73{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}(h^1x^1+h^2x^2 ) \le{\mathsf{e}}_{\mathsf{p}}z(h^1x^1+h^2x^2 ) = h^1{\mathsf{e}}_{\mathsf{p}}zx^1 = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{rd}}}{\mathsf{e}}_{\mathsf{q}}x^1,\ ] ] where @xmath350 .
combining this with the equality @xmath351 , we get that @xmath352 .
on the other hand , there exists @xmath353 , for which @xmath354 .
thus , the set @xmath355 contains measures that do not belong to @xmath317 .
@xmath75 ` remark ` .
one of techniques for pricing in incomplete markets consists in finding the representative of the set of risk - neutral measures that is the closest one to @xmath7 in some sense ( typically the relative entropy or some other measure of distance is minimized ) .
note that the set @xmath319 is exactly the set of measures @xmath356 from @xmath317 that are the closest ones to @xmath315 , the `` distance '' being measured by @xmath73{0mm}{1mm}}}\biggl\{r:\exists{\mathsf{q}}_1\in{\mathcal{pd}},\,{\mathsf{q}}_2\in{\mathcal{rd } } : \frac{1}{1+r}\,{\mathsf{q}}_1+\frac{r}{1+r}\,{\mathsf{q}}_2={\mathsf{q}}\biggr\}.\ ] ] we will now study the problem for a static model with a finite number of assets . let @xmath27 , where @xmath28 , @xmath29 , and @xmath30 is a closed convex cone .
assume that @xmath357 .
let @xmath358 be a contingent claim .
let us introduce the notation ( see figure 9 ) @xmath359 ( 150,85)(-75,-53 ) ( -40,-24 ) ( -1.7,-1.5)@xmath360 ( 8.3,19.5)@xmath361 ( 30.3,19.7)@xmath362 ( 29.5,13.7)@xmath363 ( 28.5,7.8)@xmath364 ( 48,-34)@xmath118 ( -39,28)@xmath185 ( -14,-34)@xmath58 ( -55,-6)@xmath322 ( -35,-30)(1,0)85 ( -35,-30)(0,1)60 ( -11.7,-29.5)(0,2)25(0,1)1 ( -34.5,-5)(2,0)12(1,0)1 ( -35,-5 ) ( -24,-48 ) [ aiopf1 ] we have @xmath365{0mm}{1mm}}}\{r>0:{\widetilde}d_r\cap(\{s_0\}\times{\mathbb{r}})\ne{\emptyset}\},\\ \label{saopf2 } { i_{\text{\sl nbc}}}(f)&=\{x:(s_0,x)\in{\widetilde}d_{r_*}\}.\end{aligned}\ ] ] ` proof ` .
denote @xmath366 note that @xmath367 , @xmath368 , @xmath369 , and consequently , @xmath370 , @xmath371 . combining this with the results of subsection [ og ] , we get @xmath372{0mm}{1mm}}}\{r>0:d_r\ni s_0\ } = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}\{r>0:{\widetilde}d_r\cap(\{s_0\}\times{\mathbb{r}})\ne{\emptyset}\}.\ ] ]
furthermore , for any @xmath373 , @xmath374{0mm}{1mm}}}\{r>0:{\widetilde}d_r\ni(s_0,x)\}.\ ] ] this , combined with , proves .
@xmath75 to conclude this subsection , we find the form of @xmath322 in the gaussian case .
[ aiopf2 ] consider the setting of ( * ? ? ?
* ex . 3.13 ) . clearly , @xmath150 is the solution of the equation @xmath375 ( cf .
example [ of3 ] ) .
this , combined with the form of @xmath376 found in ( * ? ? ?
* ex . 3.13 ) , shows that @xmath322 consists of a unique point @xmath377 .
let us remark that this value coincides with the fair price of @xmath270 obtained as a result of the mean - variance hedging .
note that this value does not depend on @xmath38 !
@xmath75 let @xmath8 be a probability space , @xmath38 be a coherent utility function with the weakly compact determining set @xmath31 , @xmath165 be a @xmath31-consistent convex set containing zero , and @xmath166 .
the financial interpretation is the same as in subsection [ gog ] .
[ saop1 ] a _ single - agent nbc price _ of a contingent claim @xmath270 is a real number @xmath212 such that @xmath378 the set of the nbc prices will be denoted by @xmath322 .
this pricing technique corresponds to the global single - agent optimization .
a price @xmath212 is fair if adding to the market a new instrument with the initial price @xmath212 and the terminal price @xmath270 does not increase the optimal value in the optimization problem .
[ saop2 ] for @xmath278 , @xmath379 ` remark ` .
the set of the nbc prices is nonempty only if @xmath5 is optimal in the sense that @xmath380 .
however , if @xmath5 is not optimal , then , as seen from the proof of theorem [ saop2 ] , @xmath381 , so that still holds . `
proof of theorem [ saop2 ] .
` as @xmath19 contains zero and the function @xmath382 is concave for a fixed @xmath3 , the condition @xmath325 is equivalent to : @xmath383 by proposition [ gog1 ] , this is equivalent to : @xmath73{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}(a+a(x))}{\mathsf{e}}_{\mathsf{q}}w = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}}{\mathsf{e}}_{\mathsf{q}}w,\ ] ] where @xmath321 . clearly , the latter condition is equivalent to : @xmath384 . it is easy to verify that this is equivalent to : @xmath329 for some @xmath385 .
@xmath75 let us now provide a geometric representation of @xmath322 ( see figure 10 ) .
assume that @xmath386 ( the reasoning used above shows that this is equivalent to : @xmath387 ) .
consider the generator @xmath388 and the function @xmath389{0mm}{1mm}}}\{y:(x , y)\in g\}$ ] ( we set @xmath71{0mm}{1mm}}}{\emptyset}=+\infty$ ] ) .
( 150,92.5)(-45.5,-50 ) ( 11.7,-23 ) ( 0,0)(1,0)70 ( 0,0)(0,1)40 ( 12,-0.5)(0,2)11(0,1)1 ( 20,-0.5)(0,2)9(0,1)1 ( 35,0.5)(0,2)3(0,1)1 ( 50,-0.5)(0,2)9(0,1)1 ( 58,-0.5)(0,2)11(0,1)1 ( 35,0 ) ( 68,-3)@xmath212 ( -3,38.5)@xmath390 ( 33,14.5)@xmath36 ( 33,28.5)@xmath35 ( 23,11 ) ( 24,-6 ) ( 23.5,-10 ) ( 25.5,-17 ) ( 27,-24 ) ( -2.5,-40 ) [ saop3 ] for @xmath278 , @xmath391 ` proof ` .
it is sufficient to note that @xmath392 and @xmath393{0mm}{1mm}}}\{{\mathsf{e}}_{\mathsf{q}}w:{\mathsf{q}}\in{\mathcal{d}}\cap{\mathcal{r}}(a+a(x))\},\ ] ] where @xmath321 .
thus , @xmath394 if and only if @xmath384 , which , in view of theorem [ saop2 ] , is equivalent to the inclusion @xmath325 .
@xmath75 assume that @xmath5 is optimal in the sense that @xmath395 and suppose moreover that the set @xmath396 of the nbc prices based on @xmath31 and @xmath5 ( with @xmath397 ) consists of one point @xmath398 ( this condition is satisfied if the set @xmath399 is strictly convex ; see figure 10 ) .
it is seen from the proof of theorem [ saop2 ] that condition is equivalent to : @xmath387
. then it follows from theorem [ saop2 ] that @xmath400 ( we assume that @xmath278 ) . clearly , @xmath401 . as a result , @xmath402
so , in this situation @xmath19 can be eliminated .
this situation occurs naturally as shown , in particular , by the example below .
[ saop4 ] let @xmath38 be a law invariant coherent utility function that is finite on gaussian random variables .
assume that @xmath386 and that @xmath403 has a gaussian distribution .
there exists @xmath112 such that , for a gaussian random variable @xmath113 with mean @xmath114 and variance @xmath115 , we have @xmath116 .
clearly , @xmath404 , where @xmath405 is the nbc price based on @xmath31 and @xmath5 with @xmath397 .
using corollary [ saop3 ] , we deduce that @xmath405 consists of a single point @xmath406 . as @xmath322 is nonempty , it consists of the same point .
let @xmath8 be a probability space , @xmath407 be coherent utility functions with the weakly compact determining sets @xmath408 , @xmath165 be a convex set containing zero , and @xmath409 . from the financial point of view , @xmath410 , @xmath19 , and @xmath411 are the coherent utility function , the set of attainable p&ls , and the terminal endowment of the @xmath90-th agent , respectively .
we will assume that there exists a set @xmath412 such that , for any @xmath90 , @xmath413 .
we also assume that each @xmath411 is optimal in the sense that @xmath414 .
[ maop1 ] a real number @xmath212 is a _ multi - agent nbc price _ of a contingent claim @xmath270 if there exists no element @xmath415 such that @xmath416 for any @xmath90 .
the set of the nbc prices will be denoted by @xmath322 . from the financial point of view , a price @xmath212 is fair if adding to the market a new instrument with the initial price @xmath212 and the terminal price @xmath270 does not produce a trading opportunity that is attractive to all the agents .
[ maop2 ] for @xmath417 , @xmath418 where @xmath419 is the interval of the single - agent nbc prices based on @xmath420 , @xmath19 , @xmath411 .
` proof ` .
let @xmath325 .
fix @xmath421 .
it follows from the weak continuity of the maps @xmath422 that , for each @xmath423 , the set @xmath424 , where @xmath425 , is compact . clearly , @xmath426 is convex .
suppose that @xmath427 then there exists @xmath428 such that @xmath429 and @xmath71{0mm}{1mm}}}_{x\in g_n}{\langle}h , x{\rangle}>0 $ ] for each @xmath90 .
this means that @xmath71{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_n}{\mathsf{e}}_{\mathsf{q}}y>0 $ ] for each @xmath90 , where @xmath430 .
employing ( * ? ? ?
* th . 2.16 ) , we conclude that there exists @xmath287 such that @xmath431 for any @xmath90 .
the obtained contradiction shows that , for any @xmath421 , the set @xmath432 where @xmath433 , is nonempty . as the map
@xmath434 is weakly continuous for each @xmath435 , the set @xmath436 is closed with respect to the product of weak topologies . furthermore , any finite intersection of sets of this form is nonempty .
tikhonov s theorem ensures that @xmath437 is compact .
consequently , there exists a collection @xmath438 that belongs to each @xmath439 of this form .
then @xmath440 for any @xmath90 and any @xmath441 , which means that @xmath442 .
thus , the measure @xmath443 belongs to @xmath444 and @xmath328 .
now , let @xmath329 with @xmath443 , @xmath442 .
suppose that there exist @xmath45 , @xmath445 such that , for @xmath446 , we have @xmath447 for each @xmath90 .
due to the concavity of the function @xmath448 , we get @xmath449{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_n}{\mathsf{e}}_{\mathsf{q}}(w_n+{\varepsilon}y)-u_n(w_n)\biggr ) = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{x}}_n}{\mathsf{e}}_{\mathsf{q}}y.\end{aligned}\ ] ] consequently , @xmath450 for each @xmath90 , and therefore , @xmath451 .
but , on the other hand , @xmath176 , and therefore , @xmath452 .
the contradiction shows that @xmath325 .
let @xmath8 be a probability space , @xmath407 be coherent utility functions with the weakly compact determining sets @xmath408 , @xmath453 be convex cones such that @xmath454 is @xmath420-consistent for each @xmath90 , and let @xmath409 . from the financial point of view , @xmath410 , @xmath454 , and @xmath411 are the coherent utility function , the `` personal '' set of attainable p&ls , and the terminal endowment of the @xmath90-th agent , respectively .
let us introduce the notation @xmath455 .
[ ec1 ] the _ maximal overall utility _ is defined as @xmath456 where the sum is understood as @xmath457 if any of the summands equals @xmath457 .
[ ec2 ] we have @xmath458{0mm}{1mm}}}_{{\mathsf{q}}\in\bigcap_n\!{\mathcal{d}}_n\cap{\mathcal{r}}(a_n)}{\mathsf{e}}_{\mathsf{q}}w,\ ] ] where @xmath459 and @xmath71{0mm}{1mm}}}{\emptyset}:=\infty$ ] .
[ ec3 ] let @xmath407 be coherent utility functions with the weakly compact determining sets @xmath408 . then
, for any @xmath460 , @xmath461{0mm}{1mm}}}_{{\mathsf{q}}\in\bigcap_n\!{\mathcal{d}}_n}{\mathsf{e}}_{\mathsf{q}}x.\ ] ] ` remark ` .
the left - hand side of is called the _ convex convolution _ or the _ sup - convolution _ of @xmath407 ( see @xcite , ( * ? ? ?
thus , lemma [ ec3 ] states that it is a coherent utility function with the determining set @xmath462 if @xmath463 and it is identically equal to @xmath464 if @xmath465 .
` proof of lemma [ ec3 ] . ` in the case , where @xmath463 , this statement follows by induction from a result proved in ( * ? ? ?
assume now that @xmath465 .
find @xmath114 such that @xmath466 , while @xmath467 . by the hahn - banach theorem
, there exists @xmath468 such that @xmath469{0mm}{1mm}}}_{{\mathsf{q}}\in\bigcap_{n=1}^m{\mathcal{d}}_n}{\mathsf{e}}_{\mathsf{q}}z.\ ] ] according to the part of the lemma that has already been proved , there exist @xmath470 such that @xmath471 and @xmath472 . then @xmath473 .
consequently , the left - hand side of is identically equal to @xmath474 .
@xmath75 ` proof of proposition [ ec2 ] . ` for any @xmath475 such that @xmath476 , and any @xmath477 , we have @xmath478 ( to get the second inequality , we used the inclusions @xmath479 , @xmath480 ) . consequently ,
@xmath481{0mm}{1mm}}}_{{\mathsf{q}}\in\bigcap_n\!{\mathcal{d}}_n\cap{\mathcal{r}}(a_n ) } { \mathsf{e}}_{\mathsf{q}}w.\ ] ] let us prove the reverse inequality . clearly , it is sufficient to prove it for bounded @xmath411 ( since arbitrary @xmath482 can be approximated by bounded ones ) .
proposition [ gog1 ] and lemma [ ec3 ] combined together yield @xmath483{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}_n\cap{\mathcal{r}}(a_n)}{\mathsf{e}}_{\mathsf{q}}(w_n+y_n)\\ & = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{{\mathsf{q}}\in\bigcap_n\!{\mathcal{d}}_n\cap{\mathcal{r}}(a_n ) } { \mathsf{e}}_{\mathsf{q}}w.\end{aligned}\ ] ] the following example shows that the restriction @xmath484 in the definition of @xmath485 is essential for proposition [ ec2 ] and can not be eliminated .
[ ec4 ] let @xmath486 , @xmath487 , @xmath488 @xmath489 , where @xmath490 , @xmath491 , @xmath492 , and @xmath493 .
take @xmath494 , @xmath495 , @xmath491 . then @xmath496 and @xmath497 , so that @xmath498 on the other hand , @xmath499 and @xmath500 .
@xmath75 we now pass on to various definitions of equilibrium . from the financial point of view
, the pareto - type equilibrium corresponds to the global optimum , while the arrow - debreu - type equilibrium corresponds to the competitive optimum .
[ ec5 ] a _ pareto - type equilibrium _ is a collection @xmath501 @xmath502 such that @xmath503 ; @xmath484 , @xmath476 ; there do not exist @xmath504 satisfying ( a ) , ( b ) and such that @xmath505 it is easy to see from the translation invariance property ( @xmath506 ) that condition ( c ) is equivalent to : @xmath507 .
[ ec6 ] an _ arrow - debreu - type equilibrium _ is a collection @xmath508 , where @xmath509 , such that @xmath503 ; @xmath484 , @xmath476 , @xmath510 ( so that automatically @xmath480 ) ; for any @xmath90 , @xmath511 below the notation @xmath512 for @xmath53-dimensional random vectors @xmath513 and @xmath514 means that there exist @xmath515 such that @xmath516 and @xmath517 .
we denote @xmath518 [ ec7 ] assume that @xmath519 ( by proposition [ ec2 ] , this is equivalent to : @xmath520 ) .
let @xmath503 , @xmath484 , @xmath476 .
the following conditions are equivalent : @xmath521 is a pareto - type equilibrium ; there exist @xmath509 and @xmath512 such that @xmath522 is an arrow - debreu - type equilibrium .
if these conditions are satisfied , then @xmath523 if each @xmath454 is a linear space , then ( i ) , ( ii ) are equivalent to : @xmath524 . moreover , in this case @xmath525 ` proof ` .
_ _ step 1 . _ _ let us prove the implication ( i)@xmath526(ii ) . take @xmath527 ( this set is nonempty due to ( * ? ? ? * prop .
2.9 ) ) . using proposition [ ec2 ] ,
we can write @xmath528 ( note that the expectation operator understood in the sense of ( * ? ? ? * def .
2.3 ) has the property @xmath529 ) . since the left - hand side and the right - hand side of the above inequality coincide , we get @xmath530 for any @xmath90
. we can find @xmath512 such that @xmath531 for any @xmath90 .
then , for any @xmath90 , @xmath532 , and @xmath533 such that @xmath534 , we have @xmath535 thus , @xmath522 is an arrow - debreu - type equilibrium . _
_ let us prove the implication ( ii)@xmath526(i ) .
suppose that there exist @xmath536 and @xmath537 with @xmath538 such that @xmath539 fix @xmath90 and suppose that @xmath540
. by the hahn - banach theorem , there exists @xmath541 such that @xmath542{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}_n\cap{\mathcal{r}}(a_n)}{\mathsf{e}}_{\mathsf{q}}\eta$ ] . according to proposition [ gog1 ]
, there exists @xmath532 such that @xmath543 .
this means that @xmath544
. then @xmath545{}\infty.\ ] ] in view of proposition [ ec2 ] , the condition @xmath519 implies that @xmath546 .
then , for any @xmath547 , we have @xmath548 which contradicts .
thus , @xmath477 .
in particular , @xmath480 , so that we can find @xmath549 such that @xmath550 for any @xmath90 . then @xmath551 which contradicts
. _ step 3 .
_ it was shown in step 1 that @xmath552 let us prove the reverse inclusion .
take @xmath553 and find @xmath512 such that @xmath522 is an arrow - debreu - type equilibrium .
it was shown in step 2 that @xmath477 . applying proposition [ gog1 ] to the @xmath420-consistent convex cone @xmath554 , we get @xmath555 thus , @xmath556 an application of theorem [ ec3 ] completes the proof
. _ step 4 . _
assume that each @xmath454 is linear and let us prove the inclusion @xmath557 take @xmath356 from the left - hand side of this inclusion . find @xmath512 such that @xmath531 for any @xmath90 .
clearly , @xmath558 , so that @xmath559 as @xmath560 , we have ( by the definition of @xmath561 ) that @xmath562 .
furthermore , ( by the definition of @xmath317 ) @xmath563 , so that @xmath564 . for any @xmath90 , @xmath532 , and @xmath533 such that @xmath534
, we have @xmath565 ( in the second inequality , we used the linearity of @xmath454 ) , so that @xmath522 is an arrow - debreu - type equilibrium .
_ step 5 .
_ assume that each @xmath454 is linear and let us prove the inclusion @xmath566 take @xmath553 and find @xmath512 such that @xmath522 is an arrow - debreu - type equilibrium .
it was shown in step 2 that @xmath477 . applying and proposition [ gog1 ] , we get @xmath567 consequently , @xmath568 for any @xmath90 , which means that @xmath569 . @xmath75 the assumption that each @xmath454 is linear is essential for the second part of theorem [ ec7 ] as shown by the following example . [ ec8 ]
let @xmath486 , @xmath487 , @xmath570 ( i.e. @xmath571 , @xmath572 consist of random variables that are identically equal to a negative constant ) , and @xmath493 .
take @xmath573 , @xmath574 .
then @xmath575 , but clearly @xmath521 is not a pareto - type equilibrium .
@xmath75 by theorem [ ec7 ] , the set @xmath576 does not depend on @xmath521 .
we call it the set of _ equilibrium measures _ and denote by @xmath577 ( theorem [ ec7 ] yields the representation @xmath578 ) . from the financial point of view
, @xmath577 is the set of equilibrium price systems .
thus , it is natural to define the set of _ unconstrained equilibrium prices _ of a contingent claim @xmath270 simply as @xmath579 .
let @xmath410 , @xmath420 , @xmath454 , and @xmath411 be the same as in the previous subsection .
let @xmath580 be a @xmath207-dimensional random vector whose components belong to @xmath581
. from the financial point of view , there are @xmath207 financial contracts that can be exchanged between the agents , and @xmath582 means the payoff of the @xmath583-th contract .
( there is no relation between @xmath580 and @xmath454 ; @xmath454 means the set of p&ls that can be obtained by the @xmath90-th agent without trading the assets @xmath584 . )
[ ei1 ] the _ maximal overall utility _ is defined as @xmath585 where the sum is understood as @xmath457 if any of the summands equals @xmath457 .
let us introduce the notation @xmath586{0mm}{1mm}}}\{y:(x , y)\in{\widetilde}g_n\},\quad x\in g_n,\\ g&=\bigcap_{n=1}^n g_n,\\ f(x)&=\sum_{n=1}^n f_n(x),\quad x\in g.\end{aligned}\ ] ] [ ei2 ] we have @xmath458{0mm}{1mm}}}_{x\in g}f(x),\ ] ] where @xmath71{0mm}{1mm}}}{\emptyset}:=\infty$ ] . `
proof ` . by proposition [ gog1 ]
, we have for any @xmath587 , @xmath588{0mm}{1mm}}}_{{\mathsf{q}}\in{\mathcal{d}}_n\cap{\mathcal{r}}(a_n)}{\mathsf{e}}_{\mathsf{q}}(w_n+{\langle}h_n , s{\rangle})\\ & = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in{\widetilde}g_n}{\langle}(h_n,1),x{\rangle}\\ & = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in g_n}({\langle}h_n , x{\rangle}+f_n(x)).\end{aligned}\ ] ] standard results of convex analysis ( see ( * ? ? ?
16.4 ) ) yield @xmath589{0mm}{1mm}}}_{x\in g_n}({\langle}h_n , x{\rangle}+f_n(x ) ) = { \mathop{\rm inf\rule[-0.8mm]{0mm}{1mm}}}_{x\in g}f(x).\ ] ] we now pass on to various definitions of equilibrium .
[ ei3 ] a _ pareto - type equilibrium _ is a collection @xmath590 @xmath591 such that @xmath503 ; @xmath587 , @xmath592 ; there do not exist @xmath593 satisfying ( a ) , ( b ) and such that @xmath594 it is easy to see from the translation invariance property ( @xmath506 ) that condition ( c ) is equivalent to : @xmath595 .
[ ei4 ] an _ arrow - debreu - type equilibrium _ is a collection @xmath596 , where @xmath597 , such that @xmath503 ; @xmath587 , @xmath592 ; for any @xmath90 , @xmath598 let us introduce the notation @xmath599 [ ei5 ] assume that @xmath519 ( by proposition [ ei2 ] , this is equivalent to : @xmath600 ) .
let @xmath503 , @xmath587 , @xmath592 .
the following conditions are equivalent : @xmath601 is a pareto - type equilibrium ; there exists @xmath597 such that @xmath596 is an arrow - debreu - type equilibrium . if these conditions are satisfied , then @xmath602 if each @xmath454 is a linear space , then ( i ) , ( ii ) are equivalent to : @xmath603 . moreover , in this case @xmath604 ` proof ` .
_ _ step 1 . _ _ let us prove the implication ( i)@xmath526(ii ) . take @xmath605 .
using proposition [ ei2 ] , we can write @xmath606{0mm}{1mm}}}_{x\in{\widetilde}g_n}{\langle}(h_n,1),x{\rangle}\\ & \le\sum_{n=1}^n(f_n(p)+{\langle}h_n , p{\rangle } ) = f(p ) = m.\end{aligned}\ ] ] as the left - hand side and the right - hand side of this inequality coincide , we get @xmath607 for any @xmath90 . thus ,
for any @xmath90 , @xmath532 , and @xmath608 , we have @xmath609 thus , @xmath596 is an arrow - debreu - type equilibrium .
_ step 2 . _
the implication ( ii)@xmath526(i ) follows from the inequality : for any @xmath536 and @xmath610 with @xmath611 , we have @xmath612 _ step 3 .
_ it was shown in step 1 that @xmath613 let us prove the reverse inclusion .
take @xmath614 .
fix @xmath90 and suppose that @xmath615 .
then there exists @xmath608 such that @xmath616{0mm}{1mm}}}_{x\in g_n}{\langle}\eta , x{\rangle}$ ] . according to proposition [ gog1 ]
, there exists @xmath532 such that @xmath617 .
then @xmath618{}\infty.\ ] ] in view of proposition [ ei2 ] , the condition @xmath519 implies that @xmath546 .
then , for any @xmath619 , we have @xmath620 which contradicts .
thus , @xmath621 . using proposition [ gog1 ] ,
we can write @xmath622{0mm}{1mm}}}_{x\in g_n}(f_n(x)+{\langle}\eta , x - p{\rangle})\\ & = \sum_{n=1}^n f_n(p)=f(p).\end{aligned}\ ] ] an application of proposition [ ei2 ] completes the proof .
_ step 4 .
_ assume that each @xmath454 is linear and let us prove the inclusion @xmath623 take @xmath624 from the left - hand side of this inclusion .
using the same arguments as in the proof of ( * ? ? ?
2.9 ) , we can find for every @xmath90 a measure @xmath625 such that @xmath626 ( using the @xmath420-consistency of @xmath454 , it is easy to check that @xmath627 is @xmath10-closed , so this set is weakly compact )
. then @xmath628 as @xmath629 , we have ( by the definition of @xmath561 ) that @xmath630 .
furthermore , ( by the definition of @xmath317 ) @xmath631 , so that @xmath632 .
for any @xmath90 , @xmath532 , and @xmath608 , we have @xmath633 ( in the second inequality , we used the linearity of @xmath454 ) , so that @xmath596 is an arrow - debreu - type equilibrium . _ step 5 . _
assume that each @xmath454 is linear and let us prove the inclusion @xmath634 take @xmath614 .
it was shown in step 3 that @xmath621 . using the same arguments as in the proof of (
2.9 ) , we can find for every @xmath90 a measure @xmath635 such that @xmath636 and @xmath637 . applying proposition [ gog1 ] ,
we get @xmath638{0mm}{1mm}}}_{x\in g_n}(f_n(x)+{\langle}\eta , x - p{\rangle})\\ & = \sup_{\xi\in a_n,\,\eta\in{\mathbb{r}}^d}u_n(w_n+\xi+{\langle}\eta , s - p{\rangle})\\ & = u_n(w_n+x_n+{\langle}h_n , s - p{\rangle})\\ & \le{\mathsf{e}}_{{\mathsf{q}}_n}(w_n+x_n+{\langle}h_n , s - p{\rangle})\\ & \le{\mathsf{e}}_{{\mathsf{q}}_n}w_n = f_n(p).\end{aligned}\ ] ] consequently , @xmath639 for any @xmath90 , which means that @xmath640 . @xmath75 let @xmath641 denote the relative interior of @xmath426 , and , for @xmath642 , we denote @xmath643{0mm}{1mm}}}_{x\in{\widetilde}g_n}{\langle}(\eta,1),x{\rangle}\bigr\}.\ ] ] if @xmath644 has a nonempty interior , then @xmath645 is the set of vectors @xmath608 such that @xmath646 is an inner normal to @xmath644 at the point @xmath647 .
( 150,92.5)(-80,-40 ) ( -40.5,-4.2 ) ( -45,0)(1,0)95 ( -45,0)(0,1)50 ( -15,0.5)(0,1.95)10(0,1)1 ( -10,0.5)(0,1.95)22(0,1)1 ( -3,0.5)(0,2)15(0,1)1 ( 0,0.5)(0,1.95)17(0,1)1 ( 3,0.5)(0,2)10(0,1)1 ( 10,0.5)(0,1.95)22(0,1)1 ( 15,0.5)(0,1.9)5(0,1)1 ( -44.5,32.8)(1.95,0)23(1,0)1 ( -3,30)(2,0)2(1,0)1 ( 0,20)(2,0)2(1,0)1 ( -2.5,14.7 ) ( -0.8,25 ) ( -3.2,14.7 ) ( 1,25 ) ( -15,0 ) ( 0,0 ) ( 15,0 ) ( 48,-3)@xmath212 ( -48,48.5)@xmath390 ( -32,16)@xmath648 ( 22,6)@xmath649 ( -9,41 ) ( -27.5,35.3)@xmath650 ( 22.5,24.3)@xmath651 ( -44,-7 ) ( -5,-8 ) ( 19.5,-7 ) ( -7.5,1)@xmath652 ( 3.5,1)@xmath653 ( -50,32)@xmath485 ( -52.5,-27.5 ) [ ei6 ] assume that @xmath654 .
take @xmath605 .
then there exist @xmath655 such that @xmath592 .
assume that , for each @xmath90 , there exists @xmath656 .
then @xmath657 is an arrow - debreu - type equilibrium .
conversely , any arrow - debreu - type equilibrium has such a form .
` proof ` . denote @xmath658{0mm}{1mm}}}_{x\in g_n}(f_n(x)+{\langle}\eta , x{\rangle})$ ] , @xmath608 .
standard results of convex analysis ( see ( * ? ? ?
16.4 ) ) guarantee that there exist @xmath659 such that @xmath592 and @xmath660 .
it follows from the line @xmath661 that @xmath655 for any @xmath90 . by proposition [ gog1 ] , @xmath662{0mm}{1mm}}}_{x\in{\widetilde}g_n}{\langle}(h_n,1),x{\rangle}\\ & = f_n^*(h_n ) = f_n(p)+{\langle}h_n , p{\rangle},\quad n=1,\dots , n.\end{aligned}\ ] ] consequently , for any @xmath90 , @xmath532 , and @xmath608 , @xmath663{0mm}{1mm}}}_{x\in{\widetilde}g_n}{\langle}(\eta,1),x{\rangle}-{\langle}\eta , p{\rangle}\\ & = f_n^*(\eta)-{\langle}\eta , p{\rangle}\le f_n(p)\\ & = u_n(w_n+x_n+{\langle}h_n , s - p{\rangle}),\end{aligned}\ ] ] so that @xmath596 is an arrow - debreu - type equilibrium .
conversely , let @xmath596 be an arrow - debreu - type equilibrium . according to proposition [ ei2 ] , @xmath605 . using the same arguments as in step 1 of the proof of theorem [ ei5 ]
, we deduce that @xmath655 for any @xmath90 .
the inclusion @xmath656 is clear from the definition of the arrow - debreu - type equilibrium .
@xmath75 by theorem [ ei5 ] , the set @xmath664 does not depend on @xmath521 .
we call it the set of _ equilibrium prices _ and denote by @xmath39 ( theorem [ ei5 ] yields the representation @xmath665 ) . from the financial point of view
, @xmath39 is the set of equilibrium price vectors for the multidimensional contract @xmath580 .
if @xmath666 is a one - dimensional contingent claim , we call @xmath39 the set of _ constrained equilibrium prices _ of @xmath270 and denote it by @xmath667 .
in @xcite and in the present paper , we proposed seven different pricing techniques .
they differ by the inputs they require and by the ideas behind them .
these techniques are compared by figure 12 and by table 1 .
( 150,110)(2,-55 ) ( 0,-40 ) ( 52.5,-40)utility - based ngd interval ( 50.8,-30)raroc - based ngd interval ( 53.5,-20)multi - agent nbc interval ( 50,-10)agent - independent nbc price ( 55,41)single - agent nbc prices ( 47,20)unconstrained ( 50,16)equilibrium ( 55,12)price ( 80,20)constrained ( 81,16)equilibrium ( 86,12)price ( 20,-55)*figure 12 . * the form of fair prices provided by various techniques | * abstract . *
this paper is the continuation of @xcite and deals with further applications of coherent risk measures to problems of finance .
first , we study the optimization problem . three forms of this problem are considered .
furthermore , the results obtained are applied to the optimality pricing . again
three forms of this technique are considered .
finally , we study the equilibrium problem both in the unconstrained and in the constrained forms .
we establish the equivalence between the global and the competitive optima and give a dual description of the equilibrium .
moreover , we provide an explicit geometric solution of the constrained equilibrium problem . most of the results are presented on two levels : on a general level the results have a probabilistic form ; for a static model with a finite number of assets , the results have a geometric form .
* key words and phrases .
* coherent risk measures , equilibrium , extreme measures , generating set , liquidity , no better choice , optimality pricing , optimization .
* equilibrium with coherent risk * _ * a.s .
cherny * _ _ moscow state university , _ + _ faculty of mechanics and mathematics , _ + _ department of probability theory , _ + _ 119992 moscow , russia . _
+ ` e - mail : [email protected] ` + ` webpage : http://mech.math.msu.su/~cherny ` |
WikiLeaks has announced the release of the "Kissinger Cables," a set of 1.7 million U.S. diplomatic records, dating from 1973 to 1976.
The Kissinger Cables are comprised of more than 1.3 million full diplomatic cables and 320,000 originally classified records, WikiLeaks claims. The collection also includes 205,901 records relating to former U.S. Secretary of State, Henry Kissinger (hence the name).
All in all, the Kissinger Cables contain around 700 million words, which makes it five times as large as Cablegate — WikiLeaks' release of more than 250,000 U.S. diplomatic cables in November 2010.
"The collection covers US involvements in, and diplomatic or intelligence reporting on, every country on Earth. It is the single most significant body of geopolitical material ever published," said WikiLeaks founder and publisher Julian Assange.
According to WikiLeaks, most of these records were reviewed by the U.S. Department of State's 25-year declassification process, but their declassification is "running 12 years late."
The release is a part of WikiLeaks' launch of the "WikiLeaks Public Library of US Diplomacy (PlusD)," a searchable collection of U.S. "confidential or formerly confidential" diplomatic communications. WikiLeaks claims it now holds 2 million records comprised of around 1 billion words.
Image courtesy of Flickr/Matt Erasmus ||||| WikiLeaks releases more than half a million US diplomatic cables from the momentous year of 1979
By Julian Assange
Today, 28 November 2016, marking the six-year anniversary of "Cablegate", WikiLeaks expands its Public Library of US Diplomacy (PLUSD) with more than half a million (531,525) diplomatic cables from 1979.
If any year could be said to be the "year zero" of our modern era, 1979 is it.
In the Middle East, the Iranian revolution, the Saudi Islamic uprising and the Egypt-Israel Camp David Accords led not only to the present regional power dynamic but decisively changed the relationship between oil, militant Islam and the world.
The uprising at Mecca permanently shifted Saudi Arabia towards Wahhabism, leading to the transnational spread of Islamic fundamentalism and the US-Saudi destabilisation of Afghanistan.
Osama bin Laden would leave his native Saudi Arabia for Pakistan to support the Afghan Mujahideen.
The invasion of Afghanistan by the USSR would see Saudi Arabia and the CIA push billions of dollars to Mujahideen fighters as part of Operation Cyclone, fomenting the rise of al-Qaeda and the eventual collapse of the Soviet Union.
The 1979 current of Islamification spread to Pakistan where the US embassy was burned to the ground and Pakistan Prime Minister Zulfikar Ali Bhutto was executed.
The Iranian hostage crisis would go on to fatally undermine Jimmy Carter's presidency and see the election of Ronald Reagan.
Saddam Hussein? Took power in 1979.
The rise of al-Qaeda eventually bore the September 11, 2001 attacks in the United States, enabling the US invasion of Afghanistan and Iraq and over a decade of war, leaving, at its end, the ideological, financial and geographic basis for ISIS.
The Iranian revolution and Saddam Hussein's rise to power and the subsequent Iran-Iraq War would connect with the 1979 Sandinista revolution in Nicaragua to produce the Iran-Contra affair and the indictment of 12 US administration officials including Secretary of Defense Caspar Weinberger.
Elsewhere, Thatcher won in the UK, Rhodesia became Zimbabwe, Idi Amin fled Uganda and the ANC made the decision to militarily resist Apartheid.
In the United States, the Three Mile Island nuclear incident led to a turning away from the construction and development of new nuclear reactors, increasing the reliance on oil and coal for decades.
While the 1979 SALT II agreements made some progress in reducing the risk of nuclear war, nuclear preparations and testing were stepped up elsewhere. The US decided to place Pershing and Cruise missiles in Europe and a South African/Israeli nuclear test was detected by US early warning satellites.
China officially came in from the cold and Deng Xiaoping visited the United States in a defining strategic re-orientation by both states.
In 1979 it seemed as if the blood would never stop. Dozens of countries saw assassinations, coups, revolts, bombings, political kidnappings and wars of liberation.
In the extremes and contestations of the Cold War, 1979 saw some grim culture to go with the times: ACDC produced “Highway to Hell”, Francis Ford Coppola gave us Apocalypse Now, while for Pink Floyd it was just “Another Brick in the Wall”.
The Carter Cables III bring WikiLeaks' total published US diplomatic cable collection to 3.3 million documents.
What follows are some example areas of events from 1979 covered in the new documents.
January
1 US and China resume diplomatic relations
7 Pol Pot deposed following Vietnam's invasion of Cambodia
16 Shah flees Iran
28 China's leader Deng Xiaoping visits US
February
1 Khomeni returns to Iran
3 Khomeni creates Council of Islamic Revolution
10 Iranian Revolution
17 China invades northern Vietnam
18 Snow in the Sahara
25 Rhodesia bombs Angola ZIPRA camps in Operation Vanity
March
13 Coup in Grenada
15 Herat uprising in Afghanistan
26 Anwar Sadat and Menachem Begin sign Egypt-Israel peace treaty
28 Three Mile Island nuclear incident
30 British Conservative MP Airey Neave assassinated with car bomb
April
1 Iran overthrows Shah officially: Iran becomes the Islamic Republic through national referendum
2 Anthrax epidemic in Russia following biological weapons plant accident
4 Pakistan Prime Minister Zulfikar Ali Bhutto is executed
11 Tanzanian invasion of Uganda; revolt against Idi Amin; fall of Kampala
17 IRA bombing kills four Ulster Constabulary at Bessbrook, Northern Ireland
May
1 Greenland granted partial autonomy from Denmark
4 Margaret Thatcher elected UK Prime Minister
25 American Airlines flight 191 explodes near Chicago
June
4 Canada's Pierre Trudeau defeated; Coup in Ghana
18 Carter and Brezhnev sign Salt II arms treaty
25 Baader-Meinhof assassination attempt in Belgium of NATO Supreme Allied Commander
July
16 Saddam Hussein takes power in Iraq
21 Sandinistas defeat Samoza in Nicaragua
28 Indian PM Charan Singh elected
August
3 Equatorial Guinea coup
5 Polisario Front signs peace agreement with Mauritania
11 Morocco annexes Western Sahara territory previously controlled by Mauritania
23 South Africa bombs ZIPRA camps in Zambia in Operation Motel
27 Eighteen UK soldiers killed by IRA at Warrenpoint in County Down, Northern Ireland
September
3-9 Summit of the Non-Aligned Movement
14 USColombia extradition treaty negotiated, opposed by Pablo Escobar cartel
20 Bokassa overthrown in Central African Republic via France's Operation Barracuda
22 South African and Israeli nuclear test detected by US Vela satellite in southern Atlantic Ocean
29 President Nguema of Equatorial Guinea executed
October
1 First democratic elections in Nigeria; the birth of the second republic
15 Coup in El Salvador
16 French town of Nice hit by tsunami
26 President of South Korea Park Chung-hee assassinated
November
4 Iranian hostage crisis begins; 3,000 Iranian students raid US embassy, 66 hostages taken
14 Carter issues Executive Order 12170 freezing all Iranian assets
15 Anthony Blunt outed as the “Fourth Man” in Cambridge spy ring
20 Hajj hostage crisis in Saudi Arabia
21 US embassy in Islamabad set afire after false reports from Khomeni that US occupied Mecca
December
11 Three of the ANC's "Pretoria Six" escape from Pretoria Central Prison (Moumbaris, Jenkin and Lee)
12 Decision to locate US Cruise and Pershing missiles in Europe
12 South Korea military coup
21 Lancaster House agreement signed, leading to the creation of Zimbabwe and the election of Mugabe
24 USSR invasion of Afghanistan
Search the Carter Cables III here.
WikiLeaks releases more than half a million US diplomatic cables from 1978
By Julian Assange
Today WikiLeaks has released more than half a million US State Department cables from 1978. The cables cover US interactions with, and observations of, every country.
1978 was an unusually important year in geopolitics. The year saw the start of a great many political conflicts and alliances which continue to define the present world order, as well as the rise of still-important personalities and political dynasties.
The cables document the start of the Iranian Revolution, leading to the stand-off between Iran and the West (1979 – present); the Second Oil Crisis; the Afghan conflict (1978 – present); the Lebanon–Israel conflict (1978 – present); the Camp David Accords; the Sandinista Revolution in Nicaragua and the subsequent conflict with US proxies (1978 – 1990); the 1978 Vietnamese invasion of Cambodia; the Ethiopian invasion of Eritrea; Carter's critical decision on the neutron bomb; the break-up of the USSR's nuclear-powered satellite over Canada, which changed space policy; the US "playing the China card" against Russia; Brzezinski's visit to China, which led to the subsequent normalisation of relations and a proxy war in Cambodia; with the US, UK, China and Cambodia on one side and Vietnam and the USSR on the other.
Through 1978, Zbigniew "Zbig" Brzezinski was US National Security Advisor. He would become the architect of the destabilisation of Soviet backed Afghanistan through the use of Islamic militants, elements of which would later become known as al-Qaeda. Brzezinski continues to affect US policy as an advisor to Obama. He has been especially visible in the recent conflict between Russia and the Ukraine.
WikiLeaks' Carter Cables II comprise 500,577 US diplomatic cables and other diplomatic communications from and to US embassies and missions in nearly every country. It follows on from the Carter Cables (368,174 documents from 1977), which WikiLeaks published in April 2014.
The Carter Cables II bring WikiLeaks total published US diplomatic cable collection to 2.7 million documents.
What follows are some example areas.
Lebanon
There are 5,569 new documents on Lebanon. For example, the 1978 – present Israel–Lebanon conflict is widely regarded to have started on 14 March 1978, when Israel invaded Southern Lebanon in Operation Litani. There are 386 cables containing the keyword "Litani" (see here)
Israel–Palestine
There are 11,689 new documents on Israel (see here). A portion of these refer to the September 17 Camp David Accords, signed by Egyptian President Anwar El Sadat and Israeli Prime Minister Menachem Begin, with US President Jimmy Carter as witness. The Accords called for a formal peace treaty and establishment of diplomatic relations between Israel and Egypt, Israeli withdrawal from the Sinai Peninsula in stages, and a transitional period of Israeli withdrawal from the West Bank and Gaza. Egypt and Israel later signed a formal peace treaty in 1979, ending 31 years of war between the two countries. PlusD has 855 new documents with the keywords "Camp David Accords" (see here), including numerous cables on reactions around the world.
Iran
There are 5,692 new documents on Iran (see here). 1978 saw the beginning of the Iranian Revolution, which would culminate in the 1979 overthrow of the US- and UK-installed Shah of Iran. On 8 September, a day after the Iranian government declared martial law, thousands of protesters gathered in Jaleh Square in Tehran to demonstrate. The military eventually opened fire, and later estimates claimed that thousands died. Called "Black Friday" by the media, that day is said to be a key moment in the Iranian Revolution. Large protests against the Shah were ongoing throughout 1978. PlusD has 175 new documents with TAG "Iran" and containing the keyword "demonstration" (see here). The British embassy in Tehran was also burned during this period.
Tunisia
There are 1,369 new documents on Tunisia (see here). One significant event, which has shaped Tunisian political life, occurred when a labour strike on 26 January called by the General Union of Tunisian Workers (UGTT) became a general uprising. It became known as "Black Thursday" when Tunisian security forces fired on citizens, killing an estimated 200 people. PlusD has 200 new documents containing the keywords "UGTT" (see here).
Yemen
There are 944 new documents on Yemen (see here). One example of events during the year occurred when Yemeni President Ahmad al-Ghashmi was assassinated on 24 June, which led to a political configuration in the Arabian peninsula which is still felt today. PlusD has 81 documents with keyword "al-Ghashmi" (see here), including some with speculation about who set off the explosion that killed him, which is not conclusively known.
Pakistan
There are 3,343 new documents on Pakistan (see here). For instance, on 18 March former Pakistan Prime Minister Zulfikar Ali Bhutto (father of the 1990s PM Benazir Bhutto, who was subsequently assassinated) was sentenced to death by hanging for authorising the assassination of a political opponent. PlusD has 430 new documents with keyword "Bhutto" and TAG "Pakistan" (see here).
India
There are 4,990 new documents on India (see here) covering many signficant events and still influential personalities. For example:
On 1 January, an Air India Flight 855, a Boeing 747, crashed shortly after take-off near Mumbai, killing all 213 passengers and crew on board. PlusD contains 179 new cables referring to "Air India", most of which are about the crash (see here).
Former Indian Prime Minister Indira Ghandi (daughter of PM Nehru) was re-elected to Parliament on 7 November, but then arrested on 19 December, accused of plotting against her opponents during the state of emergency she had declared from 1975 to 1977. She later became Prime Minister again in 1980 and the dynastic domination of the Congress Party continued, first through her sons Sanjay and Rajiv and later through the latter's wife, Sonia, who is current president of the party. Rajiv's son Rahul was the Congress candidate in India's 2014 election, losing to the BJP's Narenda Modi. PlusD contains 53 new documents with the keyword "Indira Gandhi" (see here) and 154 new documents with the keyword "Mrs Gandhi" (see here) as well other cables related to the Gandhi dynasty.
On 13 April, violence broke out between orthodox Sikhs and the Nirankari sect during a Nirankari convention in Amritsar, Punjab; 16 were killed and 100 injured. This event is noted as one of the starting points leading up to the Punjab insurgency during the 1980s and Indian military occupation of the region in Operation Blue Star (1984). PlusD has 3 new documents containing the keywords "Sikh" and "Nirankari" (see here).
The Indian cricket team did a two-month tour of Pakistan, ending in a finale on 18 November. Indian Information Minister Adavni attended the finale in Karachi, and the match was a political event in both countries. PlusD contains 6 new documents with the keywords "Pakistan" and "cricket" (see here).
China
There are 5,422 new documents on China (see here).
For example, a number of cables discuss US National Security Advisor Zbigniew "ZBig" Brzezinski's trip to China. US strategy was to orient China against the Soviet Union and the trip led to formal US recognition of China shortly thereafter. PlusD has 175 new documents with keyword "Brzezinski" and TAG "China" (see here).
EU
There are 9,974 new documents referring to "Europe" and 18,531 referring to "European". For example, after considerable controversy, in April President Carter decided to defer production of the neutron bomb, or Enhanced Radiation Weapon (ERW), a nuclear weapon designed to kill enemy (that is, Soviet) soldiers with radiation. Carter’s decision frustrated pro-US European leaders, who had spent political capital to support the slated US deployment of the weapons system. PlusD contains 704 new documents with the keywords "neutron bomb" (see here) and 428 new documents with the keyword "ERW" (see here).
Germany
There are 11,476 new documents on East Germany (see here) and 7,638 on West Germany (see here), some of which may overlap. For instance, in January the German magazine Der Spiegel published an SED manifesto that was strongly anti-Soviet, calling for reunification and liberal reforms. The German Democratic Republic (GDR) reacted by accusing Der Spiegel of slander and closing the East German Der Spiegel office. PlusD contains 296 new documents with the keyword "Spiegel" (see here). Some of the cables include details of and reactions to the manifesto publication, including, for example, accusations of Der Spiegel working for West Germany in subversive activity against the GDR.
UK
There are 10,253 new documents on the UK (see here). The cables contain a number of reports on Lord Carver's efforts to settle independence disputes in Rhodesia and discussions on trade, among other things. For instance, the Provisional Irish Republican Army, a paramilitary organisation wanting to separate Northern Ireland from the United Kingdom, bombed the La Mon restaurant/hotel in County Down, killing 12 people in February. Another notable event for Northern Ireland occurred in January when the European Court of Human Rights ruled that the UK was guilty of inhuman and degrading treatment of its Northern Ireland prisoners; the ruling, however, did not consider the UK's interrogation techniques to be torture. PlusD has 253 new documents with the keyword "IRA" (see here) and 787 with the keyword "Northern Ireland" (see here).
France
There are 8,892 new documents on France (see here). The following are just some examples of significant events related to France that occurred througout the year.
On 16 March, a US-owned oil tanker, Amoco Cadiz, crashed off the coast of Brittany, France and sank. It left 230,000 tons of oil along 72 km of the French shoreline, which expanded to approximately 160 km during the following month. It was then the largest recorded oil spill in history and was estimated to have caused US $250 million in damage. US scientists studying the spill said that it was the largest biological kill of marine life ever recorded. PlusD has 108 new documents with the keywords "Amoco Cadiz" (see here).
The French auto company Peugeot's purchase of Chrysler's European subsidiaries was closely followed by the US government. The Federal Trade Commission also investigated the sale that year. PlusD has 18 new cables containing the keywords "Peugeot" and "Chrysler" (see here).
France maintained a close interest in Algeria following the Algerian War and Algeria's full independence in 1962. PlusD contains 16 new cables with the keywords "Boumediene" and "Giscard" (see here).
Rebels in the Shaba separatist movement FNLC invaded Zaire's Shaba province on 11 May, capturing the city of Kolwezi on 12 May. The government of Zaire asked for French and Belgian assistance with the uprising, and French and Belgian forces later undertook an airborne operation to rescue European and Zairian hostages held by the FNLC rebels. The US provided some assistance to the operation. PlusD has 173 new documents with keywords "Zaire" and "rebels" (see here), some of which give details of the US government's reaction to the invasion, its initial concern for American citizens in Kolwezi, and its careful monitoring of press reports on the issue.
France conducted a series of 29 nuclear tests from 1975 to 1978. PlusD contains 18 new documents with keywords "nuclear" and "tests", with TAG "France" (see here).
The Hollywood film director and producer Roman Polanski fled to France in 1978 after pleading guilty to sex charges. PlusD contains 4 new documents with the keyword "Polanski" (see here).
USSR
There are 16,584 new documents on the Soviet Union (see here), reporting a number of international negotiations, agreements and events. For example, on 24 January the Soviet satellite Cosmos 954 re-entered Earth's atmosphere and scattered radioactive debris over Canada's Northwest Territories. The incident was an anti-Soviet propaganda coup for the US, which was also interested in obtaining samples of Soviet space technology. PlusD contains 182 documents with the keywords "Cosmos 954" (see here).
South Africa
There are 5,740 new documents on South Africa (see here). For example, by 1978 South Africa's nuclear weapons programme was in full swing, with assistance from Israel. PlusD contains 144 new classified cables documenting US diplomatic intelligence on the programme (see here).
Other cables document, for instance, the reaction to the killing of noted anti-apartheid activist Steve Biko, who was beaten to death in police custody in late 1977. Biko's friend, South African journalist and anti-apartheid activist Donald Woods, fled to London after severe harassment by the South African government. Woods continued his anti-apartheid work from London, and later spoke to the UN Security Council about his experiences. PlusD contains 115 new documents referring to Steve Biko, 42 of which refer to Woods (see here).
Ethiopia
There are 2,946 new documents on Ethiopia (see here). Cables document, for example, how Ethiopia's Provisional Military Government of Socialist Ethiopia (PMGSE) began a major offensive in Eritrea (which it had been prepping for some time). PlusD has 71 new documents with keywords "Ethiopia", "offensive" and "Eritrea" (see here).
Tanzania
There are 1,593 new documents on Tanzania. One particularly significant event during the year occurred when strained relations between Tanzania and Uganda broke out into war, eventually leading to the overthrow of Ugandan President Idi Amin in 1979. PlusD contains 76 new documents with the keywords "Tanzania", "Uganda" and "war" (see here). The cables contain, among other things, reports from the US ambassador to Tanzania James Spain on media coverage and public mood.
US
There are 85,893 new documents on the US (see here). One significant event occurred on 18 November when Jim Jones, founder and leader of the Peoples Temple, led hundreds of his followers to commit mass murder-suicide in his settlement of Jonestown, Guyana. In total, 909 members died, including Jones himself – 304 of these were children. They had all died of cyanide poisoning, some via injection and others via cyanide-laced Kool-Aid. PlusD has 333 new documents with the keyword "Jonestown" (see here) and 702 new documents with the keywords "Peoples Temple". For instance, one cable contains text of a note found on Jones' body (see here).
Nicaragua
There are 3,422 new documents on Nicaragua (see here). A number of cables give insight to an ongoing conflict between the Sandinistas and the ruling Somoza regime. The conflict erupted when the editor of an opposition newspaper, Pedro Joaquín Chamorro Cardenal, was assassinated on 10 January. After his murder an estimated 30,000 people rioted in Managua, and the government responded with violence and martial law. In the following two years the Sandinista National Liberation Front (FSLN) took over the country until President Somoza resigned in July 1979, leaving the revolutionaries in power. PlusD contains 230 new documents with the keyword "Sandinista" and TAG "Nicaragua" (see here).
Brazil
There are 3,740 new documents on Brazil (see here). For example, those documenting the election of ARENA party candidate João Figueiredo, who won over MDB's Euler Bentes Monteiro with 355 electoral votes to 226. PlusD contains 242 new documents with the keyword "Figueiredo" (see here).
Argentina
There are 3,354 new documents on Argentina (see here). One event mentioned extensively in these cables is a border dispute between Argentina and Chile over the possession of several islands in the Beagle Channel. The dispute nearly started a war when Argentina began Operation Soberanía, intended to occupy the islands by military force. The new cables document long negotiations throughout 1978. Afterwards, a solution for both sides was achieved through papal mediation. PlusD has 444 new documents with keywords "Argentina", "Chile" and "Beagle" (see here). Argentina also hosted the 1978 Football World Cup, which included attendance by Henry Kissinger. PlusD contains 57 new documents with the keywords "Argentina" and "World Cup" (see here).
Ecuador
There are 2,230 new documents on Ecuador (some may overlap with documents on the European Community) (see here). A number of these cables concern the constitutional referendum on 15 January. Voters chose the new constitution over a revised version of the old one. The issue held great public interest, and voter turnout was approximately 87 per cent. PlusD has 79 new documents containing the keywords "Ecuador" and "constitution" (see here).
Indonesia
There are 3,289 new documents on Indonesia (see here). By 1978 there were increasing student demonstrations protesting against various aspects of Suharto's rule, including the lack of presidential term limits. A number of student activists were imprisoned, and Suharto established the "Normalization of Campus Life" in April. PlusD contains 21 new cables with the keywords "Indonesia", "student" and "activists" (see here). There are 2 new cables containing the phrase "Normalization of Campus Life" (see here).
Australia
There are 3,168 new documents on Australia (see here). The cables document, for example, Australia's difficult relationship with Indonesia and the fall-out over Indonesia's 1975 occupation of East Timor.
WIKILEAKS SPECIAL PROJECT K: THE KISSINGER CABLES
'Investigative journalism has never been this effective!' – Publico
The Kissinger Cables are part of today's launch of the WikiLeaks Public Library of US Diplomacy (PlusD), which holds the world's largest searchable collection of United States confidential, or formerly confidential, diplomatic communications. As of its launch on April 8, 2013 it holds 2 million records comprising approximately 1 billion words.
WikiLeaks' publisher Julian Assange stated: "The collection covers US involvements in, and diplomatic or intelligence reporting on, every country on Earth. It is the single most significant body of geopolitical material ever published."
THE KISSINGER CABLES
"The illegal we do immediately; the unconstitutional takes a little longer." -- Henry A. Kissinger, US Secretary of State, March 10, 1975: http://wikileaks.org/plusd/cables/P860114-1573_MC_b.html#efmCS3CUB
The Kissinger Cables comprise more than 1.7 million US diplomatic records for the period 1973 to 1976, including 205,901 records relating to former US Secretary of State Henry A. Kissinger. Dating from January 1, 1973 to December 31, 1976 they cover a variety of diplomatic traffic including cables, intelligence reports and congressional correspondence. They include more than 1.3 million full diplomatic cables and 320,000 originally classified records. These include more than 227,000 cables classified as "CONFIDENTIAL" and 61,000 cables classified as "SECRET". Perhaps more importantly, there are more than 12,000 documents with the sensitive handling restriction "NODIS" or 'no distribution', and more than 9,000 labelled "Eyes Only".
At around 700 million words, the Kissinger Cables collection is approximately five times the size of WikiLeaks' Cablegate. The raw PDF data is more than 380 Gigabytes in size and is the largest WikiLeaks publication to date.
WikiLeaks' media partners will be reporting throughout the week on their findings. These include significant revelations about US involvements with fascist dictatorships, particularly in Latin America, under Franco's Spain (including about the Spanish royal family) and in Greece under the regime of the Colonels.
The documents also contain hourly diplomatic reporting on the 1973 war between Israel, Egypt and Syria (the "Yom Kippur war"). While several of these documents have been used by US academic researchers in the past, the Kissinger Cables provides unparalled access to journalists and the general public.
Most of the records were reviewed by the United States Department of State's systematic 25-year declassification process. At review, the records were assessed and either declassified or kept classified with some or all of the metadata records declassified. Both sets of records were then subject to an additional review by the National Archives and Records Administration (NARA). Once believed to be releasable, they were placed as individual PDFs at the National Archives as part of their Central Foreign Policy Files collection. Despite the review process supposedly assessing documents after 25 years there are no diplomatic records later than 1976. The formal declassification and review process of these extremely valuable historical documents is therefore currently running 12 years late.
The form in which these documents were held at NARA was as 1.7 million individual PDFs. To prepare these documents for integration into the PlusD collection, WikiLeaks obtained and reverse-engineered all 1.7 million PDFs and performed a detailed analysis of individual fields, developed sophisticated technical systems to deal with the complex and voluminous data and corrected a great many errors introduced by NARA, the State Department or its diplomats, for example harmonizing the many different ways in which departments, capitals and people's names were spelt. All our corrective work is referenced and available from the links in the individual field descriptions on the PlusD text search interface: https://search.wikileaks.org/plusd
RECLASSIFICATION ATTEMPTS THWARTED
The CIA and other agencies have attempted to reclassify or withhold sections of the US National Archives. Detailed minutes of US State Department meetings show that these attempts, which originated under the Bush II administration, have continued on through until at least 2009. A 2006 analysis by the US National Security Archives, an independent non-governmental research institute and library located at George Washington University, found that 55,000 pages had been secretly reclassified.
The censorship of the US National Archives was thrown into stark relief in November last year when the Archive censored all searches for 'WikiLeaks' from its records. See http://dissenter.firedoglake.com/2012/11/03/us-national-archives-has-blocked-searches-for-wikileaks/
Julian Assange, WikiLeaks' publisher, said: "The US administration cannot be trusted to maintain the history of its interactions with the world. Fortunately, an organisation with an unbroken record in resisting censorship attempts now has a copy."
Media Organizations Given Advanced Access
Australia - Fairfax (Sydney Morning Herald, The Age, the Canberra Times and the Australian Fianancial Review)
Argentina - Pagina 12
Brazil - Publica
Bulgaria - Bivol
Egypt - Al Masry Al Youm
Greece - Ta Nea
Guatemala - Plaza Publica
Haiti - Haiti Liberte
India - The Hindu
Italy - L'Espresso
Italy - La Repubblica
Lebanon - Al Akhbar
Mexico - La Jornada
Spain - Publico
Sweden - Aftonbladet
UK - Press Association
US - Associated Press
US - The Nation
PRESS CONFERENCE
WikiLeaks Special Project K: concerning the United States, Latin America, the Middle East, Africa, Central and South East Asia, Europe and the Pacific, with special focus on Israel, Russia, India, Japan, South Africa, France and Francophone Africa.
WHERE
The National Press Club The Holeman Lounge 529 14th St. NW 13th Floor Washington, DC 20045 +1 202-662-7500
WHEN
Monday April 8th at 9am (Washington time)
INTERVIEWS
WikiLeaks Spokesperson Kristinn Hrafnsson is available for interviews after the press conference please make arrangements with Melanie Lerardi [email protected] or +1 (202) 662 7502 alternatively you can call Kristinn directly on +3548217121 or email [email protected].
STATUS UPDATES
WIKILEAKS AND JULIAN ASSANGE
After WikiLeaks’ publication of Pentagon and State Department documents in 2010, the White House launched a multi-agency investigation into WikiLeaks and its publisher Julian Assange. The investigation includes the Department of Justice (DOJ), the FBI, the State Department, the CIA and the Defense Intelligence Agency (DIA) among others. The DoJ / FBI investigation is ongoing, as is its associated Grand Jury in Alexandria, Virginia, which is headed up by District Attorney Neil McBride, a current candidate for the FBI directorship.
A number of senior political figures in the United States have called for the assassination, extraordinary rendition or kidnapping of Julian Assange and other WikiLeaks staff and for the execution of WikiLeaks US sources: www.youtube.com/watch?v=ZuQW0US2sJw
The Grand Jury has coercively forced numerous people to give testimony in secret and to do so without the presence of a judge or defence lawyer. The actions of the Grand Jury, including issuing PATRIOT Act 'subpeonas' against Twitter, Google and other companies, is the subject of ongoing legal proceedings.
On 1 February this year, the Associated Press reported that the FBI was conducting an illegal investigation into WikiLeaks’ activities in Iceland. This investigation was discovered by the Icelandic Minister of the Interior, Ögmundur Jónasson, who ordered the FBI to leave and issued a formal diplomatic protest to the United States.
Julian Assange, an Australian, was granted political asylum on 19 August 2012 by the government of Ecuador. He remains under their protection in the Embassy of Ecuador in London. British police have surrounded the embassy and the British government admits to spending more than $4.5 million on this policing presence so far. Contrary to international law, the United Kingdom refuses to grant Julian Assange safe passage to Ecuador, saying that he must be extradited to Sweden to answer questions. He has not been charged with an offence in either country and the chief of the Swedish Supreme Court says there is no legal reason why Swedish police cannot go to London should they wish to speak to him.
By 8 April 2013 Julian Assange will have been imprisoned, detained under house arrest in the United Kingdom, and unable to leave the protective custody of the Ecuadorian Embassy for a total of 854 days.
On 11 April 2013 a feature film about Julian Assange’s formative years will open the Washington DC International Film Festival: http://www.filmfestdc.org
Julian Assange is a popular figure in his native Australia, where he is running for the Australian Senate. The latest poll, by Labour party polling outfit UMR, showed he had 27 per cent of the voting intention: http://wikileaksparty.org.au/
For further information see: http://justice4assange.com/extraditing-assange.html and https://usvwikileaks.org and http://justice4assange.com/
BRADLEY MANNING
An alleged WikiLeaks source, intelligence analyst Bradley Manning, now aged 25, was arrested on 26 May 2010 by US Army investigators. Manning was detained under extreme conditions in Kuwait and Marine Corps Base Quantico, Virginia. The United Nations Rapporteur on Torture Juan E. Mendez formally found these conditions to amount to "cruel and abusive treatment" akin to torture. Judge Denise Lind of the US military court found that his conditions were illegal. After the resignation of Assistant Secretary of State for Public Affairs P. J. Crowley over the issue, Manning was transferred to Fort Leavenworth, Kansas, and the Quantico barracks were decommissioned. Mr. Manning's defence team said that the abusive treatment may have been in order to break Mr. Manning into turning State's witness against WikiLeaks publisher Julian Assange.
By 8 April 2013 Bradley Manning will have been detained without trial for 1049 days, the longest detention without trial of a US soldier in modern history. His trial is said by Guantnamo beat reporters to be more secret that the military commissions held against al Quada suspects. It is scheduled for 2 June 2013 at Fort Meade, Maryland. WikiLeaks, the Center for Constitutional Rights and more than 30 other media organizations have filed suit against the US military for the abuse of secrecy used in prosecuting the case.
ECONOMIC CENSORSHIP: BANKING BLOCKADE
After documented political pressure, including from Senator Joseph Lieberman and Congressman Peter T. King, VISA, MasterCard, Bank of America, PayPal, Western Union, AMEX, Diners Club, Discover and JCB erected an extra-legal banking blockade against the WikiLeaks organization and its donors. The blockade is the subject of ongoing litigation and a resolution by the European Parliament. It has been condemned by the United Nations Special Rapporteur for Freedom of Expression, Frank La Rue, the New York Times, Reporters Without Borders, the Electronic Frontier Foundation, Amnesty International, the Council of Europe, and numerous other organizations.
The fiscal blockade against WikiLeaks is similar to that conducted against the central banks of Cuba and Iran, however, unlike these two countries, the WikiLeaks blockade is being conducted with no known legal or administrative basis. In fact, the US Secretary of the Treasury found in early 2011 that there was no legal reason to place WikiLeaks under a US embargo. Due to the market dominance of VISA, MasterCard and PayPal, the extra-legal action has cut off 95 per cent of WikiLeaks' income stream, costing the organization more than $50 million dollars.
All litigation todate has been won by WikiLeaks and its partners, but the blockade continues. An appeal, lodged by Valitor (Visa Iceland) is to be heard by the Icelandic Supreme Court on April 15, 2013.
BREAKING THE BLOCKADE: THE US FREEDOM OF THE PRESS FOUNDATION
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a promising avenue for new physics ( np ) to enter the observables of @xmath0-meson decays is given by @xmath3@xmath4 mixing . in the standard model ( sm ) ,
the phenomenon of mixing originates from box topologies and is strongly suppressed . in the presence of np
, new particles could give rise to additional box topologies or even contribute at the tree level .
should these np contributions also involve new cp - violating phases , the @xmath3@xmath4 mixing phase @xmath2 could differ sizably from the tiny sm value of @xmath7 ( see , for instance , refs .
@xcite and references therein ) .
a key channel for addressing this exciting possibility is @xmath8 .
a characteristic feature of this channel is that its final state contains two vector mesons and thereby requires a time - dependent angular analysis of the @xmath9 and @xmath10 decay products @xcite . over the last couple of years ,
measurements at the tevatron of cp - violating asymmetries in tagged " analyses ( distinguishing between initially present @xmath3 or @xmath4 mesons ) of the @xmath8 channel indicate possible np effects in @xmath3@xmath4 mixing @xcite .
these results are complemented by the measurement of the anomalous like - sign dimuon charge asymmetry at 0 , which was found to differ by @xmath11 from the sm prediction @xcite .
this summer , the lhcb collaboration has also joined the arena , reporting , however , results that disfavour large np effects @xcite . the above measurements , which we will discuss in more detail below , are typically shown in the @xmath2@xmath1 plane , where @xmath1 is the width difference between the mass eigenstates of the @xmath0-meson system . in this paper
, we point out a new method for determining further constraints in the @xmath2@xmath1 plane using measurements of the effective lifetimes of @xmath0 decays .
in particular , we show that the information provided by the lifetimes of a pair of decays into cp - even and cp - odd final states is sufficient to determine @xmath2 and @xmath1 .
the advantage of this strategy is that it only requires an untagged " analysis , i.e. it is not necessary to distinguish between initially present @xmath3 or @xmath4 mesons , which is experimentally advantageous .
specifically , we will consider the @xmath5 @xcite and @xmath6 @xcite decays , which have final states with the cp eigenvalues @xmath12 and @xmath13 , respectively . from here on we shall abbreviate the latter decay as @xmath14 .
first measurements of the effective lifetimes of these channels are already available from the cdf and lhcb collaborations @xcite . for the theoretical interpretation of these results
we also need to address hadronic uncertainties . a closer look will reveal that these decays are well suited in this respect . we will illustrate our method with the most recent data and shall compare the resulting constraints in the @xmath2@xmath1 plane with those from the alternative measurements listed above . the outline is as follows : in section [ sec : effective ] , we discuss the general formalism to calculate effective lifetimes and show in section [ sec : cubic ] how the corresponding measurements can be converted into contours in the @xmath2@xmath1 plane . in section [ sec :
control ] , we turn to the hadronic uncertainties affecting this analysis and their control through experimental data . the constraints on the @xmath3@xmath4 mixing parameters arising from the current data for the effective lifetimes of the @xmath5 and @xmath14 channels are explored in section [ sec : constraints ] , where we also illustrate the impact of future lifetime measurements with errors at the @xmath15 level .
in section [ sec : future ] , we give a collection of additional @xmath0 decays that can be added to this analysis in the future .
finally , we summarize our conclusions in section [ sec : concl ] .
we will consider a @xmath16 transition with a final state @xmath17 into which both a @xmath3 and a @xmath4 meson can decay .
the corresponding untagged rate can then be written as follows @xcite : @xmath18 where l and h denote the light and heavy @xmath0 mass eigenstates , respectively . using @xmath19
we can straightforwardly write ( [ eqn : untagged ] ) as @xmath20\end{aligned}\ ] ] with @xmath21 we define the effective lifetime of the decay @xmath22 as the time expectation value of the untagged rate @xcite , @xmath23 which is equivalent to the lifetime that results from fitting the two exponentials in to a single exponential @xcite .
by making the usual definition @xmath24 we can express the effective lifetime as @xmath25y_s^2 + { \cal o}(y_s^3 ) , \label{eqn : tauexact}\end{aligned}\ ] ] where we have also given the expansion in powers of @xmath26 up to cubic corrections .
we proceed to consider the case where @xmath17 is a cp eigenstate with eigenvalue @xmath27 . in the sm ,
the decay amplitude can be written , without loss of generality ( using the unitarity of the cabibbo kobayashi
maskawa ( ckm ) matrix ) , as @xmath28 where the @xmath29 are real and the @xmath30 and @xmath31 are cp - conserving strong and cp - violating weak phases , respectively . using the standard @xmath32@xmath33 mixing formalism @xcite , we have @xmath34 where @xmath35.\ ] ] here we have introduced the abbreviation @xmath36 and @xmath2 denotes the @xmath32@xmath33 mixing phase , which is given by @xmath37 where @xmath38 and @xmath39 are the sm and np pieces , respectively .
it is convenient for the following discussion to introduce the direct cp asymmetry of the @xmath40 decay @xcite : @xmath41 where @xmath42 subsequently , we may write @xmath43 here @xmath44 is a hadronic phase shift , which is given by @xmath45 @xmath46 yielding @xmath47 the twofold ambiguity for @xmath44 arising from the latter expression can be resolved using sign information from @xmath48 or @xmath49 .
these expressions generalize those given in refs . @xcite . using ( [ eqn : adel ] ) and ( [ xi - simpl ] ) , we thus obtain @xmath50 as we will see in section [ sec : control ]
, there are fortunate @xmath0 decays into cp eigenstates where the hadronic parameter @xmath51 and the resulting phase shift @xmath44 can be controlled through experimental data . for these decays
, we can hence use the corresponding lifetime measurements to constrain @xmath26 ( or @xmath1 ) with respect to @xmath2 .
let us now have a closer look at , which we can write as the following cubic equation for the real parameter @xmath26 : @xmath52 where @xmath53 in order to solve this cubic equation , it is useful to rewrite it in the reduced " form @xmath54 with @xmath55 applying cardano s formula then yields the solutions @xmath56{r+\sqrt{d } } + e^{-i\omega}\ , \sqrt[3]{r-\sqrt{d}}\end{aligned}\ ] ] with @xmath57 , where @xmath58 @xmath59 for @xmath60 , this solution is not valid as is then a quadratic equation in @xmath26 . furthermore , the above expressions may prove cumbersome to use in practice .
a convenient approximate solution is obtained by solving the expansion in ( [ eqn : tauexact ] ) up to quadratic order in @xmath26 : @xmath61 \pm\frac{1}{2}\sqrt{\left[\frac{{\cal a}^f_{\delta\gamma}}{2-({\cal a}^f_{\delta\gamma})^2}\right]^2 + \frac{4}{\tau_{b_s}}\left[\frac{\tau_f - \tau_{b_s}}{2-({\cal a}^f_{\delta\gamma})^2}\right]}.\ ] ] this quadratic solution is in excellent agreement with the corresponding branches of the exact solution ( [ exact - sol ] ) for the numerical analyses discussed below . given in for cp - even and cp - odd final states @xmath62 and @xmath63 , respectively .
the decay amplitudes are assumed to have no cp - violating phases .
we also show the constraint from the theoretical value of @xmath64 given in ( [ eqn : dggsm ] ) , as discussed in the text . ] for illustration we consider two @xmath0 decays to cp eigenstates , @xmath65 and @xmath66 , with positive and negative cp eigenvalues , respectively .
further , we assume @xmath67 for these decays , yielding @xmath68 and @xmath69 . in fig .
[ fig : cpillust ] , we show the lifetime constraints that are compatible with the theoretical sm calculation of @xmath1 @xcite , @xmath70 and the sm value of the @xmath3@xmath4 mixing phase , which is given as follows @xcite : @xmath71 throughout this paper , we shall use @xcite @xmath72 for the @xmath0 lifetime introduced in , resulting in the sm effective lifetimes @xmath73ps and @xmath74ps .
the difference in behaviour for cp - odd and cp - even eigenstates is due to the non - linear dependence on @xmath26 in .
said differently , if is expanded and only terms up to linear order in @xmath26 are kept the two curves in fig .
[ fig : cpillust ] would overlap . in fig .
[ fig : cpillust ] , we have included another constraint , which is related to the theoretical value in ( [ eqn : dggsm ] ) as follows : if we assume that np can only affect @xmath1 through @xmath3@xmath4 mixing , which is a very plausible assumption , we have @xcite @xmath75 where @xmath76 here @xmath39 is the np @xmath3@xmath4 mixing phase , which also enters @xmath2 defined in ( [ phis ] ) on which @xmath77 depends , whereas the sm piece takes the following value @xcite : @xmath78 the formalism developed above is also valid for non - cp eigenstates provided the final state is accessible to both @xmath3 and @xmath4 so that mixing is possible .
examples of such states are @xmath79 . for these decays the cp eigenvalue @xmath27 in should be replaced by @xmath80 , where @xmath81 denotes the relative orbital angular momentum of the decay products @xcite .
examples of effective lifetimes that have been measured for @xmath0 decays to cp - even and cp - odd final states are @xmath82 and @xmath83 , respectively . unlike our hypothetical examples from the previous section , however , the decay amplitudes of these decays are not devoid of weak phases , and can be written in the sm as follows @xcite : @xmath84\ ] ] @xmath85.\ ] ] here @xmath86 is the wolfenstein parameter of the ckm matrix @xcite , @xmath87 and @xmath88 is the usual angle of the unitarity triangle whereas @xmath89 , @xmath90 and @xmath91 , @xmath92 are hadronic , cp - conserving parameters .
consequently , the parameters introduced in and ( [ h - def ] ) take the forms @xmath93 and @xmath94 so that the hadronic phase shifts can be obtained from @xmath95\sin\gamma,\ ] ] @xmath96\sin\gamma.\ ] ] we observe that these phases are proportional to the tiny @xmath97 parameter , i.e. are doubly cabibbo - suppressed .
consequently , the @xmath98 observable given in ( [ eqn : adelcos ] ) is robust with respect to hadronic uncertainties for the decays at hand . in the case of the @xmath5 channel
, we can use the @xmath99-spin symmetry of strong interactions to relate it to the @xmath100 decay , which thereby allows us to determine @xmath88 as well as @xmath101 and @xmath102 @xcite .
the current status of an analysis along these lines , using also the direct cp violation in @xmath103 , is given by @xcite : @xmath104 where the errors include the uncertainties of the relevant input quantities and estimates of @xmath99-spin - breaking corrections .
the @xmath88 result is in excellent agreement with the current fits of the unitarity triangle @xcite , thereby excluding large cp - violating np contributions to the @xmath5 decay amplitude . using these numbers in
, we find @xmath105 where we have added the errors in quadrature .
similarly , we also find @xmath106 .
unfortunately , as discussed in ref .
@xcite , it is much more involved to control the hadronic effects in the @xmath14 decay through experimental data , and the potential control channel @xmath107 has not yet been observed . on the other hand ,
contrary to @xmath82 , the denominator of ( [ tdelphi ] ) is equal to one at leading order in @xmath97 . following ref .
@xcite , we use the conservative range @xmath108 and leave @xmath109 unconstrained .
using moreover the value for @xmath88 in , we find @xmath110\ ] ] and @xmath111 , which has , just like @xmath112 , a negligible impact on ( [ eqn : adelcos ] ) .
it is remarkable that the hadronic phase shifts @xmath113 and @xmath114 turn out to be so robust with respect to the hadronic effects and the weak phase @xmath88 , suffering from uncertainties of only @xmath115 .
future data should allow us to determine them with even higher precision . [
cols="^,^ " , ]
in the previous section we presented all the ingredients necessary to compute @xmath116 and @xmath117 as functions of @xmath2 . inserting them into the solution for @xmath26 discussed in section [ sec : cubic ] allows us to draw contours for the lifetime measurements on the @xmath2@xmath1 plane .
the first measurement of the effective @xmath118 lifetime was performed by the cdf collaboration in 2006 @xcite . in the spring of 2011 ,
the lhcb collaboration reported their first measurement of this observable @xcite : @xmath119 { \rm ps},\ ] ] which is currently the most precise .
the first measurement of the @xmath83 lifetime has recently been made by the cdf collaboration @xcite : @xmath120 { \rm ps}.\ ] ] and @xmath114 on the contours in the @xmath2@xmath1 plane for the central values of the lifetime measurements .
we also shown the impact of the present error of the @xmath0 lifetime . ] in the left panel of fig .
[ fig : dgphis ] , we show the current measurements of the effective lifetimes of the @xmath118 and @xmath83 decays as constraints on the @xmath2@xmath1 plane . we also show the 39% confidence region resulting from a @xmath121 fit of these two results .
the individual fitted values for the @xmath2 and @xmath1 parameters are given as follows : @xmath122 @xmath123 where the errors are 68% confidence levels corresponding to a @xmath121 fit of the lifetimes .
each solution has a two - fold ambiguity given by the transformation @xmath124 both lifetime measurements currently have an error of about 7% .
however , it seems feasible to reduce the uncertainty of the @xmath125 measurement at lhcb to the few - percent level @xcite . in the right panel of fig .
[ fig : dgphis ] , we show for illustration the impact of measurements of the @xmath82 and @xmath14 lifetimes with @xmath15 uncertainty , assuming no change in the central values . clearly ,
at this level of accuracy , the lifetime measurements could strongly constrain @xmath2 and @xmath1 . using ( [ ys ] )
, we also include the band corresponding to the theoretical value of @xmath64 given in ( [ eqn : dggsm ] ) .
we observe , as also noted in ref .
@xcite , that the central value of the @xmath126 measurement is too large in comparison with this constraint . to spoil the relation in ( [ ys ] )
either large np effects are required , a very contrived scenario in our opinion , or the width difference @xmath1 must be affected by hadronic long - distance effects , which are not included in the sm calculation of ( [ eqn : dggsm ] ) .
the @xmath127 effective lifetime predicted by the sm calculation is @xmath128ps @xcite .
@xmath1 plane from the left panel of fig .
[ fig : dgphis ] added to a compilation of measurements as obtained in ref .
the 0 , cdf and lhcb allowed regions refer to tagged analyses of @xmath129 .
in addition , the 0 region includes also the result for the like - sign dimuon asymmetry while lhcb has also included a first analysis of cp violation in @xmath14 . ] the uncertainties of the hadronic phase shifts given in and as well as the error of the @xmath0 lifetime in were not included in fig .
[ fig : dgphis ] or in the fit results in ( [ fit-1 ] ) and ( [ fit-2 ] ) . in fig .
[ fig : dgphis - errors ] , we illustrate the impact of these uncertainties on the lifetime contours in the @xmath2@xmath130 plane . comparing with the error bands in fig .
[ fig : dgphis ] , we observe that the effects of these uncertainties are marginal with respect to the current errors of the effective lifetime measurement .
more sophisticated fits should take these uncertainties into account as well .
it is interesting to compare our fitted results to recent measurements of cp violation in the @xmath131 channel , where the current picture of @xmath2 looks as follows : cdf finds @xmath132 \lor [ -59.6^\circ,-2.3^\circ]$ ] ( 68% c.l . ) , while 0 has recently reported @xmath133 @xcite .
the lhcb collaboration has also entered the arena , reporting @xmath134 and @xmath135 { \rm ps}^{-1}$ ] @xcite .
furthermore , lhcb has presented a first tagged analysis of the cp - violating asymmetry of the @xmath14 channel , yielding @xmath136 @xcite .
a compilation of the preliminary results from the 0 , cdf and lhcb collaborations as constraints in the @xmath2@xmath1 plane has recently been performed in ref .
@xcite . in fig .
[ fig : fits ] , we have overlaid on the corresponding plot the lifetime contours and fit results of the analysis described above .
it is intriguing to see how well the lifetime allowed region overlaps with those from 0 and cdf .
the current errors leave space for interesting future developments .
should the central values of the cp - even and cp - odd lifetimes approach the theoretical sm point , the power to pinpoint @xmath2 is lost , as illustrated by fig .
[ fig : cpillust ] .
however , because the curves are flat at this point , @xmath1 could still be determined accurately in this case .
so far we have discussed the effective lifetimes for the @xmath118 and @xmath83 channels , which have both been measured in first analyses by the cdf and lhcb collaborations .
these channels have final states with opposite cp eigenvalues and happen to be well paired for obtaining constraints in the @xmath2@xmath1 plane using the strategy proposed in this paper .
the hadronic corrections in @xmath5 can be controlled even better in the future through precise measurements of the cp - violating observables of the @xmath100 channel .
regarding @xmath14 , hadronic corrections have a minor impact on the lifetime analysis .
a potential control channel is @xmath107 , although here the situation is much more involved than in @xmath5 due to the unsettled hadronic structure of the scalar @xmath137 state @xcite .
another interesting decay that can soon be added to this picture is @xmath138 @xcite , which has been observed by the cdf and lhcb collaborations @xcite .
this channel has a final state with cp eigenvalue @xmath13 and is caused by @xmath139 quark - level processes , i.e. it has a ckm structure that is different from the decays considered above . in particular , the relevant hadronic parameter does not enter in a doubly cabibbo - suppressed way .
however , the uncertainties can be controlled through @xmath140 and are found to have a moderate impact on the effective @xmath138 lifetime @xcite , which has not yet been measured .
another @xmath0 decay with a cp - even final state is @xmath141 . here
the hadronic corrections are again doubly cabibbo - suppressed and can be controlled with the help of the @xmath99-spin - related @xmath142 decay @xcite . a first theoretical analysis of the effective lifetime of @xmath141 was performed in ref .
further decays into cp - even final states where a similar analysis can be performed are the @xmath143 channels @xcite .
decays of @xmath0 mesons into cp - selfconjugate final states with two vector mesons or higher resonances offer another laboratory for lifetime analyses . in this case
the @xmath144 and @xmath145 channels look particularly interesting .
these decays , which have already been observed experimentally @xcite , are penguin modes .
their final states are mixtures of cp - even and cp - odd eigenstates and can be disentangled by means of angular analyses
. it would be interesting to perform measurements of the lifetimes for the cp - even and cp - odd final - state configurations and to add them as contours to the @xmath2@xmath130 plane along the lines of the strategy proposed above .
a similar comment applies to the @xmath146 channel , where it would also be desirable to determine the individual lifetimes for the cp - even and cp - odd final - state configurations separately instead of making a fit to the whole time - dependent angular distribution .
this can be done by means of the moment analysis proposed in ref .
the hadronic uncertainties of the @xmath131 channel can be controlled by channels such as @xmath147 and @xmath148 @xcite . in the future ,
also decays with final states that are not cp - selfconjugate can be added to the agenda to further constrain @xmath2 and @xmath1 , provided both a @xmath3 and a @xmath4 meson can decay into the same final state ( see section [ sec : effective ] ) .
prime examples are the @xmath149 channels .
their effective lifetimes can be used to constrain @xmath150 with respect to @xmath1 ( see ref .
@xcite for an overview of the observables of these decays ) .
thanks to the sizable width difference @xmath1 of the @xmath0-meson system , effective lifetimes of @xmath0 decays offer interesting probes of @xmath3@xmath4 mixing .
the corresponding measurements require only untagged data samples and are advantageous from an experimental point of view .
thanks to non - linear terms in @xmath1 , a pair of @xmath0 decays into cp - even and cp - odd final states is sufficient to determine the @xmath3@xmath4 mixing phase and the width difference .
prime examples for implementing this strategy in practice are the decays @xmath5 and @xmath14 .
their effective lifetimes turn out to be robust with respect to hadronic uncertainties , which can be controlled or constrained with the help of further experimental data .
we have calculated the constraints in the @xmath2@xmath1 plane following from the current measurements of the @xmath5 and @xmath14 lifetimes , which both suffer from @xmath151 uncertainties .
the resulting picture is consistent with other constraints following from tevatron measurements , which have not been supported by recent lhcb data . the uncertainties still preclude us from drawing definite conclusions but leave space for interesting future developments . lifetime measurements with @xmath15 precision
would allow us to obtain much stronger constraints in the @xmath2@xmath1 plane as we have illustrated in our study .
should the central values of the lifetimes for the cp - even and cp - odd final states approach the sm values , the lifetime contours would loose their power to determine @xmath2 .
however , the width difference could still be determined in a precise way in this case .
an interesting trend of the current data is that it favours a value of @xmath1 that is larger than the one calculated in qcd . with the plausible assumption that np affects this observable only through @xmath3@xmath4 mixing ,
its absolute value can only decrease and hence the discrepancy will be even larger for sizable mixing phases .
this feature raises the question of whether the sm calculation of @xmath1 fully includes all hadronic long - distance contributions
. it will be interesting to see if this trend will be supported by future data or if it will eventually disappear . in the future , also other effective lifetime measurements of @xmath0-meson
decays can be added to the @xmath2@xmath1 plane , allowing us to overconstrain " the mixing parameters in the same spirit as the determination of the apex of the unitarity triangle .
this information will be complementary to the tagged analyses of cp violation in the @xmath0 system
. it will be intriguing to see at which point of the @xmath2@xmath1 plane all measurements will eventually converge .
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[ lhcb collaboration ] , lhcb - conf-2011 - 019 . | measurements of the effective lifetimes of @xmath0-meson decays , which only require untagged rate analyses , allow us to probe the width difference @xmath1 and the cp - violating phase @xmath2 of @xmath3@xmath4 mixing .
we point out that the dependence of the effective lifetime on non - linear terms in @xmath1 allows for a determination of @xmath2 and @xmath1 given a pair of @xmath0 decays into cp - even and cp - odd final states . using recent lifetime measurements of @xmath5 and @xmath6 decays , we illustrate this method and show how it complements the constraints in the @xmath2@xmath1 plane from other observables .
nikhef-2011 - 026 * robert fleischer and robert knegjens * _ nikhef , science park 105 , nl-1098 xg amsterdam , the netherlands _
september 2011 |
laparoscopic right colectomy ( lrc ) requires advanced skills and a specific training is recommended in order to perform this operation safely and effectively .
differences in training protocols exist among surgical teams and the need for a consensus on the key steps of lrc has been stressed by many authors .
the perceived difficulties in performing lrc are further enhanced by the introduction of the concept of complete mesocolic excision ( cme ) in the surgical treatment of colon cancer .
several techniques have been proposed for lrc with cme and good oncologic results are reported in experienced hands . despite the drive for centralization of surgery in high - volume centers ,
the majority of colectomies are still performed by low- or medium - volume surgeons and the amount of partial colectomies performed laparoscopically in nonteaching hospitals is increased in the recent years .
the development and teaching of easy - to - learn and easy - to - perform surgical techniques could help to further increase the diffusion of laparoscopy among surgeons and to achieve better results , offering good surgery to patients without forcing them to move toward reference centers . in 2000
, young - fadok and nelson described a simplified technique of lrc consisting in laparoscopic mobilization of the right colon followed by extracorporeal vascular ligation and ileocolic anastomosis .
the key point of their technique is that the right colon , once mobilized , may be exteriorized through a small supraumbilical incision that directly overlies the root of the ileocolic vessels .
we introduced some changes to further simplify the exposure of the correct planes according to the concept of cme , to reduce the need to manipulate the colon and to improve ergonomics of surgery .
since july 2010 , when the following technique was developed , all patients with cancer of the cecum and ascending colon and patients with active crohn 's disease ( cd ) of the terminal ileum and right colon were candidates for this procedure .
laparoscopic procedure was contraindicated in case of fistulizing cd , cancer infiltrating adjacent organs or perforated cancer .
cancer with suspected infiltration of the right paracolic peritoneum and previous abdominal surgery were considered relative contraindications and a laparoscopic procedure was usually attempted .
the procedure was performed by surgeons with no previous experience on lrc , who were trained by an expert surgeon for their first three cases with the eventual supervision of the main author .
data on operative time , conversion , postoperative complications ( occurring within 30 days after surgery ) , length of stay and number of harvested lymph nodes were collected retrospectively .
postoperative complications were classified according to the clavien - dindo grading system . the patient is placed supine , with both arms at the side .
the surgeon is on the patient 's left side ; the assistant stays on the surgeon 's left side ; the nurse is on the patient 's right , close to the legs ; the monitor stays on the patient 's right side .
a 10-mm hasson trocar is placed via a cut - down procedure on the left side of the umbilicus , pneumoperitoneum is established and the laparoscope is inserted .
a 5-mm trocar is then placed in the epigastric midline ( epi ) , 4 cm above the first trocar .
then , a 5-mm trocar is placed in the mcburney point ( mb ) [ figure 1 ] .
this allows the small bowel , transverse colon and omentum to fall toward the left lower quadrant , tensing the gastrocolic ligament and assisting in retraction . using the mb trocar
, the gastrocolic ligament is grasped near the transverse colon and elevated both toward the anterior abdominal wall and the feet to identify the correct plane between the gastrocolic ligament and the underlying mesentery of the transverse colon .
starting from the level of the antropyloric region and proceeding close to the colon , the ligament is then sectioned using a dissecting instrument introduced in the epi trocar .
step 1 is completed after visualization of the second portion of the duodenum [ figure 2a ] .
the peritoneum overlying the hepatic flexure and the right phrenocolic ligament is sectioned , easily identifying the profile of the kidney without entering a wrong plane behind it .
the hepatic flexure and the proximal transverse colon are separated from the anterior surface of the kidney and the duodenum by blunt dissection , as the colon is brought by its own weight toward the pelvis and the left , without any traction .
step 2 is completed when the third portion of the duodenum is visualized [ figure 2b ] .
working from the free lateral peritoneal edge of the mobilized hepatic flexure , the right paracolic gutter is opened along the ascending colon toward the cecum [ figure 2c ] .
once the peritoneal division around the cecum is completed , the right colon spontaneously falls toward the midline and is easy to detach from toldt 's fascia by blunt dissection , without any traction .
the patient is moved to trendelenburg , with the right side still banked up : this allows the small bowel and the mobilized cecum to fall toward the midline . if present , the appendix is grasped to hold the cecum upwards and straighten the terminal ileum ; otherwise , the peritoneal edge around the cecum is grasped .
the ureter is pursued via blunt dissection along the toldt 's fascia , medially to the gonadal vessels . after clear identification of the right ureter
, the terminal ileum is mobilized dissecting the peritoneum along the base of the small - bowel mesentery [ figure 2d ] until the right colon spontaneously falls toward the midline , disappearing from the monitor : this sign indicates that the dissection is sufficient for exteriorization . in few cases , little further blunt dissection along the toldt 's fascia
the appendix ( or the terminal ileus ) is firmly grasped through the mb trocar : this helps to retrieve the right colon .
the periumbilical port - site incision is extended cephalad to join the epigastric port - site incision , and the right colon is exteriorized [ figure 3 ] .
the final incision joins the epigastric and periumbilical port sites after the terminal ileum and transverse colon are divided at the chosen level , the mesocolon is severed in a v - shape - like fashion toward the supplying vessels using a sealing - dissecting device . the ileocolic vessels and if present the right colic vessels are prepared and divided at their origin [ figure 4 ] .
before closing the midline incision , if desired , a drain is placed through the mb port site .
the surgeon is on the patient 's left side ; the assistant stays on the surgeon 's left side ; the nurse is on the patient 's right , close to the legs ; the monitor stays on the patient 's right side .
a 10-mm hasson trocar is placed via a cut - down procedure on the left side of the umbilicus , pneumoperitoneum is established and the laparoscope is inserted .
a 5-mm trocar is then placed in the epigastric midline ( epi ) , 4 cm above the first trocar .
then , a 5-mm trocar is placed in the mcburney point ( mb ) [ figure 1 ] .
this allows the small bowel , transverse colon and omentum to fall toward the left lower quadrant , tensing the gastrocolic ligament and assisting in retraction . using the mb trocar ,
the gastrocolic ligament is grasped near the transverse colon and elevated both toward the anterior abdominal wall and the feet to identify the correct plane between the gastrocolic ligament and the underlying mesentery of the transverse colon . starting from the level of the antropyloric region and proceeding close to the colon ,
step 1 is completed after visualization of the second portion of the duodenum [ figure 2a ] .
the peritoneum overlying the hepatic flexure and the right phrenocolic ligament is sectioned , easily identifying the profile of the kidney without entering a wrong plane behind it .
the hepatic flexure and the proximal transverse colon are separated from the anterior surface of the kidney and the duodenum by blunt dissection , as the colon is brought by its own weight toward the pelvis and the left , without any traction .
step 2 is completed when the third portion of the duodenum is visualized [ figure 2b ] .
working from the free lateral peritoneal edge of the mobilized hepatic flexure , the right paracolic gutter is opened along the ascending colon toward the cecum [ figure 2c ] .
once the peritoneal division around the cecum is completed , the right colon spontaneously falls toward the midline and is easy to detach from toldt 's fascia by blunt dissection , without any traction .
the patient is moved to trendelenburg , with the right side still banked up : this allows the small bowel and the mobilized cecum to fall toward the midline . if present , the appendix is grasped to hold the cecum upwards and straighten the terminal ileum ; otherwise , the peritoneal edge around the cecum is grasped .
the ureter is pursued via blunt dissection along the toldt 's fascia , medially to the gonadal vessels .
after clear identification of the right ureter , the terminal ileum is mobilized dissecting the peritoneum along the base of the small - bowel mesentery [ figure 2d ] until the right colon spontaneously falls toward the midline , disappearing from the monitor : this sign indicates that the dissection is sufficient for exteriorization . in few cases , little further blunt dissection along the toldt 's fascia
the appendix ( or the terminal ileus ) is firmly grasped through the mb trocar : this helps to retrieve the right colon .
the periumbilical port - site incision is extended cephalad to join the epigastric port - site incision , and the right colon is exteriorized [ figure 3 ] .
the final incision joins the epigastric and periumbilical port sites after the terminal ileum and transverse colon are divided at the chosen level , the mesocolon is severed in a v - shape - like fashion toward the supplying vessels using a sealing - dissecting device . the ileocolic vessels and if present the right colic vessels are prepared and divided at their origin [ figure 4 ] .
before closing the midline incision , if desired , a drain is placed through the mb port site .
between july 2010 and july 2014 the above - described technique was applied in 82 consecutive patients by 16 surgeons ( 10 residents and 6 fellows ) .
average number of operations per surgeon was 5 3 ( median 5 , range 1 - 10 ) .
conversion occurred in 10 cases ( 12.2% ) : 3 for adhesions , 6 for unsuspected peritoneal metastases or locally advanced tumor and 1 for bleeding due to tearing of the henle 's gastrocolic trunk occurred in the extracorporeal phase of the operation [ table 1 ] .
patient 's characteristics and intraoperative data grade iii postoperative complications occurred in three patients ( 3.6% ) : 1 .
in the recent years an advice toward centralization of colorectal surgery to high - volume centers has been given by many authors .
nevertheless , the association between caseload and outcomes is still questionable and the majority of colorectal operations are still not performed by high - volume surgeons .
there is a growing agreement that providing local services with adequate surgical education and training could be a more effective strategy to improve outcomes and global health .
arming the growing surgeon with simplified and easy - to - learn surgical techniques could be an important step of this strategy . the original technique proposed by young - fadok and nelson
is intended to keep the laparoscopic procedure as close to the open procedure as possible , in order to make it easily reproducible .
their technique requires one left upper quadrant trocar for the camera and two trocars ( one supraumbilical and one suprapubic ) for the dissecting instruments : the laparoscopic work is to mobilize the cecum and the terminal ileum first , followed by the right colon in a clockwise fashion . as outlined by the authors themselves , it is important to keep the right colon pulled and elevated at any stage during laparoscopy in order to identify the correct planes for dissection .
this advice is particularly true during hepatic flexure mobilization , when inadvertent dissection behind the kidney , injury of the duodenum and inability to find the correct plane between the gastrocolic ligament and the underlying mesentery of the transverse colon may be causes of conversion .
the port site layout by young - fadok and nelson requires placing the camera in the upper trocar , and the surgeon works with both hands coming in sight from the left side : this lateral vision could be difficult to get used to , because our brain works with central vision and expects to see our hands coming in from their own side . moreover , the dissecting instruments are quite coaxial during hepatic flexure mobilization and triangulation is lost . our modification is conceived to respect visual ergonomics ( restoring central vision ) and to allow for the correct triangulation of port sites , especially during hepatic flexure mobilization , which is often the most critical phase .
starting from transverse colon mobilization and proceeding counterclockwise toward the cecum we take advantage of gravity for handling the colon : there is no need to hold the right colon elevated during hepatic flexure mobilization . also , there is no risk of inadvertent dissection behind the kidney because the dissection proceeds above it in a plane where the gerota 's fascia is easily identifiable . with this anterior approach to the hepatic flexure ,
the first target is the exposure of the second portion of the duodenum , which is easily detected : the novice surgeon is not tempted to start with the dissection into the mesocolon , where vascular structures are close and tearing could led to cancer cells seeding . thanks to gravity , the effort to expose the mesocolon is minimal and only a gentle blunt dissection is required to detach it from the posterior planes in a cranial to caudal direction . in a similar way , benseler et al
. found the anterior approach to be safer for mobilization of the splenic flexure during laparoscopic rectal cancer resection .
according to the principles of cme , central vascular ligation is performed after complete mobilization of the right colon , as described by hohenberger et al .
central vascular ligation is done as in open surgery : the use of a sealing - dissecting device is intended to seal the two fascial layers of the mesocolon and reduce the risk of spillage of cancer cells .
the integrity of the mesocolon is violated at the end of the dissection , proceeding from the terminal ileum and the transverse colon toward the central vascular structures .
the medial - to - lateral approach , in which the integrity of the mesocolon is disrupted close to the main colic vessels as the initial step of surgery , is deliberately avoided .
the above - presented technique was applied in 82 patients by 16 low - volume surgeons with a low rate of severe postoperative complications ( 3.6% ) and reoperation ( 2.4% ) .
our results support the advice that even low - volume surgeons , when provided with easy - to - perform surgical techniques , adequate training and a teaching - oriented environment , can achieve good outcomes .
the relationship between outcomes and the surgeon 's caseload in colorectal surgery is still unclear . in the ongoing effort to improve quality of surgery
, education and training of the surgeon may be an alternative strategy to centralization of patients to high - volume centers . as a part of the educational strategy ,
improving simplicity and reproducibility of laparoscopic surgical techniques could be an effective way to increase the diffusion of laparoscopy among surgeons and to achieve good outcomes .
our proposed surgical technique could safely put lrc in the hands of the low - volume surgeon and help the growing surgeon to achieve an increased confidence in laparoscopic colorectal surgery . | background : despite the drive toward centralization of surgery in high - volume centers , the majority of colectomies are still performed by low- or medium - volume surgeons.materials and methods : a modification of the technique of laparoscopic right colectomy ( lrc ) originally described by young - fadok and nelson was developed .
the key points of that technique were maintained , but a different port - site layout and a counterclockwise approach were adopted , to warrant better trocar triangulation , to reduce the need of right colon manipulation and to avoid dissection along false planes .
this modified technique was applied in 82 patients by 16 surgeons with no previous experience in lrc.results:average operative time was 125 35 min .
conversion occurred in 10 cases ( 12.2% ) .
grade iii postoperative complications occurred in 3 patients ( 3.6% ) .
no postoperative mortality was observed .
average number of lymph nodes retrieved was 19 6 .
average length of stay was 7 4 days.conclusion:providing low - volume surgeons with simplified and easy - to - learn surgical techniques could improve outcomes and lead to an increased use of laparoscopy . |
the laws of quantum mechanics forbid the perfect cloning of unknown quantum states @xcite .
this important result , known as the no - cloning theorem , bases on the linearity of the quantum - mechanical transformations and has been subject of continuous research in the last decades . in particular ,
the problem of approximate cloning has been exhaustively explored @xcite .
this is mainly due to the fact that it imposes a limit on our capability to manipulate and broadcast quantum information and because it can be used as an efficient eavesdropping attack on quantum key distribution ( qkd ) @xcite .
the impossibility of generating perfect copies imposed by the no - cloning theorem can be relaxed by resorting a non deterministic process .
this kind of process is called probabilistic cloning , where a set of known linearly independent nonorthogonal quantum states can be cloned perfectly at the expense of succeeding with probability less than one @xcite .
this kind of cloning is of particular interest when testing the security of the so called b92 qkd protocol @xcite , which involves only two non - orthogonal linearly independent states .
other applications and implementations are studied in @xcite and @xcite recently , this probabilistic cloning scheme has been successfully implemented via nuclear magnetic resonance @xcite in the case of generating two clones of a single qubit state .
this demonstration , however , does not allow the broadcasting of the cloned states .
this led us to propose the implementation of an optimal probabilistic cloning based on entangled twin photons @xcite .
this proposal is based on linear optics together with a pair of maximally entangled twin photons generated via spontaneous parametric down - conversion .
the states to be cloned are encoded in the polarization degree of freedom of one of the twin photons . after a sequence of measurements
the state to be cloned as well as its perfect clone are encoded in the polarization and spatial degree of freedom of the resting photon respectively .
the former photon is destroyed in a photo - detection process .
thereby , the clones are produced in a non - local way and can be broadcasted .
sources of polarized entangled pairs of photons have been shown to have very good fidelities when comparing with bell states @xcite , but additional loses can appear when distributing the entangled pairs at large distances , and also other fluctuations can make the state imperfect .
therefore even if the source is close to perfect the state shared by the different parties is not necessary close to perfect .
this is a serious issue , since perfect clones are created only when the parties share a perfect entangled state . in this work we present an example of how is still possible to have high fidelity copies even if the entanglement is not high quality .
we study the performance of the nlopc process when cloning a state from a known set of linearly independent nonorthogonal states , implemented via a partially entangled state of a pair of twin photons .
we show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process to the photon which encodes original and copy states .
this process is applied after the nlopc protocol has been carried out .
the correction procedure is based on the application of unambiguous state discrimination and does not requires information about the state undergoing the cloning process @xcite .
this procedure is complete determined by the schmidt coefficients of the partially entangled state and the measurement results of the cloning process . since
quantum state discrimination is a probabilistic process the correction succeeds with a certain probability .
the clones emerging from the correction procedure are perfect but the overall success probability of generating perfect clones is thus reduced by a factor given by the optimal probability of unambiguously discriminating two nonorthogonal states , that is the ivanovic - dieks - peres limit .
the states to be discriminated are defined by the schmidt coefficients of the partially entangled quantum channel .
we also study the possibility of local probabilistic cloning ( lpc ) where the states to be cloned are encoded in the polarization degree of freedom of one of the twin photons while a perfect clone is generated and encoded in the spatial degree of freedom of the same photon .
thus , the clones are produced locally .
the degrees of freedom of the resting photon are used as ancillary systems to implement conditional transformations .
the experimental setup for lpc turns out to be simpler than in the case of nlopc but the success probability of the lpc is the half of the success probability of nlopc .
we also study the case local probabilistic cloning via partially entangled twin photons .
this article is organized as follows : in section [ sectionii ] we summarize briefly the the optimal probabilistic cloning process . in section [ sectioniiib ]
we present the experimental setup for implementing the lpc .
section [ sectioniv ] is devoted to study the performance of the proposed setup for lpc when the entanglement it is not maximal . in section [ section5 ]
we analyze the nlopc via a partially entangled state and show that the addition of an unambiguous state discrimination stage corrects the errors generated by the partial entanglement at the expense of reducing the overall success probability of generating perfect clones . in section [ sectionv ]
we summarize our results .
the probabilistic quantum cloning machine is constructed by concatenating a unitary transformation @xmath0 and a projective measurement @xcite .
the action of the unitary transformation is @xmath1 where @xmath2 are two nonorthogonal states encoded in the original system @xmath3 .
these are the states to be cloned .
the perfect clone of each one of these states is encoded in the copy system @xmath4 as @xmath5 .
additionally , the transformation requires a third ancillary system @xmath6 spanned by the orthogonal states @xmath7 and @xmath8 .
initially , systems @xmath4 and @xmath6 are described by a joint blank state @xmath9 .
after the unitary transformation @xmath0 has been carried out a measurement on system @xmath6 projects it onto state @xmath7 .
systems @xmath3 and @xmath4 are then described by a product state formed by the original state and its clone .
this succeeds with an optimal probability @xmath10 given by @xmath11 in case of projecting system @xmath6 onto state @xmath8 systems @xmath3 and @xmath4 are left in an entangled state @xmath12 , which does not correspond to a cloning process . considering the states to be cloned as @xmath13 ,
the action of the unitary transformation @xmath0 onto the basis states @xmath14 and @xmath15 is given by @xmath16 where coefficients @xmath17 and @xmath18 are @xmath19 in this case the success probability , according to eq .
( [ success - probability ] ) , is given by @xmath20 and the state @xmath12 becomes @xmath21 . in the scheme that we study
the fidelity is unitary and the probability is given by eq . [ success - probability - particular ] , then @xmath22 .
we can compare this with the performance of the universal cloning machine , see for example @xcite , which is a deterministic process , but with limited fidelity equal to @xmath23 , in which case @xmath24 .
it is straight forward to see that our scheme of probabilistic cloning overperforms universal cloning when @xmath25 considering this particular figure of merit .
analytical solutions for the problem of cloning larger sets of linearly independent states are known in cases where the states to be cloned have a high degree of symmetry @xcite .
the experimental setup proposed for implementing the local probabilistic cloning of single - qubit states is illustrated in fig .
( [ setup ] ) .
this requires the use of a source for generating a maximally entangled polarization state of two photons .
this state can be generated via spontaneous parametric down - conversion of type - i using the scheme presented in @xcite and is of the form @xmath26 where @xmath27 and @xmath28 describe horizontal and vertical polarization for photon @xmath29 .
photon @xmath30 is directed toward interferometer @xmath31 which is defined by polarizing beam splitters @xmath32 and @xmath33 .
states @xmath34 and @xmath35 describe the spatial state of photon @xmath30 propagating at the upper or lower arm of the interferometer , correspondingly .
photon @xmath36 enters into interferometer @xmath37 whose two input ports are defined by polarizing beamsplitter @xmath38 .
the three output ports of @xmath37 are generated by polarizing beam splitter @xmath39 and beam splitter @xmath40 .
states @xmath41 and @xmath42 describe the spatial state of the photon @xmath36 propagating at the upper or lower arm of interferometer @xmath37 , respectively .
this interferometer is lossy since polarizing beamsplitter @xmath39 allows vertically polarized photons to leave the interferometer .
the state of the twin photons after polarizing beam splitters @xmath32 and @xmath38 is given by latexmath:[\ ] ] where @xmath107 . as was shown in section ( [ sectioniv ] ) ,
making use of unambiguous state discrimination is possible to perform the following transformations , @xmath162 which correct the state @xmath158 , however this transformation also introduces a non - conclusive result in the process which is characterized by a certain probability of success .
this transformation can be implemented using a conditional interferometer . in order to correct the state ( [ phi2 ] )
two interferometers are needed , one for the pair ( [ eq : alpha- ] ) and other for ( [ eq : alpha - tilde ] ) , see ( [ transformation ] ) the first interferometer , @xmath163 , acts on photons coming from path @xmath164 and is characterized by the transformation @xmath165 where @xmath90 is the angle defined by the half wave plate inside the interferometer and has to be set to @xmath166 the paths @xmath167 and @xmath168 define the result of the transformation , that means whether discrimination was successful , @xmath167 , or failed , @xmath168 .
finally , the probability of successfully discriminate the pair of states ( [ eq : alpha- ] ) is given by @xmath169 the procedure is similar for the other interferometer , @xmath170 , where the transformation is characterized by @xmath171 and the probability of success is given by @xmath172 the joint action of @xmath163 and @xmath170 over state @xmath173 is given by @xmath174 the first term describes the successful process , where the two clones are generated in the polarization and spatial degree of freedom of photon 2 , and the last term of equation ( [ eq : result ] ) describes the failure process in which an entangled state is obtained , this state is independent of the state to be cloned .
the process is the same for state @xmath175 , and is analogous for the remaining states , @xmath176 and @xmath177 , in which the tilting angle of the half wave plate in the interferometers has to be changed and an extra unitary transformation ( ruo ) is necessary before applying the two conditional interferometers .
finally , the total probability of success is determined by both the optimum probability of cloning and the probability of unambiguously discriminate between two non - orthogonal states , @xmath178
the cloning of quantum states has been a constant subject of study over the last decades .
this process has been experimentally implemented in the case of approximate universal cloning @xcite and variations .
the realization of probabilistic cloning has been only recently achieved via nuclear magnetic resonance @xcite .
since this proposal requires the use of ensemble techniques , it does not constitute cloning of individual quantum systems . here
, we have studied the possibility of implementing probabilistic cloning via twin photons in an all - optical setup .
this allows the broadcasting of the clones .
we have proposed an experimental setup for realizing the probabilistic cloning of two nonorthogonal quantum states .
the states to be cloned are encoded in the polarization degree of freedom of a single photon while the clones are encoded in the two available propagation paths of the same photon .
the resting twin photon is employed as an ancillary system to carry out conditional transformations .
this proposal achieves an overall success probability equal to the half of the optimal cloning probability .
this is due to the use of a filtering process after that the state to be cloned has been encoded .
a second characteristic of our proposal is the use of recovery operators to correct errors arisen in the cloning process itself , which is akin to quantum teleportation @xcite .
a different approach to the problem of probabilistic nonlocal cloning has also been reported @xcite but considering a ghz state of a tripartite system as initial source and make use of an additional port qubit owned by the sender which make it more difficult to implement .
additional , it is not symmetric , which means that each copy is created with a different success probability .
we have also studied the consequences of a partially entangled state as quantum channel for the cloning process and shown that the errors generated by this class of channel can be probabilistically corrected by means of unambiguous state discrimination .
the total probability of generating perfect clones is then reduced by a factor equal to the optimal probability of discriminating two nonorthogonal states which are defined by the schmidt coefficients of the quantum channel . in this way we showed that the effect of having a nonmaximal entangled state as a source and correcting after is a diminution in the rate of the perfect clones generation .
this work was supported by grant msi p010 - 30f and grants fondecyt no .
11085057 and no . 11121318
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since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but produces perfect clones .
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= 4 _ keywords _ : quantum teleportation , quantum cloning |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Agricultural Border Safeguard
Protection Act''.
SEC. 2. RESTORATION OF IMPORT AND ENTRY AGRICULTURAL INSPECTION
FUNCTIONS TO THE DEPARTMENT OF AGRICULTURE.
(a) Repeal of Transfer of Functions.--Section 421 of the Homeland
Security Act of 2002 (6 U.S.C. 231) is repealed.
(b) Conforming Amendment to Function of Secretary of Homeland
Security.--Section 402 of the Homeland Security Act of 2002 (6 U.S.C.
202) is amended--
(1) by striking paragraph (7); and
(2) by redesignating paragraph (8) as paragraph (7).
(c) Transfer Agreement.--
(1) In general.--Not later than the effective date
described in subsection (g), the Secretary of Agriculture and
the Secretary of Homeland Security shall enter into an
agreement to effectuate the return of functions required by the
amendments made by this section.
(2) Use of certain employees.--The agreement may include
authority for the Secretary of Agriculture to use employees of
the Department of Homeland Security to carry out authorities
delegated to the Animal and Plant Health Inspection Service
regarding the protection of domestic livestock and plants.
(d) Restoration of Department of Agriculture Employees.--Not later
than the effective date described in subsection (g) of this section,
all full-time equivalent positions of the Department of Agriculture
transferred to the Department of Homeland Security under section 421(g)
of the Homeland Security Act of 2002 (6 U.S.C. 231(g)) shall be
restored to the Department of Agriculture.
(e) Authority of Animal and Plant Health Inspection Service
Regarding Inspection User Fees.--The Administrator of the Animal and
Plant Health Inspection Service may, as applicable--
(1) continue to collect any agricultural quarantine
inspection user fee; and
(2) administer any reserve account for the fees.
(f) Duties of Secretary of Agriculture.--
(1) In general.--The Secretary of Agriculture (referred to
in this subsection as the ``Secretary'') shall--
(A) develop standard operating procedures for
inspection, monitoring, and auditing relating to import
and entry agricultural inspections, in accordance with
recommendations from the Comptroller General of the
United States and reports of interagency advisory
groups, as applicable; and
(B) ensure that the Animal and Plant Health
Inspection Service has a national electronic system
with real-time tracking capability for monitoring,
tracking, and reporting inspection activities of the
Service.
(2) Federal and state cooperation.--
(A) Communication system.--The Secretary shall
develop and maintain an integrated, real-time
communication system with respect to import and entry
agricultural inspections to alert State departments of
agriculture of significant inspection findings of the
Animal and Plant Health Inspection Service.
(B) Advisory committee.--
(i) Establishment.--The Secretary shall
establish a committee, to be known as the
``International Trade Inspection Advisory
Committee'' (referred to in this subparagraph
as the ``committee''), to advise the Secretary
on policies and other issues relating to import
and entry agricultural inspection.
(ii) Model.--In establishing the committee,
the Secretary shall use as a model the
Agricultural Trade Advisory Committee.
(iii) Membership.--The committee shall be
composed of members representing--
(I) State departments of
agriculture;
(II) directors of ports and
airports in the United States;
(III) the transportation industry;
(IV) the public; and
(V) such other entities as the
Secretary determines to be appropriate.
(3) Report.--Not less frequently than once each year, the
Secretary shall submit to Congress a report containing an
assessment of--
(A) the resource needs for import and entry
agricultural inspection, including the number of
inspectors required;
(B) the adequacy of inspection and monitoring
procedures and facilities in the United States; and
(C) new and potential technologies and practices,
including recommendations regarding the technologies
and practices, to improve import and entry agricultural
inspection.
(4) Funding.--The Secretary shall pay the costs of each
import and entry agricultural inspector employed by the Animal
and Plant Health Inspection Service--
(A) from amounts made available to the Department
of Agriculture for the applicable fiscal year; or
(B) if amounts described in subparagraph (A) are
unavailable, from amounts of the Commodity Credit
Cooperation.
(g) Effective Date.--The amendments made by this section take
effect on the date that is 180 days after the date of enactment of this
Act. | Agricultural Border Safeguard Protection Act - Amends the Homeland Security Act to repeal the transfer of agricultural import and entry inspection functions from the Department of Agriculture to the Department of Homeland Security (DHS).
Directs the Secretary of Agriculture to: (1) develop agricultural import and entry procedures for inspections, monitoring, and auditing; (2) ensure that the Animal and Plant Health Inspection Service has an electronic system with real-time tracking capability for monitoring, tracking, and reporting inspection activities; (3) develop and maintain an integrated, real-time communication system with respect to import and entry agricultural inspections to alert state agriculture departments about significant Service findings; and (4) establish the International Trade Inspection Advisory Committee. |
» SEE THE SLIDESHOW «
Angelina Jolie is explaining why she took the role of Elise Clifton-Ward, the woman of mystery who captivates Johnny Depp in The Tourist, which opens this month. It’s because she plans things. “I was looking for a very short thing to do before Brad started filming [Moneyball],” she says. “And I said I needed something that shoots not too long, in a nice location for my family. Somebody said there’s a script that’s been around, and it shoots in Venice and Paris. And I said, ‘Is it a character I haven’t played before?’ And they said, ‘Yes, it’s a lady.’ ” She laughs: Uhhuhhuhhehhehheh.
Sitting opposite one of the world’s most notorious beauties is an experience that requires some processing. Impressions: (1) She has a seriously filthy laugh. (2) She is graceful, straight-backed, head held high. (3) Her photogenic beauty is mesmerizing in real life. Which is quite disturbing, because it makes you “gaze and gaze” (to borrow Nancy Mitford’s phrase from Love in a Cold Climate). Women who can hypnotize people just by sitting and breathing have a spooky power. Like Princess Diana (though she was not as beautiful as Angelina). I asked her producer, Graham King, at one point if he found the beauty distracting. He said, “In The Tourist?” Me: “On her face!” King: “Oh! One hundred percent.”
She is wearing a little cropped jacket by Neil Barrett, who dresses haute Hollywood, classic pants by Helmut Lang, and Ferragamo flats. Black, black, and black. “As Brad’ll tell you—and my kids—apparently Mommy only wears black,” she says. Because she was a Goth, right? No, she says, it’s utilitarian, it’s practical: “I like to get up so every pair of pants goes with every top, every dress goes with every shoe. I’ve a very tiny closet. Brad’s always laughing at me. Some days, yes, I have the nightgown that looks like a dress that I can sleep in and pick the kids up at school. And maybe take a meeting if I switch into heels.”
She didn’t need heels today. Her choice of location for Vogue’s interview is a coolly hip hotel on Hollywood Boulevard called the Roosevelt, whose restaurant (where we have dinner later) is on “the Marilyn Monroe bridge” overlooking the Hockney pool. Oh! Glamour. On the way here, my cell phone rang and a panicky voice asked, “Where are you? Because Angelina is approaching the hotel, so she’ll be ten minutes early.” (In my entire career, no female actor has ever been early. One man has: John Cleese.) As my driver hurtled us into the hotel car park, access was blocked by two vans flanking an SUV—clearly containing a VVIP—and all I could do was watch the little figure being swooshed up, wafted aloft, and delivered inside by burly escorts. Everyone stood in line to gaze, like parlormaids in Gosford Park.
The level of (a) security and (b) logistical organization that moves the Jolie-Pitt machine probably feels normal to them now. From the inside, Brad and Angelina are two hardworking parents with in-demand skill sets who manage their work/life/family balance as best they can, while fitting in philanthropy on top. From the outside, they’re people who can shut down Toronto. I pick Toronto only because I witnessed Brad Pitt do just that in 1997, for the Seven Years in Tibet premiere. Screaming Bradmaniacs confined him to his hotel room for 48 hours, while costar David Thewlis strolled around unbothered. “For a man, being as beautiful as Brad is almost an affliction,” Thewlis told me at the after-party. When I tell Angelina this tale, her eyes dance and she gets very gurgly. “Well, he’s a handsome man.” Yes! And? “No, I think he’s an extremely sexy—extremely handsome and the most sexy. . . . When I think about him, I just think of the man who’s such a great friend and such an extraordinary father. And that’s when I fall, you know, when I have my moments of getting—whoarr!—caught up in how much I love him . . . it’s usually when I see him with the children.”
Which is often, because he’s pretty hands-on. “We take turns working. One of us is always at home with the kids—always,” says Jolie. “Taking them out to things and being there with them and bringing them to school or to the set to visit Mommy or Daddy.” But “at home” from February to May this year was a villa on the Grand Canal: Daddy was child-wrangling in Venice while Mommy filmed The Tourist. Jolie can barely get her words out about how blissful it was, how the kids loved it, and how fabulously lucky she felt to work while “living in the history of this gorgeous country.”
Click here for a slideshow of Angelina Jolie throughout the years in Vogue.
The Venetian setting makes The Tourist a nice, gift-wrapped holiday movie. The financial skulduggery and beastly villainy has a British accent, and the knowingly high-Hitchcock look has Jolie wearing fabulous clothes (costume designer Colleen Atwood used an original Charles James day dress some people I know would kill for). Plus, Johnny Depp and Angelina Jolie go head-to-head for the first time ever. Depp in Venice! Who can resist? Their onscreen chemistry in The Tourist is quite swoony. “I suppose either you spark or you don’t,” Depp told me from the set of Pirates 4.
The Tourist’s director, Florian Henckel von Donnersmarck (a smart and instantly likable man whom we shall call by his given name from now on because “Henckel von Donnersmarck” is just too Almanach de Gotha), was Jolie’s pick. She thought the film should have “a European elegance”; she’d loved The Lives of Others (2006), his extraordinary German-language debut feature. “I couldn’t believe it that he was open to doing it, and then we found out that Johnny was open to doing it. So what was always this tiny idea to do a little film in Europe suddenly became this . . . bigger movie.”
Florian really wanted to work with her, too. Are you kidding? “Literally,” he tells me in a phone call, “she gets every single script that has a female role aged between eighteen and 40—every script. And she just follows her feeling, holds her own counsel. She’s probably the only global megastar that doesn’t even have an agent—she doesn’t even have a publicist.” Mmm. And that thing of gazing and gazing? “You never lose it,” he says swiftly. “I can tell from the way that Brad looks at her that he never loses it.” Florian was intrigued when his birthday fell during filming and Angelina asked what his plans were. He thought she meant dinner. She meant his plans for the next year. “She wanted to hear what I was going to change about myself. Because that’s how she approaches life. She looks into the future.”
She does. Clear away the craziness and tabloid clatter that swirls around the Jolie-Pitt family (or “brand”), and you find a practical woman with terrific forward-planning skills. She plans in all areas: family, movies, humanitarian work, though they intertwine because she is a working mother. “I was feeding the babies”—Vivienne and Knox—“while I was reading the script [of Salt],” she remembers, “and I was feeling very round and lovely and Mom-y, and I’d been living in a nightgown for a very, very long time.” Part of the reason she did it was to get back in shape (“practicing the stunts is where you get your strength back”); another was sex-changing Tom Cruise (for whom it was written—or rumored to have been written). She says, “I felt it was a weird thing that every time you ask for a strong female role, it’s written in this strange way where it uses sexuality far too much. Or it’s all about being a woman and beating a man. So it wasn’t a surprise to me that the only way to do a strong female role properly was to not have originally written for a woman.”
Jolie has an uncanny nose for projects that will get some money into the coffers, between doing things she has a passion for. She smoldered through Tomb Raider 1 and 2 (and there is a generation of 30-year-old men who worship her for them) on the back of Girl, Interrupted, the little movie that made her an Oscar winner. She made Beyond Borders, basically about the work of Médecins Sans Frontières, because she wanted to; it tanked utterly. The movie of hers she likes best is A Mighty Heart. “Possibly because I loved Mariane [Pearl], and Brad produced it, and I think it was a well-done film about something that matters.” Voilà. She picked up a rumored $20 million paycheck from Salt, after which she wallowed happily in The Tourist and began shooting her directorial debut (still called Untitled Love Story as I write), which is about the Bosnian war of 1992–96, one of those foreign wars that many, many people can only vaguely place in geography or history (Bosnia? Herzegovina? Montenegro?), and yet the Siege of Sarajevo was one of the most vicious actions of modern times.
So “because Sarajevo, happily, has been rebuilt,” she and the family were in a rented house on location in Budapest, Hungary, in the runup to the holidays while Mommy was shooting there. Their permanent homes are on three continents (and two hemispheres) because she planned her family’s life that way. The house on stilts in the Cardamom Mountains of Cambodia that she bought for Maddox when he was a baby; the “little place in New Orleans,” where Brad’s Make It Right houses are being built; and the “little place here,” in Los Angeles. Their big place is in the South of France, which is, I think, where she plans to end up. “Hopefully, they’ll go to high school in Aix-en-Provence,” she says. Aix-en-Provence? “It looks like a great place to be a teenager.”
And that is why she does the child-rearing thing that she is most viciously excoriated for: first of all, hiring polyglot nannies in a kind of family language bank (one helper speaks Vietnamese to Pax; another, Cambodian to Maddox. “We have not yet attempted Amharic,” says Jolie—Zahara’s from Ethiopia—“but we will one day”). And second, enrolling all the school-age children at the Lycée Français, where much of the curriculum is in French. This fall, while she was in Hungary filming her Bosnian movie, Maddox, Pax, Zahara, and Shiloh trotted off to school at Budapest’s Lycée Français, picking up exactly where they left off at the Lycée in L.A. How smart is that? Angelina or Brad could make movies in Athens, Bangkok, Caracas, or Düsseldorf (and that’s only A to D) while the kids get on with lessons as normal because the instruction is the same the world over.
Did you want a big family? I ask her. She shrugs and says, “I didn’t know.” Because it’s rare, I say, especially now and here in the West, where really big families seem culturally odd and newsworthy. She looks at me levelly as I burble on about how the popular perception of women who have large broods (polygamists, Octomom) is unfavorable. Her shocked giggles are loud on my voice recorder; she loses her equanimity enough to say, “That sounds horrible.” (Not to mention rude. I can’t believe I dragged in Octomom.) But when everything in the modern world is reducing women’s fertility, compromising their ability to even have children, big families seem, um. . . . She retorts, “I didn’t have all my children.” Three, though? “I only planned for two!” says the mother of twins. “To each his own. It’s one of those things. How you build your family—you have to know what you’re capable of handling and how your children will relate to each other. Maybe if you have one child and that child has a lot of needs, you realize you cannot give more attention to another. Sometimes you just know as a parent. We felt we could handle more children, and we have a very happy, very full home. So.” With the look on her face querying whether my intellect is dull enough that show-and-tell might be better than question and answer, she takes out her white BlackBerry, automatically glances around to check that nobody else can see, and scrolls fiercely. “Wait, where is it, give me a second, I’m a mom, sorry, there’s a lot of them. . . . Now. One of my favorite pictures: This is Brad. Dinnertime.”
Interior, evening, big round table set with plates, in foreground Brad Pitt, three-quarter profile, surrounded by one, two, three . . . four (Jolie snickers as I count aloud), five, six little faces. Me: “You did very well, to even everyone up like that.” She says, “It wasn’t a plan for it to be as even as it turned out.” She takes back her BlackBerry and scrolls again: “My girls [Zahara, Shiloh, Vivienne, all spattered with great gobs of color]—they did some body painting.” They’re adorable. It is hard, she says, to think of having any fewer. I wonder if she’s overrun with cats and dogs and hamsters on top? “Well, someone found a lizard yesterday,” she says. “And Shiloh appeared.” (She checks herself momentarily, saying, “I am sure there’s going to be some comment about this, which fortunately I will not read,” before restarting.) “Shiloh found a dead bird, so she came in and said, ‘Can I have a dead pet?’ And I’m . . . ‘Uh-uh, I don’t think it’s healthy, honey. I think they have to put him in a box,’ and I had to run out to find, like, a taxidermy bird. I just worked it out for her.” Did Shiloh know about taxidermy? “No. But I figured that I couldn’t keep the actual dead bird from the yard, so I swayed her toward one that had been cleaned, at least.” We are both giggling, and Jolie says that Shiloh is indeed “hysterical.” Also that they have a bulldog called Jacques, who lives in their house in France.
And does she cook their dinner? “Sometimes. I’m not the best cook. Pax is a better cook than me. Pax likes to cook. But I try to when I can. Any house that we’re in, we all chip in. But the kids are very sweet . . . so enthusiastic anytime I cook. Especially Maddox; he’s just this little man that’s very supportive of me—it’s like he’s raised me a bit. So I cooked them all breakfast before school this morning, and he has that kind of ‘Thanks, Mom! Good job!’ ”
She starts giggling helplessly and says she didn’t burn the bacon. “I’m getting better at bacon.”
Film, family, and philanthropy are the three pillars of her life. “My children are from the countries that I work in,” she says. “I don’t see my family as a global family. I don’t see it separate. So when I look at my kids, and I wake up and hear something’s happening in Pakistan, I think: It’s Asians, and my children are from that part of the world. Those kids are very much like my kids. So I’m happy to be able to go.”
It was a different-looking, different-sounding Angelina Jolie I saw in BBC reports from flooded northwest Pakistan in early September. (She was between scouting Budapest for her Untitled Love Story and doing publicity for The Tourist.) Asked by the United Nations High Commissioner for Refugees (UNHCR) to highlight the plight of people displaced into camps by the floods, she met with women who lost children to the surging water and gave impromptu press conferences in sweaty rooms, loud with angry-seeming men. Back in Los Angeles, she tells me the country with the highest number of refugees in the world is Pakistan. Jolie was appointed UNHCR Goodwill Ambassador in 2001: She does an impressive job for them. She talks about the issues like this is her day job. I tell her Pakistan is a hard country to raise money for: Zardari’s government seems pretty unlovable. She becomes slightly heated: “The president is not the people!” And says, “If you are concerned about security in the world, the last thing you want to do is not give your support to Pakistan and Afghanistan, because that’s the most dangerous thing. That’s the least intelligent thing, as far as I’m concerned, to do.”
It was a tough trip, with security issues. “Because it was so high in the north. . . . I don’t like it when Brad has to worry.” She was happy to be back home safe. “But I got calls from the people that’d asked me to go—from the U.N. to the State Department. They felt it was effective, so I could go to sleep for two days and play with the kids and feel like. . . . ” Effective? What does it mean, effective? She says, “I don’t ask the details. They thought it was effective. I just do the best I can do.” ||||| Angelina Jolie: Brad Pitt Is 'Extremely Sexy'
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In the new issue of Vogue, 'The Tourist' star opens up about her relationship with Pitt and their six kids.
"I think he's an extremely sexy -- extremely handsome and the most sexy ... When I think about him, I just think of the man who's such a great friend and such an extraordinary father. And that's when I fall, you know, when I have my moments of getting caught up in how much I love him ... it's usually when I see him with the children," she says.
Interestingly enough, both Pitt and the children are vocal about Jolie's wardrobe choices.
"As Brad'll tell you -- and my kids -- apparently Mommy only wears black. I like to get up so every pair of pants goes with every top, every dress goes with every shoe. I've a very tiny closet. Brad's always laughing at me. Some days, yes, I have the nightgown that looks like a dress that I can sleep in and pick the kids up at school. And maybe take a meeting if I switch into heels," she explains. Angelina Jolie and Brad Pitt are arguably the most beautiful couple in the world, but Jolie finds her partner most handsome when he's playing dad.In the new issue of Vogue, 'The Tourist' star opens up about her relationship with Pitt and their six kids."I think he's an extremely sexy -- extremely handsome and the most sexy ... When I think about him, I just think of the man who's such a great friend and such an extraordinary father. And that's when I fall, you know, when I have my moments of getting caught up in how much I love him ... it's usually when I see him with the children," she says.Interestingly enough, both Pitt and the children are vocal about Jolie's wardrobe choices."As Brad'll tell you -- and my kids -- apparently Mommy only wears black. I like to get up so every pair of pants goes with every top, every dress goes with every shoe. I've a very tiny closet. Brad's always laughing at me. Some days, yes, I have the nightgown that looks like a dress that I can sleep in and pick the kids up at school. And maybe take a meeting if I switch into heels," she explains.
"I felt it was a weird thing that every time you ask for a strong female role, it's written in this strange way where it uses sexuality far too much. Or it's all about being a woman and beating a man. So it wasn't a surprise to me that the only way to do a strong female role properly was to not have originally written for a woman.""My children are from the countries that I work in. I don't see my family as a global family. I don't see it separate. So when I look at my kids, and I wake up and hear something's happening in Pakistan, I think: It's Asians, and my children are from that part of the world. Those kids are very much like my kids. So I'm happy to be able to go.""Sometimes. I'm not the best cook. Pax is a better cook than me. Pax likes to cook. But I try to when I can. Any house that we're in, we all chip in. But the kids are very sweet ... so enthusiastic anytime I cook. Especially Maddox; he's just this little man that's very supportive of me -- it's like he's raised me a bit. So I cooked them all breakfast before school this morning, and he has that kind of 'Thanks, Mom! Good job!'" | – Angelina Jolie opens up about her home life and her “extremely handsome and … most sexy” beau Brad Pitt in the December issue of Vogue, along the way relaying a funny story about Shiloh that she says will surely inspire “some comment … which fortunately I will not read.” It appears Shiloh, along with boys’ clothing, also likes dead animals, and recently asked Jolie if she could keep a dead bird she found. Mom’s solution: Buy her a dead bird “that had been cleaned, at least,” from a taxidermist. Jolie defends her family, reminding Vicki Woods—who brings up the unfavorable public opinion of many people with large families—“I didn’t have all my children.” Nor can she imagine life without any of them: “We have a very happy, very full home,” she says as she scrolls through family photos on her BlackBerry. She especially savors watching Pitt with their kids: “That’s when I fall, you know, when I have my moments of getting—whoarr!—caught up in how much I love him … it’s usually when I see him with the children.” Click here for more from the interview. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Communications Opportunity Act of
1994''.
SEC. 2. FINDINGS.
The Congress finds the following:
(1) Section 309(j)(3) of the Communications Act of 1934
requires the Federal Communications Commission to disseminate
licenses among a wide variety of applicants, including small
businesses, rural telephone companies, and businesses owned by
members of minority groups and women (hereinafter in this Act
referred to as ``designated entities'').
(2) Section 309(j)(4) of such Act requires the Commission
to ensure that small businesses, rural telephone companies, and
businesses owned by minority groups and women are given the
opportunity to participate in the provision of spectrum-based
services, and, for such purposes, requires the Commission to
consider the use of tax certificates, bidding preferences, and
other procedures.
(3) License set-asides and installment payments are
additional policy tools available to the Commission for
ensuring that licenses are disseminated to designated entities.
(4) Designated entities are greatly underrepresented in all
of the telecommunications industries. In particular, businesses
owned by members of minority groups and women suffer numerous
barriers to participating in the provision of
telecommunications services. Market entry is greatly
complicated by historically low participation and by a lack of
access to capital markets for businesses owned by members of
minority groups and women.
(5) Because the electromagnetic spectrum is a public
resource and because minorities and women face discrimination
and other barriers to entering the telecommunication market,
there is a compelling public interest to promote diversity in
the participation in the telecommunications industries in order
to promote the goals of competitive prices for services,
service innovation, full employment, and diversity of opinions
and viewpoints in public discourse.
(6) Because of the extremely capital intensive nature of
developing and deploying systems in new telecommunications
industries, and the ability of large corporations to amass
financial resources swiftly and efficiently, allocation of the
electromagnetic spectrum under a purely competitive approach
will greatly hinder access to licenses by designated entities,
especially business owned by members of minority groups and
women, wanting to provide telecommunications services. Without
the use of certain bidding preferences, in particular set-
asides, business owned by members of minority groups and women
will not make significant progress in participating in the
telecommunications industries.
SEC. 3. PARTICIPATION BY DESIGNATED ENTITIES.
(a) General Requirement.--The Commission shall ensure the
participation of small businesses, rural telephone companies, and
businesses owned by members of minority groups and women in the
provision of spectrum-based services, particularly through licenses
controlled by them.
(b) Licensing Plan.--
(1) Requirements applicable to competitive bidding.--If the
Commission decides to use competitive bidding to grant 3 or
more licenses which serve a market, the Commission shall
reserve at least one license, of up to 30 megahertz, for
bidding by designated entities only. If more than 6 licenses
serving a market are to be conferred through competitive
bidding, the Commission shall reserve at least 2 licenses, one
of which is at least 30 megahertz, for bidding by designated
entities only. In addition, the Commission shall provide
bidding preferences to designated entities which choose to bid
on other licenses, but may not substitute such preferences for
the license reservation required in this paragraph, or provide
such reservations to entities which are not designated
entities.
(2) Additional requirements.--To the maximum extent
feasible, the Commission shall equalize licenses to be bid on
initially by size and area, and shall not discriminate between
designated entity licenses and other licenses.
(3) Access to capital.--In developing rules regarding other
licenses and licensees for the same service, the Commission
shall take into account the impact of those rules on the
competitiveness and access to financing of designated entities.
To the extent possible the Commission should provide incentives
for nondesignated entities to invest as minority equity holders
in designated entity concerns. To the extent possible, the
Commission shall ensure that its preferences are not abused.
(4) Simple procedures required.--Particularly for rural
areas, the Commission shall provide a simple regulatory
approval process to allow and encourage voluntary partitioning
of licenses between overall license holders and rural telephone
companies and others which wish to serve smaller portions of
the license area.
(c) Competitive Bidding and Bid Financing.--
(1) Considerations required.--The Commission shall
carefully consider the practical effect of its auction and
related requirements on designated entities, and shall seek
wherever possible to remove or lessen regulatory and business
barriers to successful participation by designated entities,
and to provide flexibility to designated entities. This
consideration shall include--
(A) lower application fees;
(B) the initial payment or downpayment shall be no
more than 10 percent of a winning bid for successful
designated entity bidders; and
(C) installment payments of the balance due over
the term of the license.
(2) Flexibility.--The Commission shall extend similar
flexibility to requirements of financial capability for
designated entities which have won licenses. Good faith efforts
to pursue financing and construction shall meet the
requirements of title II and regulations enacted pursuant
thereto.
(3) Additional methods.--The Commission shall consider
additional methods to maximize effective participation of
designated entities in auctions and the resulting marketplace.
These methods may include devices such as tax certificates.
(d) Rules Applying to Designated Entities With Licenses.--
(1) Waivers.--In general, designated entities should be
subject to the same rules as all other parties. The Commission
shall institute a waiver process whereby a designated entity
licensee can demonstrate why the public interest will be served
by granting flexibility to such an entity.
(2) Transfers.--Designated entity licensees may freely
transfer a license to a third party, which qualifies as a
designated entity, without additional financial penalties or
obligations. A designated entity may transfer its license to a
nondesignated entity if the parties comply with the
requirements of paragraph (3).
(3) Payments by transferees.--Any party which is not a
designated entity but which buys a controlling interest in a
license from a designated entity must pay the government the
balance due of the spectrum bid immediately. Until 3 years
after award, a nondesignated entity must pay, in addition, the
difference, if any, between the amount initially bid by the
designated entity and the market price for such licenses, based
on the average of nondesignated entity bids for similar
licenses in that market. The Commission shall establish a
formula for calculating this difference taking into
consideration any bidding credits. | Communications Opportunity Act of 1994 - Requires the Federal Communications Commission (FCC) to ensure the participation of small businesses, rural telephone companies, and businesses owned by minorities and women ("designated entities") in the provision of spectrum-based services, particularly through licenses.
Directs the FCC, if it uses competitive bidding to grant three or more licenses which serve a market, to reserve at least one license, of up to 30 megahertz, for bidding by designated entities. Reserves at least two licenses for bidding by designated entities, one of which is at least 30 megahertz, if more than six licenses are to be conferred through competitive bidding. Requires the FCC to provide bidding preferences to designated entities which choose to bid on other licenses, but prohibits the FCC from substituting such preferences for the license reservations.
Directs the FCC to equalize licenses to be bid on initially by size and area and prohibits discrimination between designated entity licenses and other licenses.
Requires the FCC, in developing rules regarding licenses and licensees for the same service, to take into account the impact of those rules on the competitiveness and access to financing of designated entities.
Directs the FCC, particularly for rural areas, to provide a simple regulatory process to allow and encourage voluntary partitioning of licenses between overall license holders and rural telephone companies and others which wish to serve smaller portions of the license area.
Requires the FCC to seek to remove or lessen regulatory and business barriers to successful participation by designated entities and to provide flexibility to such entities, including flexibility to requirements of financial capability.
Authorizes designated entity licensees to freely transfer a license to a third party which qualifies as a designated entity, without additional financial penalties or obligations. Permits the transfer to non-designated entities but requires such parties to pay the balance due of the spectrum bid immediately. Requires such parties to pay the difference, if any, between the amount initially bid by the designated entity and the market price for such licenses, based on the average of non-designated entity bids for similar licenses in that market. |
in general , there are 2 ways to measure the health status of a population .
one is a subjective approach by asking the individual , and then using the self - reported health status to summarize symptoms , disease , injuries , or disability . the other is by using normative method using skilled health personnel and a clinical exam . in the first case , the individual notices changes in his / her normal state of wellness .
these perceptions ( deviations from the normal state ) are subjective , and are based on the accumulation of past experiences , both by the individual and by those around him / her . in the second case ,
the criteria are based on a normative assessment by health personnel that meets clinical standards of what constitutes a structural and/or functional deviation for the tissue , organ , system , or the body as a whole . for several years
there has been growing interest in measures of self - perceived health status in clinical scenarios , in therapy programs , and in health surveys .
self - reported health is one of the most frequently used measures of health perceptions evaluated in social epidemiology .
it is a common synthesis of health conditions that , despite lacking direct clinical equivalence , correlates with more complex health measures .
it incorporates a bio - psychosocial construct not captured by other morbidity measures . by its very nature ,
self - rated ( self - perceived ) health has a subjective component that reflects objective health evaluations of the past as well as future expectations .
it is a relatively stable measure over time , and shows high test re - test reliability .
it has also been demonstrated that self - rated health is a powerful predictor of both morbidity and mortality . in latin america and mexico
studies around the world have found changes associated with variables such as age [ 6,1518 ] , sex [ 6,1821 ] , physical activity , various indicators of socioeconomic position [ 4,12,15,1719,21,22 ] chronic diseases , body - mass index ( bmi ) and other health conditions , physical activity , having a healthy diet , religiosity , sleep quality , and consumption of alcohol and tobacco , among others . although studying variables associated with self - reported general health is not new ,
the objective of the present study was to determine if edentulism , socioeconomic position , socio - demographic variables , and presence of other health problems or disabilities were associated with self - reported general health in a mexican adult population .
the present study was derived from secondary analyses of health survey data from a nationally representative sample in mexico .
briefly , the national performance evaluation survey 20022003 ( ened ) , a cross - sectional study , was part of the technical collaboration between the ministry of health of mexico ( ssa ) and the world health organization , which used the survey instrument and sampling strategies developed by who for the world health survey ( whs ) .
information was collected from 38 746 households , with a mean of 1250 households for each state .
the sample design was probabilistic , multistage , stratified , through conglomerates , and was calculated to provide representative information at the state level , and across urban and rural areas .
the sample size considered 9% as the smaller proportion to estimate ; state estimations with a maximum relative error of 25% ; a confidence level of 95% ; non - response rate of 15% ; and a design effect of 1.7 .
data on dental conditions were only available for 20 out of the 32 states of mexico , leading to a total of 24 159 households included in the present study .
three strata were considered : a ) cities or metropolitan areas ( locations with more than 100 000 inhabitants ) ; b ) urban settings ( locations from 2500 to 99 999 inhabitants ) , and c ) rural areas ( locations with fewer than 2500 inhabitants ) .
the ened survey had 2 different questionnaires , with 1 questionnaire inquiring about household conditions and the other inquiring about individual subject factors .
in the first questionnaire , information was gathered on neighborhood public services , income , expenses , and health insurance .
the second questionnaire gathered information including health status , health risk factors , presence of key diseases , use of health services , non - clinical expectations of the population , and insurance coverage of certain clinical services .
self - reported health was our dependent variable , and was assessed by an item consisting of 5 alternatives .
the fourth and fifth options were bad and very bad . in this study ,
self - reported health was categorized into good ( the two first alternatives ) , moderate , and bad ( the 2 remaining options ) .
the main independent variable was edentulism , which refers to the absence of any natural teeth in the mouth ; it was gathered through question q6757 , have you lost all of your natural teeth ? in addition , a series of socio - demographic , socio - economic factors , and variables related to health were included : age ( 35 to 98 years ) , sex ( male or female ) , residence ( rural , urban , metropolitan ) , marital status ( single , married , divorced , widowed , cohabitating ) , indigenous ethnicity status ( do you speak an indigenous language ? : no or yes ) , schooling ( less than elementary , complete elementary , complete secondary , high school / equivalent , college studies / higher ) , occupation ( employed in the public sector , employed outside the public sector , self - employed , or not working or doing volunteer work ) , health insurance ( insured or non - insured ) , socio - economic level ( in tertiles ) , having a disability ( none or yes ) , physical activity ( high activity or low activity ) , chronic disease ( none or any ) , body mass index ( bmi ; underweight < 18.5 , normal 18.524.9 , overweight 25.029.9 , or obesity 30 ) , and tobacco use ( never / not currently , sometimes , or daily ) and alcohol use ( never and low : fewer than 4 servings for women and 5 for men in the last week on 1 occasion ; or high : 4 servings and more for women , and 5 for men in the last week on 1 occasion ) .
valid data were bmi values between 10 and 58 ; for height , we considered valid data between 130 and 200 cm .
we excluded from analysis data outside acceptable limits for bmi ( n=24 ) and for height ( n=48 ) .
this variable was constructed through interviewer s reporting problems with walking , being confined to a wheelchair , or using cane , crutches , or walker .
those reporting at least 1 limb paralyzed or amputated , and those with medically diagnosed mental health problems , were also included in this category .
the household survey included general topics , such as building materials of the house and ownership of consumable goods , which led to a wealth index using principal components analysis ( pca ) . owning a refrigerator , washing machine , dishwasher , personal computer , car , bicycle , television , etc .
the aspects incorporated to assess features of the home included the building materials for walls and floor , the number of rooms , the characteristics of bathroom and kitchen , the source of potable or indoor water , having electricity and heating , and an estimate of whether the household could be considered overcrowded .
there were some missing data for weight ( n=243 ) , height ( n=367 ) , indigenous ethnicity status ( n=113 ) , insurance ( n=30 ) , and socio - economic level ( n=1 ) , which were imputed through regression imputation .
first , a univariate analysis was conducted to report the summary measures per case ( for nominal and ordinal variables , frequencies and percentages ; for continuous variables , dispersion and central tendency measures ) .
assuming an ordinal behavior of the dependent variable , a model of ordered logistic regression was used .
it was later changed for the multinomial ( polytomous ) logistic regression model , since the assumption of similar coefficients among categories was not met ( proportional odds assumption ) in some independent variables in the bivariate analyses . in the multinomial logistic regression ,
results are established based on a comparison category . in our case , we selected as the comparison category for the dependent variable the very good / good category of self - reported health . the role of each of the variables
was thus identified while controlling for the remaining variables , and for their interactions , thus offering an overview of the associations between variables and the performance of the model as a whole .
we first ran the model using bivariate techniques , reporting odds ratio ( or ) , 95% confidence intervals ( ci 95% ) , and p - value of the test .
finally , a multivariate multinomial logistic regression model was constructed and incorporated all variables available that at the bivariate analysis level exhibited a p - value < 0.25 , to control for possible confusion.37 the criterion for inclusion of variables in the multivariate model was its association with health perception at a level of p < 0.05 , but we considered a p<0.10 as a trend to be associated with the response variable .
we used the module svy ( complex samples ) of the statistical package stata 9 .
the medical research committee of the national institute of public health in mexico granted ethics approval .
the present study was derived from secondary analyses of health survey data from a nationally representative sample in mexico .
briefly , the national performance evaluation survey 20022003 ( ened ) , a cross - sectional study , was part of the technical collaboration between the ministry of health of mexico ( ssa ) and the world health organization , which used the survey instrument and sampling strategies developed by who for the world health survey ( whs ) .
information was collected from 38 746 households , with a mean of 1250 households for each state .
the sample design was probabilistic , multistage , stratified , through conglomerates , and was calculated to provide representative information at the state level , and across urban and rural areas .
the sample size considered 9% as the smaller proportion to estimate ; state estimations with a maximum relative error of 25% ; a confidence level of 95% ; non - response rate of 15% ; and a design effect of 1.7 .
data on dental conditions were only available for 20 out of the 32 states of mexico , leading to a total of 24 159 households included in the present study .
three strata were considered : a ) cities or metropolitan areas ( locations with more than 100 000 inhabitants ) ; b ) urban settings ( locations from 2500 to 99 999 inhabitants ) , and c ) rural areas ( locations with fewer than 2500 inhabitants ) .
the ened survey had 2 different questionnaires , with 1 questionnaire inquiring about household conditions and the other inquiring about individual subject factors . in the first questionnaire ,
information was gathered on neighborhood public services , income , expenses , and health insurance .
the second questionnaire gathered information including health status , health risk factors , presence of key diseases , use of health services , non - clinical expectations of the population , and insurance coverage of certain clinical services .
self - reported health was our dependent variable , and was assessed by an item consisting of 5 alternatives .
the fourth and fifth options were bad and very bad . in this study ,
self - reported health was categorized into good ( the two first alternatives ) , moderate , and bad ( the 2 remaining options ) .
the main independent variable was edentulism , which refers to the absence of any natural teeth in the mouth ; it was gathered through question q6757 , have you lost all of your natural teeth ? in addition , a series of socio - demographic , socio - economic factors , and variables related to health were included : age ( 35 to 98 years ) , sex ( male or female ) , residence ( rural , urban , metropolitan ) , marital status ( single , married , divorced , widowed , cohabitating ) , indigenous ethnicity status ( do you speak an indigenous language ? : no or yes ) , schooling ( less than elementary , complete elementary , complete secondary , high school / equivalent , college studies / higher ) , occupation ( employed in the public sector , employed outside the public sector , self - employed , or not working or doing volunteer work ) , health insurance ( insured or non - insured ) , socio - economic level ( in tertiles ) , having a disability ( none or yes ) , physical activity ( high activity or low activity ) , chronic disease ( none or any ) , body mass index ( bmi ; underweight < 18.5 , normal 18.524.9 , overweight 25.029.9 , or obesity 30 ) , and tobacco use ( never / not currently , sometimes , or daily ) and alcohol use ( never and low : fewer than 4 servings for women and 5 for men in the last week on 1 occasion ; or high : 4 servings and more for women , and 5 for men in the last week on 1 occasion ) .
valid data were bmi values between 10 and 58 ; for height , we considered valid data between 130 and 200 cm .
we excluded from analysis data outside acceptable limits for bmi ( n=24 ) and for height ( n=48 ) .
this variable was constructed through interviewer s reporting problems with walking , being confined to a wheelchair , or using cane , crutches , or walker .
those reporting at least 1 limb paralyzed or amputated , and those with medically diagnosed mental health problems , were also included in this category .
the household survey included general topics , such as building materials of the house and ownership of consumable goods , which led to a wealth index using principal components analysis ( pca ) . owning a refrigerator , washing machine , dishwasher , personal computer , car , bicycle , television , etc .
the aspects incorporated to assess features of the home included the building materials for walls and floor , the number of rooms , the characteristics of bathroom and kitchen , the source of potable or indoor water , having electricity and heating , and an estimate of whether the household could be considered overcrowded .
there were some missing data for weight ( n=243 ) , height ( n=367 ) , indigenous ethnicity status ( n=113 ) , insurance ( n=30 ) , and socio - economic level ( n=1 ) , which were imputed through regression imputation .
self - reported health was our dependent variable , and was assessed by an item consisting of 5 alternatives .
the fourth and fifth options were bad and very bad . in this study ,
self - reported health was categorized into good ( the two first alternatives ) , moderate , and bad ( the 2 remaining options ) .
the main independent variable was edentulism , which refers to the absence of any natural teeth in the mouth ; it was gathered through question q6757 , have you lost all of your natural teeth ? in addition , a series of socio - demographic , socio - economic factors , and variables related to health were included : age ( 35 to 98 years ) , sex ( male or female ) , residence ( rural , urban , metropolitan ) , marital status ( single , married , divorced , widowed , cohabitating ) , indigenous ethnicity status ( do you speak an indigenous language ? : no or yes ) , schooling ( less than elementary , complete elementary , complete secondary , high school / equivalent , college studies / higher ) , occupation ( employed in the public sector , employed outside the public sector , self - employed , or not working or doing volunteer work ) , health insurance ( insured or non - insured ) , socio - economic level ( in tertiles ) , having a disability ( none or yes ) , physical activity ( high activity or low activity ) , chronic disease ( none or any ) , body mass index ( bmi ; underweight < 18.5 , normal 18.524.9 , overweight 25.029.9 , or obesity 30 ) , and tobacco use ( never / not currently , sometimes , or daily ) and alcohol use ( never and low : fewer than 4 servings for women and 5 for men in the last week on 1 occasion ; or high : 4 servings and more for women , and 5 for men in the last week on 1 occasion ) .
valid data were bmi values between 10 and 58 ; for height , we considered valid data between 130 and 200 cm .
we excluded from analysis data outside acceptable limits for bmi ( n=24 ) and for height ( n=48 ) .
this variable was constructed through interviewer s reporting problems with walking , being confined to a wheelchair , or using cane , crutches , or walker .
those reporting at least 1 limb paralyzed or amputated , and those with medically diagnosed mental health problems , were also included in this category .
the household survey included general topics , such as building materials of the house and ownership of consumable goods , which led to a wealth index using principal components analysis ( pca ) . owning a refrigerator , washing machine , dishwasher , personal computer , car , bicycle , television , etc .
the aspects incorporated to assess features of the home included the building materials for walls and floor , the number of rooms , the characteristics of bathroom and kitchen , the source of potable or indoor water , having electricity and heating , and an estimate of whether the household could be considered overcrowded .
there were some missing data for weight ( n=243 ) , height ( n=367 ) , indigenous ethnicity status ( n=113 ) , insurance ( n=30 ) , and socio - economic level ( n=1 ) , which were imputed through regression imputation .
first , a univariate analysis was conducted to report the summary measures per case ( for nominal and ordinal variables , frequencies and percentages ; for continuous variables , dispersion and central tendency measures ) .
assuming an ordinal behavior of the dependent variable , a model of ordered logistic regression was used .
it was later changed for the multinomial ( polytomous ) logistic regression model , since the assumption of similar coefficients among categories was not met ( proportional odds assumption ) in some independent variables in the bivariate analyses . in the multinomial logistic regression ,
, we selected as the comparison category for the dependent variable the very good / good category of self - reported health .
the role of each of the variables was thus identified while controlling for the remaining variables , and for their interactions , thus offering an overview of the associations between variables and the performance of the model as a whole .
we first ran the model using bivariate techniques , reporting odds ratio ( or ) , 95% confidence intervals ( ci 95% ) , and p - value of the test .
finally , a multivariate multinomial logistic regression model was constructed and incorporated all variables available that at the bivariate analysis level exhibited a p - value < 0.25 , to control for possible confusion.37 the criterion for inclusion of variables in the multivariate model was its association with health perception at a level of p < 0.05 , but we considered a p<0.10 as a trend to be associated with the response variable .
we used the module svy ( complex samples ) of the statistical package stata 9 .
the medical research committee of the national institute of public health in mexico granted ethics approval .
in this analysis , we included only individuals 35 years old and older ( n=13,966 ) , representing 29 853 607 inhabitants of 20 states of mexico .
the majority of participants ( 40.4% ) were 3544 years old and 57.9% were women .
the highest percentage ( 49.5% ) lived in a metropolitan zone , 67.2% were married , and 8.1% were considered of indigenous ethnicity . in relation to the socioeconomic position indicator variables , we observed that 48.9% of the subjects had completed elementary school ; most of them did not work or worked on a voluntary basis without remuneration ( 52.7% ) and of these the majority were women ( 82.8% ) ; 61.1% did not have health insurance . in the health - related variables
, we observed that 10.2% ( representing 3 052 263 individuals ) were edentulous ; a similar percentage had physical disabilities ; 92.2% reported performing moderate to vigorous physical activity ; 16.6% had a diagnosed chronic disease ; a considerable proportion of the population were overweight / obese ( 42.1% and 19.7% , respectively ) ; 77.3% had never smoked ; and 59.7% said that they did not drink alcohol . as for the percentages of the self - reported general health , we noted that the majority ( 58.2% , n=17,373,754 ) reported their health status as very good / good , 33.8% ( n=10,099,035 ) said they had a moderate health status , while 8.0% ( n=2,380,818 ) mentioned that their health was bad / very bad .
tables 1 and 2 show the bivariate distribution of self - reported general health status across the categories of the independent variables included in the study .
table 3 presents the bivariate analysis using polynomial logistic regression ( statistically significant variables are presented ) .
we observed that only age , sex , marital status , edentulism , disability , physical activity , presence of chronic disease , bmi , education , occupation , belonging to an indigenous ethnic group , and socioeconomic level were variables significantly associated in the bivariate analysis .
table 4 presents the results of the multivariate polynomial logistic regression model ; we obtained 11 main effects and an interaction between edentulism and age .
thus , the association of edentulism with self - reported health was modified by age .
we can consider : 1 ) the association of edentulism when age is constant ( e.g. , 35 years old , which was the minimum age included in the study ) on the self - report of moderate health status ( or = exp=2.05 , p=0.194 ) and of very bad / bad status ( or = exp=17.56 , p<0.001 ) and 2 ) the association of edentulism for each year that age increases ( e.g. , 3536 years ) on the self - reported health with a moderate status ( or = exp=2.03 , p>0.05 ) or a very bad / bad status ( or = exp)=16.92 , p=0.001 ) ) to reach an or of 1.68 ( p=0.001 ) at 98 years old ( which was the maximum age found in the study ) in the self - report of health as very bad / bad status .
the result for the category moderate was not statistically significant , indicating that the association of edentulism with self - reported health as bad / very bad was higher in young people than in older people , decreasing about 3.6% per each year that age increased . also , women had higher odds of reporting moderate health ( or=1.35 ) or bad / very bad health ( or=1.67 ) compared with men ( p<0.05 ) .
the results for the socio - economic status indicator variables included in the multivariate model ( table 4 ) showed that individuals with occupations placed lower in the socioeconomic scale were more likely to report moderate health status ( or=1.27 ; p<0.05 ) .
however , the significance was considered marginal for those who were considered to have bad / very bad health ( or=1.49 ; p<0.10 ) . on the other hand ,
having achieved higher levels of education decreased the likelihood of reporting moderate health ( or=0.71 ) or bad / very bad health ( or=0.62 ) ( p<0.05 ) .
individuals with better socioeconomic position had lower odds of reporting moderate health ( or=0.79 ) or bad / very bad health ( or=0.71 ) than their counterparts with lower socioeconomic level ( p<0.05 ) .
table 4 also shows data on health variables . for individuals with a disability , the odds of reporting moderate health
were 1.65 times ( 95% ci=1.332.05 ) compared to individuals without disabilities ; this contrast was even starker in those reporting bad / very bad health , 3.69 ( 95% ci=2.734.99 ) .
physical activity was not associated with a moderate health report ( p>0.05 ) , however , individuals who had physical activity had lower probabilities of reporting bad / very bad health ( or=0.47 , 95% ci=0.34 to 0.65 ) .
although being underweight or overweight were not associated with a report of moderate health status ( p>0.05 ) , obesity itself showed a positive association ( or=1.36 , p < 0.001 ) .
this situation changed when reporting bad / very bad health : when participants were considered underweight ( or=2.59 , 95% ci=1.424.73 ) or obese ( or=1.69 , 95% ci=1.112.55 ) , the odds increased .
those who had chronic disease had higher odds of reporting moderate health ( or=2.65 ; p<0.001 ) , and were even more likely to report having bad / very bad health ( or=3.68 ; p<0.001 ) .
finally , low alcohol consumption was associated with a moderate health self - report ( or=1.31 ; p<0.001 ) ; interestingly , high consumption of alcohol was not associated with moderate health ( p>0.05 ) . in an analogous way ,
those who had low alcohol consumption were 59% ( p<0.01 ) more likely to report bad / very bad health , whereas for those with high alcohol consumption , reporting bad / very bad health was marginally significant ( or=2.05 ; p=0.051 ) .
tables 1 and 2 show the bivariate distribution of self - reported general health status across the categories of the independent variables included in the study .
table 3 presents the bivariate analysis using polynomial logistic regression ( statistically significant variables are presented ) .
we observed that only age , sex , marital status , edentulism , disability , physical activity , presence of chronic disease , bmi , education , occupation , belonging to an indigenous ethnic group , and socioeconomic level were variables significantly associated in the bivariate analysis .
table 4 presents the results of the multivariate polynomial logistic regression model ; we obtained 11 main effects and an interaction between edentulism and age .
thus , the association of edentulism with self - reported health was modified by age .
we can consider : 1 ) the association of edentulism when age is constant ( e.g. , 35 years old , which was the minimum age included in the study ) on the self - report of moderate health status ( or = exp=2.05 , p=0.194 ) and of very bad / bad status ( or = exp=17.56 , p<0.001 ) and 2 ) the association of edentulism for each year that age increases ( e.g. , 3536 years ) on the self - reported health with a moderate status ( or = exp=2.03 , p>0.05 ) or a very bad / bad status ( or = exp)=16.92 , p=0.001 ) ) to reach an or of 1.68 ( p=0.001 ) at 98 years old ( which was the maximum age found in the study ) in the self - report of health as very bad / bad status .
the result for the category moderate was not statistically significant , indicating that the association of edentulism with self - reported health as bad / very bad was higher in young people than in older people , decreasing about 3.6% per each year that age increased . also , women had higher odds of reporting moderate health ( or=1.35 ) or bad / very bad health ( or=1.67 ) compared with men ( p<0.05 ) . the results for the socio - economic status indicator variables included in the multivariate model ( table 4 ) showed that individuals with occupations placed lower in the socioeconomic scale were more likely to report moderate health status ( or=1.27 ; p<0.05 )
however , the significance was considered marginal for those who were considered to have bad / very bad health ( or=1.49 ; p<0.10 ) . on the other hand ,
having achieved higher levels of education decreased the likelihood of reporting moderate health ( or=0.71 ) or bad / very bad health ( or=0.62 ) ( p<0.05 ) .
individuals with better socioeconomic position had lower odds of reporting moderate health ( or=0.79 ) or bad / very bad health ( or=0.71 ) than their counterparts with lower socioeconomic level ( p<0.05 ) .
table 4 also shows data on health variables . for individuals with a disability , the odds of reporting moderate health
were 1.65 times ( 95% ci=1.332.05 ) compared to individuals without disabilities ; this contrast was even starker in those reporting bad / very bad health , 3.69 ( 95% ci=2.734.99 ) .
physical activity was not associated with a moderate health report ( p>0.05 ) , however , individuals who had physical activity had lower probabilities of reporting bad / very bad health ( or=0.47 , 95% ci=0.34 to 0.65 ) .
although being underweight or overweight were not associated with a report of moderate health status ( p>0.05 ) , obesity itself showed a positive association ( or=1.36 , p < 0.001 ) .
this situation changed when reporting bad / very bad health : when participants were considered underweight ( or=2.59 , 95% ci=1.424.73 ) or obese ( or=1.69 , 95% ci=1.112.55 ) , the odds increased .
those who had chronic disease had higher odds of reporting moderate health ( or=2.65 ; p<0.001 ) , and were even more likely to report having bad / very bad health ( or=3.68 ; p<0.001 ) .
finally , low alcohol consumption was associated with a moderate health self - report ( or=1.31 ; p<0.001 ) ; interestingly , high consumption of alcohol was not associated with moderate health ( p>0.05 ) . in an analogous way , those who had low alcohol consumption were 59% ( p<0.01 ) more likely to report bad / very bad health , whereas for those with high alcohol consumption , reporting bad / very bad health was marginally significant ( or=2.05 ; p=0.051 ) .
using national survey data , the present study found that the degree of association between edentulism , socioeconomic status , socio - demographic variables , and the presence of general health problems or disabilities were associated with self - reported general health status among mexican adults .
self - evaluations of health generally integrate and synthesize various objective health indicators , its functions , and social and cultural values .
we observed a predominance towards health reported as very good / good ( 58.2% ) , which was similar to a study in brazil ( 60% ) but lower than that observed by laaksonen et al . in finland , and by bennet et al . and jerant et al . in the united states
using the same methodology ( world health survey ) , the observed percentage of self - reported health as very good / good was 53.3% , lower than our figures .
in general , the figures for self - reported good / very good health are higher in industrialized than non - industrialized countries .
while oral diseases and their sequelae are largely preventable [ 3944 ] , many adults experience poor oral health .
although there are no studies that directly link edentulism to self - report of general health , there is evidence of the relationship between deficient oral health and various health conditions and quality of life .
for example , in a study conducted in brazil , edentulism was associated with high blood pressure compared to individuals who had more than 10 teeth . in japan ,
aida et al . observed that mortality from cardiovascular disease and respiratory disease was higher among those who had more missing teeth . recently in mexico , medina et al
, people who reported bad health also indicated having lower quality of life related to oral health .
the overall trend from these studies suggests that oral health , specifically tooth loss , is strongly associated with general health . in the case of our study
, it should be noted that edentulism was associated with self - reported bad / very bad health ( but not on moderate health ) depending on age , the effect being greater among young people than in older adults . in terms of health ,
the variables of sex ( biological construct ) and gender ( behavioral and social construct ) are recognized as useful parameters for research and action , as differences determine specific diseases for men and for women . in this regard ,
the observed differences between men and women have been well documented by other authors , as well as in our own study , with women reporting worse health status than men .
one of the main explanations for such a difference is that women may recognize pain and discomfort more easily than men .
other explanations that have been proposed are : 1 ) the specific conditions of women ( maternal conditions , risk exposures , poverty and social exclusion , empowerment ) , especially in developing countries ; 2 ) conditions associated with increased longevity in women ( arising from aging and chronic diseases ) ; 3 ) conditions resulting from the interaction of sex and gender ( depressive symptoms ) ; and 4 ) gender - based conditions ( e.g. , violence ) . with regard to socioeconomic status , the current literature has documented that the position of an individual in society is generally a strong predictor of both morbidity and mortality .
in addition , several authors support the existence of an association between health status and social status : in general , individuals with better socioeconomic status have better health .
the results from the present study are consistent with the observed association in other publications about self - reported health and socioeconomic status variables .
this relationship has been reported using different indicators , such as the highest level of education ( schooling ) , poverty level , type of occupation , household size , or even renting the residence where people live . in the present study , it was consistently observed in all the three indicator variables that remained in the final model ( occupation , education [ measured by schooling ] , and socioeconomic status ) that individuals with better socio - economic status reported better health status than those with worse socio - economic status . among the hypotheses that can explain this association would be access to health services , access to health information , and better nutrition .
self - reported health is a valuable measure in epidemiology because it correlates with present and future morbidity , with different causes of death , and with health services utilization . as a result of several factors , including the aging of the population , a greater proportion of people develop what has been called multimorbidity , with important economic implications .
various authors around the world have found that health conditions are strong predictors of poor overall health at the individual level .
likewise , people with chronic health conditions such as hypertension and diabetes or various disabilities reported worse health levels . in the u.s .
, ayyagari et al . observed that conditions such as angina , arthritis , congestive heart failure , diabetes and renal disease were associated with worse reported health levels .
it is not surprising therefore that certain presentations of bmi ( obese individuals ) were associated with worse health reports .
similar results have been observed in the u.k . where overweight and obese patients reported worse self - rated health , and more co - morbidities and biological risk factors .
a similar situation was found in adults from brazil , as well as in the present study , in that such association was observed only among the obese subjects and not with merely overweight people . however , unlike the brazilian study , the present study found that individuals characterized as underweight also reported worse general health status .
like other studies carried out in populations of adolescents and adults , the results of the present study showed that physical activity may be a protective factor against self - reported poor health .
a sedentary lifestyle and irregular physical exercise have been previously associated with self - reported poor health in mexican women . according to the
who , physical inactivity is the fourth leading risk factor affecting overall mortality , and is the cause of almost 6% of all deaths .
it is generally accepted that physical activity is an important element of a healthy lifestyle
it improves lipid profile , blood pressure , metabolic syndrome , muscle strength and bone density , and is associated with a reduction in excess weight , emotional problems , and depressive symptoms .
numerous studies have explored the relationship between alcohol consumption and health . compared with abstention ,
moderate alcohol consumption has been linked to better health , including subjective health . on the other hand , excessive and harmful consumption of alcohol
green and pollen mentioned that studies relating alcohol to health have failed to take into account the possible heterogeneity in health history and alcohol consumption among non - drinkers and former drinkers , by combining them with lifetime abstainers in the analysis . to the extent that former drinkers stop drinking due to illness , this could increase the risk of the non - drinking category and underestimate the adverse effects of alcohol consumption on health ; diseases that lead to abstention are related to alcohol . in our study , those who had low alcohol consumption in the previous week had a higher risk of reporting moderate and bad / very bad health , along with the strong tendency to select the category of bad / very bad health . these differences could be due to methodological issues , such as the fact that in our study alcohol consumption was measured only for the previous week without taking into account the former drinkers history ; whereas in other studies the time base was between 612 months . besides the different epidemiological designs used in other studies and in ours , it is possible that by collapsing categories of those who currently drink no alcohol , we may be in fact combining people who are no longer using alcohol after substantial abuse with life - long abstainers .
the present study has limitations and strengths that should be taken into consideration when analyzing conclusions .
the main limitation is the inability to pinpoint causality between different variables , which is an inherent weakness in cross - sectional studies .
however , the ened provided reliable and internationally comparable information about a wide variety of health indicators , including measures of general health of the population and the effectiveness of health systems .
our data represent most of the country s adult population , and our study provides an initial assessment of the importance of complete loss of teeth in the context of self - perception of general health .
the association between edentulism and self - reported poor health status ( bad / very bad ) in the mexican adult population was stronger in the younger segment of the population studied .
we observed not only socioeconomic inequalities in relation to the self - report of general health , but also that people with a chronic illness or a disability reported their perceived general health status as less favorable . | backgroundto determine if edentulism , controlling for other known factors , is associated with subjective self - report health status ( srh ) in mexican adults.material/methodswe examined the srh of 13 966 individuals 35 years and older , using data from the national survey of performance assessment , a cross - sectional study that is part of the technical collaboration between the ministry of health of mexico and the world health organization , which used the survey instrument and sampling strategies developed by who for the world health survey .
sociodemographic , socioeconomic , medical , and behavioral variables were collected using questionnaires .
self - reported health was our dependent variable .
data on edentulism were available from 20 of the 32 mexican states .
a polynomial logistic regression model adjusted for complex sampling was generated.resultsin the srh , 58.2% reported their health status as very good / good , 33.8% said they had a moderate health status , and 8.0% reported that their health was bad / very bad .
the association between edentulism and srh was modified by age and was significant only for bad / very bad srh .
higher odds of reporting moderate health or poor / very poor health were found in women , people with lower socio - economic status and with physical disabilities , those who were not physically active , or those who were underweight or obese , those who had any chronic disease , and those who used alcohol.conclusionsthe association of edentulism with a self - report of a poor health status ( poor / very poor ) was higher in young people than in adults .
the results suggest socioeconomic inequalities in srh . inequality was further confirmed among people who had a general health condition or a disability . |
calculational schemes that are perturbative in the coulomb interaction are known to be inadequate for describing strongly interacting electrons in systems such as , for example , transition metal oxides , organic conductors and quantum dots @xcite and this necessitates the use of non perturbative methods , such as the renormalization group , dynamical mean field theory @xcite and various numerical methods . the @xmath4 expansion for
@xmath0 fold replicated degrees of freedom ( with subsequent extrapolation to the physical value of @xmath5 or @xmath6 ) was successfully applied to magnetic impurities @xcite and in other areas of physics @xcite . in almost all applications to electronic systems ,
this expansion uses semiclassical saddle point integration and its success in the case of the repulsive hubbard model @xcite is open to question because it is unclear where a suitable saddle point exists .
an alternative version of the @xmath7 expansion was discovered by t hooft @xcite in the context of @xmath8 quantum chromodynamics and relies instead on dominance of diagrams of simple topology for @xmath9 .
recently it was noticed @xcite that t hooft s topological classification of diagrams can be applied to the hubbard model , with collective excitations playing the role that gauge bosons play in quantum chromodynamics .
this raises the challenge of reconstructing the large @xmath0 extrapolation for electron systems from the very beginning in a way that avoids saddle point integration .
the symplectic extrapolation of the hubbard model @xcite,@xcite is interesting because , unlike the @xmath10 extension , it conserves the notion of two component spins and permits pairing . in the present paper ,
we solve this model exactly in two special cases ( i ) in the bosonic sector on an infinite lattice at @xmath2 and ( ii ) on a dimer of two points for any @xmath0 .
our solution at @xmath2 shows the existence not only of neutral spin fluctuations but also of charged pair fluctuations that are in the same multiplet and exactly degenerate with the spin fluctuations at zero doping .
our solution of the dimer for any @xmath0 indicates a smooth interpolation between @xmath3 and @xmath2 without any apparent singularity . taken together these results
indicate that ( i ) both spin and pair fluctuations must be included from the very beginning in any theory of weakly doped antiferromagnets and ( ii ) that the expansion in powers of @xmath4 about an appropriate @xmath2 limit is a legitimate procedure in this context .
the symplectic extrapolation of hubbard s model @xcite that we consider here is based on @xmath11 , the group of unitary transformations on @xmath12 quaternions and it leads to the following hamiltonian @xcite : @xmath13 + \sum_{x , y}t_{xy}% \psi _ { x}^{+}\psi _ { y } \label{symplectic }
\\ \psi _ { x}\varepsilon \psi _ { x } & = & \sum_{i=1 .. n,\alpha \beta = 1,2}\psi _ { x\alpha i}\left ( i\sigma _ { y}\right ) _
{ \alpha \beta } \psi _ { x\beta i}% \mbox{,\ \ \ } \psi _ { x}^{+}\psi _ { x}=\sum_{i=1 .. n,\alpha = 1,2}\psi _ { x\alpha i}^{+}\psi _ { x\alpha i } \nonumber\end{aligned}\ ] ] here @xmath14 denotes symmetrization and the electrons @xmath15 occur in @xmath0 copies with @xmath16 but we will often suppress this extra index . for our purposes invariance of @xmath17 under @xmath10 transformations is sufficient and @xmath18 and @xmath19 in eq([symplectic ] ) are indeed invariant under @xmath10 because @xmath20 and @xmath21 transform , by fiat , according to mutually conjugate @xmath10 transformations . if we imagine , for the moment , that the interactions in eq([symplectic ] ) come about via exchange of suitable bosons , then both neutral and charged bosons must be exchanged .
it will be shown below that this naive expectation is correct and that the symplectic extrapolation of the hubbard model contains indeed both neutral and charged collective excitations .
this paper is organized as follows . in section 2
we solve the @xmath10 hubbard model first for two points and any @xmath0 using @xmath22 pseudo spins and we also find the @xmath23 hamiltonian in the bosonic sector for an infinite lattice . in section 3
we determine the @xmath9 asymptotics of the symplectic model after mapping it onto a model of the double exchange type and we also solve the symplectic model on a dimer for any @xmath0 using the group @xmath24 as a classifying symmetry . in section 4 we identify the spectrum of the asymptotic @xmath23 and @xmath25 hamiltonians .
section 5 serves to counterbalance our extensive use of ancient boson operator methods by reformulating our problem in standard path integral language .
our conclusions are given in section 6 .
for simplicity , we begin with an @xmath10 extrapolation @xcite of the hubbard model @xcite : @xmath26 which we simplify even further by specializing it to a dimer of only two points : @xmath27 here @xmath28 , @xmath29 and @xmath16 enumerates the electron species and we have chosen hopping amplitudes with a ( naive ) bandwidth of 1 . this hamiltonian describes electrons on a ladder of length @xmath0 with hopping along the rungs @xmath30 or tunnelling between two mesoscopic quantum dots on a semiconducting substrate , each doped with @xmath0 electron donors .
the position @xmath31 on the dimer can be viewed as a pseudo spinor index and @xmath32 can be expressed entirely in terms of pseudo spin operators as follows : @xmath33 where the constant has physical meaning because it depends on electron filling .
because the hamiltonian decomposes into blocks of distinct pseudo spins we may diagonalize it separately in each block and determine the optimal value of the pseudo spin at the end ( it is impossible to diagonalize the @xmath10 dimer for large @xmath0 by brute force because the dimension of its hilbert space explodes like @xmath34 ) . it
it is useful to diagonalize the hopping term by interchanging the conventional representations of @xmath35 and @xmath36 : @xmath37 because @xmath38 as @xmath9 a naive first approximation to the ground state is @xmath39 . to understand the action of the hamiltonian on states in the vicinity of @xmath40
, we express it in terms of holstein - primakoff @xcite oscillators : @xmath41 and then diagonalize it with the help of a bogoljubov transformation : latexmath:[\ ] ] ( we have rescaled the oscillators to have conventional commutation relations ) .
the lagrangian we need is just a slight generalization of the conventional one : @xmath157 correlators ( in imaginary time ) of harmonic variables such as @xmath158 and @xmath159 are well known to be given by the inverse of the quadratic form in the imaginary time action : latexmath:[\[<b_{p_{1}q_{1}}(t)b_{p_{2}q_{2}}^{+}(0)>=<p_{1}q_{1};t|\frac{1}{{\it m}}% interaction @xmath154 which , in @xmath161 space and in terms of the rescaled variables @xmath158 , reads : @xmath162 the operator @xmath163 picks out the coincident piece of the wave function and satisfies the projector relation @xmath164 .
we decompose the full action into its freeand interacting part by writing @xmath165 with @xmath166\ ] ] where @xmath167 describes free propagation of particle hole pairs with @xmath168 .
according to general principles , the free propagator @xmath169 is just the inverse of @xmath167 : @xmath170 the last expression resembles the particle hole propagator that enters into the calculation of bubbles and lindhard s function and this indicates that we are on the right track .
next we switch on @xmath50 and exploit @xmath164 , the locality of the interaction , in a way reminiscent of the treatment of a friedel resonance : @xmath171 @xmath172 represents propagation and rescattering of particle hole pairs or a sum of bubbles .
the preceding argument shows that the spectrum of the @xmath23 hamiltonian corresponds to zeroes of the operator @xmath173 the locality of the interaction @xmath154 leads to a propagator of coincident pairs and to functions of a single label .
fourier transforming we find @xmath174 but the correlation @xmath175 for free fields is also calculable via wicks theorem : @xmath176 where @xmath177 is the hopping matrix . using conventional matsubara techniques
it is easy to check that @xmath178 we conclude that the spectrum of the boson hamiltonian corresponds to the singularities of @xmath179 where @xmath180 is a susceptibility . at half filling , in d=2 dimensions and at @xmath181 the fourier transform of @xmath182 is well known @xcite to diverge logarithmically to @xmath183 because of an incipient antiferromagnetic instability .
we conclude that the asymptotic hamiltonian @xmath184 describes bubbles that have a pole near @xmath181 at half filling .
this pole in the spin fluctuation channel is also seen in neutron scattering on cuprates @xcite . at half filling the spectrum of the asymptotic hamiltonian @xmath185 eq([rpade ] ) on an infinite lattice is very similar to that of the @xmath152 model .
again the hamiltonian describes bubbles and again the spectrum is dominated by fluctuations at @xmath181 except that there is now an extra band index .
the excitations form a triplet of spin and pair fluctuations that are exactly degenerate at half filling .
the aim of the present paper was to establish exact results on the symplectic model in order to see whether the expansion in powers of @xmath4 about @xmath2 in this model makes any sense .
the boson expansion helped us find the asymptotic hamiltonian for a finite number of points but as we have seen in the last section this method becomes inconvenient for dealing with infinite lattices where the bosons seriously overcount the degrees of freedom . in this section
we return to main stream methods of condensed matter physics and discuss how to extrapolate to from @xmath2 to @xmath3 . from the preceding sections it follows that a treatment of doped antiferromagnets and the hubbard model at low temperature near half filling requires a self consistent treatment of electron propagation and spin and pair fluctuations .
this may be done either using the topological expansion given in @xcite or by using the more conventional saddle point method . for simplicity
we adopt the saddle point method , although the topological expansion is presumably the more powerful approach .
we may set up a @xmath4 expansion of the double exchange model by conventional hubbard - stratonovich transformation : @xmath186 where @xmath187 is the hopping amplitude .
like in preceding work on the @xmath8 hubbard model at large @xmath0 ( @xcite ) the phase factor
@xmath30 is essential to get the correct coefficient @xmath188 for the coupling in the double exchange model and again the factor
causes no difficulty because @xmath189 is purely imaginary at the saddle point . to see this , we integrate over the fermionic degrees of freedom and find the stationary point of the effective action : : latexmath:[\[\begin{aligned } z & = & \int d\overrightarrow{\phi } d\psi \exp -s=\int d\phi \exp -s_{eff } \\
\frac{s_{eff}(\overrightarrow{\phi } ) } { n } & = & \int \sum_{x}\overrightarrow{% \phi } _ { x}^{2}dt-\log \det \left ( \partial _ { t}+t^{hop}+\mu \sigma _ { 3}-i% \sqrt{u}\cdot \overrightarrow{\sigma } \overrightarrow{\phi } \right ) + const \nonumber \\
s\bigskip _ { eff } & = & 0\rightarrow i\overrightarrow{\phi } ( x , t)=\frac{1% } { 2}\sqrt{u}tr\overrightarrow{\sigma } < xt|\frac{1}{\partial _ { t}+t^{hop}+\mu \sigma _ { 3}-i\sqrt{u}\cdot \overrightarrow{\sigma } \overrightarrow{\phi } } % ( there are @xmath0 species that contribute to @xmath191 , hence the factor @xmath4 ) . so the hypothesis that @xmath192 is real is consistent , but difficulties may be anticipated for @xmath193 .
numerical calculations indicate that the spin fluctuations are quickly killed by doping while the pair fluctuation channel remains intact .
the likely explanation is that the spin fluctuations correspond to longitudinal fluctuations of @xmath189 in the @xmath194 direction while the pair fluctuations correspond goldstone like rotations about the @xmath103 axis .
one may also expand @xmath195 to second order in @xmath189 and confirm the existence of degenerate spin and pair fluctuations at half filling and @xmath2 without ever using boson operators ( but we do not see how to avoid them in the dimer problem ) .
a detailed study of the extrapolation to @xmath3 via coupled integral equations will be given in a separate paper .
in this paper we have derived two exact results that serve as first steps towards a @xmath4 expansion of the symplectic hubbard model .
firstly , we diagonalized the symplectic dimer for any @xmath0 using an underlying @xmath196 classifying symmetry .
we found a smooth interpolation , without any singularities , between @xmath3 and @xmath2 which suggests that the expansion , in powers of @xmath4 , about the point @xmath2 is indeed legitimate .
secondly , we determined the hamiltonian of the symplectic model for @xmath1 and found a multiplet of collective modes containing charged pair fluctuations and neutral spin fluctuations that are exactly degenerate with each other at half filling .
this tells us that pair fluctuations in doped antiferromagnets are essential degrees of freedom on the way to establishing these results we found analogous results for the @xmath8 extrapolation of the hubbard model and we also indicated how holstein - primakoff like boson operators may be replaced by more familiar and more powerful green s function techniques .
the map of the original symplectic model onto a magnetic model that is reminiscent of a double exchange model proved crucial to our arguments .
this map is interesting in its own right because it may provide us with a simple physical picture of the superconducting instability .
the extrapolation from @xmath2 to @xmath3 requires a self consistent treatment of fermions interacting with their own triplet of collective modes and taking into account mutual renormalization of bosonic and fermionic fluctuations in a way similar to the flex approach . in the light of our results ,
the flex approach is more closely related to the @xmath10 extrapolation of the hubbard model than the @xmath11 one as it ignores the pairing fluctuations of the latter model .
the integral equations of the extrapolation to @xmath3 follow essentially from the topological classification given previously in @xcite , but the details remain to be worked out .
several scenarios for the physics of pair fluctuations have been suggested , ranging from preformed pairs @xcite to postulating a quantum phase transition at a critical doping @xcite .
also , various authors have added pair fluctuations on top of antiferromagnetic ones and obtained interesting results @xcite .
it is fair to say , however , that the details of the competition between spin and pairing fluctuations still remain to be understood .
* acknowledgements .
* we are crucially indebted to peter fulde for his continued interest in this work and for the impetus he gave to this project by inviting us to max - planck - institut fr physik komplexer systeme at dresden during a leave of d. f. from the university of bordeaux .
d. f. is indebted to p. stamp , g. t hooft , c. lhuillier and p. schuck for providing support for this leave and making it possible in the first place .
we acknowledge helpful comments and/or encouragement by many colleagues , in particular h. beck , a. georges , n. hambli , m. katsnelson , j. ranninger , d. rowe and j .- m .
we are indebted to a. lichtenstein for criticism of an earlier version of this paper and advice and code , to s. c. wang for help with preliminary numerics and to r. hayn for discussions on the manuscript .
p. fulde , electron correlations in molecules and solids , springer series in solid - state sciences * 100 * , springer , berlin , 1991 ; f. gebhardt , the mott metal - insulator transition , springer , n.y .
1997 ; m. imada , a. fujimori , y. tokura , rev .
* 70 * ( 1998 ) 1039 . to have @xmath10 invariance we need @xmath197 . with a hamiltonian corresponding more closely to tunnelling between quantum dots , the optimal value of @xmath44 depends on @xmath50 and the charge
is squeezed out of the dimer for @xmath198 .
j. ranninger , j.m .
robin and m. eschrig , phys .
lett . * 74 * , 4027 ( 1995 ) ; r. micnas , m. h. pedersen , s.schafroth , t. schneider , j. j. rodrguez - nez , h. beck phys . rev . * b 52 * ( 1995 ) 16223 ; y.m .
vilk , a .- m.s .
tremblay , j. phys .
i france * 7 * ( 1997)1309 ; v. m. loktev , r. m. quick , s. g. sharapov , cond - mat 0012082 , to appear in physics reports ; c. p. moca , b. janko , cond - mat/0105202 ; l. bartosch , p. kopietz , europ .
j. * b 17 * ( 2000 ) 555 .
s. sachdev cond - mat/0109419 quantum phase transitions of correlated electrons in two dimensions , lectures at altenberg , germany 2001 ; j. l. tallon and j. w. loram physica * c 349,1 - 2 * ( 2001)53 ; ar .
abanov , andrey v. chubukov , j. schmalian , quantum - critical theory of the spin - fermion model and its application to cuprates , cond - mat/0105308 . | we consider a symplectic extrapolation of the hubbard model of @xmath0 fold replicated electrons and solve this model exactly in two special cases , at @xmath1 in the bosonic sector and for any @xmath0 on a dimer of two points . at @xmath2
we find a multiplet of collective modes that contains neutral spin fluctuations and charged pair fluctuations that are degenerate with each other at zero doping .
our solution of the symplectic model on a dimer of two points for any @xmath0 interpolates smoothly between @xmath3 and @xmath2 without any visible discontinuity .
these results suggest that the inclusion of charged pairing modes in weakly doped antiferromagnets is essential and that an expansion about the @xmath2 limit is appropriate in this context . |
Rep. Diana DeGette (Colo.), ranking Democrat on the panel, called it a “sad day” for the committee and “an act of irresponsible partisanship,” stressing that the committee had never before subpoenaed the White House. She noted the administration had already turned over thousands of pages of documents and said a subpoena should be issued only after all alternative routes have been abandoned.
Republicans said they had hoped to avoid the step, but that the committee’s long-running investigation had failed to get to the bottom of why Solyndra, which collapsed in August and is now under criminal investigation, was selected to receive the Obama administration’s first loan guarantee under the stimulus act. President Obama last year visited the company’s California operation, whose biggest investors were venture capital funds linked to Tulsa billionaire George Kaiser, a major Obama fundraiser.
Some Republicans have questioned whether the administration rushed stimulus funding out the door to benefit its political supporters. On Oct. 14, the White House told the committee that it would not comply with a request for all internal White House communications regarding the Solyndra loan.
Following the vote, a White House official said the administration had cooperated extensively with the committee’s investigation, producing more than 85,000 pages of documents, including 20,000 pages Thursday afternoon, and having administration officials provide multiple briefings and hearings.
“The White House has also already provided over 900 pages of documents in response to requests we have received. And all of the materials that have been disclosed affirm what we said on day one: This was a merit-based decision made by the Department of Energy,” White House spokesman Eric Schultz said.
“We’d like to see as much passion in House Republicans for creating jobs as we see in this investigation. The White House has been clear with the committee that we are willing to cooperate with legitimate oversight requests that are tailored to balance the important institutional interests of both branches. We are disappointed that the committee has refused to discuss their requests with us in good faith, and has instead chosen a partisan route, proceeding with subpoenas that are unprecedented and unwarranted.”
“I regret that we have reached this place,” Rep. Cliff Stearns (R-Fla.), chairman of the subcommittee on Oversight and Investigations, said Thursday morning at a meeting of the panel. “The committee has been investigating this for over eight months and has clearly established the legitimacy of our investigation. Two of the first three companies to receive loan guarantees have now filed for bankruptcy protection. ||||| A House subcommittee investigating Solyndra voted Thursday to subpoena internal White House documents on the failed California solar company, spurning Democrats’ pleas for more time to work out a deal.
"We do not have any faith in the White House overtures that seem to simply want to delay and obstruct,” said Rep. Cliff Stearns (R-Fla.), chairman of the Energy and Commerce Committee’s oversight subpanel, minutes before the 14-9 party-line vote.
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Stearns and other GOP leaders complained that the White House had repeatedly ignored their demands for all Solyndra-related materials dating back to the start of President Barack Obama's term and said the administration wasn’t even answering basic questions about the documents.
The White House immediately expressed dismay about the vote.
“We are disappointed that the committee has refused to discuss their requests with us in good faith and has instead chosen a partisan route, proceeding with subpoenas that are unprecedented and unwarranted,” White House spokesman Eric Schultz said in an emailed statement. He added: “We'd like to see as much passion in House Republicans for creating jobs as we see in this investigation.”
The subcommittee’s action adds a legal sledgehammer to what has already been a hyperactive political clash on energy policy between both ends of Pennsylvania Avenue. It could also break new legal ground: Stearns has said he wants to see any Solyndra-related electronic messages sent to or from Obama, the first president to use a BlackBerry.
The Republicans are addressing two subpoenas to White House chief of staff Bill Daley and Bruce Reed, Vice President Joe Biden’s chief of staff.
Full committee Chairman Fred Upton (R-Mich.) told reporters that staff were still working on a final version of the subpoenas — Thursday’s vote only authorized the Republicans to send them. He said he didn’t know when the subpoenas would go out, but that the White House in general gets about a week to respond.
"We want to get this investigation done,” Upton said. “We started last February. Here it is November. … I'm sure they wish it was now off the plate, but it's not. We're going to work to get all the information we need and figure out what happens after that."
In his statement, Schultz repeated that the administration has already produced tens of thousands of pages of documents for the committee. All those records, he said, show that the administration’s handling of Solyndra’s $535 million loan guarantee “was a merit-based decision made by the Department of Energy.”
But the records released so far have also revealed that high-level White House officials were keeping a keen eye on Solyndra’s troubles.
For example, documents that the Energy Department released Wednesday showed that Carol Browner, who was Obama’s top energy and climate adviser, were part of a chain of emails in October 2010 warning that Solyndra was about to close one of its factories. Other emails showed that early this year, an aide to Biden sought information about Solyndra’s private investors — “just for background” — a day after DOE approved changes to the loan guarantee that placed taxpayers second in line for repayment.
Wednesday’s 15,000-page release brought the total number of DOE documents given to the House subpanel to more than 80,000 pages. | – Despite last-minute efforts by the White House, the House Energy and Commerce Committee panel today authorized subpoenas for internal White House documents related to the Solyndra mess. The Washington Post calls the move “apparently unprecedented.” President Obama’s top lawyer had sought a deal and White House officials had delivered some 20,000 more pages of emails and other documents to investigators yesterday, while Democrats on the panel fought the decision; the vote nonetheless came down 14-9 along party lines. The communications requested involve Bill Daley and Joe Biden’s chief of staff Bruce Reed, as well as a broad selection of other senior aides including Rahm Emanuel, Valerie Jarrett, Larry Summers, and former Biden chief of staff Ron Klain. Rep. Cliff Stearns says he also wants to see the president’s relevant BlackBerry messages, Politico reports. The panel’s ranking Democrat called the move a partisan attack and “sad day” for the committee. |
a system of neutral mesons such as @xmath7 , @xmath8 or @xmath11 , @xmath12 is a privileged laboratory for the study of weak - interaction s symmetries . even though the phenomenological framework is well understood since long time @xcite
, recent discussions in the physics community @xcite show that it may be useful to revisit a few points , in order to fully ( and correctly ) exploit the experimental results .
this process is then at the origin of the present note .
we focus on the @xmath7@xmath8 system , and refer to experimental results @xcite that have been achieved by measurements of the decay products of @xmath7@xmath8pairs created in the entangled antisymmetric state @xmath13 where the first @xmath0 in this notation moves in direction @xmath14 and the second in direction @xmath15 . within the weisskopf - wigner approximation @xcite the time evolution of a neutral @xmath0-meson , and its decay into a state @xmath16
is described by the amplitude @xmath17 , @xmath18 where @xmath19 and @xmath20 are represented by constant , complex @xmath21 matrices @xmath22 and @xmath23 , @xmath24 .
we consider experiments with final states @xmath25 or @xmath26 . here
@xmath27 , @xmath28 and @xmath29 stand for the flavour eigenstates @xmath7 ( @xmath8 ) , @xmath11 ( @xmath12 ) and @xmath30 or @xmath31 , respectively .
we recall that a symmetry is a property of the hermitian hamiltonian ( @xmath32 ) of the schrdinger equation which is defined in a space sufficiently complete to include all the particle states under consideration , also the decay products @xcite .
thus the aim of the experiments is to establish properties of the weak interaction hamiltonian @xmath33 by measuring observable combinations of the elements of @xmath34 and of @xmath19 , which represent these properties . as @xmath1 violation implies @xmath2 and/or @xmath3 violation ,
we specifically consider the classical aim posed by the discoverers of @xmath2 violation @xcite `` to express quantitatively the fraction of the observed @xmath1 violation due to @xmath2 violation and @xmath3 violation separately '' .
in passing , we show that a more recent treatment , which attempts to define @xmath2-symmetry violation as `` motion - reversal - symmetry violation '' , without reference to the weak interaction hamiltonian @xcite , is a special case within our phenomenology .
together with a parametrization of the matrices @xmath34 and @xmath19 , the equations ( 1 ) and ( 2 ) are a sufficient basis for the description of the symmetry properties of the experimental results @xcite .
symmetry properties of the hamiltonian often manifest themselves in an especially simple and direct way in relations between measured quantities . here , _ table _ 1
gives a summary , with definitions and derivations as found in @xcite , and the phase conventions of @xcite .
our approach is analogous to @xcite .
+ table 1 : _ a symmetry of @xmath33 implies vanishing values among the observables _ @xmath35 .
+ channels are assumed to have one single amplitude .
+ lll + symmetry of @xmath33 & @xmath36 for the matrix @xmath34 & @xmath36 for the matrix @xmath2 + + + @xmath2 & @xmath37 & @xmath38 + @xmath3 & @xmath39 & @xmath40 + @xmath1 & @xmath41 & @xmath42 + + + let us pose @xmath43 with real @xmath44 , @xmath45 , @xmath46 , @xmath47 , and complex @xmath48 .
for the observables of the symmetry violations in the matrix @xmath34 , i.e. in the @xmath7@xmath8 oscillation , we deduce from eqs . ( 3 ) , ( 4 ) , and _ table _ 1 @xmath49 we note that , with eqs.(3 ) , ( 4 ) and ( 5 ) , the difference of the widths of the eigenstates of @xmath20 becomes + @xmath50 .
this lets us recognize that , if @xmath51 , our matrix @xmath34 still allows for a finite @xmath47 ( @xmath52 ) , in accordance with @xcite .
this is in contrast to widely repeated affirmations @xcite , that @xmath53 would imply time - reversal symmetry of @xmath20 , i.e. @xmath54 . in terms of @xmath55 ( @xmath56 , @xmath57 ) ,
@xmath58 , the relation to eqs .
( 3 ) to ( 5 ) is given by @xmath59 , @xmath60 and @xmath61 .
we admit @xmath62 . in order to calculate the amplitude @xmath17 in eq.(2 ) , we need to evaluate the exponential in terms of @xmath34 .
we do this by summing up the power series ( as explained in @xcite ) .
let @xmath63 and find @xmath64 for the matrix @xmath65 , we assume @xmath66 with complex @xmath67 , corresponding to the @xmath68 rule " . from _ table _ 1 , and with the ( arbitrary ) normalization + @xmath69 , we deduce the useful identity among the ( diagonal ) elements of @xmath19 , @xmath70 results based on eqs .
( 1 ) to ( 11 ) will turn out to be sensitive to all the four symmetry parameters in _ table _ 1 . throughout this work
, we assume that channels have one single amplitude .
two interfering amplitudes may fake non - vanishing values of @xmath71 or @xmath72 , depending on their weak and strong phases , without the presence of the corresponding symmetry violations in the hamiltonian .
call @xmath73 the amplitude for the decay of an entangled , antisymmetric @xmath7@xmath8 pair into a final state with the two observed particles @xmath74 ( at time @xmath75 ) and @xmath76 ( at later time @xmath77 ) . with specific choices of the two final states @xmath78
, we can uniquely represent the complete set of results of the @xmath1- , @xmath2- and @xmath3-symmetry violation studies listed in _ table _ 2 and performed by @xcite through @xcite , by making use of eq .
( 12 ) below @xcite , whose derivation we sketch here .
we note with ( @xcite , section 2.7 ) , that the time evolution acts on the two - particle state @xmath79 of eq .
( 1 ) solely by a multiplicative factor , which is independent of the symmetry violations under consideration , and which does not influence the decay properties of @xmath79 .
we may thus , without loss of generality , arbitrarily choose @xmath80 , and apply eq .
( 2 ) to the single - particle components in @xmath79 , to obtain @xmath81 in rewriting ( 12 ) , we can explicitly derive the formula for the state @xmath82 , which survived the decay to @xmath83 , and its ( single particle ) time evolution and decay to @xmath84 as @xmath85 with @xmath86 the variety of expected frequency distributions is displayed in _ table _ 2 .
we find that the parameters of the data analysis are the @xmath2 and @xmath3 violation parameters of the t matrix , @xmath72 and @xmath71 , concerning the decay , and those , @xmath87 , @xmath88 , ( @xmath89 ) , concerning mainly the @xmath7@xmath8oscillation matrix @xmath34 . in the limit of @xmath1 symmetry of @xmath34
the @xmath87 , @xmath88 all vanish .
then , @xmath72 and @xmath71 are exactly associated each with its own proper time dependence : @xmath72 with @xmath90 , and + @xmath71 with @xmath91 .
_ table _ 2 also allows one to read off the relations of the measured distributions to the symmetry violating parameters of @xmath34 and t , as demonstrated below , and also to construct combinations of data which are true signatures for specific violations .
the experiments @xcite have measured in 2001/2 all the data sets listed in _ table _ 2 , and thereby discovered @xmath1 violation in the matrix t. we show now that these data furthermore establish time - reversal symmetry violation in @xmath33 , and are compatible as well with @xmath3 symmetry of the t matrix as with @xmath92 , @xmath93 , i.e. @xmath1 symmetry of @xmath34 . to this purpose
we consult _ table _ 2 and calculate @xmath94 similarly , we calculate \{5}\{6 } and summarize the results as follows . @xmath95
the experimental results for @xmath96 and @xmath97 show no time independent terms , @xmath98 , and no @xmath99 signals , @xmath100 . from this
we conclude @xmath101 , @xmath102 , and @xmath103 .
the @xmath104 amplitudes are equal but with opposite signs , and , in absolute value , @xmath105 , implying @xmath106 and @xmath107 . from ( 11 )
now follows @xmath108 and thus @xmath109 .
the @xmath87 and @xmath88 defined in _ table _
2 are thus all compatible with zero .
quantitative results for @xmath72 and @xmath71 may be read off from @xcite and @xcite , who analyze their data also with two free parameters @xcite , corresponding to @xmath72 and @xmath71 .
table 2 : _ the measurements , classified according to eq .
( 12)_. + general expressions for the expected frequency distributions in terms of @xmath110 in the limit @xmath111 , they are all of the form @xmath112 @xmath113 is a shorthand for @xmath114 or @xmath115 , @xmath116 for @xmath117 , etc . by the `` @xmath118 rule '' , a @xmath7(@xmath119 )
decays semileptonically always into @xmath120 ( @xmath121 ) .
@xmath122 has been used .
all 10 measurements have been performed .
llll + name of measurement & @xmath123 decay & @xmath124 decay & @xmath125 + & @xmath83 & @xmath84 & @xmath126 @xmath127 @xmath128 + + @xmath129 \{1 } & @xmath113 & @xmath130 & @xmath131 @xmath132 + @xmath133 \{2 } & @xmath116 & @xmath130 & @xmath134 @xmath135 + @xmath136 \{3 } & @xmath130 & @xmath137 & @xmath131 @xmath138 + @xmath139 \{4 } & @xmath130 & @xmath140 & @xmath134 @xmath141 + & & & + + @xmath142 \{5 } & @xmath113 & @xmath143 & @xmath144 @xmath145 + @xmath146 \{6 } & @xmath116 & @xmath143 & @xmath147 @xmath148 + @xmath149 \{7 } & @xmath143 & @xmath137 & @xmath144 @xmath150 + @xmath151 \{8 } & @xmath143 & @xmath140 & @xmath147 @xmath152 + @xmath153 \{9 } & @xmath116 & @xmath140 & @xmath154 @xmath155
@xmath156 + @xmath157 \{10 } & @xmath113 & @xmath137 & @xmath158 @xmath159 @xmath160 + & & & + ll the terms with @xmath161 and @xmath162 ( upper signs for @xmath163 ) . &
+ + @xmath164 + @xmath165 + @xmath166 & identity : + @xmath167 & @xmath168 + & + + table 3 : _ a selection of expectations for the experiment of ref .
@xcite_. + due to the presence of @xmath71 , of the @xmath87 and @xmath88 , our results contradict the attempt @xcite to define the differences @xmath169 to @xmath170 , each as a signature for @xmath2 violation .
in the lower part , signatures for @xmath2- and @xmath3- symmetry violations are indicated .
llll + display in @xcite & rates compared & expected @xmath171 & @xmath172 + & & @xmath173 & @xmath174 @xmath175 + + _ figure _ 2a & @xmath176 & @xmath177 & @xmath178 @xmath179 + 2b & @xmath180 & @xmath177 & @xmath178 @xmath181 + 2c & @xmath182 & @xmath183 & @xmath184 @xmath185 + 2d &
@xmath186 & @xmath183 & @xmath184 @xmath187 + + + llll & & & + signatures are & for @xmath188 & @xmath189 & @xmath190 + & @xmath191 & @xmath192 & @xmath193 + & @xmath194 & @xmath195 & @xmath196 + + the experiment @xcite has set a stringent limit on @xmath2-symmetry violation in the @xmath34 matrix of the @xmath7@xmath8 system with a direct measurement of @xmath47 .
table 2 ( entries \{9 } and \{10 } ) and _ table 3 .
the method is analogous to the one of the cplear experiment @xcite for the @xmath11@xmath12 system , where also a signature for @xmath2-violation ( `` kabir asymmetry '' ) has been directly measured .
the experiments make use of the general identity , valid in two dimensions ( see @xcite ) , @xmath197 from which @xmath198 the connection from the data to the @xmath2- symmetry violation signal @xmath47 , follows - without any assumptions on @xmath3 symmetry or on the value of @xmath199 of the @xmath34 matrix . _ _
a reanalysis of the results in 2007 of the babar and belle collaborations by @xcite has shown that the data contradict _ motion - reversal symmetry _ ( see @xcite ) in the @xmath7@xmath8 system . in summary ,
the discovered @xmath1 violation in the @xmath7@xmath8 system is @xmath2-symmetry violation in the decay - amplitude matrix @xmath19 , @xmath200 with @xmath103 . in the @xmath11@xmath12 system , however , the @xmath1-violation is @xmath2-symmetry violation in oscillations , @xmath201 with @xmath202 .
the analysis by @xcite is based on @xcite with novel notions of @xmath3- , @xmath1- , and @xmath2-symmetry , which , in contrast to the classical definitions @xcite , are not related to properties of the weak interaction hamiltonian , but to comparisons of surviving states @xmath203 with suitably motion - reversal transformed ones of type @xmath204 .
the novel definitions are less general than the classical ones as they need the assumption of @xmath205 .
this new analysis then becomes a special case of our present work , and in turn looses the possibility to address the `` classical aim '' , mentioned in our introduction .
( details below ) . to prove that the phenomenology of @xcite uses @xmath205 , it is sufficient to express their eq.(a.5 of @xcite ) in terms of the elements of the matrix @xmath206 , @xmath207 and @xmath208 , to find + @xmath209 or @xmath205 .
the work of @xcite specifies 3 sets of 4 pairs of measurements , whose comparisons are supposed to indicate the violations of the 3 symmetries mentioned above .
( see _ tables 1 , 2 , 3 of @xcite ) .
each of the 24 measurements is completely determined by the products of the first and the second decay of the antisymmetric , entangled @xmath210 pair .
their amplitudes are thus uniquely given by our eq .
the corresponding rates are listed in our _ table 2 , labeled \{1 } to \{8}. the envisaged @xmath2-violating comparisons , labelled \{2a } to \{2d } in _ table 3 , depend also on @xmath71 , and thus contradict the affirmation in @xcite , that `` any difference in these two rates is evidence for @xmath2-symmetry violation '' , since a @xmath2-symmetric , @xmath3-violating hamiltonian @xmath211(@xmath212 ) would just also create such rate differences .
_ _ _ the @xmath1-violating comparisons in _ table 2 of @xcite also depend on @xmath213 and on @xmath214 .
this confirms that @xmath2- and/or @xmath3-violation imply @xmath1-violation .
@xmath2-violation in the ( 2 by 2 dimensional ) @xmath210 system is thus never independent of @xmath1 violation .
see also @xcite .
_ the @xmath3-violating comparisons in _ table 3 of @xcite neither depend on @xmath71 nor on @xmath72 , and are thus , contrary to the authors intentions , unable to detect @xmath3 symmetry violation in the matrix @xmath206 .
_ nevertheless , the measured frequency distributions \{2a } to \{2d } show a dominant @xmath215 time - dependence , meaning , for this reason , that @xmath103 , and with the previous knowledge about the vanishing of the @xmath216 , that @xmath217 , i. e. @xmath2-symmetry violation is confirmed .
( more combinations are discussed in @xcite ) . in the lower part of _ table
_ 3 , we indicate rate combinations which are true signatures of @xmath2- or @xmath3- symmetry violations .
the experiments @xcite and @xcite have discovered @xmath1 violation in the @xmath7@xmath8 system .
our analysis shows that this @xmath1 violation is dominantly @xmath2 violation , with the same statistical significance .
furthermore , their data sets contain the information which allows for the estimation of all symmetry - violating parameters indicated in _ table _ 1 .
@xmath1 symmetry of the matrix @xmath34 , which governs the @xmath218 oscillation , is confirmed .
the novel definitions of the symmetries ( @xmath219 ) used by @xcite are more restrictive than the classical ones @xcite .
we are grateful for numerous , very helpful discussions with k. r. schubert during and around the mitp workshop in mainz , april 2013 . 99 t. d. lee , r. oehme and c. n. yang , phys .
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b@xmath236 , 95 ( 2014 ) . | we revisit various results , which have been obtained by the babar and belle collaborations over the last thirteen years , concerning symmetry properties of the hamiltonian , which governs the time evolution and the decay of neutral @xmath0 mesons .
we find that those measurements , which established @xmath1 violation in @xmath0 meson decay , 13 years ago , had as well established @xmath2 ( time - reversal ) symmetry violation .
they also confirmed @xmath3 symmetry in the decay @xmath4 and symmetry with respect to time - reversal @xmath5 and to @xmath3 @xmath6 in the @xmath7@xmath8 oscillation .
motion - reversal symmetry vs. time - reversal symmetry is discussed .
maria fidecaro@xmath9 , hans - jrg gerber@xmath10 , thomas ruf@xmath9 + @xmath9cern , ch-1211 geneva 23 , switzerland + @xmath10ethz , ipp , ch-8093 zrich , switzerland + |
portal vein thrombosis ( pvt ) is a potentially detrimental complication of liver cirrhosis that may lead to worsening of liver function , unexpected episodes of esophageal variceal bleeding , hyperdynamic circulation , and intestinal ischemia ( 1 , 2 ) . depending on the method of diagnosis and the stage of cirrhosis , the prevalence of pvt in cirrhotic patients ranges from < 0.6% in compensated cirrhosis ( 3 ) to 28% in liver transplant candidates ( 4 - 7 ) .
pvt may make liver transplantation more technically difficult ( 8 , 9 ) . in most patients ,
pvt is diagnosed as an incidental finding , but in some patients it presents with decompensation of chronic liver disease .
it is not yet completely clear whether pvt is a consequence of severe liver cirrhosis or an aggravating factor , or both .
the main pathogenic factor of pvt in cirrhosis is the decreased portal flow due to architectural liver damage , but acquired and inherited clotting abnormalities may play a role ( 10 ) .
male sex , previous surgery or endoscopic treatment for portal hypertension , history of variceal bleeding , low platelet count , hepatocellular carcinoma , and advanced liver failure have been postulated as possible risk factors for pvt ( 11 , 12 ) .
there are also contradictory findings on the role of genetic mutations in the predisposition to this condition in cirrhotic patients ( 10 , 13 ) .
the present study aimed to investigate the associations between various inherited and acquired risk factors in cirrhotic patients and the development of pvt .
this cross - sectional study was conducted from november 2010 to may 2011 at shiraz liver transplantation center at namazi general hospital in shiraz , iran ( the only national liver transplantation center in the country ) .
all cirrhotic patients ( documented clinically or by liver biopsy ) , who were > 18 years old and listed for liver transplantation , were analyzed using a questionnaire that included age , gender , child - pugh score , model for end - stage liver diseases ( meld ) score , cause of liver cirrhosis , previous surgery , history of previous variceal bleeding and subsequent endoscopic treatment , amount of diuretic use ( average use in the previous three months ) , history of intra - abdominal inflammation , abdominal trauma , oral contraceptive use , and pregnancy .
patients with end - stage renal disease , congestive heart failure , cystic fibrosis , malignancy , pylephlebitis , liver cysts or abscesses , budd chiari syndrome , inflammatory bowel disease , vascular abnormalities , or pancreatitis were excluded .
those who had a confirmed diagnosis of hepatocellular carcinoma by imaging and/or biopsy at the time of listing were also excluded .
all patients consented to participate in the study . at the time of evaluation for transplantation
, all candidates were screened by a single expert radiologist with color doppler ultrasound and contrast - enhanced multi - detector 64-slice dynamic computed tomography ( ct ) for the evaluation of portal vein patency .
laboratory studies were performed , including platelet count , alpha - feta protein , albumin levels , blood urea nitrogen , creatinine , fasting blood glucose , uric acid , protein c , protein s , antithrombin iii , activated protein c resistance ( apcr ) , factor viii , homocysteine , jak2 mutation , anticardiolipin antibody , prothrombin gene mutation ( g20210a , determined by the mbol restriction enzyme method ) , and factor v leiden mutation ( g1691a ) .
results for continuous variables were expressed as mean sd , and the mann - whitney u - test was used for comparison of means between the pvt and non - pvt groups .
results for continuous variables were expressed as mean sd , and the mann - whitney u - test was used for comparison of means between the pvt and non - pvt groups .
the chi - square test was used where appropriate for other variables . for all tests ,
the study included 219 adult cirrhotic patients who met all of the inclusion criteria and none of the exclusion criteria .
the characteristics of the patients with pvt compared to the control group are shown in table 1 .
of 219 patients , 71 were female ( nine with pvt and 62 without ) and 148 were male ( 26 with pvt and 122 without ) .
the mean age was 46 9.99 years in the patients with pvt and 45 12.71 years in those without pvt .
the mean meld score was 20 6.46 in the pvt group and 19 6.15 in the control group . according to the child classification , 32 patients had child class a cirrhosis ( 3 with pvt ) , 107 patients had child class b cirrhosis ( 20 with pvt ) , and 80 patients had child class c cirrhosis ( 12 with pvt ) .
the mean values for serum albumin , platelets , fasting blood sugar , triglycerides , cholesterol , bun , creatinine , and uric acid were not different between the two groups ( table 1 ) .
the average dose of spironolactone and furosemide taken by each patient in the previous three months was analyzed , and there was no statistically significant difference in the doses of these diuretics between the two groups .
of the 219 participants , 102 consumed both spironolactone and furosemide , while 54 used only one and 63 used neither .
there was no statistically significant difference in pvt prevalence between these three groups ( p = 0.338 , 0.329 , and 0.143 , respectively ) .
g / l in the pvt group ( sd : 144.96 ) , and 19.66 g / l in the non - pvt group ( sd : 102.72 ) .
the difference was not statistically significant ( p = 0.481 ) . among the female patients , six with pvt and 18 without pvt
there was no statistically significant difference between these two groups ( p = 0.152 ) .
the causes of cirrhosis in the participants were analyzed , and the most common etiology was hepatitis b ( table 1 ) .
there was no difference in patients with or without pvt in the etiology of cirrhosis .
the presence or absence of previous surgery was also not different between the pvt and non - pvt groups ( p = 0.327 ) . among the 219 participants ,
a history of variceal bleeding was more frequent in patients with pvt than in those without it , and this difference was statistically significant ( p = 0.023 , or : 2.526 , 95% ci : 1.200 - 5.317 ) .
however , the duration of variceal bleeding had no association with pvt . since sclerotherapy with 50% alcohol
was performed on only eight patients and all others received rubber - band ligation alone , a comparison between these two modalities was not meaningful in this study .
no patient in this study received a transjugular intrahepatic portosystemic shunt ( tips ) , shunt surgery , or cyanoacrylate injection .
a history of spontaneous bacterial peritonitis was present in four patients with pvt and 15 without pvt , with no statistically significant difference between the two groups ( p = 0.516 ) .
there was no significant difference in history of abdominal trauma between the patients with and without pvt ( p = 1.000 ) .
the same was true for histories of diabetes mellitus and ischemic heart disease ( p = 0.437 and 0.415 , respectively ) .
of the 219 participants , ascites was observed in 118 patients by the former method and in 106 by the latter .
the patients were divided into four groups based on the amount of ascitic fluid : none , mild , moderate , and severe .
first , it was compared between patients with various amounts of fluid on both sonography and ct scan , and second , the prevalence was compared between patients with moderate or severe ascites and those with mild or no ascites .
the levels of homocysteine , protein c , protein s , antithrombin iii , apcr , factor viii , and anticardiolipin antibodies showed no significant differences between the patients with pvt and the control group ( p = 0.545 , 0.625 , 0.282 , 0.678 , 0.478 , 0.479 , and 0.481 , respectively ) ( figure 1 ) .
factor v leiden polymorphism ( g1691a ) was compared between the pvt and non - pvt groups .
heterozygosity for g1691a polymorphism was detected in one patient with pvt and in six without pvt .
no statistically significant difference was noted ( p = 0.999 ) . prothrombin gene mutation and
pvt is a common complication of end - stage liver disease in patients on the waiting list for liver transplantation .
the overall prevalence of pvt in our study of cirrhotic patients was 15.9% , which was comparable to the prevalence of 8% - 25% reported in other studies of patients awaiting liver transplantation ( 4 , 12 , 14 , 15 ) . in studies that included patients with less severe disease , or that used sonography alone for the diagnosis of pvt , the prevalence of pvt was as low as 0.6% ( 3 ) . despite bleeding tendencies in cirrhotic patients , mostly related to low platelet counts and high prothrombin times
enhanced thrombin generation associated with low levels of protein c and elevated factor viii has been implicated ( 18 - 20 ) .
however , it is not clear whether this is a genetic - based abnormality or is simply related to the consequences of synthetic dysfunction in cirrhotic patients . in this prospective study
, we analyzed various predisposing factors for pvt in cirrhotic patients who were awaiting liver transplantation .
( figure 1 ) this is in contrast to some previous studies that reported thrombophilic risk factors in relationship to the prevalence of pvt in cirrhotic patients .
positivity for antiphospholipid antibodies , including anticardiolipin antibodies and lupus anticoagulant ( 10 ) , as well as prothrombin gene mutation 20210a ( 21 ) , the c677>t substitution in the methylene tetrahydrofolate reductase gene ( a mutation that causes increased plasma levels of homocysteine ) , and factor v leiden mutation , have been reported to be related to pvt ( 22 ) . in our study , the levels of homocysteine , protein c , protein s , antithrombin iii , apcr , factor viii , and anticardiolipin antibodies in the cirrhotic patients were not associated with development of pvt .
furthermore , we did not find any prothrombin gene mutations in our 219 cirrhotic patients .
this may be related to our strict inclusion and exclusion criteria , as well as to the fact that overall , it is the imbalance between procoagulants and anticoagulants that causes the hypercoagulable state of cirrhosis , rather than a single factor ( 17 , 23 ) .
a number of previous studies have found that the etiology of cirrhosis may influence the prevalence of pvt in patients , with the highest pvt incidence occurring in alcoholic and hepatitis b virus - related cirrhosis ( 24 , 25 ) .
this might be due to the high rate of hepatitis b virus - related cirrhosis in both groups . in our study , only endoscopic therapy for esophageal varices ( with sclerotherapy or variceal band ligation ) increased the risk of pvt , but the frequency of episodes of variceal bleeding had no association with pvt .
consistent with our results , in one study of 251 cirrhotic patients awaiting transplantation , a multivariate analysis showed that a past history of variceal bleeding was a predictive factor for thrombosis ( 4 ) .
episodes of variceal bleeding , reflecting the severity of portal hypertension , are more likely to be predisposing factors for , rather than a consequence of , pvt ( 4 , 26 ) .
other studies showed that endoscopic sclerotherapy for esophageal varices may represent a trigger factor for pvt in cirrhotic patients with genetic thrombophilia ( 21 ) . in one study by tripodi et al .
the theoretical risk with cyanoacrylate glue was higher than with sclerotherapy ; however , the existing evidence comes from case reports of small studies ( 17 ) .
some recent studies have shown associations between thrombopoietin receptor agonists and the development of pvt in cirrhotic patients ( 27 ) .
since esophageal variceal bleeding is an indicator of severe portal hypertension , further prospective studies should be done to evaluate the causative role of endoscopic treatment for varices in pvt .
alternatively , sluggish blood flow due to collateral formation might have a role in the development of pvt ( 7 ) .
ascites at baseline and worsening renal function have been related to new - onset pvt in patients with cirrhosis who are on waiting lists for transplantation ( 28 ) . in our study
although we performed this study in a prospective manner , we evaluated our patients only upon their addition to the waiting list , and we did not follow them to determine whether they developed pvt later .
we also did not study the patients fibrinolytic profiles , which have been recently reported to be associated with an increased risk of pvt in patients with cirrhosis ( 29 ) . in conclusion , in this study of cirrhotic patients on the waiting list for transplantation , pvt was common and was associated with previous episodes of variceal bleeding . | background : portal vein thrombosis is a fairly common and potentially life - threatening complication in patients with liver cirrhosis .
the risk factors for portal vein thrombosis in these patients are still not fully understood.objectives:this study aimed to investigate the associations between various risk factors in cirrhotic patients and the development of portal vein thrombosis.patients and methods : in this case - control study performed at the shiraz organ transplantation center , iran , we studied 219 patients ( > 18 years old ) with liver cirrhosis , who were awaiting liver transplants in our unit , from november 2010 to may 2011 .
the patients were evaluated by history , physical examination , and laboratory tests , including factor v leiden , prothrombin gene mutation , janus kinase 2 ( jak2 ) mutation , and serum levels of protein c , protein s , antithrombin iii , homocysteine , factor viii , and anticardiolipin antibodies.results:there was no statistically significant difference in the assessed hypercoagulable states between patients with or without portal vein thrombosis .
a history of previous variceal bleeding with subsequent endoscopic treatment in patients with portal vein thrombosis was significantly higher than in those without it ( p = 0.013 , or : 2.526 , 95% ci : 1.200 - 5.317).conclusions : in our population of cirrhotic patients , treatment of variceal bleeding predisposed the patients to portal vein thrombosis , but hypercoagulable disorders by themselves were not associated with portal vein thrombosis . |
human body is exposed to a continuous influence of carcinogenic factors ( physical , chemical , and biological ) , representing one of the reasons for the development of genetic mutations .
cells possess an array of mechanisms able to prevent mutations , as well as to repair dna defects and eliminate genetically altered cells , for example , by the means of apoptosis [ 1 , 2 ] . disorders of this complicated protective system lead to the development of neoplastic cells , which , in turn , may be eliminated by an array of immunological mechanisms , including those affected by the innate immune system ( monocytes , macrophages , nk cells , cytokines , etc . ) and the adaptive immunity ( induction of t and b lymphocytes ) . in order to eliminate neoplastic cells ,
the cells of the immune system must recognize them as foreign . the principles of recognition and the mechanisms of the immunological response are similar to those induced by foreign ( bacterial , viral ) or own antigens ( autoantigens ) .
foreign antigens are highly immunogenic ; that is , they induce immune response aimed at the rapid elimination of the infectious factors .
these processes lead to the selection of a pool of immunocompetent cells , specialized in the destruction of a given factor .
as previously mentioned , neoplastic cells originate from genetically altered cells of own tissues and therefore contain components that induce various degrees of immune tolerance , protecting them against the elimination by immunological mechanisms . on the other hand ,
neoplastic cells are characterized by a genetic instability , which manifests by changes in antigenic profile , which are not observed in the normal tissue . in some cases , this is accompanied by the overexpression of genes that remain inactive or exhibit low - level activity under normal conditions ; many of the factors produced in this manner act as immunomodulators .
it is widely known that neoplastic tissue can directly modulate its growth environment as a result of the activity of secreted cytokines and chemokines .
this may be due to the following : chemotactic effect on leukocytes , including monocytes and macrophages;suppression of the activity of the immune system;regulation of neovascularization processes .
chemotactic effect on leukocytes , including monocytes and macrophages ; suppression of the activity of the immune system ; regulation of neovascularization processes .
some factors synthesized and released by neoplastic cells can induce leukocyte chemotaxis , including peripheral monocytes and macrophages located in the surrounding tissues .
these cells represent the predominant component of leukocytic infiltrate of many tumors and , due to their pleotropic biological activity control , the majority of immunological processes proceeding in the region of neoplastic growth .
chemotaxis of monocytes and macrophages is a receptor - dependent process , directly associated with the polarization of these cells towards pro- or anti - inflammatory cells .
monocyte chemotactic protein-1 ( mcp-1/ccl2 ) , showing affinity to ccr2 receptor , constitutes one of the principal monocyte / macrophage chemokines [ 6 , 7 ] .
moreover , the concentration of ccl2 correlates positively with the stage of the tumor in cancer of urinary bladder and breast .
high level of this cytokine is associated with poor prognosis ; it is observed in patients with higher clinical stages of the tumor [ 8 , 9 ] .
in contrast , a proportional decrease in the concentration of ccl2 is observed with increasing stages of gastric malignancies , both in the serum and in neoplastic tissue . perhaps , this phenomenon results from enhanced
interestingly , mcp-1 can be released also by macrophages located in the region of neoplastic growth .
it should be noted , however , that the impaired expression of ccr2 receptor on the surface of tumor - associated macrophages leads to the reversal of the effect exerted on these cells by the discussed chemokine . plausibly , this is one of the mechanisms enabling the maintenance of rich macrophage infiltrate in the region of neoplastic growth .
expression of mcp-1 correlates positively with the level of vascular endothelial growth factor ( vegf ) , tnf- , and il-8 , which suggests its involvement in the processes of neovascularization .
the migration of peripheral monocytes to the site of neoplastic growth can be also induced by monocyte chemotactic protein-2 ( mcp-2/ccl-8 ) and monocyte chemotactic protein-3 ( mcp-3/ccl-7 ) .
these cytokines show both a structural similarity to mcp-1 and an affinity to the ccr2 receptor .
the chemotaxis of monocytes is also induced by ccl5 ( rantes ) , whose level of expression correlates with the degree of macrophage infiltration and lymph node metastases of neoplastic cells .
rantes and ccl2 stimulate monocytes to secrete metalloproteinase-9 ( mmp-9 ) and metalloproteinase-19 ( mmp-19 ) , which suggests indirect involvement of the discussed chemokines in the degradation of basal membrane , and hence in the process of neovascularization [ 15 , 16 ] .
furthermore , high concentration of ccl5 increases the probability of metastases in patients with gastric malignancies .
also , factors released by the neoplastic cells , such as vegf , il-8 , and angiopoietin-2 ( ang-2 ) , exert chemotactic effect on monocytes / macrophages ; additionally , they are involved in the processes of angiogenesis .
formation of new blood vessels is critical for neoplastic growth and results from the predominance of proangiogenic factors over those inhibiting angiogenesis .
enhanced angiogenesis can be observed in very early stages of malignant growth [ 19 , 20 ] .
molecules such as ( vegf ) , interleukin-8 ( il-8/cxcl8 ) , basic fibroblast growth factor ( bfgf ) , angiopoietin-1 ( ang-1 ) , and angiopoietin-2 ( ang-2 ) are the main mediators of neovascularization released by the neoplastic cells , including the cells of gastric malignancies .
vegf is synthesized and secreted by many types of neoplasms [ 2123 ] and although high levels of this molecule can be observed both in the plasma and in the serum of patients , the serum concentration of vegf is higher .
this results from the secretory activity of thrombocytes , which release high amounts of this factor during the coagulation of blood .
vegf acts in the receptor - dependent manner , inducing the chemotaxis of peripheral monocytes as a result of interacting with vegf - r1 . in response to vegf ,
activated monocytes / macrophages synthesize molecules , for example , metalloproteinase-9 [ 27 , 28 ] , which , as previously mentioned , is involved in the processes of angiogenesis .
although tumor - associated macrophages ( tam 's ) constitute the principal source of mmp9 in the zone of neoplastic growth , it should be noted that this molecule may be also synthesized by neoplastic cells , stromal neutrophils , fibroblasts , and mastocytes .
moreover , the activity of vegf leads to an increased permeability of blood vessels within the neoplastic tissue , proliferation of vascular endothelial cells , and the inhibition of dendritic cell maturation .
the majority of these processes are associated with the activation of vegf - r2 receptor .
therefore , the vegf / vegf - r2 system is connected with the initiation of neovascularization processes . similarly to vegf , interleukin-8 is a chemokine with pro - angiogenic activity .
high expression levels of this molecule have been observed in various types of neoplasms , directly correlated with the vascularization of proliferating tissue and poor prognosis , being the highest in the advanced stages of tumor development .
gastric cancer cells also show the expression of a ( cxcr1 ) and b ( cxcr2 ) receptors for il-8 . during in vitro il-8 stimulation
, they show increased expression of epidermal growth factor receptor ( egfr ) , mmp-9 , vegf , and il-8 . similarly to vegf , interleukin-8 induces the migration of monocytes / macrophages to the site of neoplastic growth .
basic fibroblast growth factor ( bfgf ) is one of the strongest stimulators of angiogenesis , acting via fgf - r1 and fgf - r2 receptors .
high level of bfgf correlates positively with poor prognosis , and its expression in neoplastic cells is associated with the vascularization of the tumor .
moreover , this factor stimulates the chemotaxis of macrophages , which acquire the potential to synthesize and secrete this molecule in response to mediators released by neoplastic cells .
this suggests indirect tams - dependent influence of bfgf on the processes of tumor neovascularization .
angiopoetin-1 ( ang-1 ) and angiopoetin-2 ( ang-2 ) are the main representatives of angiopoietin family . the activity of ang-2 during the development of neoplastic disease is associated with the progression of the disease and the neovascularization of the tumor .
angiopoietin-1 activates tie-2 receptor ( angiopoietin receptor ) , in this way stimulating in vitro migration of endothelial cells ; moreover , it recruits pericytes into the newly formed vessels in order to stabilize their structure .
ang-2 inhibits the maturation of vessels resulting from ang-1 activity in a vegf - independent manner and causes their regression .
the activity of ang-2 leads to the destabilization of vessels , which is necessary for the initiation of neovascularization process .
interestingly , vegf causes an increase in ang-1 expression , but it does not modulate the synthesis of ang-2 .
the level of ang-2 expression correlates significantly with the clinical stage of disease ( lymph node and organ metastases ) while the expression of ang-1 is significantly higher in poorly differentiated tumors .
the angiopoietin / tie-2 system is involved in the remodeling and maturation of blood vessels and is , therefore , complementary to the activity of vegf .
moreover , the evaluation of ang-1 , ang-2 , and tie-2 serum concentrations seems to be useful in preoperative differentiation of malignant thyroid tumors .
additionally , angiopoietins are able to stimulate the chemotaxis of tie-2-positive peripheral monocytes , which , constituting cells with pro - angiogenic potential , support the proliferation of neoplastic tissue .
cancer cells and tumor - infiltrating leukocytes ( primarily macrophages ) modulate the activity of the immune system , also by means of immunosuppression , via the profile of released factors ( cytokines and chemokines ) . il-10 and tgf- are released by these cells and show an array of immunosuppressive effects , for example : blockade of the activity of cytotoxic nk cells , macrophages , and cytotoxic t lymphocytes ( cd8 ) ; reduced expression of class ii mhc molecule on the surface of antigen presenting cells ; polarization of immune response towards th2 ; inhibition of dendritic cell maturation ; inhibition of certain functions of t lymphocytes ; stimulation of tumor cell b7-h3 expression .
blockade of the activity of cytotoxic nk cells , macrophages , and cytotoxic t lymphocytes ( cd8 ) ; reduced expression of class ii mhc molecule on the surface of antigen presenting cells ; polarization of immune response towards th2 ; inhibition of dendritic cell maturation ; inhibition of certain functions of t lymphocytes ; stimulation of tumor cell b7-h3 expression . together with a strong anti - inflammatory signal , neoplastic cell - released chemotactic factors for monocytes and macrophages induce their differentiation into mii macrophages , and hence into cells showing an array of functions promoting the proliferation of neoplastic tissue .
consequently , it should be noted that aside from direct immunosuppressive activity , growing neoplasm induces anti - inflammatory activity of infiltrating cells , thus escaping from the control of the immune system .
macrophages are terminally differentiated cells of bone marrow origin that reside in tissues and are derived from peripheral monocytes ( figure 1 ) .
depending on the activating factor , monocytes and macrophages can be involved in an array of biological processes , such as : presentation of antigen;cytotoxicity;phagocytosis;secretion of biologically active molecules;control of inflammatory processes;rearrangement and reconstruction of destroyed tissues .
presentation of antigen ; secretion of biologically active molecules ; control of inflammatory processes ; rearrangement and reconstruction of destroyed tissues .
as previously mentioned , the proliferation of neoplastic tissue modulates the activity of immune cells , including the function of monocytes and macrophages .
it is widely known that macrophages residing at the site of neoplastic growth , referred to as tams , constitute the predominant component of infiltrate in many neoplasms , including gastric malignancies [ 5254 ] . due to their pleotropic biological properties
, tams can have both progressive and regressive effects on the development of neoplastic tissue . moreover
the pro- or anti - neoplastic activity of macrophages is directly associated with their pro- or anti - inflammatory activity , respectively , and tightly depends upon monocyte - activating factors , which define the relevant polarization of these cells ( figure 1 ) .
as peripheral cells , monocytes do not have direct contact with a neoplastic tissue . indirectly , however , they are subject to its immunomodulatory effect , responding to chemotactic factors and neoplastic antigens present in peripheral blood , as well as to circulating neoplastic cells .
all these factors directly induce the differentiation of monocytes to macrophages and their polarization towards pro- or anti - inflammatory cells . in the case of some malignancies , such as colorectal cancer ,
monocytes are heterogeneous population of cells in terms of morphology , phenotype , and effector properties . on the basis of the level of expression of lipopolysaccharide ( lps ) receptor ( cd14 ) and fc receptor iii ( cd16 )
, they can be classified into three well - characterized subpopulationsthose showing strong expression of cd14 receptor and lacking the expression of cd16 receptor ( cd14cd16);those showing strong expression of cd14 and the presence of cd16 receptor ( cd14cd16);those showing weaker expression of cd16 receptor than in the above - mentioned groups expression of cd14 receptor , with simultaneous ( cd14cd16 ) .
those showing strong expression of cd14 receptor and lacking the expression of cd16 receptor ( cd14cd16 ) ; those showing strong expression of cd14 and the presence of cd16 receptor ( cd14cd16 ) ; those showing weaker expression of cd16 receptor than in the above - mentioned groups expression of cd14 receptor , with simultaneous ( cd14cd16 ) .
monocytes with cd14cd16 phenotype are referred to as classical monocytes and correspond to 8595% of all peripheral monocytes under physiological conditions .
the remaining two populations showing strong expression of cd16 receptor differ from each other in terms of cd14 expression level and , under physiological conditions , represent up to 15% of peripheral monocytes [ 57 , 58 ] . despite phenotypic similarities associated with the expression of cd16 receptor , stronger ,
as compared to classical monocytes , expression of hla - dr , cd86 , and cd54 , and lower level of cd64 expression , both of the aforementioned subpopulations of monocytes show different biological activities .
an increase in the fraction of cd14cd16subpopulation of peripheral monocytes was observed during infections and inflammatory processes [ 60 , 61 ] , in septic states , and in some types of neoplasms [ 63 , 64 ] .
cd14cd16 cells are referred to as proinflammatory monocytes , because in contrast to classical monocytes upon stimulation they synthesize and release high amounts of tumor necrosis factor - alpha ( tnf- ) without concomitant secretion of il-10 or with low secretion of this cytokine .
the cells from this population show an array of similarities to tissue macrophages , and they are , therefore , postulated to be more mature and macrophage - like cells than the classical monocytes [ 66 , 67 ] .
higher fraction of monocytes from cd14cd16 subpopulation has been observed in a number of conditions , including septic neonatal states and gastric malignancies .
additionally , compared to the pro - inflammatory subpopulation and classical monocytes , these cells show a higher expression of cd11b and tlr4 .
moreover , they differ from the cd14cd16 subpopulation in terms of characteristics such as higher phagocytic activity and the presence of anti - inflammatory properties , constituting the principal source of il-10 amongst peripheral monocytes .
the presence of this subpopulation in peripheral blood is thought to constitute an intermediate stage in the differentiation of monocytes to macrophages . in spite of the lack of direct contact with neoplastic tissue , peripheral monocytes represent an interesting object during the assessment of the developmental stage of the disease .
as previously mentioned , they undergo a continuous stimulation by chemokines and cytokines released by neoplastic cells and tumor - infiltrating cells , as well as by neoplastic antigens and circulating neoplastic cells .
cd14cd16 cells are the main subpopulation of monocytes showing in vitro antineoplastic activity , which is directly associated with the enhanced synthesis and secretion of cytokines such as tnf- , il-12p40 , and il-12p70 , lack of synthesis and release of il-10 , enhanced synthesis of reactive nitrogen species , and higher cytotoxic and cytostatic activities .
the influence of il-12p70 is associated with the activation of ifn- synthesis in lymphocytes , which in turn contributes to the polarization of immune response towards th1 , that is , a proinflammatory response against neoplastic cells .
additionally , il-12p70 activates cytotoxic t lymphocytes ( cd3cd8 ) and nk cells , both showing an array of antineoplastic properties .
il-12p40 is a chemotactic factor for monocytes , which differentiate into macrophages and migrate to the tissue .
therefore , il-12p40 enhances the infiltration of macrophages into the site of neoplastic proliferation , where , as pro - inflammatory cells , they can exert many antineoplastic effects .
the results of in vitro studies suggest that increased fraction of cd16 monocytes in patients with malignancies can represent a natural consequence of immune response against neoplastic tissue as well as against circulating neoplastic cells .
spontaneous increase in this population of peripheral monocytes was also observed in vivo , including gastrointestinal malignancies .
additionally , a decrease in the fraction of the subpopulation 1 of t - helper lymphocytes ( th1 ) was observed in peripheral blood of cancer patients in relation to the subpopulation 2 ( th2 ) ; this was associated with lower plasma concentration of molecules such as il-2 and ifn- , and higher level of cytokines , such as il-4 , il-10 , and il-13 , as compared to healthy individuals . in view of the elevated concentration of anti - inflammatory factors , circulating monocytes should gain anti - inflammatory properties and differentiate into mii macrophages , which are involved in the processes of neovascularization , among others .
proangiogenic activity is also characteristic for monocytes that show the surface expression of angiopoietin receptor ( tie-2 ) , although this receptor is mostly expressed on epithelial cells and is considered as a specific feature of vascular epithelial cells .
tie-2 monocytes represent a separate population of cells referred to as the tie-2-expressing monocytes ( tems ) .
even though their physiological fraction in peripheral blood is low and corresponds to only 1 - 2% of peripheral leukocytes , approximately 20% of circulating monocytes are tie-2 [ 43 , 76 ] .
an increase in the fraction of tie-2-expressing monocytes , even up to 10% of all peripheral blood mononuclear cells ( pbmcs ) , has been observed in cancer patients .
murine model studies revealed strong pro - angiogenic properties of tems during the processes of neoplastic tissue neovascularization .
moreover , these cells are considered the precursors of pro - angiogenic tissue macrophages , which correspond to up to 30% of all tams in certain parts of the neoplastic tissue .
macrophages are the predominant cells of the leukocytic infiltrate of many neoplasms and are able to polarize their immune response in both a pro- or anti - inflammatory direction .
monocytes , activated by microorganisms or their parts , certain pro - inflammatory cytokines ( e.g. , ifn- ) , gm - csf , and m - csf , migrate into tissues and differentiate into pro - inflammatory cells , referred to as mi macrophages , which are involved in the destruction of microorganisms and neoplastic cells , among others ( table 1 ) .
their function includes the activation of immune system and the support of adaptive response by means of : enhanced synthesis and secretion of pro - inflammatory cytokines such as tnf- , il-1 , il-6 , il-12 , and il-23 [ 7880];enhanced synthesis and secretion of chemokines such as ccl5 , ccl8 , cxcl2 , and cxcl4 [ 8183];polarization of immune response towards th1 and/or th17 ; high capacity for presentation of antigen to antigen - naive t lymphocytes;cytotoxic potential .
enhanced synthesis and secretion of pro - inflammatory cytokines such as tnf- , il-1 , il-6 , il-12 , and il-23 [ 7880 ] ; enhanced synthesis and secretion of chemokines such as ccl5 , ccl8 , cxcl2 , and cxcl4 [ 8183 ] ; polarization of immune response towards th1 and/or th17 ; high capacity for presentation of antigen to antigen - naive t lymphocytes ; cytotoxic potential .
monocytes activated by factors such as il-4 , il-13 , il-10 , and m - csf show typical activities of anti - inflammatory cells ; when present in tissues , they are referred to as mii macrophages ( table 1 ) .
these cells are characterized by : enhanced synthesis and secretion of anti - inflammatory cytokines such as il-10 , tgf- , and il-1ra;enhanced synthesis and secretion of chemokines such as ccl16 , ccl18 , and ccl22;polarization of immune response towards th2;induction of t - regulatory ( treg ) lymphocyte formation;low capacity for the presentation of antigen to antigen - naive t lymphocytes;strong expression of arginase-1 ( its activity alters the metabolism of l - arginine into ornithine and polyamines , which results in the blockade of inducible nitric oxide synthase ( inos));lack of cytotoxic activity;higher expression of certain membrane receptors , including type 2 fc receptor for igg ( fc - r2 , cd23 ) , mannose receptor ( mr ) , and receptor for lps ( cd14 ) .
enhanced synthesis and secretion of anti - inflammatory cytokines such as il-10 , tgf- , and il-1ra ; enhanced synthesis and secretion of chemokines such as ccl16 , ccl18 , and ccl22 ; polarization of immune response towards th2 ; induction of t - regulatory ( treg ) lymphocyte formation ; low capacity for the presentation of antigen to antigen - naive t lymphocytes ; strong expression of arginase-1 ( its activity alters the metabolism of l - arginine into ornithine and polyamines , which results in the blockade of inducible nitric oxide synthase ( inos ) ) ; lack of cytotoxic activity ; higher expression of certain membrane receptors , including type 2 fc receptor for igg ( fc - r2 , cd23 ) , mannose receptor ( mr ) , and receptor for lps ( cd14 ) . the principal tasks of mii include the suppression of adaptive response , inhibition of cytotoxic cell activity , rearrangement and reconstruction of destroyed tissues , and their neovascularization . therefore , mii macrophages play a regulatory function in pro - inflammatory response via the control of mi cell - dependent activities . consequently
, the maintenance of body homeostasis requires maintaining a proper ratio of both discussed subpopulations of macrophages , namely , mi and mii .
this balance is disturbed during such pathological conditions as the proliferation of neoplastic cells , leading to the impaired activity of immune system and uncontrolled progression of the disease .
however , the secretory activity of macrophages residing within the tumor should not be forgotten .
the activity of macrophages in the course of neoplastic disease has been studied extensively as they can exert both progressive ( mii macrophages ) and regressive ( mi macrophages ) effects on the development of neoplastic tissue . the balance between mi and mii macrophages seems to be controlled by nfb signaling , because targeting of this transcription factor switched macrophages from an mii to an mi phenotype .
the consequence of which is the regression of tumor tissue in vitro . as pro - inflammatory cells ,
macrophages are involved in stromal remodeling releasing a slate of pro - inflammatory factors that constitute a signal of danger for immune cells .
this macrophage activity may result in the following : activation of cytotoxic t lymphocytes and nk cells;influx of dendritic cells;migration and differentiation of monocytes in a pro - inflammatory direction .
activation of cytotoxic t lymphocytes and nk cells ; influx of dendritic cells ; migration and differentiation of monocytes in a pro - inflammatory direction . activated mi
macrophages synthesize and release il-12 , which , as was mentioned previously , shows indirect antineoplastic activity .
additionally , it exerts stimulatory effect on nk cells , inducing the synthesis and secretion of ifn- and enhancing their cytotoxic potential . stimulated with this cytokine , macrophages release factors such as roi , il-1 , il-6 , arginase , and tnf- , that is , pro - inflammatory factors exerting cytostatic and cytotoxic effects upon neoplastic cells .
moreover , these cells show a strong cytotoxic activity in both the antibody - dependent ( adcc ) and antibody - independent ( mtc ) mechanisms .
unfortunately , the majority of macrophages infiltrating neoplastic tissue have phenotype characteristic for mii , and thus they present an array of activities promoting the growth of neoplastic tissue .
the level of their infiltration is used as an independent prognostic factor in many tumor types .
however , it should be noted that in the case of some malignancies , for example , colorectal and gastric cancers , higher fraction of these cells does not necessarily correlate negatively with patients ' survival .
for example , higher infiltration of tams to the region of tumor cell nests is associated with improved survival . despite the small fraction of nest tams , as compared to their overall count in the other regions of the tumor , enhanced apoptosis of neoplastic cells
consequently , it should be emphasized that antineoplastic activities controlled by macrophages with mi phenotype can be induced in certain regions of neoplastic tissue .
however , they represent a minority of pro - neoplastic activities of mii macrophages , associated with the following : suppression of adaptive response;promotion of tumor growth;promotion of the metastases of neoplastic cells;involvement in the recruitment of peripheral monocytes and macrophages from the surrounding tissues . suppression of adaptive response ; promotion of tumor growth ; promotion of the metastases of neoplastic cells ; involvement in the recruitment of peripheral monocytes and macrophages from the surrounding tissues .
the mii macrophages release an array of anti - inflammatory factors , such as il-10 and prostanoids , causing the attenuation of type th1 immune response , as well as an impaired activity of cytotoxic t lymphocytes and nk cells .
moreover , they secrete a variety of specific cytokines ( e.g. , ccl17 and ccl22 ) , inducing the inflow of regulatory t cells and th2 subpopulation of helper lymphocytes .
these effects are reflected by the suppression of pro - inflammatory activities of the immune system , that is , by the inhibition of activities oriented against neoplastic cells .
moreover , tumor - associated macrophages are capable of modifying subunit of tcr receptor ( tcr- ) of t - helper lymphocytes [ 9092 ] , which plays a crucial role in the activation of the latter cells . the disorders of tcr- expression or inactivation of this subunit are reflected by the anergy of t lymphocytes , leading to their apoptosis . intensified proliferation of neoplastic tissue is associated with an increased requirement for nutrients and growth factors and leads to the hypoxia of the tumor .
high efficiency of pro - neoplastic mii macrophage activity is associated with their ability to accumulate within the oxygen - deficient regions of the tissue .
tams synthesize and release an array of growth and pro - angiogenic factors that are concurrently chemotactic factors for monocytes and macrophages , including vegf , bfgf , cxcl8 , pdgf , egf , and tgf- [ 89 , 94 ] .
pdgf promotes the proliferation of neoplastic tissue ; additionally , it acts as a pro - angiogenic factor and recruits pericytes stabilizing the newly formed vessels .
aside from the chemotaxis of macrophages from the surrounding tissues , m - csf induces the differentiation and migration of peripheral monocytes .
this constitutes one of the mechanisms behind the enhanced infiltration of macrophages into the tumor , which is in turn reflected by an enhanced synthesis of egf .
egf / m - csf feedback cycle leads to macrophage - dependent , growth factor - induced intensive proliferation of neoplastic tissue .
macrophages present at the invasive front of the tumor ( margin tams ) participate in the creation of promoting environment for neoplastic cells , enabling them to reach vascular and lymphatic system .
as previously mentioned , tams constitute a source of metalloproteinases ( such as mmp-2 and mmp-9 ) and an urokinase - type plasminogen activator ( upa ) , which facilitate tumor invasion due to their involvement in the degradation of basal membrane and extracellular matrix .
this process seems to a large extent to be egf and m - csf dependent .
the blockade of egf and m - csf activities is reflected by inhibited migration of neoplastic cells and macrophages , respectively [ 98 , 99 ] .
therefore , the m - csf - stimulated tams induce the migration of neoplastic cells on egf - dependent pathway . most likely , this process is also modulated by il-4 , which polarizes macrophages towards promoting the invasiveness and spread of the tumor ; these functions are blocked in the lack of il-4 [ 101 , 102 ] .
the invasiveness of neoplastic cells can be also modulated in tnf--dependent manner , with macrophages being the principal source of tnf- [ 104 , 105 ] .
the migration of neoplastic cells through the stroma is markedly more efficient if supported by collagen fibers ( type i collagen ) , formed with the involvement of tams .
these fibers expand towards blood vessels , significantly facilitating the migration of neoplastic cells and thus promoting the formation of distant metastases . in summary , due to their pro - angiogenic activity
, synthesis of collagen fibers , and the induction of neoplastic cell migration , tams actively promote the invasion and spread of the tumor .
the process of neoplastic tissue proliferation is directly related to the modulatory effect on the immune system .
this results in a switch from a protective function into one that promotes neoplastic proliferation . in the case of many malignancies ( e.g. , breast , prostate , or endometrial cancer ) ,
high percentage of tams is associated with poor prognosis . in practice , high percentage of tumor - associated macrophages may be an independent prognostic factor , providing a thorough examination of all the regions of the tumor and a precise assessment of the phenotype of these cells .
tams also seem to be a promising target for antineoplastic therapy , the aim of which should be , for example , the reversal of the unfavorable balance between mi and mii macrophages . on the other hand , monocytes | due to the profile of released mediators ( such as cytokines , chemokines , growth factors , etc . )
, neoplastic cells modulate the activity of immune system , directly affecting its components both locally and peripherally .
this is reflected by the limited antineoplastic activity of the immune system ( immunosuppressive effect ) , induction of tolerance to neoplastic antigens , and the promotion of processes associated with the proliferation of neoplastic tissue .
most of these responses are macrophages dependent , since these cells show proangiogenic properties , attenuate the adaptive response ( anergization of nave t lymphocytes , induction of treg cell formation , polarization of immune response towards th2 , etc . ) , and support invasion and metastases formation .
tumor - associated macrophages ( tams ) , a predominant component of leukocytic infiltrate ,
cooperate with the neoplastic tissue , leading to the intensified proliferation and the immune escape of the latter .
this paper characterizes the function of macrophages in the development of neoplastic disease . |
All of us at the University of Arizona are shocked and saddened by the loss of our recent graduate, Bakari Henderson.
Our hearts and prayers are with his friends and family. I can only imagine the deep sense of loss they must be feeling at his untimely death. It is always a tragedy when a young life ends before it has really yet to begin.
Our staff in the Dean of Students office are reaching out to the faculty and staff across campus. We also are working with his student organizations and the affiliations he had on campus to offer support to those who knew Bakari.
I know I speak for the university community as I express deepest condolences to Bakari’s family and friends.
President Robert C. Robbins
The University of Arizona ||||| ATHENS, Greece (AP) — Greek police say a 22-year-old American tourist has been fatally injured in a fight at a bar on the island of Zakinthos.
Police said in a statement Friday that the man, whose identity was not publicly announced, was beaten to death by a group of people at the bar early Friday in Lagana, an area of the island known for frequently rowdy behavior by young foreign tourists.
Police say a 34-year-old Greek and a 32-year-old British man of Serbian origin have been arrested and were to appear before a prosecutor on murder charges. They say an investigation to identify the rest of the people involved is ongoing.
It was not immediately clear why the fight broke out. ||||| Story highlights Bakari Henderson, 22, was visiting the Greek island of Zakynthos
Two people have been arrested, police say
(CNN) An American tourist was beaten to death by a group of 10 men while visiting a Greek island in the Mediterranean, state media reported.
Bakari Henderson, 22, was at a bar in the Greek island of Zakynthos with his friends Friday when a man approached him and they began fighting, according to state news agency ANA-MPA.
The fight escalated into a brawl on the streets after the bar's security asked the men to leave, ANA-MPA reported.
Two people, a 32-year-old Serbian and a 34-year-old Greek national, have been arrested. Police are searching for others who may be involved.
Zakynthos, an island in the west coast of mainland Greece, is popular among tourists for its cliffside beaches and sea caves.
Read More | – An American was beaten to death by a group of 10 men in a bar fight on the Greek island of Zakynthos, CNN reports. Bakari Henderson, 22, was out with friends on Friday night when a man approached him and a fight broke out, state news agency ANA-MPA reports via CNN. After the bar's security asked the men to leave, the fight spilled into a brawl on the street. Police arrested a 32-year-old British man of Serbian origin and a 34-year-old Greek. They were to appear before a prosecutor on murder charges, per the AP. Police were searching for others who may be involved. It was not immediately clear why the fight broke out. Henderson, a recent graduate of the University of Arizona, was in Greece working on a photo shoot for a new clothing line, his family tells KXAN via CNN. Henderson's Linkedin profile says he studied business finance and entrepreneurship. "Bakari loved spending time with family and friends, traveling, and meeting new people," his family says in a statement. "He was a big thinker and enjoyed coming up with new business ventures." University of Arizona President Robert C. Robbins extended his sympathies to the family in a statement. |
the electric resistivity in magnetic metals has been studied for years .
the main effect of spin - independent resistivity is unanimously attributed to phonons . as far as spin - dependent resistivity
is concerned , we had to wait until de gennes and friedel s first explanation in 1958@xcite which was based on the interaction between spins of conduction electrons and magnetic lattice ions .
experiments have shown that the resistivity indeed depends on the spin orientation.@xcite therefore , the resistivity was expected to depend strongly on the spin ordering of the system .
experiments on various magnetic materials have found in particular an anomalous behavior of the resistivity at the critical temperature where the system undergoes the ferromagnetic - paramagnetic phase transition.@xcite the problem of spin - dependent transport has been also extensively studied in magnetic thin films and multilayers .
the so - called giant magnetoresistance ( gmr ) was discovered experimentally twenty years ago.@xcite since then , intensive investigations , both experimentally and theoretically , have been carried out.@xcite the so - called `` spintronics '' was born with spectacular rapid developments in relation with industrial applications . for recent overviews ,
the reader is referred to refs . and .
theoretically , in their pioneer work , de gennes and friedel@xcite have suggested that the magnetic resistivity is proportional to the spin - spin correlation . in other words ,
the spin resistivity should behave as the magnetic susceptibility .
this explained that the resistivity singularity is due to `` long - range '' fluctuations of the magnetization observed in the critical region .
craig et al@xcite in 1967 and fisher and langer@xcite in 1968 criticized this explanation and suggested that the shape of the singularity results mainly from `` short - range '' interaction at @xmath1 where @xmath2 is the transition temperature of the magnetic crystal .
fisher and langer have shown in particular that the form of the resistivity cusp depends on the interaction range .
an interesting summary was published in 1975 by alexander and coworkers@xcite which highlighted the controversial issue . to see more details on the magnetic resistivity
, we quote an interesting recent publication from kataoka.@xcite he calculated the spin - spin correlation function using the mean - field approximation and he could analyze the effects of magnetic - field , density of conduction electron , the interaction range , etc . although many theoretical investigations have been carried out , to date very few monte carlo ( mc ) simulations have been performed regarding the temperature dependence of the dynamics of spins participating in the current . in a recent work,@xcite
we have investigated by mc simulations the effects of magnetic ordering on the spin current in magnetic multilayers .
our results are in qualitative agreement with measurements.@xcite due to a large number of parameters which play certainly important roles at various degrees in the behavior of the spin resistivity , it is difficult to treat all parameters at the same time .
the first question is of course whether the explanation provided by de gennes and friedel can be used in some kinds of material and that by fisher and langer can be applied in some other kinds of material . in other words
, we would like to know the validity of each of these two arguments .
we will return to this point in subsection [ discuss ] .
the second question concerns the effects of magnetic or non - magnetic impurities on the resistivity .
note that in 1970 , shwerer and cuddy@xcite have shown and compared their experimental results with the different existing theories to understand the impurity effect on the magnetic resistivity .
however , the interpretation was not clear enough at the time to understand the real physical mechanism lying behind .
the third question concerns the effects of the surface on the spin resistivity in thin films .
these questions have motivated the present work .
in this paper we use extensive mc simulation to study the transport of itinerant electrons traveling in a ferromagnetic thin film .
we use the ising model and take into account various interactions between lattice spins and itinerant spins .
we show that the magnetic resistivity depends on the lattice magnetic ordering .
we analyze this behavior by using a new idea : instead of calculating the spin - spin correlation , we calculate the distribution of clusters in the critical region .
we show that the resistivity depends on the number and the size of clusters of opposite spins .
we establish also a boltzmann s equation which can be solved using numerical data for the cluster distribution obtained by our mc simulation .
the paper is organized as follows .
section ii is devoted to the description of our model and the rules that govern its dynamics .
we take into account ( i ) interactions between itinerant and lattice spins , ( ii ) interactions between itinerant spins themselves and ( iii ) interactions between lattice spins .
we include a thermodynamic force due to the gradient of itinerant electron concentration , an applied electric field and the effect of a magnetic field . for impurities ,
we take the rudermann - kittel - kasuya - yoshida ( rkky ) interaction between them . in section iii
, we describe our mc method and discuss the results we obtained .
we develop in section iv a semi - numerical theory based on the boltzmann s equation . using the results obtained with hoshen and kopelmans@xcite cluster - counting algorithm
, we show an excellent agreement between our theory and our mc data . concluding remarks are given in section v.
we consider in this paper a ferromagnetic thin film .
we use the ising model and the face - centered cubic ( fcc ) lattice with size @xmath3 .
periodic boundary conditions ( pbc ) are used in the @xmath4 planes .
spins localized at fcc lattice sites are called `` lattice spins '' hereafter .
they interact with each other through the following hamiltonian @xmath5 where @xmath6 is the ising spin at lattice site @xmath7 , @xmath8 indicates the sum over every nearest - neighbor ( nn ) spin pair @xmath9 , @xmath10 being the nn interaction . in order to study the spin transport in the above system
, we consider a flow of itinerant spins interacting with each other and with the lattice spins .
the interaction between itinerant spins is defined as follows , @xmath11 where @xmath12 is the itinerant ising spin at position @xmath13 , and @xmath8 denotes a sum over every spin pair @xmath14 .
the interaction @xmath15 depends on the distance between the two spins , i.e. @xmath16 . a specific form of @xmath15 will be chosen below .
the interaction between itinerant spins and lattice spins is given by @xmath17 where the interaction @xmath18 depends on the distance between the itinerant spin @xmath12 and the lattice spin @xmath6 .
for the sake of simplicity , we assume the same form for @xmath15 and @xmath18 , namely , @xmath19 where @xmath20 and @xmath21 are constants .
the procedure used in our simulation is described as follows .
first we study the thermodynamic properties of the film alone , i.e. without itinerant spins , using eq .
( [ eqn : hamil1 ] ) .
we perform mc simulations to determine quantities as the internal energy , the specific heat , layer magnetizations , the susceptibility , ... as functions of temperature @xmath0.@xcite from these physical quantities we determine the critical temperature @xmath2 below which the system is in the ordered phase .
we show in fig .
[ fig : m(t ) ] the lattice magnetization versus @xmath0 for @xmath22 , @xmath23 .
once the lattice has been equilibrated at @xmath0 , we inject @xmath24 itinerant spins into the system .
the itinerant spins move into the system at one end , travel in the @xmath25 direction , escape the system at the other end to reenter again at the first end under the pbc .
note that the pbc are used to ensure that the average density of itinerant spins remains constant with evolving time ( stationary regime ) .
the dynamics of itinerant spins is governed by the following interactions : \i ) an electric field @xmath26 is applied in the @xmath25 direction .
its energy is given by @xmath27where @xmath28 is the velocity of the itinerant spin , @xmath29 its charge ; \ii ) a chemical potential term which depends on the concentration of itinerant spins ( `` concentration gradient '' effect ) .
its form is given by @xmath30 where @xmath31 is the concentration of itinerant spins in a sphere of radius @xmath32 centered at @xmath33 .
@xmath34 is a constant taken equal to @xmath20 for simplicity ; \iii ) interactions between a given itinerant spin and lattice spins inside a sphere of radius @xmath35 ( eq . [ eqn : hamil3 ] ) ; \iv ) interactions between a given itinerant spin and other itinerant spins inside a sphere of radius @xmath32 ( eq . [ eqn : hamil2 ] ) .
let us consider the case without an applied magnetic field .
the simulation is carried out as follows : at a given @xmath0 we calculate the energy of an itinerant spin by taking into account all the interactions described above .
then we tentatively move the spin under consideration to a new position with a step of length @xmath36 in an arbitrary direction .
note that this move is immediately rejected if the new position is inside a sphere of radius @xmath37 centered at a lattice spin or an itinerant spin .
this excluded space emulates the pauli exclusion principle in the one hand , and the interaction with lattice phonons on the other hand .
if the new position does not lie in a forbidden region of space , then the move is accepted with a probability given by the standard metropolis algorithm.@xcite to study the case with impurities , we replace randomly a number of lattice spins @xmath38 by impurity spins @xmath39 .
the impurities interact with each other via the rkky interaction as follows @xmath40 where @xmath41 @xmath42 being a constant and @xmath43 the fermi wave number of the lattice .
the impurity spins also interact with nn lattice spins .
however , to reduce the number of parameters , we take this interaction equal to @xmath44 as that between nn lattice spins ( see eq .
[ eqn : hamil1 ] ) with however @xmath45 .
we will consider two cases @xmath46 and @xmath47 in this paper .
we let @xmath24 itinerant spins travel through the system several thousands times until a steady state is reached .
the parameters we use in most calculations , except otherwise stated ( for example , in subsection [ surf ] for @xmath48 ) are @xmath49 and @xmath50 and @xmath51 .
other parameters are @xmath52 ( in unit of the fcc cell length ) , @xmath53 , @xmath54 , @xmath55 ( namely one itinerant spin per fcc unit cell ) , @xmath56 , @xmath57 , @xmath58 . at each @xmath0
the equilibration time for the lattice spins lies around @xmath59 mc steps per spin and we compute statistical averages over @xmath59 mc steps per spin . taking @xmath44 , we find that @xmath60 for the critical temperature of the lattice spins ( see fig .
[ fig : m(t ) ] ) .
we define the resistivity @xmath61 as @xmath62 where @xmath63 is the number of itinerant spins crossing a unit area perpendicular to the @xmath25 direction per unit of time .
we show in figs .
[ m_size ] and [ r_size ] the simulation results for different thicknesses . in all cases ,
the resistivity @xmath61 is very small at low @xmath0 , undergoes a huge peak in the ferromagnetic - paramagnetic transition region , decreases slowly at high @xmath0 .
we point out that the peak position of the resistivity follows the variation of critical temperature with changing thickness ( see fig .
[ m_size ] ) and @xmath61 at @xmath1 becomes larger when the thickness decreases .
this is due to the fact that surface effects tend to slow down itinerant spins .
we return to this point in the next subsection .
the temperature of resistivity s peak at a given thickness is always slightly higher than the corresponding @xmath2 .
let us discuss the temperature dependence of @xmath61 shown in fig .
[ r_size ] : \i ) first , @xmath61 is very low in the ordered phase .
we can explain this by the following argument : below the transition temperature , there exists a single large cluster of lattice spins with some isolated `` defects '' ( i. e. clusters of antiparallel spins ) , so that any itinerant spin having the parallel orientation goes through the lattice without hindrance .
the resistance is thus very small but it increases as the number and the size of `` defect '' clusters increase with increasing temperature .
\ii ) second , @xmath61 exhibits a cusp at the transition temperature .
we present here three interpretations of the existence of this cusp .
note that these different pictures are not contradictory with each other .
they are just three different manners to express the same physical mechanism .
the first picture consists in saying that the cusp is due to the critical fluctuations in the phase transition region .
we know from the theory of critical phenomena that there is a critical region around the transition temperature @xmath2 . in this region ,
the mean - field theory should take into account critical fluctuations .
the width of this region is given by the ginzburg criterion .
the limit of this `` ginzburg '' region could tally with the resistivity s peak and ginzburg temperature.@xcite the second picture is due to fisher - langer@xcite and kataoka@xcite who suggested that the form of peak is due mainly to short - range spin - spin correlation .
these short - range fluctuations are known to exist in the critical region around the critical point .
the third picture comes from our mc simulation@xcite which showed that the resistivity s peak is due to the formation of antiparallel - spin clusters of sizes of a few lattice cells which are known to exist when one enters the critical region .
note in addition that the cluster size is now comparable with the radius @xmath35 of the interaction sphere , which in turn reduces the height of potential energy barriers .
we have checked this interpretation by first creating an artificial structure of alternate clusters of opposite spins and then injecting itinerant spins into the system .
we observed that itinerant spins do advance indeed more slowly than in the completely disordered phase ( high-@xmath0 paramagnetic phase ) .
we have next calculated directly the cluster - size distribution as a function of @xmath0 using the hoshen - kopelman s algorithm.@xcite the result confirms the effect of clusters on the spin conductivity .
the reader is referred to our previous work@xcite for results of a multilayer case .
we will show in the next section a cluster distribution for the film studied in this paper .
\iii ) third , @xmath61 is large in the paramagnetic phase and decreases with an increasing temperature . above @xmath2 in the paramagnetic phase ,
the spins become more disordered as @xmath0 increases : small clusters will be broken into single disordered spins , so that there is no more energy barrier between successive positions of itinerant spins on their trajectory . the resistance , though high , is decreasing with increasing @xmath0 and saturated as @xmath64 .
\iv ) let us touch upon the effects of varying @xmath35 and @xmath32 at a low temperatures .
@xmath61 is very small at small @xmath35 ( @xmath65 ) : this can be explained by the fact that for such small @xmath35 , itinerant spins do not `` see '' lattice spins in their interaction sphere so they move almost in an empty space .
the effect of @xmath32 is on the other hand qualitatively very different from that of @xmath35 : @xmath61 is very small at small @xmath32 but it increases to very high value at large @xmath32 .
we conclude that both @xmath35 and @xmath32 dominate @xmath61 at their small values .
however , at large values , only @xmath32 has a strong effect on @xmath61 .
this effect comes naturally from the criterion on the itinerant spins concentration used in the moving procedure .
also , we have studied the effect of the electric field @xmath66 both above and below @xmath2 .
the low - field spin current verifies the ohm regime .
these effects have been also observed in magnetic multilayer.@xcite the reader is referred to that work for a detailed presentation of these points .
let us show now the effect of magnetic field on @xmath61 .
as it is well known , when a magnetic field is applied on a ferromagnet , the phase transition is suppressed because the magnetization will never tend to zero .
critical fluctuations are reduced , the number of clusters of antiparallel spins diminishes . as a consequence
, we expect that the peak of the resistivity will be reduced and disappears at high fields .
this is what we observed in simulations .
we show results of @xmath61 for several fields in fig .
[ r_b ] . the picture suggested above on the physical mechanism causing the variation of the resistivity helps to understand the surface effect shown here .
since the surface spins suffer more fluctuations due to the lack of neighbors , we expect that surface lattice spins will scatter more strongly itinerant spins than the interior lattice spins .
the resistivity therefore should be larger near the surface .
this is indeed what we observed .
the effect however is very small in the case where only a single surface layer is perturbed . to enhance the surface effect ,
we have perturbed a number of layers near the surface : we considered a sandwich of three films : the middle film of 4 layers is placed between two surface films of 5 layers each .
the in - plane interaction between spins of the surface films is taken to be @xmath67 and that of the middle film is @xmath68 . when @xmath69 one has one homogeneous 14-layer film .
we have simulated the two cases where @xmath69 and @xmath70 for sorting out the surface effect . in the absence of itinerant spins ,
the lattice spins undergo a single phase transition at @xmath71 for @xmath69 , and two transitions when @xmath70 : the first transition occurs at @xmath72 for `` surface '' films and the second at @xmath73 for `` middle '' film .
this is seen in fig .
[ surf1 ] where the magnetization of the surface films drops at @xmath74 and the magnetization of the middle film remains up to @xmath75 .
the susceptibility has two peaks in the case @xmath70 .
the resistivity of this case is shown in fig .
[ surf2 ] : at @xmath76 the whole system is ordered , @xmath61 is therefore small .
when @xmath77 the surface spins are disordered while the middle film is still ordered : itinerant spins encounter strong scattering in the two surface films , they `` escape '' , after multiple collisions , to the middle film . this explains the peak of the surface resistivity at @xmath74 .
note that already far below @xmath78 , a number of surface itinerant spins begin to escape to the middle film , making the resistivity of the middle film to decrease with increasing @xmath0 below @xmath74 up to @xmath75 , as seen in fig .
[ surf2 ] .
note that there is a small shoulder of the total resistivity at @xmath74 .
in addition , in the range of temperatures between @xmath74 and @xmath75 the spins travel almost in the middle film with a large density resulting in a very low resistivity of the middle film . for @xmath79 , itinerant spins flow in every part of the system .
in this subsection , we take back @xmath50 and @xmath51 .
to treat the case with impurities , we replace randomly a number of lattice spins @xmath38 by impurity spins @xmath46 .
we suppose an rkky interaction between impurity spins ( see eq .
[ eqn : hamili1 ] ) . figure [ m_mag ] shows the lattice magnetization for several impurity concentrations .
we see that critical temperature @xmath2 increases with magnetic impurity s concentration .
we understand that large - spin impurities must reinforce the magnetic order . in figs .
[ mag1 ] , [ mag2 ] and [ mag5 ] , we compare a system without impurity to systems with respectively 1 and 2 and 5 percents of impurities .
the temperature of resistivity s peak is a little higher than the critical temperature and we see that the peak height increases with increasing impurity concentration ( see fig .
[ mag5 ] ) .
this is easily explained by the fact that when large - spin impurities are introduced into the system , additional magnetic clusters around these impurities are created in both ferromagnetic and paramagnetic phases .
they enhance therefore @xmath61 .
for the case with non - magnetic impurities , we replace randomly a number of lattice spins @xmath38 by zero - spin impurities @xmath47 .
figures [ m_nmag ] , [ nmag1 ] and [ nmag5 ] show , respectively , the lattice magnetizations and the resistivities for non - magnetic impurity concentrations @xmath80 and @xmath81 .
we observe that non - magnetic impurities reduce the critical temperature and the temperature of the resistivity s peak .
this can be explained by the fact that the now `` dilute '' lattice spins has a lower critical temperature so that the scattering of itinerant spins by lattice - spin clusters should take place at lower temperatures .
de gennes and friedel@xcite have shown that the resistivity @xmath61 is related to the spin correlation @xmath82 .
they have suggested therefore that @xmath61 behaves as the magnetic susceptibility @xmath83 .
however , unlike the susceptibility which diverges at the transition , the resistivity observed in many experiments goes through a finite maximum , i. e. a cusp , without divergence . to explain this , fisher and langer@xcite and
then kataoka@xcite have shown that the cusp is due to short - range correlation .
this explanation is in agreement with many experimental data but not all ( see ref . for review on early experiments ) .
let us recall that @xmath84 where the sum is taken over nn ( or short - range ) spin pairs while @xmath85 where the sum is performed over _ all _ spin pairs .
this is the reason why short - range correlation yields internal energy and long - range correlation yields susceptibility . roughly speaking ,
if @xmath86 is short - ranged , then @xmath61 behaves as @xmath87 so that the temperature derivative of the resistivity , namely @xmath88 , should behave as the specific heat with varying @xmath0 .
recent experiments have found this behavior(see for example ref . ) .
now , if @xmath86 is long - ranged , then @xmath61 behaves as the magnetic susceptibility as suggested by de gennes and friedel.@xcite in this case , @xmath61 undergoes a divergence at @xmath2 as @xmath83 .
one should have therefore @xmath89 at @xmath90 and @xmath91 at @xmath92 . in some experiments ,
this has been found in for example in magnetic semiconductors ( ga , mn)as@xcite ( see also ref . for review on older experiments ) .
we think that all systems are not the same because of the difference in interactions , so one should not discard a priori one of these two scenarios . in this paper
, we suggest another picture to explain the cusp : when @xmath2 is approached , large clusters of up ( resp . down )
spins are formed in the critical region above @xmath2 . as a result ,
the resistance is much larger than in the ordered phase : itinerant electrons have to steer around large clusters of opposite spins in order to go through the entire lattice .
thermal fluctuations are not large enough to allow the itinerant spin to overcome the energy barrier created by the opposite orientation of the clusters in this temperature region .
of course , far above @xmath2 , most clusters have a small size , the resistivity is still quite large with respect to the low-@xmath0 phase .
however , @xmath61 decreases as @xmath0 is increased because thermal fluctuations are more and more stronger to help the itinerant spin to overcome energy barriers .
what we have found here is a peak of @xmath61 , not a peak of @xmath93 .
so , our resistivity behaves as the susceptibility although the peak observed here is not sharp and no divergence is observed .
we believe however that , similar to commonly known disordered systems , the susceptibility peak is broadened more or less because of the disorder .
the disorder in the system studied here is due the lack of periodicity in the positions of moving itinerant spins .
in this paragraph , we show a theory based on the boltzmann s equation in the relaxation - time approximation . to solve completely this equation , we shall need some numerical data from mc simulations for the cluster sizes as will be seen below . using these data
, we show that our mc result of resistivity is in a good agreement with this theory .
let us formulate now the boltzmann s equation for our system .
when we think about the magnetic resistivity , we think of the interaction between lattice spins and itinerant spins . we recognize immediately the important role of the spin - spin correlation function in the determination of the mean free - path .
if we inject through the system a flow of spins `` polarized '' in one direction , namely `` up '' , we can consider clusters of `` down '' spins in the lattice as `` defect clusters '' , or as `` magnetic impurities '' , which play the role of scattering centers .
we therefore reduce the problem to the determination of the number and the size of defect clusters . for our purpose
, we use the boltzmann s equation with uniform electric field but without gradient of temperature and gradient of chemical potential .
we write the equation for @xmath94 , the fermi - dirac distribution function of itinerant electrons , as @xmath95 where @xmath96 is the wave vector , @xmath29 and @xmath97 the electronic charge and mass , @xmath98 the electron energy .
we use the following relaxation - time approximation @xmath99 where @xmath100 is the relaxation time . supposing elastic collisions , i. e. @xmath101 , and using the detailed balance we have @xmath102 where @xmath103 is the system volume , @xmath104 the transition probability between @xmath105 and @xmath106 .
we find with eq .
( [ eqn : equ2 ] ) and eq .
( [ eqn : equ3 ] ) the following well - known expression @xmath107 where @xmath108 and @xmath109 are the angles formed by @xmath110 with @xmath111 , i. e. spherical coordinates with @xmath112 axis parallel to @xmath111 .
we use now for eq .
( [ eqn : equ4 ] ) the `` fermi golden rule '' and we obtain @xmath113 we give for the potential @xmath114 the following expression which reminds the form of the interactions ( [ eqn : hamil5])-([eqn : hamil6 ] ) @xmath115 where @xmath116 is the size of the defect cluster and @xmath117 a constant
. we resolve eq .
( [ eqn : equ5 ] ) with eq .
( [ eqn : equ6 ] ) and we have the following expression @xmath118 where @xmath119 is given by @xmath120^{1/2 } , \label{eqn : equ8}\ ] ] integrating eq .
( [ eqn : equ7 ] ) we obtain @xmath121 \label{eqn : equ9}\end{aligned}\ ] ] where @xmath122 is the number of clusters of size @xmath123 .
we integrate eq .
( [ eqn : equ9 ] ) for the interval @xmath124 $ ] and we obtain finally @xmath125 \label{eqn : equ10}\end{aligned}\ ] ] note that although the relaxation time @xmath126 is averaged over all states in the fermi sphere , i. e. states at @xmath127 , its temperature dependence comes from the parameters @xmath123 and @xmath122 .
these will be numerically determined in the following .
if we know @xmath126 we can calculate the resistivity by the drude expression @xmath128 let us use now the hoshen - kopelman s algorithm@xcite to determine the mean value of @xmath123 and the number of the cluster s mean size , for different temperatures .
the hoshen - kopelman s algorithm allows to regroup into clusters spins with equivalent value for @xmath90 or equivalent energy for @xmath92 . using this algorithm during our mc simulation at a given @xmath0
, we obtain a `` histogram '' representing the number of clusters as a function of the cluster size . for temperature @xmath0 below @xmath2
, we call a cluster a group of parallel spins surrounded by opposite spins , and for @xmath0 above @xmath2 a cluster is a group of spins with the same energy . at a given @xmath0 , we estimate the average size @xmath123 using the histogram as follows : calling @xmath129 the number of spins in the cluster and @xmath130 the probability of the cluster deduced from the histogram , we have @xmath131 in doing this we obtain @xmath123 for the whole temperature range .
we note that we can fit the cluster size @xmath123 with the following formula @xmath132 where @xmath133 is a fitting parameter and @xmath134 a constant .
these parameters are different for @xmath90 and @xmath92 .
figure [ rayon ] and figure [ nbre_cluster ] show the average size and the average number of cluster versus temperature . to simplify our approach
we consider that the cluster s geometry is a sphere with radius @xmath123 .
note that due to the fact that our fitting was made separately for @xmath90 and @xmath92 , no effort has been made for the matching at @xmath135 exactly , but this does not affect the behavior discussed below .
we distinguish hereafter temperatures below and above @xmath2 in establishing our theory .
we write @xmath136),\\ \xi=(\dfrac{3a_{inf}}{16\pi})^{1/3}(t_c - t)^{\nu_{inf}/3},\\ n_{c}=(\dfrac{b_{inf}}{2\alpha \pi})\times \exp[\dfrac{-(t - t_g)^2}{2\alpha^2 } ] .
\end{array } \right .\ ] ] @xmath137 @xmath138),\\ \xi=(\dfrac{3a_{sup}}{16\pi})^{1/3}(t - t_c)^{\nu_{sup}/3},\\ n_{c}=b_{sup}\exp[-d(t - t_c)]+n_0 .
\end{array } \right .\ ] ] @xmath139 in eq .
( [ eqn : equ14 ] ) we call @xmath140 the temperature on which the cluster of small size are gathering to form bigger cluster .
this temperature marks the limit when one enters the critical region from below . in eq .
( [ eqn : equ14 ] ) , @xmath141 is the half - width of the peak of @xmath122 shown in fig .
[ nbre_cluster ] .
@xmath142 is the resistivity at @xmath127 and @xmath143 is that at @xmath144 .
we summarize in table 1 the different results obtained for the cases studied by mc simulations shown above .
other parameters @xmath145 , @xmath146 , @xmath147 , @xmath148 , @xmath149 and @xmath150 are fitting parameters which are not of physical importance and therefore not given here for the sake of clarity . using the numerical values of table 1 and the average cluster size and cluster number shown in fig .
[ rayon ] and fig .
[ nbre_cluster ] , we plot eqs .
( [ eqn : equ14 ] ) and ( [ eqn : equ17 ] ) by continuous lines in figs . [ mag1]-[nmag5 ] to compare with mc simulations shown in these figures .
we emphasize that our theory provides a good `` fit '' for simulation results . [ cols=">,^,^,^,^,^,^,^",options="header " , ] of magnetic clusters versus temperature @xmath0 for both above and below @xmath2.,width=151,height=302 ] for both above and below @xmath2.,width=151,height=302 ] based on those results , we can extract the resistivity @xmath151 corresponding only to the addition of impurities .
@xmath151 is defined as @xmath152 where @xmath153 is the resistivity without impurities ( see the first line of table 1 ) .
we compare now the resistivity @xmath151 with experiments realized by shwerer and cuddy.@xcite it is important to note that the change of behavior can be explained if we use the correct value for @xmath133 , @xmath2 , @xmath140 , etc .
figure [ romag ] shows @xmath151 with magnetic impurities corresponding to the ni - fe system , while fig .
[ ronmag ] shows @xmath151 in the case of non - magnetic impurities corresponding to the ni - cr case .
we see that the form of @xmath151 of the alloys ni - fe(@xmath80 ) and ni - fe(@xmath154 ) experimentally observed@xcite can be compared to the curves of @xmath80 and @xmath155 of magnetic impurities shown in fig .
[ romag ] . for ni - cr(@xmath80 ) and ni - cr(@xmath155 ) , experimental curves are in agreement with our results of non - magnetic impurities shown in fig .
[ ronmag ] . finally , to close this section , let us show theoretically from the equations obtained above , the effects of the density of itinerant spins on the resistivity .
figure [ densite ] shows that , as the density @xmath156 is increased , the peak of @xmath61 diminishes .
it is noted that this behavior is very similar with that obtained by kataoka.@xcite in our mc simulation shown above , we have chosen @xmath157 .
such a weak density has allowed us to avoid the flip of lattice spins upon interaction with itinerant spins . in the case of strong density
, we expect that a number of lattice spins , when surrounded by a large number of itinerant spins , should flip to accommodate themselves with their moving neighbors
. so the lattice ordering should be affected . as a consequence , critical fluctuations of lattice spins
are more or less suppressed , so is the peak s height , just like in the case of an applied magnetic field .
kataoka@xcite has found this in his calculation by taking into account the spin flipping : the resistivity s peak disappears then at the transition
. it would be interesting to perform more mc simulations with varying @xmath156 .
this is left for a future investigation .
we have shown in this paper results of mc simulations on the transport of itinerant spins interacting with localized lattice spins in a ferromagnetic fcc thin film .
various interactions have been taken into account .
we found that the spin current is strongly dependent on the lattice spin ordering : at low @xmath0 itinerant spins whose direction is parallel to the lattice spins yield a strong current , namely a small resistivity . at the ferromagnetic transition ,
the resistivity undergoes a huge peak . at higher temperatures , the lattice spins are disordered , the resistivity is still large but it decreases with increasing @xmath0 . from the discussion given in subsection [ discuss ]
, we conclude that the resistivity @xmath61 of the model studied here behaves as the magnetic susceptibility with a peak at @xmath2 .
@xmath158 , differential resistivity is thus negative for @xmath92 .
the peak of the resistivity obtained here is in agreement with experiments on magnetic semiconductors ( ga , mn)as for example.@xcite of course , to compare the peak s shape experimentally obtained for each material , we need to refine our model parameters for each of them .
this was not the purpose of the present paper .
instead , we were looking for generic effects to show physical mechanisms lying behind the temperature dependence of the spin resistivity . in this spirit
, we note that early theories have related the origin of the peak to the spin - spin correlation , while our interpretation here is based on the existence of defect clusters formed in the critical region .
this interpretation has been verified by calculating the number and the size of clusters as a function of @xmath0 by the use of hoshen - kopelman s algorithm .
we have formulated a theory based on the boltzmann s equation .
we solved this equation using numerical data obtained for the number and the size of average cluster at each @xmath0 .
the results on the resistivity are in a good agreement with mc results .
finally , let us conclude by saying that the clear physical picture we provide in this paper for the understanding of the behavior of the resistivity in a single ferromagnetic film will help to understand properties of resistivity in more complicated systems such as antiferromagnets , non - ising spin systems , frustrated spin systems , disordered media , ... where much has to be done . | the magnetic phase transition is experimentally known to give rise to an anomalous temperature - dependence of the electron resistivity in ferromagnetic crystals .
phenomenological theories based on the interaction between itinerant electron spins and lattice spins have been suggested to explain these observations . in this paper , we show by extensive monte carlo ( mc ) simulation the behavior of the resistivity of the spin current calculated as a function of temperature ( @xmath0 ) from low-@xmath0 ordered phase to high-@xmath0 paramagnetic phase in a ferromagnetic film .
we analyze in particular effects of film thickness , surface interactions and different kinds of impurities on the spin resistivity across the critical region .
the origin of the resistivity peak near the phase transition is shown to stem from the existence of magnetic domains in the critical region .
we also formulate in this paper a theory based on the boltzmann s equation in the relaxation - time approximation .
this equation can be solved using numerical data obtained by our simulations .
we show that our theory is in a good agreement with our mc results .
comparison with experiments is discussed . |
localization - delocalization ( ld ) or anderson localization transitions of non - interacting electrons are continuous phase transitions driven by disorder.@xcite when disorder is weak , the single - electron wave functions are extended over the whole sample .
sufficiently strong disorder localizes electrons within a finite region in space .
the linear size of this region is the localization length @xmath5 characterizing the typical size of the wave functions @xmath6.@xcite as the disorder strength is reduced , the localization length increases and eventually diverges at an ld transition point .
the localization length is the analogue of the correlation length at non - random continuous phase transitions . at the ld transition point ,
wave function amplitudes obey scale - invariant , multifractal statistics;@xcite that is , the disorder - averaged @xmath7-th moment of the square of the absolute value of wave function has a power - law dependence on the linear dimension @xmath8 of the system , with an exponent that is a non - linear function of @xmath7.@xcite let us recall that continuous phase transitions in _ non - random _ systems are known to be quite generally described by conformally - invariant field theories .
conformal symmetry is especially powerful in two dimensions ( 2d ) , where its presence leads to an infinite number of symmetry constraints .
this , in many cases , allows for a rather complete description of critical properties.@xcite effective ( field ) theories describing the _ random _ ld transitions are also expected to possess conformal symmetry .
in fact , we have recently shown by numerical simulations of a standard ld transition occurring in two dimensions , namely of the metal - insulator transition in the 2d spin - orbit ( symplectic ) symmetry class,@xcite that multifractal exponents of critical wave functions evaluated on a straight boundary and those at a corner are related through a simple relation dictated by conformal symmetry.@xcite conformal symmetry is known to impose strong constraints on finite - size scaling ( fss ) for phase transitions in _ non - random _ systems with quasi - one - dimensional ( q1d ) geometry .
for these systems cardy has shown@xcite that the correlation length @xmath5 which characterizes the decay of the two - point correlation function of any ( conformal primary@xcite ) operator along a cylinder or a strip of width @xmath9 , is related to the bulk ( @xmath10 ) or surface ( @xmath11 ) scaling dimension of the operator in two dimensions through @xmath12 here bc stands for boundary conditions imposed in the transverse direction . the generalization of eq .
( [ eq : cardy ] ) to scale - invariant disordered 2d systems was first provided in the study of random 2d diluted ferromagnets in ref .
[ ] [ for the 2d bulk exponents and q1d cylinder geometry ( periodic bcs ) ] . in a random system
the scaling of an observable ( such as , for example , a `` spin '' ) is in general characterized by the set of scaling dimensions @xmath13 of all its @xmath7-th moment disorder averages .
equation ( [ eq : cardy ] ) generalizes@xcite to all these moments .
in particular , the correlation length @xmath14 characterizing the exponential decay of the @xmath7-th moment of a correlation function of the observable in q1d cylinder geometry is related to the 2d scaling exponent by @xmath15 at the same time , by using an expansion about @xmath16 of the @xmath7-th moments in the 2d system and in the q1d cylinder geometry , it was demonstrated in ref .
[ ] that such a relationship holds also for the corresponding `` _ typical _ '' quantities referring to a fixed disorder realization . in particular , if @xmath0 denotes the _
typical_@xcite 2d bulk scaling dimension of the observable , and if @xmath17 denotes the lyapunov exponent characterizing the inverse of the _ typical _ q1d correlation length in cylinder geometry , then again the relationship @xmath18 holds .
[ cols="<,^,^,^,^,^,^",options="header " , ] in this section we have to distinguish off - critical and critical values of the q1d localization lengths , @xmath5 and @xmath19 , and the corresponding fss amplitudes , @xmath20 and @xmath1 ( for both periodic and open bcs ) .
all @xmath5 and @xmath20 that have appeared in the previous sections denoted values at the critical point . to compute the localization length at the ld transition in the symplectic class , we employed the so - called su(2 ) model,@xcite a tight - binding model on the square lattice , with random on - site disorder and fully random su(2 ) hopping .
we obtained the typical localization length from the smallest lyapunov exponent of transfer matrices for very long q1d lattices .
we imposed hard - wall , i.e. , reflecting bcs in the transverse direction and hence our q1d samples had strip geometry .
our systems had a maximum size @xmath21 in the transverse direction .
figure [ fig : su(2)](a ) shows the fss amplitude @xmath22 of the typical q1d localization length as a function of the on - site disorder strength @xmath23 for various system sizes @xmath9 and at fixed energy @xmath24 ( band center ) .
the curves for the various system sizes intersect at different points reflecting large finite - size effects , in contrast to the case of periodic bcs.@xcite to determine the critical value of the fss amplitude @xmath25 , we performed a fss analysis incorporating corrections to scaling arising from the leading irrelevant scaling variable.@xcite specifically , we took a scaling function for the fss amplitude of the form @xmath26 , where @xmath27 is the relevant scaling variable , and @xmath28 is the leading irrelevant scaling variable whose scaling exponent @xmath29 . the exponent @xmath30 characterizes the divergence of the 2d localization length @xmath5 upon approaching the ld transition point , @xmath31 .
we expanded the scaling function around the critical point @xmath32 , setting @xmath33 , @xmath34 we fitted the numerical data to eq .
( [ eq : scaling_series ] ) with @xmath35 by taking @xmath36 , @xmath37 , @xmath38 , @xmath30 , and @xmath39 as fitting parameters .
we obtained @xmath40 the details of the fitting are summarized in table [ tab : lambda ] .
these results are in good agreement with those obtained by asada _
et al . _
for the su(2 ) model@xcite with periodic bcs : @xmath41 and @xmath42 at @xmath43 .
the good quality of the fit can be seen from the scaling collapse , shown in fig .
[ fig : su(2)](b ) , of the data for the corrected fss amplitude @xmath44 defined by @xmath45 on @xmath23 at @xmath24 for various values of @xmath9 .
@xmath46 at @xmath24 .
( b ) scaling plot of @xmath46 at @xmath24
see eq.([eq : lambda ] ) .
the obtained parameters are @xmath47 , @xmath48 , @xmath49 , @xmath50 , @xmath51 , @xmath52 , @xmath53 , @xmath54 , and @xmath55 . ,
width=302 ] in our previous publication@xcite we reported the value @xmath56 for the surface exponent , which was obtained from numerical simulations on @xmath57 lattices of system sizes up to @xmath58 .
we performed averaging over more than @xmath59 disorder realizations .
the lattices had periodic bc imposed in one of the two directions , but open bc in the other direction , so our system had the geometry of a finite cylinder . here
we update the value for @xmath3 reported in our previous work.@xcite we use larger system sizes up to @xmath60 , and average over up to @xmath61 disorder realizations .
the surface exponent @xmath3 was obtained from the system size dependence of the wave function amplitude in the vicinity of the boundary , according to @xmath62 here @xmath63 , @xmath64 , and @xmath65 is a constant of order @xmath66 .
the double angular brackets represent both ensemble average and spatial average along the boundary of the cylinder in each disorder realization .
first we tried a linear fitting to eq .
( [ eq:<ln|psi| > ] ) of our numerical data for the left hand side of eq .
( [ eq:<ln|psi| > ] ) , using system sizes @xmath67 , with two fitting parameters @xmath3 and @xmath65 .
this resulted in the value @xmath68 substitution of this value into eq .
( [ eq : lambda_obc ] ) gave @xmath69 this analysis , however , ignored corrections from irrelevant scaling variables and was not quite correct , since we now know from the previous subsection that such corrections are appreciable for the fss amplitude @xmath20 for open bc .
we therefore re - analyzed the data , assuming scaling with corrections from the leading irrelevant variable.@xcite we define @xmath70 where we take @xmath71 , as suggested by eq .
( [ eq : su(2 ) ] ) .
the fitting of the same data to eq .
( [ eq:<ln|psi|>_correction ] ) yielded @xmath72 which leads to @xmath73 with the help of eq .
( [ eq : lambda_obc ] ) .
we see that the @xmath25 obtained from the transfer matrix method ( [ eq : su(2 ) ] ) is consistent with these results .
the value of @xmath3 reported in eq .
( [ alpha_0^s_su(2 ) ] ) has larger error bars , which needs to be improved in future numerical work .
the @xmath4 topological insulator is a time - reversal invariant topological insulator in two dimensions , which possesses a topologically protected kramers pair of extended edge states at its boundaries.@xcite the @xmath4 topological insulating states can be realized in materials with strong spin - orbit interactions , as evidenced by recent experiments on hgte/(hg , cd)te quantum wells.@xcite in the presence of disorder , this system undergoes a two - dimensional metal - insulator transition from a @xmath4 topological insulator to a metal , as one changes the fermi energy . on symmetry grounds , this ld transition is expected to belong to the spin - orbit ( symplectic ) symmetry class.@xcite indeed , the critical exponent @xmath30 for the diverging localization length ( a bulk property ) at the metal to @xmath4 topological insulator transition is found to agree with the value obtained for the su(2 ) model,@xcite which describes the metal to ( ordinary ) insulator transition in this symmetry class .
similar agreement is found for the multifractal exponents for critical wave functions in the bulk.@xcite however , the multifractal exponents characterizing wave function amplitudes at the sample _ boundary _ turn out to be different at the two metal - insulator transitions . here
we show that , at the metal to @xmath4 topological insulator transition , the fss amplitude @xmath25 ( eq.([deflambdac ] ) ) for the typical q1d correlation length in strip geometry , is related by conformal invariance to the boundary multifractal exponent @xmath3 at the same transition .
to compute the localization length at the metal to @xmath4 topological insulator transition , we employed the quantum spin hall network model.@xcite an important parameter in this network model is the one controlling the probability of tunneling at the nodes of the network , which we denote by @xmath74 . the numerical results shown below were obtained at the critical point @xmath75 with fully random su(2 ) spin rotation symmetry on each link.@xcite figure [ fig : lambda_qsh ] shows the dependence of the fss amplitude @xmath76 of the typical q1d localization length @xmath77 on a strip of width @xmath9 ( @xmath78 ) . here
@xmath9 is the number of nodes of the network model in the transverse direction across the q1d strip .
this corresponds to transfer matrices of size @xmath79 . in order to find the critical value @xmath25 of the fss amplitude @xmath80 in the large @xmath9 limit
, we assumed that @xmath80 at @xmath81 has a power - law finite - size correction due to a leading irrelevant variable with dimension @xmath82 : @xmath83 fitting the data to this form ( see fig .
[ fig : lambda_qsh ] ) , we obtained @xmath84 with @xmath85 and @xmath86 .
the details of the fitting are summarized in table [ tab : lambda ] .
the surface multifractal exponent at the metal to @xmath4 topological insulator transition was obtained in ref .
[ ] . by using larger system sizes this value
was recently improved in ref .
[ ] to @xmath87 substituting the improved value into eq .
( [ eq : lambda_obc ] ) yields the fss amplitude @xmath88 this value is consistent with eq .
( [ eq : lambda_c_qsh ] ) . the larger error bar in eq . ( [ lambda-7 ] )
results from the fact that the denominator in eq .
( [ eq : lambda_obc ] ) ( with @xmath89 ) contains @xmath90 .
neither of the numerical analyses in refs .
[ , ] , used to obtain eq .
( [ newequation ] ) , included effects of the leading irrelevant variable , in contrast to eq .
( [ eq : lambda_c_qsh ] ) .
these effects may influence the value of @xmath3 and possibly result in better agreement with eq .
( [ eq : lambda_c_qsh ] ) .
dependence of @xmath80 at the metal to topological quantum spin hall insulator transition .
the solid curve is a fit to eq .
( [ eq : lambda_c_correction ] ) with @xmath91 , @xmath92 , and @xmath93 .
, scaledwidth=43.0% ] to compute the localization length @xmath94 and the surface multifractal exponent @xmath3 at the plateau transition in the iqh effect , we employed the chalker - coddington network model@xcite in strip geometry with @xmath9 nodes in the transverse direction across the strip .
this corresponds to transfer matrices of size @xmath95 .
the plateau transition is reached by tuning a parameter @xmath96 which controls the tunneling probability at the nodes of the network model . for this model
the critical value @xmath97 is known exactly .
on the node parameter @xmath96 in the chalker - coddington model of the strip geometry .
the vertical dashed line indicates the critical point @xmath98 .
inset : @xmath9 dependence of @xmath80 at @xmath99 ; the solid curve is a fit to eq .
( [ eq : lambda_c_correction ] ) .
( b ) scaling plot from fss analysis including corrections from the leading irrelevant scaling variable .
the parameters used for the plot are @xmath100 , @xmath101 , @xmath102 , @xmath103 , @xmath104 , @xmath105 , and @xmath106 .
, scaledwidth=43.0% ] the typical localization length @xmath94 in q1d strip geometry was computed numerically from the smallest lyapunov exponent of the transfer matrices .
the largest system size ( the number of network model nodes in the transverse direction ) that we studied , was @xmath107 .
figure [ fig : lambda_iqh](a ) shows the fss amplitude @xmath108 of the typical localization length as a function of the network model tunneling parameter @xmath96 for various transverse system sizes @xmath9.@xcite for @xmath109 the network model is in the quantum hall phase.@xcite as seen from fig .
[ fig : lambda_iqh ] , the crossing point of the curves moves towards @xmath99 as @xmath9 increases , indicating the presence of finite - size corrections . to find the critical value of the fss amplitude @xmath80 of the typical q1d correlation length in the large @xmath9 limit
, we fitted the data to eq.([eq : lambda_c_correction ] ) [ see the inset of fig .
[ fig : lambda_iqh](a ) ] , to obtain @xmath110 @xmath111 , and @xmath112 .
the details of the fitting are summarized in table [ tab : lambda ] .
figure [ fig : lambda_iqh](b ) shows the data collapse from the fss analysis using eqs .
( [ eq : scaling_series ] ) and ( [ eq : lambda ] ) with @xmath113 and the values of @xmath25 , @xmath39 , and @xmath114 obtained above .
this fss analysis also yielded @xmath100 for the critical exponent of the diverging ( 2d bulk ) localization length , which is close to the value obtained in a recent large - scale numerical study , @xmath115.@xcite the surface multifractal exponent @xmath3 at the plateau transition was recently obtained by the present authors@xcite and by evers , mildenberger , and mirlin.@xcite it was found in these works that the multifractal analysis for the chalker - coddington model suffers from large finite - size corrections . to reduce these corrections ,
we have used , in the multifractal scaling analysis in ref .
[ ] , numerical data obtained only for large system sizes . here we used an alternative approach by taking into account corrections to scaling arising from a leading irrelevant scaling variable using eq.([eq:<ln|psi|>_correction ] ) .
@xmath116 on this figure .
there are @xmath117 links , and the unitary evolution operator @xmath118 is a @xmath119 matrix.,scaledwidth=30.0% ] the geometry of the chalker - coddington network model that we used is shown in fig .
[ fig : cc - network - square ] .
there are two types of nodes forming two sub - lattices ( denoted @xmath120 and @xmath121 in the figure ) , such that the @xmath120 sublattice has the size @xmath122 ( @xmath116 in the figure ) .
the links of the network form zigzag shaped rows and columns ; there are @xmath123 such rows and @xmath123 such columns so that the total number of links is @xmath124 .
integer @xmath125 and @xmath39 coordinates are assigned to the centers of links .
we imposed periodic bc in the vertical @xmath39 direction , and reflecting bc in the horizontal @xmath125 direction .
the links in the first and the last columns at @xmath126 and @xmath127 are called the edge links .
the discrete time evolution of wave functions defined on links of the network model is governed by a unitary evolution operator @xmath118 for one discrete time step , which is determined by the scattering @xmath128 matrices at the nodes of the network model.@xcite in our case this operator is a @xmath129 unitary matrix . for each disorder realization , we obtained one critical wave function that is the eigenvector of @xmath118 at @xmath99 and whose eigenvalue is closest to unity among all the eigenvectors .
the largest system size we studied was @xmath130 , and the disorder average was taken over @xmath131 realizations for @xmath132 , over @xmath133 realizations for @xmath134 , and over @xmath135 realizations for @xmath136 . .
the system size is changed as @xmath137 from the top to the bottom .
( b ) dependence of @xmath138 on the effective system size @xmath139 at @xmath140 ( squares , @xmath141 ) , 2 ( open circles , @xmath141 ) and at edge plaquettes with coarse - graining ( filled circles , @xmath142 ) , where @xmath143 is the ( linear ) size of boxes used to define the coarse - grained wave function probabilities .
the solid curves are the fits to eq .
( [ eq:<ln|psi|>_correction ] ) . also shown by crosses is the dependence of @xmath144 $ ] on the width @xmath9 and its fit ( dashed curve ) to eq .
( [ eq : lambda_c_correction ] ) . , scaledwidth=45.0% ] figure [ fig : wfa](a ) shows the @xmath125 dependence of @xmath145 , where the double angular brackets stand for both the average over disorder realizations and the spatial average along the periodic @xmath39 direction .
we clearly observe in fig .
[ fig : wfa](a ) friedel - like oscillations near the edges of the cylinder , which become less pronounced as @xmath8 is increased .
( such oscillations are absent in the su(2 ) model discussed in the previous section . )
figure [ fig : wfa](b ) shows how @xmath146 approaches a constant value with increasing @xmath8 at the left boundary ( @xmath147 ) .
the solid curves show the fitting of @xmath148 to eq .
( [ eq:<ln|psi|>_correction ] ) at @xmath140 ( squares ) and @xmath149 ( open circles ) .
to minimize the corrections coming from the friedel - like oscillations , we defined the coarse - grained wave function amplitude on each plaquette and calculated the corresponding @xmath120 for the plaquettes along the edge ( shown as red filled circles ) . fitting this coarse - grained data to eq .
( [ eq:<ln|psi|>_correction ] ) with @xmath150 obtained in sec .
[ sec : iqh_lambda ] yielded @xmath151 where the error bars reflect only statistical errors .
this result is consistent with that of ref .
[ ] ( @xmath152 ) .
figure [ fig : wfa](b ) shows that fitting of @xmath153 and @xmath154 gives similar values of @xmath3 . substituting eq .
( [ eq : alpha_0^s ] ) into eq .
( [ eq : lambda_obc ] ) yields @xmath155 which should be compared with @xmath156 [ eq . ( [ eq : lambda_c^o - iqh ] ) ] obtained from the transfer matrix calculation . as we see in fig .
[ fig : wfa](b ) , finite - size corrections to @xmath120 and @xmath80 are still quite large at @xmath130 .
this makes the extrapolation of these quantities to @xmath157 difficult ; we can not exclude the possibility of having systematic errors in addition to the statistical errors included in eqs .
( [ eq : lambda_c^o - iqh ] ) and ( [ lambda_c^o - iqh ] ) . given the presence of this uncertainty ,
we conclude that our numerical results are consistent with eqs .
( [ eq : ours - surface ] ) and ( [ eq : lambda_obc ] ) . in this section
we discuss the verification of eqs .
( [ eq : ours - bulk ] ) and ( [ eq : ours - surface ] ) for symmetry class c , which is known to possess a vanishing critical dos ( @xmath158 ) . in our simulations
we used an appropriate generalization of the chalker - coddington network model,@xcite which we refer to as the class c network model .
this model has a control parameter @xmath159 ( in the notation of ref . [ ] ) , and is critical at @xmath160 .
exact values for critical exponents , @xmath161 and @xmath162 , were obtained through mapping to classical percolation.@xcite the exact values of the bulk@xcite and surface@xcite multifractal wave function exponents @xmath163 are also known at @xmath164 . however , exact results for the fss amplitudes of the typical q1d correlation lengths , @xmath165 and @xmath25 , and the typical wave function scaling exponents @xmath166 are not available . on @xmath159 for several values of @xmath9 in the class c network model of cylinder geometry .
a critical point is known to be located at @xmath167 .
( b ) scaling plot of @xmath168 , obtained after subtracting corrections to scaling from a leading irrelevant scaling variable .
the parameters used for the plot are @xmath169 , @xmath170 , @xmath171 , @xmath172 , @xmath173 , @xmath174 , and @xmath175 .
( c ) @xmath9 dependence of @xmath176 at @xmath177 .
the solid curve is a fit to eq .
( [ eq : lambda_c_correction ] ) .
, scaledwidth=43.0% ] we numerically obtained the fss amplitudes of the typical q1d localization length of the class c network model for both cylinder and strip geometries . a previous numerical study@xcite of fss of the typical localization length in cylinder geometry did not report the value of @xmath165 . here
we present results for the fss amplitudes @xmath165 and @xmath25 corresponding to cylinder and strip geometries , respectively .
_ cylinder geometry _ : figure [ fig : lambda_classc_pbc](a ) shows the dependence of the fss amplitude @xmath178 of the typical q1d correlation length on the parameter @xmath159 for various values of the transverse width @xmath9 , obtained in cylinder geometry .
the fss amplitude @xmath176 is symmetric about the critical point @xmath167 when periodic bcs are imposed .
hence in the fss analysis we have to use an expansion in even powers of @xmath159 , @xmath179 the result of fitting of the data in fig .
[ fig : lambda_classc_pbc](a ) to eq.([eq : scaling_series_even ] ) is shown in fig.[fig : lambda_classc_pbc](b ) .
the dependence of @xmath180 on the width @xmath9 at the critical point @xmath167 is plotted in fig .
[ fig : lambda_classc_pbc](c ) .
we obtained @xmath181 and @xmath182 .
the details of the fitting are summarized in table [ tab : lambda ] .
the latter result is consistent with the exact value @xmath161 , indicating good accuracy of our numerical results .
_ strip geometry _ : on @xmath159 for several values of @xmath9 in the class c network model of strip geometry .
the critical point is located at @xmath167 .
( b ) scaling plot of @xmath46 from the fss analysis with subtraction of corrections from a leading irrelevant scaling variable .
the parameters used for the plot are @xmath183 , @xmath184 , @xmath185 , @xmath186 , @xmath187 , @xmath188 @xmath189 , @xmath190 , and @xmath191 .
( c ) the @xmath9 dependence of @xmath80 at @xmath160 .
the solid curve is a fit to eq .
( [ eq : lambda_c_correction]).,scaledwidth=43.0% ] figure [ fig : lambda_classc_obc](a ) shows the fss amplitude of the typical q1d correlation length in strip geometry .
with reflecting bcs imposed in the transverse direction , the model possesses edge states for @xmath192 ( the spin quantum hall phase , possessing topological order).@xcite since @xmath80 is not a symmetric function of @xmath159 , we use the fss function in eq .
( [ eq : scaling_series ] ) .
figures [ fig : lambda_classc_obc](b ) and ( c ) show the result of the fss analysis and the width @xmath9 dependence of the fss amplitude @xmath193 for the typical correlation length in the strip , respectively . from this analysis
we obtained @xmath194 and @xmath184 .
the details of the fitting are summarized in table [ tab : lambda ] .
the bulk and surface multifractal exponents @xmath195 and @xmath3 for the class c network model have been obtained numerically in refs .
[ , ] : @xmath196 substitution of these values into eqs .
( [ eq : lambda_bdg_pbc ] ) and ( [ eq : lambda_obc ] ) , respectively , with @xmath162 yields @xmath197 these values are consistent with the values presented in eqs .
( [ eq : lambda_classc_pbc ] ) and ( [ eq : lambda_classc_obc ] ) obtained by our fss analysis .
in this paper we have generalized the formula relating the multifractal exponent @xmath0 of the typical wave function amplitude in a 2d sample to the fss amplitude @xmath1 of the typical localization length in a q1d sample .
our generalization is twofold , resulting in eqs .
( [ eq : ours - bulk ] ) and ( [ eq : ours - surface ] ) .
( [ eq : ours - bulk ] ) extends the relation to unconventional symmetry classes where the global density of states vanishes at criticality .
( [ eq : ours - surface ] ) extends the relation to the case when the q1d sample has strip geometry , instead of cylinder geometry which was always considered in earlier studies . in this case
the multifractal exponent @xmath3 describes the scaling of typical wave function amplitude near the sample boundary .
we have verified generalized eqs .
( [ eq : ours - bulk ] ) and ( [ eq : ours - surface ] ) numerically for systems in four different universality classes : ( a ) the metal - to - insulator transition in the spin - orbit ( symplectic ) symmetry class , ( b ) the metal - to-(@xmath4 topological insulator ) transition also in the spin - orbit ( symplectic ) class , ( c ) the integer quantum hall plateau transition , and ( d ) the spin quantum hall plateau transition .
our numerical results are summarized in tables [ tab : alpha_0 ] and [ tab : lambda ] .
we acknowledge helpful discussions with a. mirlin , c. mudry and s. ryu .
this work was partly supported by the next generation super computing project , nanoscience program from mext , japan .
numerical calculations were performed on the riken super combined cluster system .
is supported by jsps research fellowships for young scientists .
the work of a.f . was supported by a grant - in - aid for scientific research from mext and jsps , japan ( no . 16gs0219 , no .
21540332 ) .
was partially supported by nsf grant no .
dmr-0448820 and nsf mrsec grant no .
the work of a.w.w.l . was supported in part by nsf grant no .
dmr-0706140 . at any conventional non - random second order phase transition in two dimensions ,
all scalar scaling operators which possess scaling dimensions smaller than two are examples of conformal primary operators .
these assumptions have been numerically verified in ref .
[ ] for one of the standard symmetry classes which possess a ld transition in 2d , namely for the 2d metal - insulator transition in the spin - orbit ( symplectic ) class . it is known@xcite that the exponents @xmath198 are positive only within some range @xmath199 . outside this range @xmath200 , which leads to ldos moments @xmath201^q}$ ] that are exponentially growing away from the cylinder boundary
this can be explained by the following argument . in cylinder geometry ,
the wave functions are localized , and the level broadening @xmath202 created by the metallic lead attached at the edge @xmath203 is strongly coordinate dependent . indeed , the overlap of a wave function localized at a point @xmath204 away from the cylinder edge with the extended wave functions in the lead is exponentially small , which results in an escape rate , that is , a level broadening that is exponentially decaying away from the edge : @xmath205 here @xmath5 is the typical localization length .
thus , away from the edge , the profile of the ldos ( as a function of energy ) consists of well resolved narrow lorentzian peaks ( see eq.([lorentzian ] ) ) of width of order @xmath206 and height proportional to @xmath207 . only within the range @xmath199 corresponding to @xmath208
are the moments of the ldos determined by the minima of the ldos profile ( where the ldos is proportional to @xmath206 ) . for other values of @xmath7
the dominant contribution to the moments of ldos comes from the maxima in the ldos profile . in the described situation
the behavior of the moments of the wave functions is very different from that of the moments of the ldos .
however , we can directly relate the latter to the transmission through the cylinder from the metallic lead .
essentially , the transmission will be exponentially small away from the edge of the cylinder if the energy of the incoming wave ( in the lead ) corresponds to a minimum in the ldos profile , but will be of order one ( it can not be bigger ) if the energy is in resonance with one of the broadened energy levels ( that is , a peak in the ldos profile ) . | we generalize universal relations between the multifractal exponent @xmath0 for the scaling of the typical wave function magnitude at a ( anderson ) localization - delocalization transition in two dimensions and the corresponding critical finite size scaling ( fss ) amplitude @xmath1 of the typical localization length in quasi - one - dimensional ( q1d ) geometry : ( i ) when _ open _ boundary conditions are imposed in the transverse direction of q1d samples ( strip geometry ) , we show that the corresponding critical fss amplitude @xmath2 is universally related to the _ boundary _ multifractal exponent @xmath3 for the typical wave function amplitude along a straight boundary ( surface ) . ( ii ) we further propose a generalization of these universal relations to those symmetry classes whose density of states vanishes at the transition .
( iii ) we verify our generalized relations [ eqs .
( [ eq : ours - bulk ] ) and ( [ eq : ours - surface ] ) ] numerically for the following four types of two - dimensional anderson transitions : ( a ) the metal - to-(ordinary insulator ) transition in the spin - orbit ( symplectic ) symmetry class , ( b ) the metal - to-(@xmath4 topological insulator ) transition which is also in the spin - orbit ( symplectic ) class , ( c ) the integer quantum hall plateau transition , and ( d ) the spin quantum hall plateau transition . |
quantum optimal control theory ( qoct ) which incorporates the optimal control theory with the quantum theory is a powerful tool and has attained various physical achievements @xcite .
it has also been introduced to quantum gate control to obtain the optimal control pulses in quantum gate operations . in the literature , quantum gate control employing qoct in closed or open systems
are studied @xcite . however , in most investigations where the environment effect is taken into account , the dynamics are often derived perturbatively , involving born @xcite or born - markov approximations @xcite . despite the broad applicability of the perturbative master equation , the approximations made in the derivation results in unwanted intrinsic error , which in turn contributes to the gate error as the pulse sequence for the gate operation is obtained through the approximated master equation . in cases
where the models can be exactly solved , resorting to the exact dynamics can help reduce these possible intrinsic errors . in this paper , we adopt an exact master equation of a qubit @xcite and combine it with qoct based on the krotov iteration method @xcite to find the optimal control pulse for state - independent single - qubit gate control in a general non - markovian environment with an arbitrary spectral density .
to be specific , the model we consider is a qubit linearly coupled to a dissipative zero - temperature environment through a qubit lowering operator @xmath1 .
the exact master equation for this model can be derived from either the pseudo mode method @xcite or the quantum state diffusion equation @xcite .
reasonable trends of gate error for this model under various conditions are observed and discussed . moreover ,
if the bath spectral density is chosen to be a lorentzian type , this dissipative qubit model can be shown to be equivalent to the damped jaynes - cummings model describing the coupling of a qubit to a single cavity mode which in turn is coupled to a markovian reservoir @xcite .
thus our optimal control results would also have direct applications , for example , to superconducting circuit quantum electrodynamic ( qed ) systems @xcite that are described very well by the damped jaynes - cummings model and are controlled relatively easily by external fields . another important property
we wish to investigate is whether or not in open systems , qoct is able to correct the gate error due to the environment effect .
a quantity , improvement @xmath0 , is defined to quantify such correction . for a system where the improvement is large , including the environment effect becomes essential to the control problem .
whereas for a system with negligible improvement , the optimal control pulse developed while the system is considered closed would suffice .
we further explore the region of parameters where significant improvement is achieved , and find that improvement is in close relation to the structure of the environment .
we note here that in cases where the open quantum system models are not exactly solvable , one will have to turn to the perturbative master equation approaches for the optimal control solution @xcite . however , in certain models where the exact master equations are available , our present treatment bears the advantage of ruling out the intrinsic errors due to the perturbative dynamics .
only a few non - markovian open quantum system models can be exactly solved @xcite , and exact dissipative models of a two - level system are even fewer .
the total hamiltonian @xmath2 of the two - level qubit model we consider consists of three parts @xcite ( set @xmath3 ) : @xmath4 here @xmath5 is the qubit transition frequency ; @xmath6 is the pauli-@xmath7 matrix ; and @xmath8 , @xmath9 are the creation and annihilation operator for the bath oscillator with eigenfrequency @xmath10 . in this exactly solvable model , the qubit is linearly coupled to the zero - temperature environment through the lindblad operator @xmath11 with coupling constant @xmath12 .
we choose the qubit transition frequency as the time - dependent control parameter , @xmath13 .
in real experiments , @xmath5 is often tunable and is a possible agent of external control .
the exact master equation reads @xcite @xmath14 + 2\text{re}\left[f(t)\right]\notag\\ & \times\left(\sigma_{-}\rho(t)\sigma_{+}-\frac{1}{2}\left\ { \sigma_{+}\sigma_{-},\rho(t)\right\ } \right)+i\text{im}\left[{f(t)}\right]\left[\sigma_{+}\sigma_{-},\rho(t)\right],\end{aligned}\ ] ] where @xmath15 $ ] and @xmath16 $ ] stand for the real and imaginary parts of a complex function , @xmath17 satisfying the differential equation @xmath18 and the bath correlation function is defined as @xmath19 where we have taken the continuum limit and @xmath20 is the environment spectral density .
equation ( [ eq : f_diff_eq ] ) is a nonlocal integro - differential equation and is not easy to solve for a general bath spectral density and thus to incorporate within the framework of qoct .
one important observation to deal with this time - nonlocal equation is to express the bath correlation function in a multi - exponential form @xcite , @xmath21 where @xmath22 and @xmath23 are complex constants and can be found by numerical methods .
then we see from eqs .
( [ eq : f ] ) and ( [ eq : f_diff_eq ] ) that the relevant function @xmath24 in eq .
( [ eq : master equation ] ) satisfies @xmath25 and @xmath26+\sum_{k\neq j}f_{k}(t)\right]\notag\\ + & f_{j}^{2}(t ) , \end{aligned}\ ] ] along with the initial condition @xmath27 .
equation ( [ eq : partialf ] ) forms a set of coupled time - local equations that yield a simple , fast and stable iterative scheme to incorporate with the krotov qoct method that we will employ .
for the convenience of numerical computation , we treat the density matrix as a column vector @xmath28 and eq .
( [ eq : master equation ] ) can be put in the form @xmath29 .
the propagator @xmath30 is defined such that @xmath31 and can be viewed as a state - independent gate operation .
the differential equation for @xmath30 is @xmath32 and @xmath30 is identity when @xmath33 . in qoct , it is necessary to define a quantity , or the cost function , we wish to maximize or minimize after each iteration @xcite . in open system gate control
, this quantity corresponds to the gate error defined at the final gating time @xmath34 @xcite , @xmath35^{\dagger}[\mathcal{o}-\mathcal{g}(t_{f})]\right\},\ ] ] where @xmath36 is the control target to be specified and @xmath37 is the dimension of @xmath30 in the column vector representation .
this error @xmath38 or fidelity @xmath39 definition can be mapped to the trace fidelity commonly used in closed systems when the dynamics becomes unitary . for the dissipative two - level model with control over the @xmath6 term , we perform @xmath7-gate and identity gate control . for the @xmath7-gate control , the target @xmath40 in the column vector representation is defined as @xmath41 and for identity - gate control @xmath42 , where @xmath43 is the identity matrix in the column vector representation .
the update algorithm of the optimization iteration based on the krotov method is as follows @xcite : ( 1 ) an admissible initial control @xmath44 is constructed either by guess or experience .
find the trajectory @xmath45 by intergrating the equation of motion along with the initial condition using the control @xmath46 .
( 2 ) an auxiliary backward propagator @xmath47 is found by integrating the differential equation @xmath48 with its boundary condition @xmath49/2\mathcal{n}$ ] .
( 3 ) solve the equation of motion for @xmath30 and the control update rule @xmath50\right)\ ] ] self - consistently to yield the updated control and propagator @xmath51 and @xmath52 for a small enough @xmath53 to ensure the monotonic convergence of the algorithm . ( 4 ) substitute @xmath51 and @xmath52 for @xmath46 and @xmath54 in step ( 1 ) and repeat steps ( 1 ) to ( 3 ) until the error converges to a saturated value ( a preset error threshold is reached or a given number of iterations has been performed ) .
we constrain the control parameter in our case the time - dependent transition frequency to an allowable range . in real experiments
, there exists an attainable range of qubit frequency determined by the external control agent and the physical system . beyond this range ,
the control is unattainable or simply destroys the original system .
an example can be the critical magnetic field in the superconducting circuit qed system @xcite .
thus for most of the results presented here , we set the range to be @xmath55 , i.e. , @xmath56 .
the value of @xmath5 is determined by the actual physical system implementing this model .
we will present results with large range control @xmath57 in sec .
[ sec : suppression ] . in our model , the optimal pulses for @xmath7-gates and identity gates in closed systems can be obtained straightforwardly .
an important question to be addressed is , how much can qoct improve the gate fidelity in an open quantum system , given that we take the ideal closed system optimal pulse as our initial guess . for a fixed gating time @xmath58 and a constant magnitude control pulse , @xmath59 where @xmath60 is even for the identity gate and odd for the @xmath7-gates .
we take this ideal closed system pulse as the initial guess for optimal control in open systems .
define the quantity , improvement @xmath0 : @xmath61 where @xmath62 denotes the gate error before the qoct iteration , and @xmath63 is the saturated gate error after the iteration .
improvement characterizes the order of magnitude of the gate error improved by the qoct iteration .
in principle , we can deal with any environment spectral density resulting in a bath correlation function that can be expanded in the form of a multi - exponential function . here
we consider two kinds of environment spectral densities or environment correlation functions : the lorentzian - like correlation function and the ohmic correlation function .
the lorentzian spectral density @xmath64 yields the lorentzian - like exponential decaying bath correlation function @xcite @xmath65 } .\ ] ] the environment effect is characterized by the correlation strength @xmath66 , the correlation time @xmath67 , and the central frequency of the environment spectrum @xmath68 .
the ohmic correlation function can be derived analytically from the ohmic spectral density @xmath69 as @xcite @xmath70^{-2 } } , \ ] ] where @xmath71 is the dimensionless coupling strength and @xmath72 is the cutoff frequency .
note that function fitting is required to put eq .
( [ eq : ohmic correlation ] ) in a multi - exponential form .
we present below the numerical results with the parameters in units of @xmath5 if not stated otherwise .
figure [ fig : iteration and pulse ] shows typical optimal pulses ( in the insets ) and the monotonic converging behavior of the qoct iteration , a favorable feature of the krotov method , and the saturation of gate error near the optimal trajectory .
the smooth shape of the optimal control pulses can be easily engineered .
identity gates serve as quantum memories and thus favor long gating times .
figure [ fig : i gate ] shows the gate error after qoct iteration and improvement vs gating time of the identity - gate control in both the lorentzian - like environment [ figs .
[ fig : i gate](a ) and [ fig : i gate](b ) ] and the ohmic environment [ figs .
[ fig : i gate](c ) and [ fig : i gate](d ) ] .
it appears that high - fidelity identity gates with error @xmath73 can be achieved for gating times longer than the system decay time for moderate system decay parameters .
gate control is better performed with weaker qubit - environment coupling strength ( @xmath66 or @xmath71 small ) and with smaller @xmath74 or @xmath72 in both cases .
note that improvement increases as the gating time gets longer .
the anomalous crossing in fig .
[ fig : i gate](d ) results from gate error saturation in extreme conditions .
a @xmath7-gate operation is desired to be fast and thus requires a short gating time .
we set a fixed @xmath7-gate gating time @xmath75 , which is the smallest multiples of @xmath76 within which an ideal closed system @xmath7-gate can be fulfilled in the admissible control range .
the results are shown in tables [ tab : lorentz z ] and [ tab : ohmic z ] .
the trends are similar to the identity - gate control . the parameters @xmath74 and @xmath72 determine the bath correlation time and the shape of the correlation function .
from eqs .
( [ eq : lorentz correlation ] ) and ( [ eq : ohmic correlation ] ) , it can be shown that larger @xmath74 or @xmath77 corresponds to a bath correlation function of shorter correlation time and a stronger correlation strength near @xmath78 , namely , a relatively markovian correlation . in table
[ tab : lorentz z ] , we demonstrate the effect of @xmath68 on @xmath7-gate control .
the gate error becomes smaller when @xmath68 increases .
mathematically , this can be inferred from eq .
( [ eq : lorentz correlation ] ) that large @xmath68 results in mutual cancellation of the bath correlation function in , for example , the integration of eq .
( [ eq : f ] ) and thus minor environment effect .
physically , the peak of the spectral density is detuned away from the qubit frequency by large @xmath68 and results in weak environment - induced decoherence .
figures [ fig : z improvement](a)[fig : z improvement](c ) show the plots of the improvement of @xmath7-gate control under various conditions in lorentzian environment .
apparently there is hardly any improvement when @xmath68 is in the vicinity of the system transition frequency .
as the detuning @xmath79 grows large , we observe great improvement in the @xmath7-gate control .
the increase in the improvement is not monotonic . in the ohmic environment [ fig .
[ fig : z improvement](d ) ] , the improvement grows with the cutoff frequency @xmath72 as in the identity - gate control [ fig .
[ fig : i gate](d ) ] . in all cases ,
neither @xmath66 nor @xmath71 plays a role in improvement . to study the trend of improvement
, we shall study the exact dynamics and explore the agent of error correction in the qoct iteration for the dissipative system we investigate .
cccc + @xmath66 & @xmath80 & @xmath81 & @xmath82 + 0.01 & @xmath83 & @xmath84 & @xmath85 + 0.1 & @xmath86 & @xmath87 & @xmath88 + 1 & @xmath89 & @xmath90 & @xmath91 + + @xmath66 & @xmath80 & @xmath81 & @xmath82 + 0.01 & @xmath92 & @xmath93 & @xmath94 + 0.1 & @xmath95 & @xmath96 & @xmath97 + 1 & @xmath98 & @xmath99 & @xmath100 + + @xmath66 & @xmath80 & @xmath81 & @xmath82 + 0.01 & @xmath101 & @xmath102 & @xmath103 + 0.1 & @xmath104 & @xmath105 & @xmath106 + 1 & @xmath107 & @xmath108 & @xmath109 + .[tab : ohmic z ] errors of the @xmath7-gate control in an ohmic environment under various conditions .
[ cols="^,^,^,^",options="header " , ] the dissipation and the phase shift are directly related to the nature of @xmath24 , which is determined by its differential equation , eq .
( [ eq : partialf ] ) .
mathematically , it is possible to find conditions such that the gate error contributed by @xmath110ds\right|$ ] is relatively larger than that by @xmath111ds\right|$ ] and thus determine the conditions for significant improvement .
physically , the effect of phase shift and dissipation can be understood as the result of qubit transition frequency shift , namely , lamb shift , and qubit decay . in the lorentzian environment with zero detuning , @xmath112
, the spectral density is peaked at and symmetric with respect to @xmath113 .
as the numerical results indicate , the decay rate becomes large and the dissipation effect becomes prominent . on the other hand ,
the lamb shift is relatively small due to the symmetric distribution of spectral density with respect to qubit frequency @xmath113 . in this case
the dissipation effect dominates over the phase shift effect , and the improvement due to the optimal control is small .
however , if the environment central frequency is detuned from the qubit frequency , our numerical results indicate that qubit decay drops dramatically , but the lamb shift does not change much .
this is due to the asymmetric distribution of the spectral density with respect to qubit frequency @xmath113 and the result consequently leads to significant improvement .
this is in agreement with the trend of improvement observed in the previous sections .
note that this behavior is more prominent as the lorentzian distribution gets narrower ( @xmath74 small ) .
similar arguments apply to the ohmic case .
the overall coupling strength @xmath66 ( or @xmath71 ) is irrelevant to the improvement since it does not affect the shape of the spectral density but only the overall value .
so far , we have observed very limited suppression of dissipation applying qoct to the two - level dissipative model .
this consequence is model specific , and is due to the control range we specify . in eq .
( [ eq : rho21 ] ) , the control pulse can be designed to directly cancel the environment - induced phase shift , but can hardly suppress the dissipation effect through minimizing the magnitude of @xmath114ds\right]$ ] .
however , one can observe in eq .
( [ eq : partialf ] ) that @xmath115 follows the unit imaginary number @xmath116 , so @xmath24 oscillates faster when the control @xmath115 is large in magnitude .
the integral @xmath117 is then small in magnitude due to mutual cancellation .
therefore , if we allow the optimal control pulse to be considerably large in magnitude compared to the initial guess and other parameters , the dissipation can be reduced remarkably after the qoct iteration . a @xmath7-gate control with large range control @xmath57 is shown in fig . [ fig : large control ] .
note that the gating time is shorter than that of the small range control , and furthermore the gate error is smaller than that of the small ranged control by several orders .
this is due to both phase shift correction and dissipation suppression . the question would , however , be whether such high values of the control strength are physically attainable and admissible in realistic qubit systems .
if so , very high - fidelity gate operations are practically possible .
-gate control error vs gating time in a lorentzian - like environment with @xmath112 and large range control @xmath118 .
the reduced @xmath119 and @xmath120 ratio is responsible for the much smaller gate error .
the evolution time scale is shortened ( compared to @xmath76 ) , as well as the gating time.,scaledwidth=45.0% ]
in this work , we show that an exact open non - markovian qubit dynamics can be readily put in the framework of the qoct to attain single - qubit gate control .
high - fidelity identity gates and @xmath7-gates can be achieved for moderate qubit decaying parameters with small magnitude control .
the optimal pulses are smooth in shape and easy to implement in experiments . in cases where the open quantum system models are not exactly solvable ,
the perturbative master equation approaches should be employed for the optimal control solutions @xcite . however , for models where the exact master equations are available , our present treatment , in contrast to the commonly used perturbation method , is valid for all orders and free from intrinsic error .
the dissipative model and the qoct method discussed above can be readily applied to realistic physical systems such as the circuit qed system @xcite . in circuit qed ,
the system is realized by a josephson charge qubit or a transmon qubit @xcite coupled to a coplanar waveguide resonator and the qubit frequency can be controlled by external electric voltage and magnetic flux @xcite . in principle , this formalism can be applied to any two - level system embedded in a structured environment @xcite , e.g. , nitrogen vacancy center in diamond embedded in photonic band - gap @xcite .
we introduce the definition of improvement and find that , improvement is directly related to the mathematical nature of @xmath24 . physically , improvement is in close relation to the shape of the spectral density with respect to the qubit transition frequency .
the concept of improvement does not need to be limited to this specific exactly solvable model , but can also be extended to more general systems that allow no exact solutions . gaining the insight of improvement ,
one is able to determine in which condition the improvement is notable , and that applying qoct to the environment - included open system is necessary . in the model ( dissipative model ) and
the control problem @xmath121 control ) discussed in our work , the suppression of dissipation is substantial only when we increase the control strength or , in a physically equivalent sense , enlarge the ratio of the qubit frequency to the qubit - environment coupling strength .
this result is in agreement with that implicitly stated in @xcite where nonperturbative dynamical decoupling is applied to the same model .
h.s.g . acknowledges support from the national science council in taiwan under grant no .
100 - 2112-m-002 - 003-my3 , from the national taiwan university under grants no .
103r891400 , no .
103r891402 and 102r3253 , and from the focus group program of the national center for theoretical sciences , taiwan .
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link:\doibase 10.1103/revmodphys.73.357 [ * * , ( ) ] link:\doibase 10.1103/physreva.80.012104 [ * * , ( ) ] link:\doibase 10.1126/science.1158340 [ ] * * , ( ) link:\doibase 10.1103/physreva.88.022333 [ * * , ( ) ] | we apply quantum optimal control theory ( qoct ) to an exactly solvable non - markovian open quantum bit ( qubit ) system to achieve state - independent quantum control and construct high - fidelity quantum gates for moderate qubit decaying parameters .
an important quantity , improvement @xmath0 , is proposed and defined to quantify the correction of gate errors due to the qoct iteration when the environment effects are taken into account . with the help of the exact dynamics ,
we explore how the gate error is corrected in the open qubit system and determine the conditions for significant improvement . the model adopted in this paper
can be implemented experimentally in realistic systems such as the circuit qed system . |
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Jailers discovered the 12 inmates missing about 6:30 p.m. Sunday. Authorities have not yet said how they broke out.
The Jasper Police Department posted this message on its Facebook page: "JPD has activated additional personnel to assist the Walker County Sheriff's Office in locating multiple escaped inmates from the Walker County Jail. We ask that downtown residents stay indoors and turn on all outdoor lighting."
Walker County Chief Deputy Dayron Bridges said sheriff's official activated off-duty employees to help in the search. Jasper and Parrish police, constables also joined in the hunt. ALEA's Aviation Unit also assisted.
As of 5 a.m. Monday, only one - Brady Andrew Kilpatrick - remained at large. The Cordova man was jailed for possession of a controlled substance,possession of drug paraphernalia, and possession of marijuana.
Those who escaped and were quickly recaptured are:
-John Richard Hunter, 26, of Jasper - in jail for burglary, theft, possession of burglary tools and escape.
-Christopher Cole Spain, 18, of Jasper - in jail for failure to appear on disorderly conduct.
-Kristopher Keith Secrest, 20, of Oakman - in jail for felony domestic violence and giving false information to law enforcement.
-Quadrekas Latoddrick Key, 21, of Parrish - in jail for possession of a controlled substance, possession drug parpahernalia and attempting to elude.
-Timothy Chaz Cooper, 28, of Cordova - in jail for breaking and entering a motor vehicle and fourth-degree theft.
-Steven Sanford Hartley, 27, of Hoover - in jail for first-degree theft of property.
Those who escaped and were taken back into custody late Sunday and early Monday are:
-Michael Adam McGuff, 30, of Jasper - in jail for third-degree escape and obstructing government operations. He was back in custody by 10:30 p.m.
-Steven Blake Lamb, 28, of Quinton - in jail for attempted murder, first-degree robbery, first-degree theft, reckless endangerment and probation revocations. He was recaptured at 10:42 p.m. Sunday.
- Christopher Micheal Smith, 19, of Jasper - in jail for attempted murder, first-degree burglary, unlawful breaking and entering, second-degree theft. He was captured at 4:21 a.m. Monday in Townley.
-Larry Inman Jr, 29, of Parrish, - in jail for two counts of receiving stolen property, attempting to elude, failure to appear. Inman was recaptured by sheriff's deputies and Birmingham police at the Flying J of of I-65 about 1:52 a.m. Monday.
-Ethan Howard Pearl, 24, of Jasper -in jail for resisting arrest, obstructing government operations, possession of drug paraphernalia, promoting prison contraband, and failure to appear. Pearl was also captured by Walker County and Birmingham lawmen at the Flying J. He was taken into custody at 2:06 a.m.
A $500 reward was offered for information that led to the arrest of the escapees. Contact the Sheriff's Office at (205) 302-6464.
This story will be updated | – A dozen inmates broke out of the Walker County Jail in Alabama Sunday evening, but they weren't all on the loose for long: Authorities say eight of the men had been recaptured by 10:42pm, about four hours after they escaped, AL.com reports. Police, who asked area residents to stay indoors and turn on outdoor lighting, say they're investigating how so many inmates managed to escape the Jasper facility, which only holds around 250 inmates. The New York Daily News reports that those still listed as on the loose late Sunday include Christopher Smith, a 19-year-old charged with attempted murder. |
The number of tremors recorded during an earthquake swarm in Irving climbed to eight Tuesday, according to the United States Geological Survey; three additional quakes were reported Wednesday morning and a fourth that afternoon.
The USGS said the two strongest of Tuesday's quakes, a 3.5 and a 3.6, each ranked as an MMI V on the Modified Mercalli Intensity Scale, which indicates they had the strength to be felt by nearly everyone, wake those sleeping, break windows and dishes and to overturn unstable objects.
No injuries or significant damage have been reported in connection with the earthquakes and police have requested people stop calling 911 to report only shaking. Atmos Energy said Wednesday the earthquakes have not caused any gas leaks in the area.
The recent earthquake swarm, where a number of quakes are concentrated in a single area over a few days, is centered in an area of Irving where more than 20 quakes have been recorded since October 2014, but where only one earthquake was ever recorded before 2008, according to a scientist at Dallas' Southern Methodist University.
Irving Quake Swarm (Jan. 6-7) Tuesday
1. 7:37 a.m. Jan. 6, 2.3M
2. 3:10 p.m. Jan. 6, 3.5M
3. 6:52 p.m. Jan. 6, 3.6M
4. 8:11 p.m. Jan. 6, 2.9M
5. 8:12 p.m. Jan. 6, 2.7M
6. 9:54 p.m. Jan. 6, 1.7M
7. 10:05 p.m. Jan. 6, 2.4M
8. 11:02 p.m. Jan. 6, 1.6M Wednesday
1. 12:59 a.m. Jan. 7, 3.1M
2. 8:34 a.m. Jan. 7, 2.6M
3. 9:57 a.m. Jan. 7, 2.7M
4. 1:24 p.m. Jan. 7, 2.3M
Scientists at SMU said these are some of the largest quakes to hit North Texas in recent history. Before this most recent swarm, the largest magnitude quake recorded in the Irving area since October 2014 was a 3.3-magnitude quake on Nov. 22. The most recent temblor before this swarm was a 2.4 MMI III recorded at 8:29 p.m. on New Year's Day.
Since 2008, more than 100 quakes have hit North Texas; 45 were in the Irving area alone and more than 20 happened in just the last three months.
Geologists and seismologists at SMU are trying to figure out what is causing the increase in earthquakes, whether they are induced or if they are simply the result of natural, believed to be dormant, fault lines.
SMU researchers are taking a hard look at disposed waste water as a possible cause, but experts add that earthquakes of this size can happen virtually anywhere in the world at any time.
“There’s been some indication that disposable fluids can trigger small earthquakes,” said Dr. Brian Stump, a professor of earth sciences at SMU. “That's still an open question in this particular case.”
Scientists are also trying to determine if the earthquakes indicate whether something more catastrophic may be possible. The largest earthquake ever recorded in Texas occurred in the Big Bend area, near Valentine, where a 5.8-magnitude quake was recorded in 1931.
Tuesday's Earthquakes
7:37 a.m. -- The first earthquake, measuring as a 2.3-magnitude, was recorded at 7:37 a.m. Wednesday near the University of Dallas Irving location on East Northgate Drive.
3:10 p.m. -- At 3:10 p.m Tuesday a magnitude-3.5 earthquake was recorded near Texas 183 and Texas 114, east of the former site of Texas Stadium in Irving.
“All of a sudden you hear a 'boom.' That's why we thought somebody hit the building. And then everything started shaking,” said Melissa Lockard, who works in Irving.
3.5 Earthquake Felt in FW, Dallas
The United States Geological Survey confirms a 3.5 magnitude earthquake rumbled across North Texas Tuesday afternoon with the epicenter located near the former site of Texas Stadium in Irving. (Published Tuesday, Jan. 6, 2015)
6:52 p.m. -- The strongest of the day, was recorded at 6:52 p.m. and was measured as a magnitude-3.6. Its epicenter was in the Trinity River basin near the Bachman Branch in East Irving.
“We said, ‘Oh, my God, this is another one,” said Dania Medina, who works at the Days Inn off Texas 183 in Irving. “And we didn't believe it.”
8:11, 8:12 p.m. -- The fourth and fifth quakes, one of them magnitude-2.9 and the other magnitude-2.7, occurred within seconds of each other, again in Irving near the former site of Texas Stadium. One was located along Loop 12 at Texas 114 while the other was just south of Texas 183 at the Trinity River.
9:54 p.m. -- A sixth earthquake was recorded as a magnitude-1.7 at 9:54 p.m. near the intersection of Harry Hines Boulevard and West Northwest Highway in Dallas.
Earthquake Hits Irving, Felt Across NTX
A magnitude 3.5 earthquake hit Irving Tuesday afternoon. (Published Tuesday, Jan. 6, 2015)
10:05 p.m. -- The seventh earthquake followed minutes later at 10:05 p.m. and was measured as a magnitude-2.4 on the University of Dallas campus near Texas 114 and Tom Braniff Drive in Irving.
11:02 p.m. -- The USGS recorded an eighth earthquake, measured as a 1.6-magnitude, at 11:02 p.m. near the Trinity River south of Storey Lane.
NBC 5's Johnny Archer, Kevin Young and Alex Russell contribtued to this report.
Copyright Associated Press / NBC 5 Dallas-Fort Worth ||||| Update at 5:35 p.m. on January 7 from Marissa Barnett in Austin: In an afternoon press conference, Craig Pearson, a seismologist for the state’s oil and gas regulatory agency, reiterated his position that wastewater disposal wells in North Texas are not to be blamed for the rash of quakes in Irving and Dallas in recent weeks.
The Texas Railroad Commission’s Pearson, who has talked with SMU researchers but will not be conducting research, said he will review their findings and decide what action, if any, oil and gas regulators need to make. The agency’s seismologist is not responsible for investigating seismic events or conducting research on the ground, the commission said.
At this time, the agency has no plans to suspend services or collect additional information, including pressure of injection rates, from disposal well operators in surrounding areas. The nearest disposal well is 10.3 miles away.
Update at 4:50 p.m. on January 7: Someone call Lee Marvin.
Moments ago the U.S. Geological Survey confirmed that at 1:24 this morning there was a smaller quake that went previously undetected — a 2.3-magnitude quake just north of the old Texas Stadium site. From the looks of the map it was in a pond off N. Walton Walker Blvd.
And if you’re wondering why we’re just now seeing this …
“When they are this little, either we have immediate inquiry or people will submit reports saying they felt something,” says a USGS seismologist. “My colleague then goes sorting through those. That’s why this one showed up later than the others.”
Update at 3:22 p.m. on January 7: Our Avi Selk already broke the news that Irving’s getting close to two dozen more sensors intended to keep tabs on the quakes that have been rattling Irving and North Texas in recent weeks. Now comes SMU to explain how this will go down.
A release from the Hilltop says their seismology team will deploy 22 more seismographs in coming days. Fifteen monitors are being deployed today; two more, coming from the U.S. Geological Survey, will be added tomorrow; and five more, on their way from the Incorporated Research Institutions for Seismology, will be put in place Friday.
“In the near term, our first step is to put out seismographs to confirm and refine the location of the quakes and define the faults in the area,” says associate physics professor Heather DeShon. “Only after we get that data will we be in a position to investigate the potential cause of the earthquakes.”
As SMU notes, and you’re no doubt aware at this point, this current swarm is “the fourth sequence of felt earthquakes recorded in the Fort Worth Basin since 2008,” once you include the previous clusters located near Dallas/Fort Worth International Airport, Cleburne and Reno-Azle.
“SMU studies of the DFW and Cleburne quakes cited wastewater injection wells as a plausible cause of the seismicity in those areas,” says SMU. The Texas Railroad Commission has already said it doesn’t believe wastewater injection plays a role in the Irving quakes.
“It’s premature to speculate on the cause of this current series of seismic events,” says Brian Stump, SMU’s Albritton Chair of Geological Sciences, in a statement released Wednesday. “We’re just getting started. We want to support the local community in understanding these earthquakes, and the team appreciates the cooperation of the city of Irving, the United States Geological Survey and IRIS in helping us get the best information possible.”
Update at 1:57 p.m. on January 7: Earlier this morning, Irving Mayor Beth Van Duyne and Dallas Mayor Mike Rawlings said, separately, that they’d spoken about preparing an emergency response to the swarm of quakes that have shaken the ground and rattled the nerves of North Texans in recent weeks — and the last 24 hours, in particular. Moments ago, Dallas County Judge Clay Jenkins issued a statement noting that the county’s Emergency Management staff had been talking with the Texas Division of Emergency Management and Irving and Dallas’ respective offices of emergency management as well.
“In Dallas County, we use an ‘All Hazards Approach’ to emergency response and preparedness, which includes earthquake planning,” says Jenkins. “This week our emergency management staff will conduct a conference call with SMU and city emergency managers to discuss technical information and develop additional guidance to better ensure our plans and procedures are up-to-date and specific to this type of hazard. While the cause of these earthquakes is still being investigated and the threat for a major earthquake in Dallas County remains low, I would encourage our residents to review important earthquake preparedness and safety information from FEMA and the American Red Cross.”
Update at 1:37 p.m. on January 7 from Avi Selk and Robert Wilonsky: Earthquakes, beware: You are being monitored.
Irving is about to get wired to the hilt with seismometers, which help researchers pinpoint and study the temblors.
Currently, three devices are in the city, the latest installed Monday, just before Tuesday’s massive swarm. But Irving Mayor Beth Van Duyne said that SMU researchers will install 15 more seismometers by the end of the day—and later this week they will add seven fancier versions that can transmit data in real time.
Just call it Seismometer City.
Meanwhile, Atmos Energy Corporation says it’s keeping a close eye on gas lines during this current swarm of quakes. Some folks on social media have noted gas-line breaks they believe to have been caused by the quakes. But Jennifer Altieri, Atmos’ director of media relations, says that’s not the case, as far as she’s aware.
“Atmos Energy is closely monitoring the number of recent, minor earthquakes that have occurred in and around Irving in recent weeks,” she says via email. “As of today, Atmos Energy has no indications of any abnormalities or integrity issues on its natural gas system as a result of these earthquakes.
“In addition to monitoring our system following an earthquake, Atmos Energy routinely assesses the condition of our pipelines through leak surveys, foot and air patrols, and monitoring devices that help pinpoint areas of needed repair. Once again — these surveying measures have not yielded any natural gas leaks directly connected to the recent earthquakes.”
The city of Dallas said the same thing yesterday about water main breaks that occurred following the 3.5-magnitude temblor that rattled most of North Texas around 3 p.m.
Update at 12:47 p.m. on January 7 from Robert Wilonsky and Avi Selk: Just to be clear: You can get earthquake coverage in Texas. And according to one Dallas State Farm agent, it’s not terribly expensive, for the most part — around $85 annually for a 2,400-square-foot brick-veneer house built in the 1960s, let’s say, if you take the 2-percent deductable. Farmers says the same thing on its website: You can get it added, and it’s “relatively inexpensive” if you don’t live a part of the country known for its temblors. Till a few months ago, that included Irving and Dallas.
We’ve got a long way to go before quakes surpass hail and water damage as the top two claims filed in the state of Texas. A long way. But it’s do-able, if you must. And a lot of people must, says one State Farm agent who didn’t want to be named. “We have gotten tons — tons of calls. No one asked for it two years ago. Now, tons of calls.”
“Insurance companies offer separate policies that cover damages caused by earthquakes,” says the Texas Department of Insurance. “The cost is low because earthquakes are rare in Texas.”
In North Dallas, Amy Wallace Bradley’s two children came home from school Tuesday, rattled by the afternoon quake. That evening, she held and hugged them as the biggest temblor rolled beneath her kitchen floor.
“After that it was like a running joke,” Wallace Bradley said—quakes straight through to bed time, until the last one woke her 12-year-old up after midnight.
“She said, ‘Was that a little earthquake?’ I said, ‘No, honey. That was a big one.’”
Come morning, Wallace Bradley phoned up her insurance company and added earthquake coverage for $63 a year.
“It was not even a question,” she said. “I’m a single mom raising two kids. If something happens to the house I want to take care of them.”
Update at 11:22 a.m. on January 7 from Avi Selk: Irving Mayor Beth Van Duyne was on the phone with her city manager Tuesday evening, talking about the 3.5-magnitude afternoon quake, when an even bigger tremblor interrupted their conversation.
“I’ll admit I was startled,” she said. So were many residents.
“I’ve gotten responses across the board,” Van Duyne said. “Some are blaming fracking, though from what I understand we don’t current have any fracking in Irving.
“Some are blaming the fact we imploded Texas Stadium. Some are blaming DART and 183 construction. Some are saying it’s because of the drought. Some are saying it’s not a city issue—please don’t waste time and taxplayer dollars; it’s an earthquake; you’re not God.”
So Van Duyne also called up Dallas Mayor Mike Rawlings yesterday.
“Since these occurrences are happening in both our cities — it’s right on the fault line between Irving and Dallas — I’d be interested in a partnership to find out the nature of these quakes, and what types of preparations the cities can have.
“He said he thought that was a good idea. We’re discussing now creating a joint task force, using resources from both our cities to find the cause.”
Update at 10:45 a.m. on January 7: The 11th quake since Tuesday morning has been confirmed: a 2.7-magnitude quake at 9:57 a.m. … and you will never guess where! OK. Fine. It’s along what Twitter and Facebook posts now refer to as The Jerry Jones Fault. Which is brilliant.
Update at 10:15 a.m.: In the words of Nigel Tufnel, this one goes to 11.
The U.S. Geological Survey confirms what Twitter and email told me just before 10 — there was another one in Irving. We’re not yet sure precisely where or just how strong it was. That data’s on its way, says Julie Dutton, a seismologist at the USGS. Patience.
Anyway. While I had Dutton on the phone I asked her what many readers have been wondering: Are these individual quakes or aftershocks or … something?
“They are considered ‘a swarm,’” she says, if that makes you feel better. “They’re all related to the same geological region, so they’re all related. But it’s not necessarily a foreshock-aftershock series. We just call it a swarm.”
In the meantime, Irving police just sent a note asking people not to call 911 after a quake, because, look, why?
“In the minutes following these earthquakes, many people have called 911 to report their experience,” says a release that just landed in the in-box. “Consequently, the 911 system was overwhelmed and operators were quickly trying to reach callers with a true emergency. The Irving Police Department requests that you refrain from calling 911 following an earthquake unless you are in immediate need of medical attention or other emergency services. An unnecessary call to 911 may prevent someone with a critical need from reaching an emergency operator.”
And as our Avi Selk notes this morning, all Irving ISD students will be drilled in earthquake safety Wednesday.
“It’s similar to what we do for tornadoes, but not quite the same,” district spokeswoman Lesley Weaver tells Avi.
Weaver knew of no damage to schools, and only a few calls from concerned parents had been reported. Nevertheless, periodic “duck, cover and hold-on” earthquake drills will become a part of the school year going forward.
Update at 9:08 a.m. January 7: We’re now into the double digits.
The U.S. Geological Survey says there was a 10th quake since Tuesday morning, and it occurred at 8:34 this morning — a 2.6-magnitude temblor. And, as always, it was at the 183-114 split otherwise known as The Road Formerly Known as The Road to Texas Stadium. This was our second today, counting this one just before 1 a.m.
We’ve asked SMU if their seismologists if they have a second to chat — since there have been nine more recorded since Tuesday’s hastily called press conference. We were told to be patient, as they need to “regroup” because “as you can imagine, they have a lot to process.” Don’t we all.
Meanwhile, Dallas Mayor Mike Rawlings told the Dallas City Council today that he is meeting with Irving Mayor Beth Van Duyne to discuss the rise in quakes and come up with a possible emergency-management plan should they become stronger in coming days (weeks, hours, minutes?). The city’s Emergency Management department has been told to come up with a plan to present to the council’s Public Safety Committee.
Update at 1:20 a.m. January 7: Another one!
The USGS has reported a 3.1 magnitude temblor in the Irving area that occurred at 12:59 a.m.
The quake is the ninth in the last 18 hours. It was centered near Highways 114 and 183 and Loop 12.
Update at 12:20 a.m. January 7: Early Tuesday morning we asked the U.S. Geological Survey to check on reports of an earthquake felt in Northwest Dallas around 7:30 a.m. At the time we were told one couldn’t be found, but if it turned up they’d post to their earthquake map. Well, it just showed up, which means we actually had eight quakes on Tuesday.
Says the USGS, it was a 2.3-magnitude temblor at 7:37 a.m. And you’ll never guess … oh, all right, it was near all the others, across Northgate Drive from the University of Dallas campus. Near the old Texas Stadium site.
“People reported feeling it,” says a USGS seismologist, “so we searched for the data.” She confirms it was just added to the site.
Update at 11:20 p.m.: And it’s Lucky Number Seven!
Says the U.S. Geological Survey, we end the day (fingers crossed) with another minor temblor, this one a 1.6-magnitude at 11:02 p.m. close to most its siblings, along the Elm Fork of the Trinity River near the old Texas Stadium site.
Update at 10:20 p.m.: So … make that six quakes confirmed today in North Texas.
The fifth, per the U.S. Geological Survey, occurred a 1.7-magnitude quake at 9:54 p.m. near Denton Drive and W. Northwest Highway in Northwest Dallas. The sixth followed a few minutes later: a 2.4-magnitude temblor at 10:05 p.m. on the University of Dallas campus.
At least they’re getting smaller?
Update at 9:45 p.m.: There have been numerous water main breaks throughout the city today, including a major one at Dykes Way and Hughes Lane in North Dallas off Preston Road. But when asked about the link between those events and today’s quakes — especially the 3.5-magnitude temblor this afternoon — city officials say they have no definitive proof.
“The main break on Dykes Way occurred nearly two hours after earthquake,” says Sana Syed, the spokesperson for Dallas City Hall. “There are many contributing factors to main breaks, especially during cold weather. We experienced some failures prior to earthquake as well. We are unable to correlate the two or state that it was the cause.”
Actually, it appears the one on Dykes Way occurred a little before 4 p.m., says Thor Johnson, who posted videos of the break to his Facebook page.
Update at 8:50 p.m.: And here’s the fourth — a 2.7-magnitude quake at 8:12 p.m., according to the U.S. Geological Survey. This one was located smack in the middle of the Loop 12-John Carpenter Freeway tangle. Also, in my house. It’s not the rattling that gets you. It’s the boom that precedes it.
So that’s it. Four. For now.
Update at 8:28 p.m.: The quake at 8:11 p.m. was indeed a 2.9, says the U.S. Geological Society, and was close to the one that rattled a 3.6 before 7 p.m. — along the East Fork of the Trinity River. It could be felt from Addison to North Richland Hills to Dallas.
Still waiting for info about the fourth that followed one minute later. USGS says that is a “distinct, different event with a smaller magnitude,” and more information is coming.
Update at 8:16 p.m.: There were just two more quakes, according to the U.S. Geological Survey (and my nerves).
The first occurred at 8:11 p.m., and according to a seismologist “it preliminarily registered a 2.9 magnitude.” The second was one minute later — and, says the USGS seismologist, “it was definitely smaller than a 2.9.”
Reports are just coming in. Final confirmation momentarily.
Update at 7 p.m.: There was yet another earthquake at 6:52 p.m. — and according to a seismologist at the U.S. Geological Survey, it was a 3.6-magnitude temblor.
And it was — you guessed it — near the old Texas Stadium site, along the Elm Fork of the Trinity River.
Here’s the USGS list of cities where people report having felt the latest quake, and at this point it would be easier to report who didn’t feel it. Reports one reader living near Marsh and Royal Lanes, “That was amazing. Mortar from inside my chimney fell in fireplace. Dogs freaking out. Knocked a hurricane lamp off of buffet. Big bang.”
Multiple readers report items falling off shelves and walls during the second quake. Here, another reader, who lives not far away along Joe’s Creek near Marsh Lane, shows off some of the damage:
Update at 4:54 p.m.: SMU seismologist Brian Stump says today’s 3.5-magnitude temblor near the old Texas Stadium site was “well-felt, so I am sure people are concerned.” But, he cautions: Researchers have no idea what caused it — or whether it’s a precursor to larger quakes.
“We cannot predict the size of the largest events, and that motivates a need to study these events,” he said, “to try to address those questions.”
One thing is certain: While many people in North Texas felt it, some didn’t — even if they were in the same building. Said SMU seismologist Heather DeShon, she felt it on campus. Stump, who was on a different floor in the same building, did not.
“Sitting still makes a huge difference” when it comes to feeling a quake, DeShon said.
SMU has three seismometers now recording quakes in Irving in an attempt to better locate the quakes. They’re also attempting to discover what’s causing them. But that won’t be an easy thing.
“Even this part of Texas has old faults, and those old fault have stored stress,” said Stump. “The disposal of fluids [wastewater] in some cases can trigger small quakes.” But, he said, that remains an “open question.”
Dr. Craig Pearson, a seismologist with the Texas Railroad Commission, says in a statement sent to The Dallas Morning News that “there are no oil and gas disposal wells in Dallas County. And I see no linkage between oil and gas activity and these recent earthquakes in Irving.”
Update at 4:15 p.m.: The U.S. Geological Survey is now reporting that there was also a 3.5-magnitude quake in Snyder at 3:55 p.m. Snyder’s 262 miles west of Dallas — a straight shot on Interstate 20.
In a few moments we’ll have an update on today’s Irving quake from SMU. Seismologists are studying the data from the 3:10 p.m. temblor, and are expected to address the media concerning some preliminary findings at 4:30 p.m.
Original post at 3:21 p.m.: The US Geological Survey confirms what you probably felt if you live in North Texas: There was a pretty decent-sized earthquake at 3:10 p.m.
It was a 3.5-magnitude quake, reports the USGS, once again very close to the Texas Stadium site and along the Balcones Fault, which had been inactive until recently. Indications are the temblor rumbled through at 3:10 p.m. near the State Highway 183-114 split. It was measured at a depth of three miles.
Until today, the strongest recorded in Irving during this recent cluster of quakes was the 3.3-magnitude quake on November 22. Most have been in the mid-2 range.
But today’s was something entirely different: It could be felt all the way from Arlington to Argyle, Grand Prairie to Plano and McKinney to downtown Dallas based on USGS reports and, ya know, Twitter.
Good timing too: Only yesterday SMU researchers placed a seismograph in Irving to see if they could better locate the quakes that appear to now be a regular occurrence in this part of the world. SMU says its seismologists will be speaking to the media around 4:30 this afternoon. Updates after that. | – Nerves were jangled and items were jolted off shelves by four earthquakes in North Texas yesterday, but no major damage was reported. All four quakes were centered in the same location in Irving, Dallas County, where there have been 20 quakes reported since October 2014, NBC reports. The four quakes—ranging in strength from magnitude 2.7 to 3.6—were centered near the old Texas Stadium site, former home of the Dallas Cowboys, and Southern Methodist University scientists are trying to determine the cause. The United States Geological Survey says the quakes—two of which happened within seconds of each other starting at 8:11pm—were strong enough to break windows and be felt by many people in the area. Researchers say the quakes could be linked to stored stress in old fault lines, although the disposal of wastewater from the energy industry can also trigger small quakes. But "there are no oil and gas disposal wells in Dallas County," a seismologist with the Texas Railroad Commission tells the Dallas Morning News. "And I see no linkage between oil and gas activity and these recent earthquakes in Irving." |
transient low - mass black hole x - ray binaries show distinct changes of their spectral and variability properties as they evolve during an outburst , that are interpreted as evidence for changes in the accretion flow and x - ray emitting regions .
this behavior can be classified by different phenomenological states through which the black hole transient ( bht ) evolves during an outburst . at the beginning of a typical outburst bhts
are usually in the low hard state ( lhs ) where their power density spectra ( pds ) are dominated by band - limited noise ( bln ) on which narrow quasi - periodic features ( quasi - periodic oscillations ; qpos ) are superimposed . during the evolution through the lhs and into the hard intermediate state ( hims ) the amplitude as well as the centroid frequency of the qpos increases . in the energy range covered by the rxte / pca detector ( @xmath02 kev )
the pds show a smooth transition from the lhs to the hims .
this picture changes dramatically when softer energies are included , as they reveal the existence of two distinct power spectral states at soft and hard x - rays with the onset of the hims @xcite .
the transition to the soft intermediate state ( sims ) is marked by the appearance of another type of qpo , and an overall fractional rms in the 5 10 per cent interval @xcite . in the high soft state ( hss )
the variability is even lower and the pds is dominated by power - law noise . after experiencing a substantial decrease in luminosity during the hss the bht returns back to the lhs again usually passing the hims and sims @xcite . in the lhs
the x - ray emission is very noisy and the fractional rms can reach values up to 4050 per cent .
the first detection of a difference in time scales between the soft and hard flux from a bht was found in observations of the hims of gs112468 andgx 3394 obtained with ginga .the shape of the pds , which is dominated by bln , can be fitted with a combination of lorentzian components @xcite .
four main components have been identified ( 0.001 @xmath1 a few 100 hz ) : a low - frequency one fitting the flat - top part , a peaked ( sometimes qpo - like ) component , and two broad lorentzians at higher frequencies .
these components are characterized by their characteristic frequency and by the amount of variability they contribute , where the latter one is measured as factional rms .
studying the fractional rms as a function of energy ( the `` rms spectrum '' ) it was shown that it is either flat or decreases by a few per cent in the energy range covered by rxte / pca ( * ? ? ?
* and references therein ) .
this shape has been interpreted in the framework of comptonization models @xcite .
using covariance spectra and ratios obtained from data , an increased disc blackbody variability with respect to the comptonized emission was detected below 1 kev at time scales longer than one second , while on shorter time scales the disc variability is driven by variability of the comptonized component , consistent with propagating models modified by disc heating at short time scales @xcite .
in addition to the bln component type - c qpos @xcite can be present .
they can be observed over a relatively large range of frequencies roughly from 0.01 to 30 hz and their fractional rms is of the oder of 3 15 per cent . in recent years
much work has gone into developing and exploring models to describe qpos and noise components .
an excellent summary of these models can be found in the extensive recent review of ( * ? ? ?
* see also references therein ) .
bln can be explained within the `` propagating fluctuation '' model @xcite , where variability is caused by variations in the mass accretion rate which propagate through the disc , so that shorter time - scale variations either from coronal flares or fluctuation in the mass accretion rate or similar processes in the inner parts of the disc are superimposed on longer time - scale variations from further out .
bln is also seen in neutron star low mass x - ray binaries .
likely indicators of the orbital frequency in the innermost accretion flow such as the khz qpo frequency in neutron star low mass x - ray binaries are found to vary with the flux corresponding to the time scale of the bln in a manner similar to that established for variability on longer time scales which is due to modulation in the mass accretion rate , providing an independent evidence that the bln corresponds to the modulation in the mass accretion rate which causes changes in the inner edge or characteristic frequencies in the accretion flow @xcite .
in this paper , we study the variability properties of the characteristic frequency and variability amplitude of the bln in different energy bands during the lhs for a sample of bhts .
we used observations of gx3394 , h1743322 , xtej1650500 , xtej1752223 , and swiftj1753.50127 .
details on the individual observations are given in table [ tab : obs ] .
all observations were taken during the lhs .
we filtered and extracted the pn event files , using standard sas ( version 13.0.0 ) tools , paying particular attention to extract the list of photons not randomized in time . for our study
we selected the longest , continuous exposure available in each observation ( see table [ tab : obs ] ) .
we used the sas task ` epatplot ` to investigate whether the observations are affected by pile - up , and in the case of pile - up excluded the column(s ) with the highest count rate until the selection results in an observed pattern distribution that follows the theoretical prediction quite nicely .
we selected single and double events ( pattern@xmath24 ) for our study .
we extracted power density spectra ( pds ) in two different energy bands , namely 1 2 and 4 8 kev . after verifying that the noise level at frequencies above 30 hz is consistent with the one expected for poissonian noise @xcite
, we subtracted the contribution due to poissonian noise , normalised the pds according to @xcite and converted to square fractional rms .
the pds were fitted with models composed of zero - centered lorentzians for bln components , and lorentzians for qpos .
the resulting power spectra in the two energy bands thus contain only source variability and can be compared with each other .
in addition , we derived rms spectra for each component of the pds using the amplitude ( normalisation ) of the lorentzians . furthermore , we derived covariance spectra following the approach described in @xcite . to study variability on shorter time scales we used 0.1 s time bins measured in segments of 4 s. for longer time scales 2.7 s time bins in segments of 270 s were used . as reference band we used the energy range between 1 and 4 kev , taking care to exclude energies from the reference band that are in the channel of interest .
we extracted energy spectra of all observations , using the rawx values given in table [ tab : obs ] for the source spectra . to extract background spectra we used columns 3@xmath3rawx@xmath35 . in the case of burst mode observations we used rawy @xmath4 140 following the procedure outlined in .
we payed special attention to generate arf files of the pile - up corrected source region , following the steps laid down in the users guide .
as it is known that energy spectra obtained form epic - pn fast - readout modes can be affected by gain shift due to charge - transfer inefficiency ( cti ) , which leads to an apparent shift of the instrumental edges visible at low energies , we also generated spectra applying the sas task epfast to the data .
apart form the observation of 1743 no significant changes between the energy spectra obtained with and without epfast are noticeable at low energies , and a residual feature at @xmath52 kev , related to small shifts in energy gain at the si - k and au - m edges of the instrumental response , remains present in the data obtained with epfast @xcite . as there are no significant changes of the energy spectra at low energies and as epfast leads to an over - correction of the cti at higher energies ( see * ? ? ? * ; * ? ? ?
* ) , we fitted the spectra obtained without epfast and limited our spectral study to the 1 10 kev energy range .
llrlrrrr & & & & & & & + 1 & gx3394 & 0204730201 & 2004 march 16 & t & 135.067 & 93.20 & 31 36 & 40
43 + 2 & gx3394 & 0605610201 & 2009 march 26 & t & 33.529 & 32.234 & 31 37 & 39 45 + 3 & h1743322 & 0554110201 & 2008 sep .
29 & t & 22.148 & 13.5 & 32 35 & 39 44 + 4 & swiftj1753.50127 & 0311590901 & 2006 march 24 & t & 41.948 & 40.643 & 31 45 + 5 & swiftj1753.50127 & 0691740201 & 2012 sep . 10 &
t & 40.091 & 37.890 & 31 36 & 39 45 + 6 & swiftj1753.50127 & 0694930501 & 2012 oct .
08 & t & 30.938 & 28.740 & 31 36 & 39 45 + 7 & xtej1650500 & 0136140301 & 2001 sep .
13 & b & 24.947 & 23.201 & 30 44 + 8 & xtej1752223 & 0653110101 & 2010 april 06 &
t & 41.917 & 19.700 & 30 46 + notes : + @xmath6 : t for timing mode , b for burst mode + @xmath7 : exposure used in this study + @xmath8 : detector columns from which source photons have been selected [ tab : obs ] llrrl & & & & l@xmath7 + 1 & gx3394 & @xmath9 & @xmath10 & l@xmath11 + 1 & gx3394 & @xmath12 & @xmath13 & l@xmath14 + 1 & gx3394 & @xmath15 & @xmath16 & l@xmath17 + 2 & gx3394 & @xmath18 & @xmath19 & l@xmath11 + 2 & gx3394 & @xmath20 & @xmath21 & l@xmath17 + 2 & gx3394 & @xmath22 & @xmath23 & l@xmath14 + 3 & h1743322 & @xmath24 & @xmath25 & l@xmath11 + 3 & h1743322 & @xmath26 & @xmath27 & l@xmath28 + 3 & h1743322 & @xmath29 & @xmath30 & l@xmath17 + 4 & swift1753.50127 & @xmath31 & @xmath32 & l@xmath11 + 4 & swift1753.50127 & @xmath33 & @xmath34 & l@xmath14 + 5 & swift1753.50127 & @xmath35 & @xmath36 & l@xmath11 + 5 & swift1753.50127 & @xmath37 & @xmath38 & l@xmath14 + 6 & swift1753.50127 & @xmath39 & @xmath40 & l@xmath11 + 6 & swift1753.50127 & @xmath41 & @xmath42 & l@xmath14 + 7 & xte1650500 & @xmath43 & @xmath44 & l@xmath11 + 8 & xtej1752223 & @xmath45 & @xmath46 & l@xmath11 + 8 & xtej1752223 & @xmath47 & @xmath48 & l@xmath17 + 8 & xtej1752223 & @xmath49 & @xmath50 & l@xmath14 + notes : + l@xmath7 : pds component : l@xmath11 , l@xmath17 , and l@xmath14 are used in the way shown in fig .
[ fig : pdscomp ] , while l@xmath28 denotes the harmonic of the qpo + [ tab : nub ]
investigating the pds of the individual sources in the two energy bands , we find that in general the overall shape of the components is consistent between the soft ( 1 2 kev ) and hard ( 4 8 kev ) band ( see fig .
[ fig : pds ] ) .
for some observations , an additional qpo or peaked noise component is present in one of the two energy bands but missing in the other one . in order to study the shapes of the pds in a more quantitative way
, we determined the characteristic frequency , defined by @xmath51 , where @xmath52 is the centroid frequency , and @xmath53 is the half width at half maximum @xcite , of each component . in the case of bln ,
where @xmath54 , the characteristic frequency equals the break frequency .
a visualization of the different components fitted to the hard band pds of gx3394 and named following the nomenclature used in @xcite and @xcite can be found in fig . [
fig : pdscomp ] .
figure [ fig : numax ] ( see also tab . [
tab : nub ] ) shows the characteristic frequency obtained in the soft band versus the one derived from the hard band .
apart from the 2006 observation of swiftj1753.5 - 0127 and the observation of 1743 , we detect at least one component for which the characteristic frequency obtained in the soft band is lower than the one obtained in the hard band . for the remaining noise components , the characteristic frequencies in both bands are equal within errors . in cases where the characteristic frequency in the soft band is lower than in the hard band ,
this is always true for the component with the highest characteristic frequency ( l@xmath11 ) .
@xcite studied the variability of the 2004 observation of gx3394 and the 2006 observation of swiftj1753.50127 in the 0.5 1 kev and 2 10 kev bands .
they reported qualitatively , without obtaining characteristic frequencies through fits of the pds , that in the case of gx3394 the higher frequency component in the pds appears `` to be shifted to even higher frequencies in the hard band '' , while in the case of swiftj1753.50127 the soft and hard pds appear to overlap more closely at higher frequencies " . in a study of the smbh system ark 564
a similar energy dependence of the characteristic frequency of the higher frequency component has been found , while the lower frequency component did not show any energy dependence between the 0.6 2 and 2 10 kev bands @xcite .
xte j1753 - 223 that has been observed during outburst decay shows the highest break frequency and rather big error bars .
a clear energy dependence of the characteristic frequency can be seen in the four observations that show break frequencies between 1 and 2 hz in the hard band .
to rule out the possibility that the change of the characteristic frequency is mimicked by the emergence of a type - c qpo in the hard band , we added an additional lorentzian to the fits of the hard band pds and redetermined the characteristic frequencies .
the allowed frequency range for the added lorentzian was obtained from the relation of characteristic frequency and centroid qpo frequency presented in fig .
11 of @xcite . for each observation
, we used the lowest characteristic frequency found in the soft band to select the range of allowed centroid qpo frequencies .
in addition the added lorentzian had to be narrow .
we found that the changes of the characteristic frequency caused by the added lorentzian are within the errors of the values without added component .
we estimated the significance of the added lorentzian from its normalisation .
this showed that the added lorentzian is not significant at all ( 0.7 1.4 @xmath55 ) .
we also checked for the presence of additional disc variability at low frequencies in the soft band by adding a power law component to the model used to fit the pds .
a power law component was used to test for disc variability , as in the hss , which is dominated by emission of the accretion disc , the pds is consistent with power law noise at all frequencies . in all observations
fitting returned the normalisation of the power law component as zero , which implies that none of the pds shows additional disc variability at low energies . in fig .
[ fig : diff ] we show the difference in the characteristic frequency between the hard and soft band , determined by @xmath56 , versus the characteristic frequency in hard band .
as can be seen from fig .
[ fig : diff ] there is no clear correlation between the change of the characteristic frequency and the characteristic frequency itself . using the characteristic frequency in the softer band instead of
the one from the hard band on the x - axis leads to a shift to lower frequencies by @xmath57 for points with @xmath58 and to higher frequencies for those with @xmath59 .
in addition , fig .
[ fig : diff ] also shows the relative changes of the characteristic frequency , defined as @xmath60 versus the characteristic frequency in hard band .
again no clear correlation between the parameters shown can be seen .
in addition to the energy dependence of the characteristic frequency , we investigate the energy dependence of the variability amplitude of the bln .
the rms spectra of all pds components are shown in fig .
[ fig : rms_spec ] .
the bln component with the highest characteristic frequency ( l@xmath11 ) is indicated by ( red ) crosses . in the observations of 339 , 1743 , and the september 2012 observation of swiftj1753.50127 this component does not show a strong energy dependence and it is either rather flat or slowly decreasing with increasing energy .
this behaviour of the rms spectra has been observed in the hard state observations presented in @xcite .
the remaining two observations of swiftj1753.50127 show a jump in variability around 4 5 kev , while variability remains rather constant at lower and higher energies . a behaviour observed in the hard intermediate state @xcite .
the observations of xtej1650500 and xtej1752223 show much lower variability in the 1 2 kev band compared to the rather constant variability above 2 kev .
we performed our investigation of the /epic - pn energy spectra within isis v. 1.6.2 @xcite in the 1 10 kev energy range , taking into account a systematic error of 1% . to obtain comparable spectral parameters
, we fitted all spectra with the same model consisting of an absorbed disc blackbody plus thermal comptonisation component ( nthcomp ; * ? ? ?
* ; * ? ? ?
* ) , including a high - energy cut - off .
the foreground absorption is modeled with tbabs @xcite and the values of @xmath61 are taken from the literature : @xmath62@xmath63 @xmath64 for xtej1650500 @xcite , @xmath65@xmath63 @xmath64 for swiftj1753.50127 @xcite , @xmath66@xmath63 @xmath64 for 339 @xcite , @xmath67@xmath63 @xmath64 for xtej1752223 @xcite and @xmath68@xmath69 @xmath64 for h1743322 @xcite .
the temperature at the inner edge of the accretion disc is taken as temperature of the seed photons for the comptonised component .
in addition , a gaussian is added to model the residual visible in all observations at @xmath52 kev ( see sect .
[ subsec : specana ] ) . in the case of 339
a second gaussian is need to fit the fe - emission line at 6.4 kev . in the case of 1743
we used the data with correction of cti effects at low energies , and fitted those with the same model that has been used for 339 . for 1743
the obtained fit implies a large disc normalization ( @xmath70 ) and a very low inner edge temperature ( @xmath71kev ) .
a more detailed study of the spectrum showed that the disc blackbody component is not need to obtain a decent fit .
hence , we removed this component , and fixed the seed temperature for the comptonization model at the disc temperature mentioned above .
figure [ fig : spec ] shows the behaviour of the photon index , inner disc temperature and normalization of the disc component depending on the difference in the characteristic frequency @xmath57 of the component with the highest characteristic frequency .
the values for 1743 are omitted in this figure as no disc component was need to obtain an acceptable fit for this source .
for the three observations of swiftj1753.5 - 0127 a slide increase in the disc normalization with increasing @xmath57 is visible .
this behaviour is not observed in the two observations of 339 , which span a smaller range in @xmath57 than the ones of swiftj1753.5 - 0127 .
taken into account all observations again no clear correlation is evident . having a look at the ratio of the flux contributed by the disc blackbody component to the one coming for the componized component in the soft ( 1 2 kev ) band ( the values are given in the last row of table [ tab : specpar ] ) , we find that this ratio is below @xmath57% for the two observations for which the characteristic frequencies are consistent within errors ( observation of 1743 and 2006 observation of swiftj1753.5@xmath720127 ) , while it is above 20% for those observations where we found @xmath73 . in the case of xtej1650500 and xtej1752223 , the ratio exceeds one hundred per cent , which means that the flux of the disc component contributes more than 50% of the total flux in the soft band . for xtej1752223
this high value might be attributed to the fact that the source is observed during outburst decay , but this is not true for xtej1650500 which was observed during outburst rise . in fig.[fig : nuflux ] we show the flux ratio versus the absolute and relative difference in the characteristic frequency of the component with the highest characteristic frequency . even ignoring the two data points with a flux ratio larger than one ,
there no clear correlation that a larger absolute or relative change of the characteristic frequency would be related to a larger flux ratio .
lllllllll & & & & & & & & + n@xmath74 & @xmath75 & @xmath76 & @xmath77 & @xmath78 & @xmath79 & @xmath80 & @xmath81 & + t@xmath82 [ kev ] & @xmath83 & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 & @xmath89 & 0.001@xmath90 + e@xmath91 [ kev ] & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 & @xmath97 & @xmath98 & @xmath99 + e@xmath100 [ kev ] & @xmath101 & @xmath102 & @xmath72 & @xmath103 & @xmath104 & @xmath105 & @xmath106 & @xmath107 + n@xmath108 & @xmath109 & @xmath110 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 + @xmath117 & @xmath118 & @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125 + kt@xmath126 [ kev ] & @xmath127 & @xmath128 & @xmath129 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & @xmath134 + @xmath135/dof & @xmath136 & @xmath137 & @xmath138 & @xmath139 & @xmath140 & @xmath141 & @xmath142 & @xmath143 + f@xmath74/f@xmath144 $ ] & 23.1 & 20.0 & 6.8 & 31.6 & 31.0 & 167.1 & 172.8 & 0 + notes : + @xmath7 : ratio of the flux contributed by the disc emission to the one of the comptonized emission in the 1 2 kev band + @xmath90 : value used as seed temperature in the nthcomp model ( fixed ) [ tab : specpar ] to investigate variability of spectral components we derived covariance spectra on long ( segments of 270 s with 2.7 s time bins ) and short ( segments of 4 s with 0.1 s time bins ) time scales ( fig .
[ fig : cove_spec ] ) .
the covariance spectra have been fitted with the same model used for the averaged energy spectra in section [ sect : espec ] .
we adjusted the binning of the response files to the number of bins present in the covariance spectra using the ftool rbnrmf .
in the cases where 50 bins have been used ( 339 and 1743 ) the rebinding led to an artificial feature consisting of a spike and a trough - like structure at energies between 5.8 and 6.8 kev ( the energy range of the iron k@xmath145 emission ) .
hence , this energy range has been ignored in the fits of the covariance spectra .
for both observations of 339 it is not possible to obtain formally acceptable fits as the data points stagger around the obtained best fit at energies below 2 2.5 kev . in the spectral fitting of all covariance
spectra a systematic uncertainty of one per cent has been included .
the covariance spectra of xtej1650500 and xtej1752223 do not require a high - energy cut - off component to obtain acceptable fits .
for these two observations the photon indices and inner disc temperatures obtained from the covariance spectra are larger than those obtained from the mean energy spectra . for the remaining observations
a comparison of the behaviour of the photon index and inner disc temperature between short and long term covariance spectra as well as between covariance and mean energy spectra can be found in table [ tab : speccomp ] .
lllllllll & & & & & & & & + + n@xmath74 & @xmath146 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath152 & + t@xmath82 [ kev ] & @xmath153 & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath158 & @xmath159 & 0.001@xmath90 + e@xmath91 [ kev ] & @xmath95 & @xmath160 & @xmath161 & @xmath162 & @xmath163 & @xmath72 & @xmath72 & @xmath164 + e@xmath100 [ kev ] & @xmath165 & @xmath160 & @xmath160 & @xmath166 & @xmath160 & @xmath72 & @xmath72 & @xmath167 + n@xmath108 & @xmath168 & @xmath169 & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 + @xmath117 & @xmath176 & @xmath177 & @xmath178 & @xmath179 & @xmath180 & @xmath181 & @xmath182 & @xmath183 + kt@xmath126 [ kev ] & @xmath184 & @xmath185 & @xmath163 & @xmath186 & @xmath187 & @xmath163 & @xmath163 & @xmath188 + @xmath135/dof & @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath193 & @xmath194 & @xmath195 & @xmath196 + + n@xmath74 & @xmath197 & @xmath198 & @xmath199 & @xmath200 & @xmath201 & @xmath202 & @xmath203 & + t@xmath82 [ kev ] & @xmath204 & @xmath205 & @xmath206 & @xmath207 & @xmath208 & @xmath209 & @xmath210 & 0.001@xmath90 + e@xmath91 [ kev ] & @xmath211 & @xmath160 & @xmath212 & @xmath213 & @xmath160 & @xmath72 & @xmath72 & @xmath214 + e@xmath100 [ kev ] & @xmath215 & @xmath160 & @xmath160 & @xmath160 & @xmath160 & @xmath72 & @xmath72 & @xmath216 + n@xmath108 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & @xmath223 & @xmath224 + @xmath117 & @xmath225 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & @xmath232 + kt@xmath126 [ kev ] & @xmath233 & @xmath234 & @xmath235 & @xmath187 & @xmath236 & @xmath163 & @xmath237 & @xmath238 + @xmath135/dof & @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 & @xmath244 & @xmath245 & @xmath246 + [ tab : covspecpar ] notes : + @xmath90 : value used as seed temperature in the nthcomp model ( fixed ) lllllll & & & & & & + + @xmath117 & smaller & agree & agree ( s ) & agree ( s ) & @xmath247 & agree + & & & smaller ( l ) & bigger ( l ) & & + t@xmath82 & smaller & agree ( s ) & agree & smaller & smaller & smaller + & & smaller ( l ) & & & & + + @xmath117 & agree & agree & agree & agree & do not agree & agree + t@xmath82 & do not agree & agree & agree & agree & agree & agree + [ tab : speccomp ] notes : + @xmath7 : for the october 2012 observation of swiftj1753.5 - 0127 the photon index obtained from the mean energy spectrum lies between the values obtained from the covariance spectra and agrees within error bars with the one obtained from long scale covariance spectrum .
+ ( s ) , ( l ) : short , long term scale covariance spectra , respectively + agree : short for : agree within error bars + table should be read like this : for the 2004 observation of 339 the photon indices obtained from the long and short term covariance spectra are smaller than the one obtained from the mean energy spectrum .
the consistency of photon indices of short and long time scale covariance spectra of the 2004 observation of 339 and the 2006 observation of swiftj1753.5 - 0127 agrees with the results presented by @xcite .
they also obtained a bigger photon index from the mean energy spectrum compared to the one obtained from covariance spectra for the 2006 observation of swiftj1753.5 - 0127 . in the case of the 2004 observation of 339
@xcite found a smaller photon index from the mean energy spectrum compared to the one obtained from covariance spectra , contrary to what we found .
this difference can be related to the inclusion of a reflection component in the study of @xcite that becomes obvious at higher energies covered by rxte but inaccessible with .
apart form the observation of xtej1650 - 500 and the october 2012 observation of swiftj1753.5 - 0127 the disc normalisation obtained from the long time scale covariance spectra are larger than the one obtained from the short time scale covariance spectra , although they all agree within their rather big error bars . in case of consistent photon indices
, this higher disc blackbody normalisation indicates additional disc variability on long time scales @xcite . a model - independent way to compare variability on long and short time scales are covariance ratios , which we show in fig .
[ fig : cov_ratio ] . the observations of 339 , xtej1752223 and the 2006 and october 2012 observations of swiftj1753.50127
show a clear increase in the covariance ratio at energies below about one kev .
apart from the october 2012 observations of swiftj1753.50127 we found a higher disc blackbody normalisation for the long time scale covariance spectra in these observations , which is consistent with the increase found in the covariance ratios .
this increase has been interpreted as a sign of additional disc variability on longer time scales by @xcite . in case of the october 2012 observation of swiftj1753.50127 we found a change of the photon index between short and long time scale covariance spectra which may explain why the additional long - term disc variability observed in the covariance ratio
does not show up in a higher disc normalisation in the long time scale covariance spectrum .
we also found significantly different photon indices for the short and long time scale covariance spectra of xtej1752223 .
as changes in the photon index indicate changes of the overall spectral shape , the difference in photon index may explain the increase of covariance ratio with increasing energy seen in xtej1752223 .
at the beginning of this section we would like to summarise the main results : * in obs .
1 , 2 , 5 , 6 , 7 , 8 the band limited noise component with the highest characteristic frequency shows a lower characteristic frequency in the soft band compared to the one observed in the hard band . * in all these observations
the ratio of the disc blackbody flux to the flux of the comptonized component in the soft band exceeded @xmath510% . in obs .
7 and 8 it even exceeds 100 per cent . in obs . 3 and 4 the ratio is below 10 per cent .
* in obs . 1 , 2 , 3 , 5 the rms spectrum is either flat or slowly decreasing with energy . obs .
4 and 6 show a jump in variability around 4 5 kev , while variability remains rather constant at lower and higher energies .
obs . 7 and 8 show much lower variability in the 1 2 kev band compared to the rather constant variability above 2 kev .
* the covariance ratios of obs .
1 , 2 , 4 , 6 , 8 show a clear increase at lower energies . in obs . 7 and 8 the photon indices and inner disc temperatures obtained from the covariance spectra are larger than those obtained from the mean energy spectra .
obs . 1 , 2 , 5 , 6
do not show a general correlation between spectral parameters obtained from covariance and mean energy spectra .
our investigations of the characteristic frequency of the band limited noise in a hard and soft energy band revealed that for observations where the ratio of the disc blackbody flux to the flux of the comptonized component in the soft band exceeded @xmath510% , the band limited noise component with the highest characteristic frequency shows a lower characteristic frequency in the soft band compared to the one observed in the hard band .
the energy dependence of the characteristic frequency is more obvious at characteristic frequencies above 1 hz in the hard band .
the energy dependence of the characteristic frequency observed in the 2004 observation of gx3394 and the 2006 observation of swiftj1753.5 - 0127 concur with the energy dependence found in a qualitative study of the pds shape that was based on the same observations @xcite .
this study of wilkinson & uttley also presented the increase of covariance ratios at lower energies and interpreted it as additional variability of the accretion disc relative to the power - law component at low frequencies ( @xmath41 hz ) , while the soft band blackbody variations at frequencies above 1 hz are probably mostly produced by x - ray heating caused by the reprocessing of comptonized photons in the accretion disc . in a study of xtej1650 - 500 and xtej1550 - 564 , based on rxte / pca data
, @xcite showed pds in the @xmath52 @xmath513 and @xmath513
@xmath5 25 kev bands for different states .
it is interesting to notice that for their lhs pds of xtej1650 - 500 the pds of their hard band lies below the pds of their soft band ( the power in the hard band is smaller than the power in the soft band at the same frequency ) , while for the energy bands used here the soft band pds lies below the hard band pds ( see fig .
[ fig : pds ] ) .
in addition to the pds @xcite also showed rms spectra for different states . in their study of xtej1650 - 500 and xtej1550 - 564 they observed flat rms spectra and an rms slightly decreasing with increasing energy in the lhs .
we found a similar behaviour in the observations of 339 , 1743 , and the september 2012 observation of swiftj1753.5 - 0127 .
the behaviour of the rms observed in the remaining observations of swiftj1753.5 - 0127 corresponds to the one of the hims in the @xcite study
. the observed energy dependence of the characteristic frequency which is more obvious at characteristic frequencies above 1 hz in the hard band can be either explained by variable seed photon input for the comptonized photons in different energy bands @xcite or by x - ray heating of the accretion disc caused by the reprocessing of comptonized photons @xcite .
the variability properties observed in our study show characteristics of variability associated with comptonized photons down to the lowest observed energies , that the pds can be described by bln and qpos in all energy bands and that a power - law shape observed in the hss when disc variability dominates in not needed .
the energy dependence of the characteristic frequency suggests that the seed photon input for the comptonized photons varies between different energy bands , as has been discussed in @xcite based on rxte data .
it is therefore expected that such an effect would become more obvious when the corona is cooled down and the electron temperature is getting lower . thus the energy dependence becomes more obvious in narrower energy bands .
the presence of the energy dependence of the characteristic frequency can be interpreted within the picture where the photons in the soft and hard energy bands come from different locations in the system .
a schematic sketch of this picture , which was also used in our recent studies @xcite , is given in fig .
[ fig : sketch ] .
when the thermal disc component emerges in the soft band of but does not dominate , a significant number of photons in the soft energy band will still come from the comptonization component ( originating either from an optically thin hot corona ( see * ? ? ? * ) or from a jet flow ( see * ? ? ? * ) ) .
however , the soft band photons should origin further away from the black hole than the hard band ones and thus suffer less up - scattering .
this brings lower characteristic frequencies and softer energies together .
the change of the characteristic frequency can be interpreted as a hint of a temperature gradient in the comptonization component .
the observation that the energy dependence of the characteristic frequency is mainly observed at higher frequencies ( @xmath01 hz ) can be interpreted as a moving in of the inner disc radius during outburst evolution . in early outburst stages
the disc ends far away from the black hole and the characteristic frequency , which is below 1 hz , is consistent between both bands , since the photons in both bands experience a similar number of scatterings . with ongoing evolution of the outburst the boundary region between the disc and
the comptonizing corona moves inwards and the characteristic frequency as well as the contribution of the direct disc emission in the soft band increases @xcite .
notice that the radius at which the cold disc ends may be not the radius at which the cold disc terminates , since a hot flow or corona would cover the innermost cold disc so the radius one determines from the cut - off frequency of the power - law noise would correspond to the radius to which the hot flow or corona extends ( while the disc can reach down to the isco as assumed in * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
interpreting the energy dependence of the characteristic frequency by additional intrinsic disc variability at low energies is not a convincing alternative , as intrinsic disc variability contributes at low frequencies @xcite while the observed energy dependence of the characteristic frequency is more pronounced at frequencies above 1 hz . in addition , the subsample of observations that show an increased covariance ratio at low energies does not agree with the subsample of observations that show the energy dependence of the characteristic frequency .
we would like to point out that the additional disc variability on long time scales shows up only in the covariance spectra and ratios , but that there is no hint of an additional disc component in the pds at low energies .
as pds fitting does not require any disc variability ( see sect .
[ subsec : time_prop ] ) , we can exclude that the observed energy dependence of the characteristic frequency is caused by underlying disc variability not taken into account properly during pds fitting .
thus we prefer to interpret the energy dependence of the characteristic frequency to be caused by variable seed photon input for the comptonized photons in different energy bands .
a challenge to our interpretation might be the observations of xte j1650@xmath72500 and xte j1752@xmath72223 . in both observations
the contribution of the disc emission to the overall emission in the soft band exceeds 50 per cent , and based on the results obtained in @xcite and @xcite we would expect that the sources are in the hard intermediate state .
the fact that the signal - to - noise ratio at higher energies is lower in these two observations compared to the other observations used in this study can not explain why the contribution of the disc emission to the overall emission in the soft band exceeds 50 per cent , as taking the error bars on the spectral parameters into account does not affect the flux ratio to always exceed 50 per cent .
we notice that for these two observations the variability amplitude in the softest band is lower than the variability amplitude at higher energies .
furthermore , fitting of the covariance spectra of these two sources does not require a high - energy cut - off and the photon indices and inner disc temperatures obtained from the covariance spectra are larger than those obtained from the mean energy spectra . for xte j1752@xmath72223
this discrepancy can be explained by the fact that xte j1752@xmath72223 is observed during outburst decay returning to the lhs , while the results of @xcite and @xcite are based on the evolution from the hard to the soft state . in the case of xte j1650@xmath72500 , it is more difficult to find an explanation as the source is observed during outburst rise when it evolves from the lhs to the hss .
a possible explanation can be that in this source the contribution of the disc emission to the soft band is in general higher than in those sources studied by @xcite and @xcite .
a thorough investigation of this possibility as well as a detailed study of the differences between outburst rise and decay will be the targets of future studies .
please notice that in these two observations the signal - to - noise ratio at higher energies is lower compared to the other observations used in this study .
however , the lower signal - to - noise ratio can not explain why the contribution of the disc emission to the overall emission in the soft band exceeds 50 per cent .
regarding the absence of correlations between the characteristic frequencies in different energy bands and between the characteristic frequency and spectral parameters , it is mainly the data points of 339 with well constraint parameters that do not agree with possible trends seen in the remaining data points with bigger uncertainties .
higher quality data that would allow to constrain the characteristic frequency more precisely would be helpful to foster the absence of correlations . in conclusion
, the energy dependence of the break frequency of the band - limited noise component supports a picture that the power spectra in black hole x - ray binaries depend on which spectral components we are looking at .
energy - resolved timing observations can be sensitive enough to trace not only the accretion geometry by detecting power - law noise as evidence of the emergence of a disc component but can also probe the properties of the corona from studies of the band - limited noise break frequency . in this work we provide evidence that the energy dependence of the characteristic frequency may be used to probe the extension of the corona .
we would like to acknowledge useful discussions with jon miller , mike novak , diego altamirano , omer blaes and tomaso belloni .
this work makes use of software tools provided by simon vaughan .
this work was supported by the national natural science foundation of china under grant no .
11073043 , 11333005 , and 11350110498 , by strategic priority research program `` the emergence of cosmological structures '' under grant no . xdb09000000 and the xtp project under grant
xda04060604 , by the shanghai astronomical observatory key project and by the chinese academy of sciences fellowship for young international scientists grant . | black hole low - mass x - ray binaries show a variety of variability features , which manifest themselves as narrow peak - like structures superposed on broad noise components in power density spectra in the hard x - ray emission . in this work we study variability properties of the band - limited noise component during the low - hard state for a sample of black hole x - ray binaries .
we investigate the characteristic frequency and amplitude of the band - limited noise component and study covariance spectra . for observations that show a noise component with a characteristic frequency above one hz in the hard energy band ( 4 8 kev ) we found this very same component at a lower frequency in the soft band ( 1 2 kev ) .
this difference in characteristic frequency is an indication that while both the soft and the hard band photons contribute to the same band - limited noise component , which likely represents the modulation of the mass accretion rate , the soft photons origin actually further away from the black hole than the hard photons .
thus the soft photons are characterized by larger radii , lower frequencies and softer energies , and are probably associated with a smaller optical depth for comptonisation up - scattering from the outer layer of the corona , or suggesting of a temperature gradient of the corona .
we interpret this energy dependence within the picture of energy - dependent power density states as a hint that the contribution of the up - scattered photons originating in the outskirts of the comptonising corona to the overall emission in the soft band is becoming significant .
[ firstpage ] x - rays : binaries x - rays : individual : 1743 , 339 , , xtej1752 - 223 , swiftj1753.5 - 0127 binaries : close black hole physics |
Chance the Rapper is one charitable guy. Last year, the Chicago native donated millions of dollars to Chicago Public Schools and to its arts programs. He has become the superhero to swoop in at just the right time, the rapper with millions who saves the day. And he’s doing it again for former Chicago local news site and Gothamist sister site, the Chicagoist.
Per WNYC, Chance is buying the assets for the news site, which WNYC had previously taken over.
Last fall, Gothamist, its sister sites, and site DNAinfo were shut down suddenly by C.E.O Joe Ricketts. The billionaire decided to discontinue Gothamist, and, effectively, Chicagoist in a sudden move that shocked employees. As Huffington Post noted then, the decision put 115 staffers out of work. In an interview with The New York Times, a DNAInfo spokesperson cited the staff’s recent decision to “unionize is simply another competitive obstacle making it harder for the business to be financially successful.” WNYC acquired Gothamist in February and has continued running it as a news organization. WNYC also acquired the assets for Chicagoist at the same time. Though Gothamist is a live site again, Chicagoist has been dormant since November.
“I’m extremely excited to be continuing the work of the Chicagoist, an integral local platform for Chicago news, events, and entertainment,” Chance the Rapper said, via the press release. “WNYC’s commitment to finding homes for the ‘ist’ brands, including Chicagoist, was an essential part of continuing the legacy and integrity of the site. I look forward to re-launching it and bringing the people of Chicago an independent media outlet focused on amplifying diverse voices and content.”
Appropriately, he announced his latest financial heroism in a new single on his Web site called “I Might Need Security.” ||||| Breaking News Emails Get breaking news alerts and special reports. The news and stories that matter, delivered weekday mornings.
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Chance the Rapper is now a local-media mogul.
He announced the deal to buy Chicagoist, a local news site covering the Windy City, in one of his four new tracks released at midnight ET Wednesday. In the song, “I Might Need Security,” he explains why.
“I bought the Chicagoist just to run you racist b-----s outta business,” Chance says in the song, which includes a backing-vocal loop throughout that repeats “f--k you.”
Chicagoist.com has been dormant since November 2017, when owner Joe Ricketts, the billionaire founder of TD Ameritrade, summarily shut down the site along with Gothamist, DNAinfo and others. That came after the sites’ staffers voted to join the Writers Guild of America East as their collective-bargaining rep.
In a statement, Chance the Rapper said, “I’m extremely excited to be continuing the work of the Chicagoist, an integral local platform for Chicago news, events and entertainment… I look forward to relaunching it and bringing the people of Chicago an independent media outlet focused on amplifying diverse voices and content.”
Chance the Rapper acquired Chicagoist from New York Public Radio’s WNYC, through the artist’s newly formed Social Media LLC, which aims to promote local investigative journalism, diversity, and representation for people of color in media. Terms of the deal for Chicagoist weren’t disclosed.
The 25-year-old rapper-songwriter-actor-producer, born Chancelor Bennett, hails from Chicago’s West Chatham neighborhood.
WNYC had initially taken ownership of the Chicagoist assets, including the site’s archives, internet domain, and social-media channels, when it acquired Gothamist and its associated sites in February. The public radio station has since relaunched Gothamist in New York City and hosts the archives of DNAinfo. (LAist.com is now part of Southern California Public Radio’s KPCC, and DCist.com is owned by Washington, D.C., public radio station WAMU.)
“We are delighted that the Chicagoist assets are finding a new home in the hands of a proud Chicagoan,” Laura Walker, president and CEO of New York Public Radio, which includes WNYC, said in a statement released early Thursday.
“WNYC has a strong commitment to local journalism and building community, and we are pleased that these assets will be used to support local coverage in the great city of Chicago.” ||||| "This whole 'tell it like it is' business, that's nonsense" said the former First Lady, who then diplomatically assured us she had no one in particular in mind. | – Chance the Rapper is also a songwriter, actor, and producer—and as of Wednesday, he's in the media business, too. The 25-year-old rapper, who is from Chicago, announced his purchase of Chicagoist, a local news site that former owner Joe Ricketts shut down in November 2017 along with Gothamist, DNAinfo, and other sites. The rapper calls it an "integral local platform" and notes that when he relaunches it, it will be "an independent media outlet focused on amplifying diverse voices and content." He also mentioned the deal in one of four new tracks released Wednesday, NBC News reports: "I bought the Chicagoist just to run you racist b-----s outta business," he says in "I Might Need Security." Vanity Fair is hailing the move as saving Chicago journalism, "or at least a significant part of it." |
women are making up an increasing part of the
acquired immune deficiency syndrome ( aids ) epidemic in the
united states . in 2001 hiv infection was the 6th leading cause of death among all women aged 2534 years and the 4th
leading cause of death among all women aged 3544 years . by the
end of 2003 ,
women and adolescents represented 22% of the
people living with aids . with the considerable number of women of childbearing age with aids ,
as we have made great strides to
reduce vertical transmission to less than 2% in the us , there
has been an increased focus on maternal health .
while childbirth in developed countries is relatively safe , there
exists a risk of morbidity .
of significance , cesarean section is
associated with an increased risk and , in particular , infectious
morbidity . risk factors for morbidity include prolonged
rupture of membranes , obesity , immune suppression , and type of
anesthesia , nonelective cesarean delivery , and a number of vaginal
examinations among others .
women with aids are severely
immunocompromised and may be at increased risk for postpartum
morbidity . while studies have indicated that the risk may be
greater for hiv - infected patients , few studies have estimated the
risk among the most immunocompromised of these patients .
this study sought to estimate the risk of
postpartum morbidity among patients with aids compared to more
immunocompetent hiv - infected patients and hiv - uninfected women .
an
additional objective was to determine the impact of their
diagnosis on the management of puerperal infections .
this retrospective chart review was approved by the institutional
review board at wayne state university .
cases consisted
of patients with a diagnosis of hiv infection who delivered from
january 1 , 2000june 1 , 2005 .
uninfected controls were selected
utilizing a computerized perinatal database and random number
allocation .
charts with incomplete medical records or undocumented
hiv testing during the current pregnancy were excluded .
medical
charts were reviewed for demographic data , clinical
characteristics , antenatal course , delivery data , and postpartum
management . among hiv - infected patients ,
treatment data were
recorded including cd4 cell count , hiv-1 rna viral load
measurements , and use of highly active
antiretroviral therapy ( haart ) .
group 1 consisted of patients
diagnosed with aids as defined by a current or prior history of a
cd4 cell count < 200 cells/l or an opportunistic infection .
group 2 consisted of relatively immunocompetent
hiv - infected patients ( cd4 200 cells/l ) and group 3
consisted of hiv - uninfected patients .
febrile morbidity was
defined as a temperature 38.0c 24 hours or greater
postdelivery .
postpartum endometritis was defined as persistently
elevated temperature with uterine tenderness in the absence of
evidence of a nonuterine etiology .
postpartum morbidity was
defined as anemia requiring a blood transfusion , endometritis ,
other infectious morbidity , wound complication , repeat admission
for a pregnancy - related complication within 6 weeks postdelivery ,
or unexpected surgery .
infectious morbidity was defined as the
presence of endometritis , wound infection , or pneumonia .
data
regarding the indication for use of intravenous antibiotics , the
use of imaging in assessment of febrile morbidity , and the time
from the first fever until initiation of intravenous ( iv )
antibiotics were collected as well .
postdelivery length of stay
( los ) was defined as the time from delivery until discharge from
the hospital .
statistical analysis was performed utilizing the spss statistical
software ( version 14.0 spss inc , chicago , il ) .
wilcoxon ranks
sum test and the kruskal - wallis test were utilized for discrete
and continuous variables .
the variables included were government
insurance , age , body mass index ( bmi ) , nulliparity , drug abuse
history , smoking , cesarean section after labor , intrapartum fever ,
general anesthesia , duration of membrane rupture , and cesarean
delivery .
there were 148 hiv - infected patients with complete data . of that
group ,
33 were diagnosed with aids by cdc criteria and 7 of those
women had symptomatic aids .
hiv - infected women were more likely to
smoke ( 24.2 and 28.9 versus 15.8% , p = .03 ) , have a drug
abuse history ( 33.3 and 24.6 versus 5.3% , p < .0001 ) ,
were older ( median 28 and 28 versus 24 years , p < .0001 ) , and had
a lower bmi ( median 27 and 27 versus 32 kg / m ,
p < .0001 ) .
overall , 82% of the hiv - infected women were
adherent with their antretroviral therapy .
women with aids were more likely
to have a cesarean delivery ( 59.4 versus 35.1 and 15.8% ,
p < .0001 ) and there was no difference in the use of prophylactic
antibiotics at the time of cesarean section . among women with a
vaginal delivery , patients with aids had a shorter duration of
rupture of membranes ( median 50 minutes versus 63 and 193 minutes ,
p < .0001 ) but there was no difference in the number of vaginal
exams or the duration of labor .
women with aids were more likely
to have a postpartum morbidity ( 32.3 versus 19.3 and
13.2% , p = .03 ) or an infectious morbidity ( 22.6 versus
11.54 and 5.3% , p = .007 ) .
the highest rate of infectious
morbidity was among women with symptomatic aids ( 66% ) .
there
was no difference in febrile morbidity , hemorrhage , wound
complications , and multiple complications among the three groups .
women with aids were more likely to have radiological imaging in
the evaluation of febrile morbidity and a resultant delay in
initiation of iv antibiotics but there was no difference in the
rate of antibiotic use ( table 3 ) . among the imaging
modalities ,
abdominal and pelvic computed axial tomography was
performed in 4 of the 19 of the patients , yielding the diagnosis
of a pelvic abscess in one patient and a small bowel obstruction
in another .
two patients had a head and neck magnetic resonance
imaging ( mri ) ; one demonstrated lesions suggestive of
cryptococcal meningitis . in a logistic regression controlling for
potential confounders , cesarean delivery ( or 19.5 , 95% ci
5.469.8 ) and not advanced hiv disease were associated with
an increased risk of postpartum morbidity ( see table 4 ) .
in particular , infectious morbidity was
diagnosed more frequently in women with advanced hiv disease than
in relatively immunocompetent hiv - infected women and in
hiv - uninfected women . when controlling for potential confounders ,
the majority of the risk appeared to be associated with cesarean
delivery and not hiv immune status . additionally , in the
management of postpartum febrile morbidity , there was an increased
use of imaging and a delay in initiation of antibiotics among
women with aids .
our finding is similar to a previously published study by
marcollet et al . in a retrospective review of 401 hiv - infected
women , marcollet et
al found that women with aids were more likely
to have febrile morbidity but there was no difference in
postpartum complications . in that study
watts et al in a study
of 497 women participating in the pediatric aids clinical trial
group study of hiv - infected women with a cd4 count below 500
cells/l demonstrated an increased risk of postpartum
morbidity but that risk was associated with cesarean delivery
. other studies that estimated risk focused only on
patients undergoing cesarean delivery .
in those studies , risk
appeared to be associated with the degree of immune suppression .
semprini et al in a study of 156 hiv - infected women undergoing
cesarean delivery and controlling for potential confounding
variables demonstrated that profound immunodeficiency ( defined as
a cd4 count below 200 cells/l ) was the predominant risk
factor for postpartum morbidity .
similarly ,
maiques - montesinos et al in a case control study of hiv - infected
women undergoing cesarean section demonstrated that the lowest
risk of morbidity was among hiv - infected women with a cd4 count
> 500 cells/l compared to more immunosuppressed patients .
the obvious inconsistencies in the findings among the
different studies cited may be related to differences in sample
size and patient population . in our study , we found an increased use of imaging in the
evaluation of febrile morbidity among women with aids and a
resultant delay in initiation of antibiotics .
the management of
febrile morbidity among these immunosuppressed women is a question
that has yet to be answered . in the uninfected population
,
prophylactic antibiotics have been demonstrated to decrease
perioperative morbidity associated with cesarean delivery
[ 2 , 10 ] .
however , those studies did not include the evaluation
of hiv - infected women .
our data indicate that interventions for
decreasing postcesarean infectious morbidity in women with aids
warrant investigation . in our cohort ,
the predominant indication for elective cesarean
delivery was a high viral load ( data not shown ) . in a randomized
trial , the european mode of delivery collaborative demonstrated a
50% reduction of vertical transmission with the use of
scheduled cesarean section .
the findings of these studies
resulted in the release of a committee opinion by the american
college of obstetricians and gynecologists , which indicated that
patients with a viral load > 1000 copies / ml should be counseled
and offered an elective cesarean section at 38 weeks of gestation
to decrease the risk of vertical transmission . since that time , the use of cesarean section as a tool in the prevention
of maternal - to - child transmission has increased . while this has been an effective part of the management to decrease
perinatal transmission , it does so at a maternal cost . among
high - risk patients who may present late for prenatal care , prompt
diagnosis and initiation of highly active retroviral treatment
play a crucial role .
in particular , women with advanced hiv
infection may have a higher baseline viral load or therapeutic
resistance requiring therapy manipulation .
effective therapy may decrease the number of women requiring a cesarean
delivery thus decreasing the associated perioperative morbidity .
this study is limited in that it is a retrospective review at a single
institution .
the patient population was particularly in
high risk with regards to entry to care and substance abuse .
as such ,
that information may have impacted their management decisions .
additionally , the small - sample sizes may preclude us from
detecting an association that may truly exist .
regardless , this
study illustrates that women with aids face additional risks with
cesarean delivery .
these findings would confer an additional duty
for the perinatal care provider to include more information about
these risks in the extensive counseling given to women with aids
when planning for mode of delivery prior to initiation of labor .
these findings emphasize further the importance of early
initiation of prenatal care to allow time for viral load suppression and
place hiv care providers for women of childbearing age
at the leading edge of this most important care initiative .
demographic data by group . data presented as n ( % ) or median ( interquartile range ) .
* represents comparison across groups . logistic regression modeling for risk factors for postpartum
morbidity . | objective . to investigate the postpartum morbidity and postpartum management of febrile morbidity associated with advanced hiv
infection . methods . a case control study of hiv infected women at a tertiary care center during january 2000june 2005 was performed .
postpartum morbidity was defined as endometritis , blood
transfusion , wound complication , readmission , infectious morbidity ,
or unexpected surgery .
results .
women in group 1 had aids ( n = 33 ) , group 2 were relatively immunocompetent hiv infected women ( n = 115 ) , and group 3 were uninfected women ( n = 152 ) .
group 1 was more likely to have a postpartum morbidity ( 32.3 versus 19.3 and 13.2% , p = .03 ) and to have postpartum imaging 18.8 versus 7.9 and 2.6% , p = .002 .
after controlling for potential confounders , cesarean delivery ( or 6.2 , 95% ci 2.1505.5 ) but not advanced hiv disease was associated with an increased risk of postpartum morbidity .
conclusion .
cesarean delivery and not advanced hiv disease increases the risk of postpartum morbidity in women with aids . |
the significance of magnetic fields in the dynamics of molecular clouds , and in star formation itself , is still uncertain .
theory and modelling have demonstrated that the strength of magnetic fields can have a profound influence on the processes which lead to the formation of stars .
there is a critical ratio of magnetic flux to mass above which magnetic fields can prevent gravitational collapse ( magnetically subcritical ) and below which they can not ( magnetically supercritical ; e.g. mouschovias & spitzer 1976 ) . redistribution of magnetic flux by ambipolar diffusion in a magnetically subcritical region can lead to loss of support against self - gravitation , and eventually to low mass star formation ( see shu , adams , & lizano 1987 , myers & goodman ( 1988 ) , porro & silvestro ( 1993 ) , ciolek & mouschovias 1993 , 1994 , 1995 , safier , mckee , & stahler 1997 , ciolek & knigl 1998 ) .
however , magnetically subcritical regions do not appear to reproduce observations of molecular cloud cores ( nakano 1998 ) , nor can this scenario explain the large fraction of cloud cores containing protostellar objects ( ward - thompson , motte , & andr 1999 ) .
it is possible that magnetically supercritical regions can be supported by turbulence ( bonazzola et al .
1987 , mckee & zweibel 1995 ) , which , to support a highly supercritical region , must be quite nonlinear ( myers & zweibel 2001 ) .
recent 3d simulations ( heitsch , mac low , & klessen 2001 , hereafter hmk , ostriker , stone , & gammie 2001 ) demonstrate that strong turbulence can provide large - scale support against collapse , though it can not prevent collapse on small scales .
the degree to which clouds are supported at all , of course , depends on their lifetimes and on the star formation rate ( ballesteros - paredes , hartmann , & vazquez - semadeni 1999 , elmegreen 2000 ) .
magnetic fields affect other dynamical processes in clouds besides gravitational collapse . in a strong magnetic field , weakly compressible turbulence is anisotropic ( sridhar & goldreich 1994 ; goldreich & sridhar 1995 , 1997 ) and energy dissipation is relatively more in waves and less in shocks ( smith , mac low , & zuev 2000 ) , although the overall rate of energy dissipation is not strongly dependent on the fieldstrength ( mac low 1999 ) .
magnetic fields may also play a role in collimating molecular outflows , and in transferring their momentum to the ambient medium .
the actual strength of magnetic fields in molecular clouds will ultimately determine which theoretical picture is correct , so observations of field strengths are crucial .
the integrated line of sight component of the field , weighted by the density of the tracer species , can be measured through the zeeman effect .
however , zeeman mapping is time consuming and requires high sensitivity and the presence of particular tracers ( most commonly oh ) .
moreover , this technique does not probe the field in the plane of the sky . for all of these reasons ,
it is desirable to have a complementary method of mapping the field . following the first detection by cudlip et al .
( 1982 ) , it has been shown that the polarization of the far infrared thermal radiation emitted by magnetically aligned dust grains can be used to map the orientation of the magnetic field on the plane of the sky ( see hildebrand et al 2000 for methodology ) .
this has been done , at various wavelengths , for a number of nearby clouds ( gonatas et al .
1990 , jarrett et al 1994 , dotson 1996 , rao et al .
1998 , schleuning 1998 , glenn , walker , & young 1999 , dotson et al .
2000 , schleuning et al .
2000 , valle , bastien , & greaves 2000 , ward - thompson et al 2000 ) and near the galactic center ( werner et al .
1988 , hildebrand et al . 1990 , 1993 , dowell 1997 , novak et al . 1997 , 2000 ) .
far infrared polarization maps display the morphology of the field relative to other structures in the cloud , and can also be used to estimate the strength of the mean field according to a dynamical method originally proposed by chandrasekhar & fermi ( 1953 , hereafter cf ) .
applications of the cf - method generally suggest fieldstrengths in the milligauss range or above .
such fieldstrengths are larger than what is typically measured by the zeeman effect ( e.g. glenn et al . 1999 ,
lai et al .
2000 ) .
the cf - method is subject to errors arising from line of sight and angular averaging , and rests on the assumptions of equipartition between turbulent kinetic and magnetic energy , and isotropy of fluid motions .
spatial averaging , by smoothing the maps , can give misleading impressions about the magnetic field morphology .
however , since the information carried in the maps is unique , it is difficult to test the magnitude of these effects with astronomical observations .
numerical simulations of turbulent , magnetized molecular clouds offer the means to calibrate the accuracy of polarization maps and develop new techniques to analyze them .
the actual strength and structure of the field are known at all gridpoints and at selected times , as are the gas velocity and density .
it is possible to create synthetic polarization maps , analyze them as though they were astronomical data , and check the accuracy of the results .
that is the subject of this paper .
ostriker , stone , & gammie ( 2001 ) have used a set of simulations to calibrate the cf - method in this manner . in section [ sec : models - methods ] , we describe the numerical models and the method by which we generate polarization maps .
most of the results relevant to polarization maps are in section [ sec : results ] , in which we discuss the morphology shown in the maps , implement the cf - method , devise an alternative to it , and show what can be learned about the spectrum of magnetic field fluctuations .
section [ sec : conclusions ] is a summary and discussion .
we base our investigation on full 3d models of driven mhd - turbulence in a cube with periodic boundary conditions , simulating a portion of the interior of a molecular cloud .
we chose an isothermal equation of state , because the cooling times are much shorter than the dynamical times at the high densities typical of molecular clouds .
we performed the simulations at @xmath3 and @xmath4 grid zones resolution using zeus-3d , a well - tested eulerian finite - difference code ( stone & norman 1992a , 1992b , clarke 1994 ) with second - order advection and a von neumann artificial viscosity to capture shocks .
the mhd induction equation is followed using the method of consistent transport along characteristics ( hawley & stone 1995 ) .
we employed the massively - parallel version of the code , zeus - mp ( fiedler 1998 , norman 2000 ) , to produce a data set at resolution @xmath5 .
we used the uniform driving mechanism described in mac low ( 1999 ) . at each timestep
, a fixed pattern of velocity perturbations is added , with the amplitude adjusted such that the energy input rate is kept constant .
the driving results in an _ rms _ mach number of @xmath6 for models of series @xmath7 and of @xmath8 for such of series @xmath9 ( see table [ tab : models ] ) .
the mechanism for generating the perturbation field allows us to select fixed spatial ranges .
all models presented in this work employ driving at wavenumbers k=@xmath10 waves per box length @xmath11 .
our measurements begin at system time @xmath12 = 0.0 , when the model has reached an equilibrium state between the energy dissipation rate due to shock interaction and numerical diffusion , and the driving energy input rate .
self - gravity is implemented via an fft - poisson solver for cartesian coordinates ( burkert & bodenheimer 1993 ) .
it is activated as soon as the model reaches the dissipation equilibrium at @xmath12 = 0.0 .
the isothermal equation of state renders the system scale free . in code units ,
the length of the box is @xmath13 and the mass is @xmath14 .
we dimensionalize the results by choosing the jeans length @xmath15 , jeans mass @xmath16 , and free fall time @xmath17 ( see klessen , heitsch , & mac low 2000 for discussion of the scaling ) . the number of jeans masses and jeans lengths in each run are given in table [ tab : models ] .
all the models are initialized with a uniform magnetic field stretching across the box along the @xmath18-direction .
the field becomes distorted over time , but the magnetic flux @xmath19 through the boundaries should be constant according to the equations of ideal mhd , and is typically preserved by the code to a relative accuracy of 10@xmath20 - 10@xmath21 . as in hmk , we scale the initial magnetic fieldstrength by the plasma beta @xmath22 .
the parameter @xmath23 is directly related to the critical magnetic flux required to prevent global gravitational collapse ( see mckee et al 1993 ) @xmath24 where the constant @xmath25 is found to be 0.13 for a uniformly magnetized sphere ( mouschovias & spitzer 1976 ) and 0.16 for a uniformly magnetized sheet ( nakano & nakamura 1978 ) . here
we choose the latter value .
we find @xmath26 where @xmath27 is the ratio of mass to critical mass as in hmk .
the models discussed in this paper span the range @xmath28 and @xmath29 .
the alfvn mach number @xmath30 is related to @xmath23 and the sonic mach number @xmath31 by @xmath32 .
thus , we consider both sub - alfvnic and super - alfvnic models . a detailed discussion of the model sets is given by hmk .
here we describe their physical properties just briefly .
the supersonic turbulence supports the gravitationally unstable region against global collapse , however , it can not prevent local collapse , even in the presence of magnetic fields too weak to provide magnetostatic support .
collapsing regions evolve from shock - induced filaments and cores .
the models reach density contrasts of @xmath33 orders of magnitude above and below the mean density .
the gravitationally bound regions can be interpreted as the initial stages of a protostellar core which may subsequently evolve into stars . once a core begins to collapse
, we can not resolve it well enough to follow its evolution further ( truelove et al .
1997 , hmk ) .
the isotropy of a model depends largely on its field strength . for the weak - field - model @xmath34 ,
the resulting distribution of magnetic energy is fairly isotropic , whereas for the models with stronger fields ( e.g. @xmath35 ) , the field imprints its initial direction onto the gas flows .
the flows , in turn , act on the field .
two quantities of interest for the polarization studies are the ratio of the mean field energy to the total magnetic energy , @xmath36 , and the dispersion in the angle @xmath37 between the local magnetic field direction and the mean direction , @xmath38 ( the two are not equivalent ; for example , the energy in the field could be increased by collecting it into strong unidirectional filaments with no dispersion in angle ) .
both quantities are given in table [ tab : turbcharacter ] .
equipartition between turbulent kinetic and turbulent magnetic energy is often assumed in astrophysics ; it has been shown to hold rigorously only in certain cases , such as weak alfvn wave turbulence ( zweibel & mckee 1995 ) and the incompressible alfvnic turbulence modelled by goldreich & sridhar ( 1997 ) .
observations do not yet yield clear evidence for or against equipartition , although data collected by crutcher ( 1999 ) tend to speak against it .
the models discussed here are not in exact equipartition ; the ratio @xmath39 of turbulent magnetic to turbulent kinetic energy for each model is listed in table [ tab : turbcharacter ] , and is typically a few tenths .
it is unclear whether these departures from equipartition occur for physical reasons related to the nature of nonlinear , compressible mhd turbulence or occur because of numerical diffusivity or the nature of the forcing .
we take the deviation from equipartition into account in [ subsec : res - cf ] to correctly interpret our polarization maps .
the model cubes include density , magnetic fields and velocity fields .
these data allow us to derive the stokes parameters @xmath40 and @xmath41 , and the polarized intensity @xmath42 according to zweibel ( 1996 ) @xmath43 where @xmath44 and @xmath45 give the field vectors in the plane of sky perpendicular to the line of sight and are taken directly from the simulations .
we integrate along the line of sight in @xmath46-direction .
the function @xmath47 is a weighting function which accounts for the density , emissivity , and polarizing properties of the dust grains . in this paper , we take it to be the gas density normalized by the mean density .
the polarized intensity is @xmath48 , and the polarization angle is @xmath49 equation ( [ equ : stokesparm ] ) is an approximate solution of the full radiative transfer equation for the stokes parameters ( martin 1974 , lee & draine 1985 ) , valid for small polarization and low optical depth . at far infrared wavelengths , and at typical column densities for molecular clouds ,
the medium can safely be assumed to be optically thin ( hildebrand et al . 2000 ) .
polarization maps are made at finite resolution .
we simulate the telescope beam by applying a gaussian filter of the form @xmath50 to the complex polarization @xmath42 given in equation ( [ equ : stokesparm ] ) .
the width @xmath51 of the smoothing filter should not exceed one eighth of the box length @xmath11 . for @xmath52 , the tails of the filter exceeding the map s area
would contribute to such an extent that neglecting them would yield a too small average .
for each model , we generated polarization maps with a set of smoothing widths @xmath53 .
the 2d polarization maps serve a threefold purpose : we discuss how their structure depends on self - gravity and limited observational resolution ( [ subsec : res - struct ] ) , and we show that there is no preferred alignment between filamentary structures in our simulations and the magnetic fields ( [ subsec : res - filament ] ) . finally , in [ subsec : res - cf ] we discuss the chandrasekhar - fermi method of determining the mean field and an extension , which determines the rms field , both of which we test and calibrate .
the polarization maps showing column density and polarization vectors ( fig .
[ fig : polmap - maps ] left column , model @xmath35 ) are highly structured .
shock fronts moving through the gas initiate formation of filaments and knots .
after one free - fall time ( lower left panel in fig .
[ fig : polmap - maps ] ) , the filaments fragment and concentrate due to self - gravity .
qualitatively , no influence of self - gravity on the large - scale structure of the field is discernible , although there is some effect on the smallest scales . smoothing these maps with a gaussian filter of @xmath54 pixels width ( fig . [
fig : polmap - maps ] right column , @xmath35 ) leads to a clumpier appearance of the previously well - defined filaments .
any substructure in these is lost .
single shock structures are smeared out .
as expected , the field appears more uniform , thus in our case indicating more and more its initial orientation .
small scale variations in the field indicating turbulence and defining the turbulent cascade are lost due to the smoothing .
figure [ fig : smoothphi ] quantifies this effect in model @xmath35 .
it shows the power spectrum of the angle between the local and the mean magnetic field .
this is equivalent to the line of sight averaged spectrum of the magnetic field fluctuation amplitude ( recall that the total power in fluctuations is given in table [ tab : turbcharacter ] ) .
increasing the smoothing width from @xmath55 to @xmath56 results in a power loss of @xmath57% .
structures at a wave number of @xmath58 are suppressed by more than two orders of magnitude .
the diamonds in figure [ fig : smoothphi ] indicate the power spectrum of perturbed against mean field energy @xmath59 , where @xmath60 is the magnetic energy corresponding to the perturbed field components perpendicular to the mean field .
we use this as a measure of the true disorder in the magnetic field and as a gross check whether the polarization angles mirror the behaviour of the energies .
some power loss between the true angular dispersion and even the unsmoothed fluctuation amplitude is inevitable , because the latter involves line of sight averaging while the former is a true 3d quantity .
inspection of figure ( [ fig : polmap - maps ] ) shows no dramatic effects caused by self gravity after one free - fall time .
figure ( [ fig : ang - dist ] ) shows that the width of the distribution of polarization angles does not change significantly under the effect of self - gravitation , but does certainly decrease with increasing beam width , as expected .
the emerging asymmetry results from the reduced statistics due to the increasing beam width .
although every pixel contributes to the histogram , the number of independent measurements decreases with increasing beam width .
there is an ongoing debate on the mechanisms generating the observed filamentary structures of molecular clouds ( e.g. loren 1989 , johnstone & bally 1999 , matthews & wilson 2000 ) .
shocks come to mind as a natural explanation , either compressing the material ( as in the simulations presented ) or generating downstream flows resulting in the filaments ( loren 1989 ) .
the alignment of the magnetic field with the filaments has been used as a test for the validity of different filament models .
the observations seem to favour no definite alignment .
maps of omc - iii ( matthews & wilson 2000 ) show a perpendicular alignment , thus perhaps supporting the model of fiege & pudritz ( 2000a , 2000b ) , in which they propose helical fields to confine filamentary structures . rizzo et al .
( 1998 ) found parallel and perpendicular alignment in their maps of background starlight polarization for lupus 1 and lupus 4 , whereas rao et al .
( 1998 ) find varying alignments for orion - kl .
further examples of varying field alignments can be found in dotson ( 1996 ) and ward - thompson et al .
( 2000 ) .
in the simulations presented here , the filaments are solely due to shock interactions . we do not find a preferred alignment of the magnetic field with the filaments .
we illustrate this in figure [ fig : highresmap ] , which shows the full polarization map for the @xmath5 zone model @xmath61 , and with a selection of filaments of the same model in figure [ fig : highresfil ] . a detailed study of the filaments will be presented in a forthcoming paper .
chandrasekhar & fermi ( 1953 ; cf ) suggested a method of estimating the mean magnetic field strength @xmath62 in the galactic spiral arms .
it relates the line of sight velocity dispersion @xmath63 to the dispersion of polarization angles @xmath64 around a mean field component .
the cf method rests on two main assumptions : that the fluctuations are isotropic about the direction of the mean field , and that there is equipartition between the mean kinetic and magnetic energies in the fluctuations . under these conditions , the mean field component @xmath62 is given by @xmath65 where @xmath66 stands for the mean density . because of the angular variations in the denominator , the result depends strongly on the actual mean field strength , and will in fact only be meaningful if there is a noticable mean field component . in terms of the parameter @xmath67
, the ratio of turbulent magnetic to turbulent kinetic energy listed in table [ tab : turbcharacter ] , equation ( [ equ : cf - original ] ) generalizes to @xmath68 we initially set @xmath69 when implementing the cf - method , because observations do not yield clear evidence for or against equipartition ( e.g. crutcher 1999 ) , but we correct for @xmath70 later ( see table [ tab : turbcharacter ] ) . in the following paragraphs , we present a modification of the cf - method ( [ subsubsec : res - cf - method ] ) ,
compare both methods with the help of model data ( [ subsubsec : res - cf - calib ] ) and discuss the effect of limited telescope resolution on the resulting field strength estimates in
[ subsubsec : res - cf - powerloss ] . the cf - method in its original form estimates the mean magnetic field .
when the mean field is much less than the rms field , the dispersion in fluctuation angle @xmath71 is dominated by points where @xmath72 . since @xmath73 ( see eq .
( [ equ : cf - original ] ) ) , the result is usually an underestimate of @xmath62 .
the cf - method can be extended to yield an estimate @xmath74 which is free of this problem .
suppose @xmath75 and the @xmath76 plane is the plane of the sky
. then @xmath77 by definition of the angle @xmath37 @xmath78 squaring and averaging equation ( [ equ : per - b ] ) , assuming that the magnetic field fluctuations energies are the same for all components ( see [ subsubsec : res - cf - claimtest ] ) , and using equation ( [ equ : cf - original ] ) , equation ( [ equ : rms - b ] ) becomes @xmath79 when the field is highly disordered , and the dispersion in polarization angles is large , equation ( [ equ : cf - modified ] ) reflects the underlying physical assumptions of equipartition between kinetic and magnetic energy together with isotropy .
the formula is valid for arbitrary ratios of turbulent magnetic to turbulent kinetic energy if we multiply the rhs by @xmath67 .
when the field is highly ordered , comparison of equation ( [ equ : cf - modified ] ) with equation ( [ equ : cf - original ] ) shows that the mean and rms fields are nearly the same .
we plotted the ratio of the estimated and model field strength @xmath80 in figure [ fig : cf - variation ] .
the upper left panel displays @xmath81 for the cf - method , averaged over two lines of sight perpendicular to the mean field direction and over three physical times .
the lower left panel shows the dispersion of a single measurement relative to the corresponding mean value .
it decreases with increasing field strength . for strong fields , the cf - method overestimates the field strength derived from the unsmoothed maps ( star symbols in fig .
[ fig : cf - variation ] ) by a factor of @xmath0 to @xmath82 .
thus we confirm the claim made by ostriker et al .
( 2001 ) . for weaker fields
however , the method starts to develop a significant scatter , as shown in figure [ fig : cf - variation ] ( lower panel ) . the right column in figure [ fig : cf - variation ]
show the corresponding results for the cf - method in its modified version according to equation ( [ equ : cf - modified ] ) . for the unsmoothed case ( again star symbols ) ,
the strongest field is overestimated by @xmath83 .
whereas the original method breaks down at a field strength of @xmath84 , the modified version still yields acceptable results for @xmath85 .
the minimum field strength alone however does not tell us much about the reliability of the method .
the parameter of interest is the alfvn mach number @xmath86 , as the angular variations @xmath64 of polarization not only depend on the energy content in the field , but on the turbulent kinetic energy as well .
a field strength of @xmath85 would correspond to @xmath87 , in the parameter set of models @xmath7 . with typical parameters of @xmath88 and @xmath89 ,
we can then scale @xmath90 . field strengths in molecular clouds are seen to be mostly larger than @xmath91 ( crutcher 1999 ) . in denser regions ,
the field strengths seem to increase with density as @xmath92 ( crutcher 1999 ) , whereas the nonthermal line widths ( the `` turbulence '' ) decreases with decreasing size as @xmath93 ( caselli & myers 1995 ) .
thus we conclude , that both methods should yield acceptably accurate results for molecular cloud regions up to their densest parts , _ as long as the observations sample the angular variations sufficiently _ ( see [ subsubsec : res - cf - powerloss ] ) .
we have to address the question of energy equipartition .
since @xmath67 is generally less than unity in our models ( see table [ tab : turbcharacter ] ) , the cf - method and its extension overestimate both @xmath62 and @xmath74 by a factor of @xmath94 .
figure [ fig : cf - corrected ] shows @xmath95 `` corrected '' for non - equipartition .
both methods now hit the model field strength at a factor between @xmath96 and @xmath97 , at least for sufficiently large field strengths and for unsmoothed maps .
the correction slightly reduces the largest deviations of the weak - field estimates .
we conclude , that for a sufficiently well resolved ( see below ) polarization map and for large field strength , both methods yield reliable results .
a main uncertainty factor is the ratio of magnetic to kinetic energy @xmath67 in the observed region .
whereas the original cf - method underestimates low field strengths , the modified version overestimates them . for weak fields
, the polarization angles can reach @xmath98 with respect to the mean field , which yields @xmath99 in equations ( [ equ : cf - original ] ) and ( [ equ : cf - modified ] ) . as the original cf - method , the modified version yields overestimated field strengths with increasing smoothing beam width . from the lower row in figure [ fig : cf - variation ] we conclude that even for the strongest fields the relative scatter is of order @xmath100% .
smoothing the maps leads to smaller scatter except for the weakest field strengths .
the effect of self - gravity on the field strength estimates is minute ( fig .
[ fig : cf - gravsigma ] ) . for small smoothing widths
@xmath51 , the varying small scale structure due to self - gravity leads to some statistical scatter , which is averaged out for large @xmath51 .
the cf - methods seem to be insensitive to effects of self - gravity on small scales . the fact that @xmath101 and @xmath102 vary by roughly the same logarithmic range , but with opposite signs
, suggests that by taking the geometric mean @xmath103 we would arrive at a more accurate estimate for the actual field strength . applying this recipe yields figure [ fig : cf - varcormean ] ( corresponding to fig . [ fig : cf - corrected ] )
clearly , the large deviations of @xmath101 and @xmath102 cancel sufficiently to yield estimates accurate to a factor of @xmath104 even for the weakest , unsmoothed fields , and is more accurate than that for moderately strong fields . smoothed maps of course lead again to a systematic overestimation , here up to a factor of @xmath105 .
we would like to emphasize that equation ( [ equ : res - cf - recipe - agm ] ) is only motivated by the ( logarithmically ) comparable deviations of @xmath101 and @xmath102 . to test this recipe , we applied it to a set of models with varying physical properties ( fig .
[ fig : cf - vcrest ] ) . models @xmath106 , @xmath107 and @xmath108 are a time series of decaying turbulence taken from mac low ( 1999 ) .
models @xmath109 , @xmath110 and @xmath111 ( mac low et al .
1998 ) are simulations of driven turbulence as series @xmath7 , but with driving wave length of @xmath112 ( @xmath111 ) and @xmath113 ( @xmath110 , @xmath109 ) .
see tables [ tab : models ] and [ tab : turbcharacter ] for their parameters .
all these models have weak initial fields , corresponding to @xmath114 . as in figure
[ fig : cf - varcormean ] , the scatter of @xmath115 is more than one order of magnitude lower than for @xmath101 and @xmath102 .
the unsmoothed estimates are accurate again up to a factor of @xmath104 .
again , smoothed fields are likely to be overestimated .
note that @xmath102 on the whole leads already to slightly more accurate estimates than @xmath101 .
we conclude that the geometric mean @xmath115 gives more reliable estimates than @xmath101 or @xmath115 even for very weak fields , being more accurate as well for moderate and strong fields .
thus , this recipe may prove useful when being applied to observational data .
field estimates derived from smoothed maps tend to overestimate the field strength with increasing `` beam width '' ( fig .
[ fig : cf - variation ] , all symbols except stars ) .
we will discuss how limited telescope resolution in polarization maps of turbulent regions can lead to this overestimation .
both cf - methods rely on perturbations of the magnetic field around a mean component .
if all the power of these perturbations resided on spatial scales @xmath116 , increasing the smoothing width above @xmath51 would have no effect on the power distribution of polarization angles , and varying smoothing widths would yield identical results .
on the other hand , if the perturbations grew with increasing length scale , as e.g. in a turbulent power spectrum , a larger smoothing width @xmath51 would result in a greater power loss on larger scales , and thus to an overestimation of the field .
note that in equations ( [ equ : cf - original ] ) and ( [ equ : cf - modified ] ) we find the angular variations in the denominator .
so losing power in the variations increases the field estimate .
the turbulence is driven between wave numbers @xmath117 in our simulations , thus letting the code evolve a turbulent cascade down to the dissipation scale at grid cell size . this turbulent cascade in our models
is well reflected in the power spectrum of angular variations @xmath118 ( fig .
[ fig : smoothphi ] ) .
we lose more and more power when applying larger smoothing widths @xmath51 .
this power loss should depend on the steepness of the power spectrum .
this suggests that it might be possible to measure the spectrum of magnetic field fluctuations by smoothing polarization maps by different filter widths , and comparing the dispersion of polarization angles . to illustrate this relation
, we will describe the smoothing as a convolution and then will determine analytically the loss of power in a spectrum due to smoothing .
the convolution would be @xmath119 with the wave function @xmath120 @xmath121 and the gaussian filter function @xmath122 as in equation ( [ equ : gaussfilter ] ) .
we identify @xmath120 with the @xmath123 of equation ( [ equ : per - b ] ) . instead of convolving directly , we use the fourier transforms @xmath124 $ ] and @xmath125 $ ] of equations ( [ equ : def - wave ] ) and ( [ equ : gaussfilter ] ) to derive the power spectrum of the convolved function @xmath126|$ ] via the convolution theorem @xmath127 where the hatted quantities denote fourier transformations .
the fourier transform of a gaussian yields again a gaussian , in our case with an additional phase shift .
the frequency space variable is @xmath128 .
@xmath129 applying the fourier transform to the wave function @xmath120 and integrating over @xmath130 $ ] , we get @xmath131 now we can multiply @xmath132 and @xmath133 , and taking the absolute value gives us the power spectrum of the convolved function @xmath134 . @xmath135 as we are interested in the loss of power caused by the smoothing , we now try to determine the amount of power remaining in the spectrum after smoothing , i.e. the quantity @xmath136 for @xmath137 , @xmath138 .
figure [ fig : cf - powerloss ] illustrates the behaviour of @xmath139 for several values of @xmath140 .
note that this is a log - linear plot , so that , for example , @xmath141 . curves for @xmath142 have negative , the ones for @xmath143 positive curvature . normalizing the curves for @xmath143 with @xmath144 and plotting them together with the inverse of the ratio of estimated to model field strength @xmath101 of model @xmath145 yields figure [ fig : cf - powerlosscomp ] .
we normalized @xmath101 to @xmath55 as well , in order to compare the measurements to the analytic curves @xmath139 .
we note that the measurements start to flatten off for small @xmath146 because of line of sight averaging , which we do not include in the analytic derivation .
the same argument applies for observations .
thus , even in the ideal case of @xmath55 , the measurement may not reach @xmath147 but may overestimate the actual field strength .
of course , this would crucially depend on the length of line of sight and , generally , on optical depth effects .
they , however , are neglegible in the far - infrared regime . because we need a certain length in the line of sight in order to derive a meaningful velocity dispersion @xmath63 , this overestimate due to line - of - sight averaging gives an intrinsic error in the cf - methods .
the power spectrum of angular variations in the simulations is by no means a clear power law , due to numerical dissipation and the signatures of the driving scale .
thus , the measured @xmath148 ( fig . [ fig : cf - powerlosscomp ] ) does not correspond clearly to one of the analytic curves .
however , if observations show a well defined power law in the angular variations @xmath64 , and provide sufficient resolution to create a series of maps smoothed over larger and larger areas , then it should be possible to extract information about the exponent of the power law and to correct the field estimate as well .
once a power law description is found for the observed region , @xmath149 supplies a correction factor for the field strength estimate @xmath150 . in polarization maps derived from observations ,
an additional effect could potentially lead to a systematic overestimation .
when we derive the field estimates from our models , we use the complete domain , thus including all wave lengths occurring in the problem . however , it is not clear whether the observations do trace the largest scales in the field perturbations .
if the power of angular variations is distributed in a power spectrum which decreases with increasing wave number , we will lose overproportionally much power when estimating the field strength within a domain which is smaller than the largest wave length contributing to the perturbations .
figure [ fig : cf - subframes ] illustrates this effect contributing to a systematic overestimation of the field strength .
it shows the ratios @xmath151 for subframes of @xmath152 , @xmath153 and @xmath154 cells for model @xmath145 at @xmath4 resolution .
we averaged the estimates from all possible subframes .
the error bars indicate the standard deviations of the means . with decreasing frame size , the field is overestimated slightly , thus indicating a decrease of @xmath64 .
however , bearing in mind the large scatter around the mean values in figure [ fig : cf - subframes ] , this effect is not very distinct .
we conclude that , although the cf - methods are applicable in principle to molecular clouds , the resulting field strengths are most likely to be systematically overestimated for two reasons : ( a ) any smoothing introduced by the finite telescope beam size will lead to a systematic removal of large - scale perturbations and thus to an overestimation of the field strength .
( b ) deriving field estimates for a domain smaller than the maximum perturbation wave length present leads to power loss on large scales and thus as well to an overestimated field strength .
this systematic overestimation due to limited resolution is different from uncertainties because of non - equipartition as discussed in
[ subsubsec : res - cf - calib ] . in order to draw these conclusions
we assume that the underlying power spectrum of perturbations follows a power - law - like distribution , at least , that it decreases with increasing wave number .
figure [ fig : resolution - cf ] presents a test for resolution with models @xmath155 and @xmath145 at @xmath3 and @xmath4 grid cells . the beam width @xmath156 is given in pixels .
note that in order to compare both models , we have to compare them at the same _ physical _ beam width , i.e. we have to shift a data point of model @xmath155 at @xmath157 such that it corresponds to a point of @xmath158 .
we corrected all estimates with @xmath159 ( see table [ tab : turbcharacter ] ) in order to account for non - equipartition .
discrepancies at small scales are to be expected as model @xmath155 then already reaches the grid scale .
figure [ fig : resolution - cf ] allows us to conclude that numerical resolution does not affect our calibration of the cf - methods .
thus we feel justified to draw conclusions for observations of turbulent regions from our simulated observations of computational turbulence . we still have to substantiate the claim leading to equation ( [ equ : rms - b ] ) , namely , that our simulated turbulent flows are isotropic enough to validate that the field components perpendicular to the mean field @xmath160 obey @xmath161 and that the field perturbations in all three directions fulfill @xmath162 .
the upper panel of figure [ fig : cf - claim - test ] supports the second assumption .
there occur only minor differences in the _ rms _ values .
note that the initially homogeneous background field is oriented along the @xmath18-direction .
thus , we had to subtract this background in order to determine the corresponding mean values , yielding @xmath163 ( lower panel of fig .
[ fig : cf - claim - test ] ) .
the scatter of the means is considerably larger , however their absolute values are three to four orders of magnitudes lower than the corresponding field strengths .
ideally , the means should vanish , especially in the directions perpendicular to the initial field , namely the @xmath164- and @xmath46-direction .
deviations from this ideal case are probably due to numerical diffusion in the code .
this results in not conserving the total flux per coordinate direction .
the small shifts in the means thus indicate how well the code actually does conserve the total flux .
reliable methods for measuring and mapping magnetic fields in molecular clouds are urgently needed in order to assess the role of magnetic fields in the dynamics of molecular clouds and in star formation .
probes based on far infrared polarimetry of the thermal emission from magnetically aligned dust are now in widespread use .
far - ir polarimetry is complementary to the zeeman method , which is the traditional means of measuring the field .
there are few independent checks of its accuracy as a diagnostic of magnetic fields . in this paper we used numerical simulations of turbulent , magnetized , self gravitating molecular clouds to assess the reliability of polarization maps .
although such simulations qualitatively reproduce many of the features seen in molecular clouds , we do not expect the computed densities , velocities , and magnetic fields to be completely realistic .
we undertook the project with the expectation that analysis of simulated data would bring out the same issues as analysis of real data .
we assumed that the polarized emission is optically thin and proportional to gas density .
the first assumption should be excellent .
the second could be modified , for example by modelling the grain temperature point to point within the cloud .
it might be possible to pick out particular structures along the line of sight by comparing maps at different wavelengths , but establishing this is beyond the scope of the present paper .
1 . filaments produced by shocks do not show a preferred alignment with the magnetic field .
self - gravity has no discernible effect on the structure of the magnetic fields in our simulations .
however , we have to bear mind that our self - gravitating regions are small with respect to the simulated region .
3 . the chandrasekhar - fermi method in its original version yields field estimates accurate up to @xmath165 .
a modified version determining the rms field @xmath166 results in in @xmath167 .
this version proves to work more reliably for slightly weaker field strengths .
both methods should be applicable to magnetic fieldstrengths typical of molecular clouds .
the geometrical mean @xmath168 yields field estimates accurate up to a factor of @xmath169 even for the weakest fields . for moderate and stronger fields , @xmath170 .
thus , this recipe improves the reliability of field strength estimates for the whole range of physically realistic fields in molecular clouds , and may prove useful when applied to observational data .
the original and modified chandrasekhar - fermi methods are based on the assumption of equipartition between turbulent kinetic and magnetic energy .
the field fluctuations in the models are below equipartition , leading to an overestimate of the field .
limited angular resolution again leads to systematic overestimation of the magnetic field strength for both methods .
two effects can cause this overestimation : ( a ) in a power spectrum decreasing with increasing wave number , smoothing leads to an overproportionally large power loss on larger scales .
thus the angular variations are underestimated , which leads to larger field strengths .
( b ) if the domain used for deriving the field estimate does not trace the largest wave modes , this again leads to power loss on the largest scales .
if the power spectrum of magnetic field fluctuations is a power law , field estimates made from a series of maps with different smoothing widths can in principle be used to estimate the exponent of the fluctuation spectrum , assuming that this is well enough defined over at least two decades . with this information
, one could correct for the overestimated field strengths .
fh , egz and m - mml express special thanks to the itp at university of california at santa barbara ( nsf grant no .
phy94 - 07194 ) , the hospitality of which during the astrophysical turbulence program has made possible this research .
the work of egz was supported in part by nsf ast 98 - 00616 .
m - mml was partially supported by an nsf career fellowship nsf ast 99 - 85392 , and by nasa atp grant nag5 - 10103 .
computations presented here were performed on sgi origin 2000 machines of the rechenzentrum garching of the max - planck - gesellschaft and the national center for supercomputing applications ( ncsa ) . zeus-3d and
zeus - mp were used by courtesy of the laboratory for computational astrophysics at the ncsa .
we have made use of nasa s astrophysics data system abstract service .
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san francisco : asp ; |c1996 ; edited by wayne g. roberge and doug c. b. whittet , p.486 zweibel , e.g. & mckee , c.f .
1995 , , 439 , 779 ccccccc @xmath61 & @xmath5 & @xmath10 & @xmath171 & @xmath172 & @xmath173 & @xmath174 + @xmath34 & @xmath4 & @xmath10 & @xmath171 & @xmath172 & @xmath173 & @xmath174 + @xmath35 & @xmath4 & @xmath10 & @xmath175 & @xmath176 & @xmath173 & @xmath174 + @xmath177 & @xmath3 & @xmath10 & @xmath171 & @xmath172 & @xmath178 & @xmath179 + @xmath114 & @xmath3 & @xmath10 & @xmath180 & @xmath181 & @xmath178 & @xmath179 + @xmath182 & @xmath3 & @xmath10 & @xmath183 & @xmath184 & @xmath178 & @xmath179 + @xmath185 & @xmath3 & @xmath10 & @xmath186 & @xmath187 & @xmath178 & @xmath179 + @xmath188 & @xmath3 & @xmath10 & @xmath189 & @xmath97 & @xmath178 & @xmath179 + @xmath190 & @xmath3 & @xmath10 & @xmath191 & @xmath192 & @xmath178 & @xmath179 + @xmath193 & @xmath3 & @xmath10 & @xmath194 & @xmath195 & @xmath178 & @xmath179 + @xmath155 & @xmath3 & @xmath10 & @xmath196 & @xmath197 & @xmath178 & @xmath179 + @xmath145 & @xmath4 & @xmath10 & @xmath196 & @xmath197 & @xmath178 & @xmath179 + @xmath11 & @xmath4 & @xmath198 & @xmath199 & @xmath200 & ( ... ) & ( ... ) + @xmath109 & @xmath3 & @xmath201 & @xmath199 & @xmath200 & ( ... ) & ( ... ) + @xmath110 & @xmath3 & @xmath201 & @xmath199 & @xmath200 & ( ... ) & ( ... ) + @xmath111 & @xmath3 & @xmath202 & @xmath199 & @xmath200 & ( ... ) & ( ... ) + cccccc @xmath61 & @xmath171 & @xmath203 & @xmath204 & @xmath205 & @xmath206 + @xmath34 & @xmath171 & @xmath207 & @xmath208 & @xmath209 & @xmath210 + @xmath35 & @xmath175 & @xmath211 & @xmath212 & @xmath213 & @xmath214 + @xmath177 & @xmath171 & @xmath215 & @xmath216 & @xmath217 & @xmath218 + @xmath114 & @xmath180 & @xmath219 & @xmath220 & @xmath221 & @xmath222 + @xmath182 & @xmath183 & @xmath223 & @xmath224 & @xmath225 & @xmath226 + @xmath185 & @xmath186 & @xmath227 & @xmath228 & @xmath229 & @xmath214 + @xmath188 & @xmath189 & @xmath230 & @xmath228 & @xmath231 & @xmath226 + @xmath190 & @xmath191 & @xmath232 & @xmath233 & @xmath234 & @xmath235 + @xmath193 & @xmath194 & @xmath236 & @xmath212 & @xmath237 & @xmath235 + @xmath155 & @xmath196 & @xmath238 & @xmath239 & @xmath240 & @xmath241 + @xmath145 & @xmath196 & @xmath242 & @xmath199 & @xmath243 & @xmath244 + @xmath106 & @xmath199 & @xmath245 & @xmath246 & @xmath247 & @xmath248 + @xmath107 & @xmath199 & @xmath249 & @xmath250 & @xmath251 & @xmath252 + @xmath108 & @xmath199 & @xmath204 & @xmath253 & @xmath254 & @xmath255 + @xmath109 & @xmath199 & @xmath256 & @xmath183 & @xmath257 & @xmath258 + @xmath110 & @xmath199 & @xmath259 & @xmath260 & @xmath261 & @xmath262 + @xmath111 & @xmath199 & @xmath263 & @xmath227 & @xmath264 & @xmath248 + | the dynamical state of star - forming molecular clouds can not be understood without determining the structure and strength of their magnetic fields .
measurements of polarized far - infrared radiation from thermally aligned dust grains are used to map the orientation of the field and estimate its strength , but the accuracy of the results has remained in doubt . in order to assess the reliability of this method , we apply it to simulated far - infrared polarization maps derived from three - dimensional simulations of supersonic magnetohydrodynamical turbulence , and compare the estimated values to the known magnetic field strengths in the simulations .
we investigate the effects of limited telescope resolution and self - gravity on the structure of the maps . limited observational resolution affects the field structure such that small scale variations can be completely suppressed , thus giving the impression of a very homogeneous field .
the chandrasekhar - fermi method of estimating the mean magnetic field in a turbulent medium is tested , and we suggest an extension to measure the rms field . both methods yield results within a factor of @xmath0 for field strengths typical of molecular clouds , with the modified version returning more reliable estimates for slightly weaker fields .
however , neither method alone works well for very weak fields , missing them by a factor of up to @xmath1 .
taking the geometric mean of both methods estimates even the weakest fields accurately within a factor of @xmath2 .
limited telescope resolution leads to a systematic overestimation of the field strengths for all methods .
we discuss the effects responsible for this overestimation and show how to extract information on the underlying ( turbulent ) power spectrum . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Comprehensive Child Welfare Services
Reform Act of 1993''.
SEC. 2. ESTABLISHMENT OF COMPREHENSIVE CHILD WELFARE SERVICES PROGRAM.
(a) In General.--Title IV of the Social Security Act (42 U.S.C. 601
et seq.) is amended--
(1) in part F, by redesignating sections 481 through 487
(42 U.S.C. 681-687) as sections 491 through 497, respectively;
(2) by striking the heading for part E and inserting the
following:
``PART E--FOSTER CARE, ADOPTION ASSISTANCE, AND COMPREHENSIVE CHILD
WELFARE SERVICES.
``Subpart 1--Foster Care and Adoption Assistance'';
(3) in section 474(a) (42 U.S.C. 674(a)), by striking
paragraph (3), and redesignating paragraph (4) as paragraph
(3); and
(4) by adding at the end of part E the following:
``Subpart 2--Comprehensive Child Welfare Services
``SEC. 480. PURPOSE; APPROPRIATION.
``For the purposes of assisting each State to meet the needs of
children (including children ineligible for assistance under the
programs under subpart 1) for comprehensive child welfare services, and
enabling each State to administer its programs under subpart 1, there
are authorized to be appropriated--
``(1) $1,328,000,000 for fiscal year 1994;
``(2) $1,449,000,000 for fiscal year 1995;
``(3) $1,585,000,000 for fiscal year 1996;
``(4) $1,734,000,000 for fiscal year 1997; and
``(5) $1,892,000,000 for fiscal year 1998.
``SEC. 481. RESERVATION OF FUNDS FOR SECRETARY; ALLOTMENTS TO STATES;
REALLOTMENTS.
``(a) Reservation of Funds.--1 percent of the amount appropriated
pursuant to section 480 for each fiscal year shall be reserved to the
Secretary for expenditure in accordance with section 484.
``(b) Allotments.--The allotment for each State for each of fiscal
years 1994 through 1998 shall be an amount which bears the same ratio
to 99 percent of the amount authorized to be appropriated under section
480 for the fiscal year as the total payment to which the State is
entitled under section 474(a)(3) for fiscal year 1992 bears to the
total amount to which all States are entitled under such section for
the fiscal year (as determined on the basis of claims submitted by the
State and received by the Secretary on or before March 31, 1993, and
found by the Secretary to be allowable on or before July 31, 1993).
``(c) Reallotment.--The amount of any allotment to a State under
subsection (b) for any fiscal year which the State certifies to the
Secretary will not be used by the State to carry out the State plan
under section 482 shall be available for reallotment from time to time,
on such dates as the Secretary may fix, to other States which the
Secretary determines will be able to use such excess amounts during
such fiscal year, in addition to amounts already allotted or reallotted
to such other States, under the State plans under such section. The
amount reallotted to each State eligible for reallotted funds shall
bear the same ratio to the amount available for reallotment as the
State's allotment under subsection (b) bears to the total amount
allotted to all States so eligible.
``SEC. 482. STATE PLAN FOR COMPREHENSIVE CHILD WELFARE SERVICES.
``In order to be eligible for payments under this subpart for a
fiscal year, a State shall publish in the State and furnish to the
Secretary a plan of the State for expenditure of funds under this
subpart. The plan shall provide that--
``(1) expenditures will be made under the plan only for--
``(A) provision of child welfare services (as
defined in section 425) in accordance with section
422(b), other than foster care maintenance payments and
adoption assistance payments, but including
nonrecurring adoption expenses (as defined in section
473(a)(6)); and
``(B) administration of the programs of the State
under subpart 1 (including training of current or
prospective State or local agency personnel, and of
foster care and adoptive parents, related to
administration of such program); and
``(2) the State share of expenditures under this subpart
shall be an amount not less than the amount of the State share
of expenditures for which payment was made under section
474(a)(3) for fiscal year 1993.
``SEC. 483. PAYMENTS TO STATES.
``Each State shall be entitled to a payment for each fiscal year in
an amount equal to the lesser of--
``(1) the allotment of the State under this subpart for the
fiscal year; or
``(2) 75 percent of amounts (other than amounts for which
the State receives payment under part B) expended in the fiscal
year in accordance with the State plan under section 482.
``SEC. 484. SECRETARY'S DISCRETIONARY ACTIVITIES.
``The Secretary shall use the amounts reserved under section 481(a)
to provide, through grants to or contracts with public or private
entities, for--
``(1) technical assistance and training for State and local
public and private agencies to enable them to improve their
administration of the program under subpart 1, including--
``(A) States or cities with large numbers of
children at risk of foster care placement, or with
substantial deficiencies in program operation; and
``(B) State agencies in greatest need of assistance
in meeting the requirements of section 479 or other
Federal data collection requirements;
``(2) evaluation of State programs under this part and part
B; and
``(3) demonstrations designed to--
``(A) develop or identify more effective programs
to support and strengthen families;
``(B) improve child protective, foster care, and
adoption assistance services; and
``(C) reduce burdens on caseworkers.''.
(b) Coordination With Other Programs Providing Services to Children
and Families.--Section 422(b)(2) of such Act (42 U.S.C. 622(b)(2)) is
amended by striking ``under part E'' and inserting ``under subpart 1,
and the State plan published under subpart 2, of part E''.
(c) Elimination of Conditional Part E of Title IV Ceiling and
Authority to Transfer Funds to Part B of Title IV.--Section 474 of such
Act (42 U.S.C. 674) is amended--
(1) by striking subsections (b) and (c), and redesignating
subsection (d) as subsection (b); and
(2) in subsection (b), as so redesignated--
(A) by striking ``subsections (a), (b), and (c)''
and inserting ``subsection (a)'';
(B) by striking ``such estimates'' and inserting
``such estimate''; and
(C) by striking ``such subsections'' and inserting
``such subsection''.
(d) Conforming Amendments.--(1) Part E of title IV of such Act (42
U.S.C. 470-479) is amended by striking ``this part'' each place such
term appears and inserting ``this subpart''.
(2) Section 403(a)(3)(D) of such Act (42 U.S.C. 603(a)(3)(D)) is
amended by striking ``486(a)'' and inserting ``496(a)''.
(3) Section 403(l)(1)(A) of such Act (42 U.S.C. 603(l)(1)(A)) is
amended--
(A) by striking ``482(a)'' and inserting ``492(a)''; and
(B) by striking ``482(i)(2)'' and inserting ``492(i)(2)''.
(4) Section 403(l)(4)(A)(i) of such Act (42 U.S.C. 603(l)(4)(A)(i))
is amended by striking ``482(d)(1)'' and inserting ``492(d)(1)''.
(5) Section 403(l)(4)(A)(ii) of such Act (42 U.S.C.
603(l)(4)(A)(ii)) by striking ``482'' and inserting ``492''.
(6) Section 473(a)(6) of such Act (42 U.S.C. 673(a)(6)) is
amended--
(A) by striking ``(6)(A)'' and inserting ``(6)''; and
(B) by striking subparagraph (B).
(7) Section 477(e)(3) of such Act (42 U.S.C. 677(e)(3)) is amended
by striking ``(a)(1), (a)(2), and (a)(3)'' and inserting ``(a)(1) and
(a)(2)''.
(8) Section 492(e)(2)(B) of such Act, as so redesignated by
subsection (a) of this section, is amended by striking ``484'' and
inserting ``494''.
(9) Section 492(f) of such Act, as so redesignated by subsection
(a) of this section, is amended by striking ``section 482(a)(1)'' and
inserting ``subsection (a)(1)''.
(10) Section 493(a)(1) of such Act, as so redesignated by
subsection (a) of this section, is amended by striking ``482(a)(1)''
and inserting ``492(a)(1)''.
(11) Section 494(c) of such Act, as so redesignated by subsection
(a) of this section, is amended by striking ``482(e)'' and inserting
``492(e)''.
(12) Section 494(d)(2) of such Act, as so redesignated by
subsection (a) of this section, is amended by striking ``482(f)'' and
inserting ``492(f)''.
(13) Section 495(c) of such Act, as so redesignated by subsection
(a) of this section, is amended by striking ``482(a)(1)'' and inserting
``492(a)(1)''.
(14) Section 497(a)(1) of such Act, as so redesignated by
subsection (a) of this section, is amended by striking ``486'' and
inserting ``496''.
(15) Section 1902(a)(10)(A)(i)(I) of such Act (42 U.S.C.
1396a(a)(10)(A)(i)(I)) is amended by striking ``482(e)(6)'' and
inserting ``492(e)(6)''.
(16) Section 1928(a)(1)(D) of such Act (42 U.S.C. 1396s(a)(1)(D))
is amended by striking ``482(e)(6)'' and inserting ``492(e)(6)''.
(17) Any other reference in law or regulation, as of the effective
date of this Act, to section 481, 482, 483, 484, 485, 486, or 487 of
the Social Security Act shall be considered to be a reference to
section 491, 492, 493, 494, 495, 496, or 497 of such Act, respectively.
SEC. 3. SECTION 1115 DEMONSTRATION WAIVERS.
Section 1115(a) of the Social Security Act (42 U.S.C. 1315(a)) is
amended--
(1) in the matter preceding paragraph (1), by striking
``part A or D'' and inserting ``part A, B, D, or E'';
(2) in paragraph (1), by striking ``454,'' and inserting
``422, 454, 471, 472, 473,''; and
(3) in paragraph (2), by striking ``455,'' and inserting
``423, 455, 474,''.
SEC. 4. RECOVERY OF TRAINING COSTS.
(a) Under Part E of Title IV.--Section 471(a) of the Social
Security Act (42 U.S.C. 671(a)) is amended--
(1) by striking ``and'' at the end of paragraph (16);
(2) by striking the period at the end of paragraph (17) and
inserting ``; and''; and
(3) by adding at the end the following:
``(18) provide that the State agency--
``(A) will require each individual who receives, at
an institution of higher education, education or
training in child welfare or a related field supported
by funds from the State agency under this part or part
B to enter into a written agreement either--
``(i) to work, after the completion of such
education or training, for the State agency or
another public child welfare agency, or for a
private child welfare agency operating under a
contract with a public child welfare agency,
for a period not less in duration than the
period of such education or training; or
``(ii) to repay to the State agency the
full amount expended by it for such education
or training for the individual;
``(B) will enforce compliance with such agreements;
and
``(C) will repay to the Secretary the Federal share
of amounts recovered in accordance with this
requirement, to the extent that such amounts exceed
amounts necessary to reimburse the State agency for
costs reasonably incurred to obtain recovery.''.
(b) Under Section 426.--Section 426 of such Act (42 U.S.C. 626) is
amended--
(1) in subsection (a)(1)(C), by inserting ``subject to
subsection (d),'' after ``(c)''; and
(2) by adding at the end the following:
``(d) As a condition of eligibility for grants under subsection
(a)(1)(C), a public or other nonprofit institution of higher learning
shall undertake--
``(1) to require each individual who receives education or
training in child welfare or a related field supported by a
stipend or other financial assistance under this section to
enter into a written agreement either--
``(A) to work, after the completion of such
education or training, for a public child welfare
agency, or for a private child welfare agency operating
under a contract with a public child welfare agency,
for a period not less in duration than the period of
such education or training, or
``(B) to repay to the institution the full amount
of such stipend or other assistance;
``(2) to enforce compliance with such agreements; and
``(3) to repay to the Secretary amounts recovered in
accordance with this requirement, to the extent that such
amounts exceed amounts necessary to reimburse the institution
for costs reasonably incurred to obtain recovery.''.
SEC. 5. EXTENSION OF THE INDEPENDENT LIVING PROGRAM.
Section 477 of the Social Security Act (42 U.S.C. 677) is amended--
(1) in subsection (a)(1), by striking the last sentence;
(2) in subsection (c), by striking ``In the case of'' and
all that follows through ``1992, such'' and inserting ``Such'';
(3) in subsection (e)(1)(A), by striking ``of the fiscal
years 1987 through 1992'' and inserting ``fiscal year'';
(4) in subsection (e)(1)(B), by striking ``fiscal years
1991 and 1992'' and inserting ``each fiscal year'';
(5) by amending subsection (e)(1)(C) to read as follows:
``(C) As used in this section:
``(i) The term `basic ceiling' means
$45,000,000.
``(ii) The term `additional ceiling' means
$25,000,000.'';
(6) in subsection (f), by striking the last sentence; and
(7) in subsection (g)--
(A) by striking ``(g)(1)'' and inserting ``(g)'';
and
(B) by striking paragraphs (2) and (3).
SEC. 6. ACCUMULATION OF ASSETS BY OLDER CHILDREN RECEIVING FOSTER CARE
MAINTENANCE PAYMENTS.
Section 472 of the Social Security Act (42 U.S.C. 672) is amended
by adding at the end the following:
``(i) In determining the eligibility of an individual who has
attained age 16 for foster care maintenance payments under this
subpart, the State agency shall disregard from the resources of the
individual an amount of funds not exceeding an amount the agency
determines to be reasonable for the purpose of achieving self-
sufficiency.''.
SEC. 7. REPEAL OF ANNUAL REPORT ON VOLUNTARY PLACEMENT.
Section 102(e) of the Adoption Assistance and Child Welfare Act of
1980 (Public Law 96-272; 42 U.S.C. 672 note) is repealed.
SEC. 8. EFFECTIVE DATE.
The amendments made by this Act shall become effective with respect
to fiscal years beginning on or after October 1, 1993. | Comprehensive Child Welfare Services Reform Act of 1993 - Amends title IV of the Social Security Act (SSA) to establish a new comprehensive child welfare services program under part E (Foster Care and Adoption Assistance). Authorizes appropriations.
Amends SSA title IV part B (Child-Welfare Services) to provide for coordination with other programs providing services to children and families.
Amends SSA title XI to revise demonstration waiver provisions.
Amends SSA title IV parts B and E to provide for recovery of training costs.
Amends SSA title IV part E to make permanent the independent living program and to maintain basic and additional ceiling amounts at the latter amounts authorized under current law. Provides that in determining the eligibility of an individual aged 16 for foster care maintenance payments under such part, the State agency shall disregard from the resources of the individual an amount not exceeding what the agency determines to be reasonable for the purpose of achieving self-sufficiency.
Amends the Adoption Assistance and Child Welfare Act of 1980 to repeal provisions respecting the annual report on voluntary placement. |
Japan to resume 'research' whaling in Antarctic, move to conflict with ruling by International Court of Justice
Updated
Japan has decided to resume whaling in the Antarctic Ocean by the end of March after a hiatus since last year, a move likely to prompt international outrage.
The International Court of Justice (ICJ) last year ruled that Japan's decades-old whale hunt in the Antarctic should stop, prompting Tokyo to cancel the bulk of its whaling in the 2014-2015 season.
But the Japanese Fisheries Agency has now notified the International Whaling Commission (IWC) that it will resume whaling in the 2015-2016 season under a revised plan.
The plan, which calls for cutting annual minke whale catches by two-thirds to 333, is "scientifically reasonable", the agency said in a document filed with the IWC.
Japanese media said whalers were expected to depart for the ocean possibly by the end of December.
There was no immediate comment from the IWC or the ICJ.
Environment Minister Greg Hunt said Japan had previously said it would abide by the ruling, and added that there is no need to kill whales in the name of research.
Japan began what it calls scientific whaling in 1987, a year after an international whaling moratorium took effect.
It hunts the whales under an exemption in the moratorium that allows for lethal research.
Japan makes no secret of the fact that meat from the mammals - killed ostensibly for research - is processed into food, and says the whale population in any case is big enough to allow sustainable whaling.
It accuses opponents of being emotional about whales and disregarding what it says is evidence to support its position.
Japan killed 251 minke whales in the Antarctic in the 2013-14 season and 103 the previous year, far below its target because of direct action by activist group Sea Shepherd.
Reuters/AFP
Topics: environment, conservation, whaling, mammals---whales, japan
First posted ||||| Image copyright AFP Image caption Japan says it will catch only a third of the minke whales it caught under its previous programme - 333 instead of 1,000
Japan has announced it will resume whaling in the Antarctic early next year after a break of more than a year.
The decision comes despite an International Court of Justice (ICJ) ruling that Japan cease all whaling.
The Japanese government says it has taken into account the court ruling and its "scientific" whaling programme will be much smaller.
But the announcement has been condemned by environmental groups and the Australian and UK governments.
"We do not accept in any way, shape or form the concept of killing whales for so-called 'scientific research'," said Australian Environment Minister Greg Hunt.
"We are deeply disappointed with Japan's decision to restart whaling in the Southern Ocean," said the UK environment ministry, Defra. "This undermines the global ban on commercial whaling which the UK strongly supports."
Image copyright Twitter
A guide to the great whales
Japan's whaling fleet could set sail again within weeks and head for the Southern Ocean, says the BBC's Rupert Wingfield Hayes in Tokyo.
Under Japan's revised plan, it will reduce the number of minke whales caught each year by two thirds to 333.
The Japanese authorities believe their plan is scientifically reasonable but it is unlikely to placate opponents, in particular the Australian government.
"Japan cannot unilaterally decide whether it has adequately addressed" scientists' questions, Mr Hunt was quoted as saying.
Image copyright AFP Image caption This is the latest move in a years-long struggle pitting Japan against other governments, activists and the international court
Image copyright AFP Image caption Japan makes no secret of the fact that the meat resulting from its so-called scientific whaling programme ends up on the plate
'Sentimental' critics
In 2014 Australia won a case against Japan in the international court of justice in the Netherlands.
The court ruled that Japan's "scientific" whaling program was not scientific at all - and ordered Tokyo to recall its fleet.
Crucially, the ruling stated that it did not believe it was necessary for Japan to kill whales in order to study them, our correspondent says.
Japan started its whaling programme in 1987, a year after an international moratorium was enacted.
It accuses critics of being sentimental about whales and disregarding scientific evidence about the sustainability of whaling.
The ICJ says Japan has caught some 3,600 minke whales since its current programme began in 2005. ||||| Japan should toe the line and hold off on resuming whaling in the Antarctic until the International Whaling Commission looks at it, New Zealand says.
Japan wants to resume whaling in the Antarctic Ocean by the end of March.
Tokyo cancelled the bulk of its whaling for the 2014-15 season following a ruling from the International Court of Justice.
But the Japanese Fisheries Agency has notified the International Whaling Commission that Japan will resume whaling in the 2015-16 season under a revised plan.
The plan, which calls for cutting annual minke whale catches by two-thirds to 333, is scientifically reasonable, the agency said in a document filed with the commission.
New Zealand's Acting Foreign Minister Todd McClay says the decision is disappointing and Japan should heed the court's decision and international scientific evidence.
The whaling commission's expert panel was very clear this year that Japan had not made the case for lethal research, Mr McClay said.
"New Zealand's long-standing and fundamental opposition to this practice remains unchanged," Mr McClay said.
"It is clear that Japan's research objectives can be met using non-lethal means.
"We call on Japan to heed the expert panel's advice and postpone any whaling this season. Our strong view is that Japan should at least afford the International Whaling Commission the opportunity to consider the proposal in 2016."
Japan began what it calls scientific whaling in 1987, a year after an international whaling moratorium took effect.
Japan has long maintained that most whale species are not endangered and that eating whale is part of its food culture.
Last year, New Zealand Prime Minister John Key told his Japanese counterpart Shinzo Abe during his visit to Auckland that Kiwis want to see the end of whaling.
Mr Key at the time would not rule out getting the Navy involved if Japan breaches the court's ruling.
NZN | – Japan's whale meat restaurants are set to get fresh supplies with the resumption of what the country's government insists is scientific whaling. The country has decided to buck last year's International Court of Justice ruling and send its whalers back to sea under a revised plan. Under the plan submitted to the International Whaling Commission on Friday, Japan say the "scientifically reasonable" program will catch 333 minke whales in the Antarctic Ocean during the 2015-16 season, a two-thirds drop from the usual target of 1,000 reports Reuters. Japan says the new plan takes the United Nations court's concerns about the program into account. In its ruling, the ICJ said the former program, which allowed Japan to get around a ban on commercial whaling, was "not driven by scientific considerations." The court decided that scientists did not need to kill the whales in order to study them, reports the BBC, which notes that Japan doesn't hide the fact that the meat from the whales is eaten. When the program resumes, which could be before the end of this year, Australia is expected to strongly protest, as is New Zealand, where Prime Minister John Key warned last year that the country's navy might get involved if Japan decides to defy the ban, 3 News reports. (Scientists from other nations determined that what little scientific research is conducted on the whales is mostly useless and often very strange.) |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Veterans Day Off Act''.
SEC. 2. DEFINITIONS.
In this Act:
(a) Eligible Employee.--
(1) In general.--The term ``eligible employee'' means an
employee who--
(A) is a veteran, as that term is defined in
section 101 of title 38, United States Code; and
(B) has been employed for at least 12 months by the
employer with respect to whom leave is requested under
section 3.
(2) Exclusions.--The term ``eligible employee'' does not
include an individual employed by a public agency, as that term
is defined in section 3(e)(2) of the Fair Labor Standards Act
of 1938 (29 U.S.C. 203(3)(e)(2)).
(b) Employ; Employee.--The terms ``employ'' and ``employee'' have
the same meanings given such terms in subsections (e) and (g) of
section 3 of the Fair Labor Standards Act of 1938 (29 U.S.C. 203 (e)
and (g)).
(c) Employer.--The term ``employer'' means any person engaged in
commerce or in any industry or activity affecting commerce who employs
50 or more employees during a calendar year, and includes any person
who acts, directly or indirectly, in the interest of any employer to
any of the employees of such employer and any successor in interest of
an employer. In the previous sentence, the terms ``commerce'' and
``industry or activity affective commerce'' have the meaning given such
terms in section 101(1) of the Family and Medical Leave Act of 1993.
(d) Person.--The term ``person'' has the same meaning given such
term in section 3(a) of the Fair Labor Standards Act of 1938 (29 U.S.C.
203(a)).
(e) Secretary.--The term ``Secretary'' means the Secretary of
Labor.
SEC. 3. LEAVE REQUIREMENT.
(a) Entitlement to Leave.--
(1) In general.--Except as provided in paragraph (2), an
eligible employee shall be entitled to leave on Veterans Day
upon request if such employee would otherwise be required to
work on Veterans Day.
(2) Exceptions.--An employer may deny leave to an eligible
employee if providing leave to the employee would--
(A) negatively impact public health or safety; or
(B) cause the employer significant economic or
operational disruption.
(b) Type of Leave.--
(1) Unpaid leave permitted.--Leave granted under subsection
(a) may consist of unpaid leave.
(2) Substitution of paid leave.--An eligible employee may
elect, or an employer may require the employee, to substitute
any of the accrued paid vacation leave or personal leave of the
employee for leave provided under subsection (a).
(c) Duties of Employee.--Not less than 30 days before the Veterans
Day on which leave is requested to be taken, an employee requesting
leave under subsection (a) shall provide the employer with the
following:
(1) Written notice of the employee's intention to take
leave under subsection (a).
(2) Documentation verifying that the employee is a veteran.
(d) Duties of Employer.--
(1) Notice of decision.--Not less than 10 days before the
Veterans Day on which leave is requested to be taken, the
employer shall notify an employee requesting leave under
subsection (a)--
(A) whether the employee shall be provided leave;
and
(B) if so, whether the leave shall be paid or
unpaid.
(2) Denial of leave request.--If an employer receives
multiple requests for leave under subsection (a)(1) and denies
leave to more than one eligible employee in accordance with
subsection (a)(2), the employer should deny leave to the
minimum number of eligible employees practicable.
SEC. 4. PROHIBITED ACTS.
(a) Interference With Rights.--
(1) Exercise of rights.--It shall be unlawful for any
employer to interfere with, restrain, or deny the taking of or
the attempt to take, any leave provided under this Act.
(2) Discrimination.--It shall be unlawful for any employer
to discharge or in any other manner discriminate against any
individual for opposing any practice made unlawful by this Act.
(b) Interference With Proceedings or Inquiries.--It shall be
unlawful for any person to discharge or in any other manner
discriminate against any individual because such individual--
(1) has filed any charge, or has instituted or caused to be
instituted any proceeding, under or related to this Act;
(2) has given, or is about to give, any information in
connection with any inquiry or proceeding relating to any leave
provided under this Act; or
(3) has testified, or is about to testify, in any inquiry
or proceeding relating to any leave provided under this Act.
SEC. 5. INVESTIGATIVE AUTHORITY.
The Secretary shall have investigative authority with respect to
the provisions of this Act in the same manner and under the same terms
and conditions as the investigative authority provided under section
106 of the Family and Medical Leave Act of 1993, and the requirements
of section 106 of such Act shall apply to employers under this Act in
the same manner as such requirements apply to employers under section
106 of such Act.
SEC. 6. ENFORCEMENT.
The provisions of section 107 of the Family and Medical Leave Act
of 1993 shall apply with respect to the enforcement of the requirements
of this Act in the same manner and under the same terms and conditions
as such provisions apply with respect to the enforcement of the
requirements of title I of such Act.
SEC. 7. NOTICE.
(a) In General.--Each employer shall post and keep posted, in
conspicuous places on the premises of the employer where notices to
employees and applicants for employment are customarily posted, a
notice, to be prepared or approved by the Secretary, setting forth
excerpts from, or summaries of, the pertinent provisions of this title
Act information pertaining to the filing of a charge.
(b) Penalty.--Any employer that willfully violates this section may
be assessed a civil money penalty not to exceed $100 for each separate
offense. | Veterans Day Off Act - Entitles veterans who have been employed by an employer for at least 12 months, except those employed by a public agency, to leave from such employer on Veterans Day upon request if such veteran would otherwise be required to work on Veterans Day. Authorizes employers who employ 50 or more employees to deny leave if providing leave to veterans would negatively impact public health or safety or cause the employer significant economic or operational disruption.
Authorizes leave granted to consist of unpaid leave. Authorizes an employee to elect, or an employer to require the employee, to substitute accrued paid vacation leave or personal leave for leave provided under this Act.
Prohibits: (1) such employers from interfering with, restraining, or denying the taking of any leave provided under this Act; (2) such employers from discharging or discriminating against individuals for opposing practices made unlawful by this Act; and (3) any person from discharging or discriminating against individuals for filing any charge or instituting any proceeding under this Act, giving any information in connection with inquiries or proceedings relating to such leave, or testifying in inquiries or proceedings related to such leave.
Gives the Secretary of Labor investigative authority with respect to the provisions of this Act in the same manner and under the same terms and conditions as the investigative authority provided under the Family and Medical Leave Act of 1993.
Requires such employers to post in conspicuous places on their premises a notice with information pertaining to the filing of a charge under this Act. |
peripheral neurotoxicity induced by antineoplastic drugs ( vinca - alkaloids , taxanes , and platin - based compounds ) is a clinically significant complication that can be dose limiting and can substantially diminish the quality of life .
vincristine is a chemotherapeutic agent that can be used in the treatment of many types of human cancer , including leukemias , lymphomas , and sarcomas [ 1 , 2 ] .
the antitumor action of vincristine is due to its binding to beta - tubulin , which leads to disorganization of the axonal microtubule cytoskeleton .
however , peripheral neuropathy is a relatively common side effect of chemotherapeutic treatment with vincristine , sometimes greatly reducing patients ' quality of life and their ability to perform activities of daily living .
antidepressants and anticonvulsants have suppressive effects on neuropathic pain [ 4 , 5 ] , and antidepressants are widely used for the treatment of neuropathic pain .
indeed , antidepressants , particularly tricyclic antidepressants ( tcas ) , are regarded as first - line drugs for the treatment of neuropathic pain .
recently , newer antidepressants have become available , the antidepressant function of which is better understood than that of tcas ; they work by selectively inhibiting monoamine reuptake , namely , serotonin ( 5-ht ) and noradrenaline ( na ) .
these serotonin / noradrenaline reuptake inhibitors ( snris ) are also used clinically as a treatment modality for neuropathic pain [ 6 , 7 ] .
the antinociceptive effects of snris have been examined using a variety of animal models of pain .
the snris milnacipran and duloxetine have been shown to be efficacious for the prevention and/or reversal of pain in several preclinical models of acute and chronic pain in rodents .
yokogawa et al . demonstrated that milnacipran significantly attenuated late phase paw licking behavior in the formalin test and also reversed mechanical allodynia in the chronic constriction injury model and spinal nerve ligation model of neuropathic pain [ 1012 ] .
in addition , milnacipran had an antiallodynic effect in the paclitaxel - induced neuropathic pain model and the streptozotocin - induced diabetic neuropathy model and potentiated the antihyperalgesic effect of tramadol .
for duloxetine , clinical studies have confirmed its efficacy against pain in diabetic patients [ 1517 ] . in vivo ,
duloxetine significantly attenuated late phase paw licking behavior in the formalin test and also reversed mechanical allodynia in the spinal nerve ligation model of neuropathic pain .
importantly , duloxetine has also been shown to alleviate allodynia in several inflammatory and neuropathic pain models [ 1923 ] .
however , the antiallodynic effects of milnacipran and duloxetine on vincristine - induced mechanical allodynia have not yet been investigated .
the purpose of the present work was to examine the efficacy and validity period of the snris milnacipran and duloxetine on vincristine - induced neuropathic pain in mice .
male ddy - strain mice ( japan slc , hamamatsu , japan ) weighing an average of 2325 g at the time of testing were used in the experiments .
mice were housed individually in a colony maintained in a controlled environment ( 12 h light / dark cycle , room temperature 23c , 5060% relative humidity ) and had unlimited access to food pellets and water .
all behavioral experiments took place during the light period between 10:00 and 16:00 in a quiet room .
the animals belonging to the various treatment groups ( n = 10 per group ) were tested in randomized order . all experiments followed the guidelines on ethical standards for investigation of experimental pain in animals . additionally , the study was approved ( number 13012 ) by the committees of animal care and use of tohoku pharmaceutical university .
vincristine sulfate ( oncovin ; nippon kayaku company , tokyo , japan ) was administered intraperitoneally ( i.p . ) to mice at doses of 0.0250.1 mg / kg , once per day for 7 consecutive days .
milnacipran hydrochloride or duloxetine hydrochloride ( wako pure chemical industries , ltd , osaka , japan ) was administered i.p . to mice .
all drugs were dissolved in physiological saline , in an injection volume of 0.1 ml/10 g body weight . in the vehicle control group , physiological saline alone
mechanical allodynia of the hind paw was assessed using von frey filaments with 0.4 g bending force .
briefly , mice were placed individually in a plastic cage with a wire mesh bottom . after they had adapted to the testing environment for 60 min ,
the von frey filament was pressed perpendicularly against the mid - plantar surface of the hind paw from below the mesh floor and held for 35 s with the filament slightly buckled .
stimulation of the same intensity ( 0.4 g filament ) was applied to the point of bending 10 times to the hind paw at intervals of 5 s. mechanical allodynia was designated as the percentage of withdrawal responses ( % response ) to stimulation of the hind paw .
testing was performed for 2 days before the start of the experiment to accustom the mice to the testing procedures .
the statistical significance of the differences between groups was determined using one - way analysis of variance ( anova ) followed by dunnett 's test or two - way anova followed by bonferroni 's test .
the level of statistical significance was set at 5% ( p < 0.05 ) in all experiments .
statistics were performed using graphpad prism software ( graph pad software , inc . , san diego , ca ) .
vincristine or vehicle ( saline ) was administered to mice once per day for 7 days ( days 06 ) .
we evaluated withdrawal responses to mechanical stimulation applied to the hind paw using a von frey filament ( 0.4 g ) from day 0 to day 35 in ddy mice .
mechanical allodynia was not observed when vincristine was administered i.p . at a dose of 0.025
mg / kg , as measured on day 14 . however , when the dose was increased to 0.05 or 0.1 mg / kg , mechanical allodynia became marked ( figures 1(a ) and 1(b ) ) . with repeated daily dosing of 0.05 or 0.1 mg / kg of vincristine , mechanical allodynia peaked at day 14 after the start of administration and then decreased gradually , almost completely subsiding by day 35 . in 0.1 mg
/ kg vincristine - treated mice , mechanical allodynia was significant on days 328 compared with the saline control group ( figure 1(b ) ) .
thus , we subsequently used 0.1 mg / kg as the working dose of vincristine to induce mechanical allodynia .
in contrast to the repeated dosing regimen , mechanical allodynia was not observed after a single administration of vincristine ( 0.05 , 0.1 mg / kg ; data not shown ) .
the effect of vincristine on the overall health of the mice appeared to be minimal .
no mouse presented with weight loss or died within 35 days after administration . a single administration of milnacipran ( 40 mg / kg , i.p . ) or duloxetine ( 20 mg / kg , i.p . ) on day 14 , when allodynia peaked , had no effect on vincristine - induced mechanical allodynia ( figures 2(a ) and 2(b ) ) .
however , repeated milnacipran administration ( 20 or 40 mg / kg , once per day , i.p . ) or duloxetine administration ( 5 , 10 , or 20 mg / kg , once per day , i.p . ) for 7 days ( days 06 ) , in combination with vincristine , significantly attenuated vincristine - induced mechanical allodynia on day 7 in a dose - dependent manner ( figures 3(a ) and 4(a ) ) . similarly , when administered on days 713 ( after cessation of vincristine treatment ) , these repeated dosing regimens significantly attenuated vincristine - induced mechanical allodynia on day 14 in a dose - dependent manner for milnacipran or duloxetine ( figures 3(b ) and 4(b ) ) .
the single or chronic administration of milnacipran ( 40 mg / kg , i.p . ) or duloxetine ( 20 mg / kg , i.p . ) had no influence on the mechanical allodynia ( figures 2 , 3 , and 4 ) .
in this study , we demonstrated that repeated but not acute administration of vincristine ( 0.05 or 0.1 mg / kg , i.p . ) produced dose - dependent mechanical allodynia in male ddy - strain mice .
the mechanical allodynia was observed even after cessation of vincristine administration in this experimental model ( figures 1(a ) and 1(b ) ) .
these observations are consistent with those of other reports of vincristine inducing mechanical allodynia in mice .
the present study further demonstrated a significant attenuation of vincristine - induced mechanical allodynia by repeated milnacipran or duloxetine treatment .
snris such as milnacipran and duloxetine are used for the treatment of acute , persistent , neuropathic pain as supplementary analgesics [ 4 , 8 ] .
there have been several reports indicating that milnacipran and duloxetine have significant antinociceptive effects against nociceptive and inflammatory pain [ 913 , 1823 , 26 ] .
however , their efficacy for attenuating vincristine - induced mechanical allodynia remains to be established . in this study ,
repeated but not acute administration of the two agents significantly attenuated vincristine - induced mechanical allodynia , during both the development ( days 06 ) and maintenance ( days 714 ) stages of the allodynia . 5-ht and na are implicated in modulating descending inhibitory pain pathways .
the antiallodynic effects of snri in neuropathic pain models were predominantly attenuated by the noradrenergic system rather than by the serotonergic system at the spinal level .
recently , nakajima et al . reported that activation of the descending noradrenergic system and a subsequent increase of na in the spinal dorsal horn in a rat neuropathic pain model contributed to the antihyperalgesic effects of antidepressants such as tcas and snris .
in addition , the 2-adrenergic receptor agonists significantly inhibited chronic constriction injury of sciatic nerve - induced neuropathic pain in mice , thermal hyperalgesia , and spinal astrocyte activation in a rat model of monoarthritis , further implicating adrenergic signaling in analgesia .
central glial cells such as astrocytes and microglia play a prominent role in pain modulation [ 31 , 32 ] .
for instance , spinal astrocytes and microglia have been found to play critical roles in facilitating central plasticity following both nerve injury and inflammation [ 31 , 32 ] .
indeed , spinal glial cells contribute to the development of vincristine - induced painful neuropathy in a mouse model .
recently , ji et al . reported that spinal astrocytes also contribute to the pathogenesis of vincristine - induced painful neuropathy in a rat model and also the neuropathy induced activation of the spinal astrocyte .
the neuronal na transporter is functionally expressed in cultured rat astrocytes and snri potently inhibits na uptake in these cells .
the na uptake system in astrocytes is sensitive to milnacipran and duloxetine , and the therapeutic effects of snris may thus be mediated to some extent by their action on astrocytes . together with these findings
, our data suggest that chronic but not single milnacipran or duloxetine treatment attenuates vincristine - induced neuropathic pain , that is , at least in part , through the inhibition of astrocyte activation .
these results suggest that chronic vincristine administration induces mechanical allodynia and that repeated milnacipran and duloxetine administration may be an effective approach for the treatment of neuropathic pain caused by vincristine treatment for cancer . | vincristine is an anticancer drug used to treat a variety of cancer types , but it frequently causes peripheral neuropathy .
neuropathic pain is often associated with the appearance of abnormal sensory signs , such as allodynia .
milnacipran and duloxetine , serotonin / noradrenaline reuptake inhibitors , have shown efficacy against several chronic pain syndromes . in this study , we investigated the attenuation of vincristine - induced mechanical allodynia in mice by milnacipran and duloxetine . to induce peripheral neuropathy ,
vincristine was administered once per day ( 0.1 mg / kg , intraperitoneally ( i.p . ) ) for 7 days .
mechanical allodynia was evaluated by measuring the withdrawal response to stimulation with a von frey filament . in vincristine - treated mice ,
mechanical allodynia was observed on days 328 of vincristine administration . a single administration of milnacipran ( 40 mg / kg , i.p . ) or duloxetine ( 20 mg / kg , i.p . ) had no effect on vincristine - induced mechanical allodynia .
however , repeated administration of milnacipran ( 20 or 40 mg / kg , once per day , i.p . ) or duloxetine ( 5 , 10 , or 20 mg / kg , once per day , i.p . ) for 7 days significantly reduced vincristine - induced mechanical allodynia .
these results suggest that chronic vincristine administration induces mechanical allodynia , and that repeated milnacipran and duloxetine administration may be an effective approach for the treatment of neuropathic pain caused by vincristine treatment for cancer . |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Mothers' and Infants' Good Health
Act of 1995''.
SEC. 2. REQUIRED COVERAGE FOR CHILD BIRTH.
(a) In General.--A health plan that provides maternity benefits
that include benefits for child birth shall ensure that--
(1) in the case of delivery in a hospital or other
inpatient setting, coverage is provided for a minimum of 48
hours of inpatient care following a vaginal delivery and a
minimum of 96 hours of inpatient care following a caesarean
section for a mother and her newly born child in a health care
facility; and
(2) in the case of delivery in the home or other outpatient
setting, coverage for appropriate home health care in the
setting is provided for a minimum of 48 hours following
delivery.
(b) Terms of Coverage.--A health plan fails to provide coverage
required under subsection (a) if the plan imposes cost-sharing with
respect to care described in such subsection which varies depending on
the length of stay within the minimum period required under such
subsection.
(c) Prohibition.--In implementing the requirements of this section,
a health plan may not modify the terms and conditions of coverage based
on the determination by an enrollee to request less than the minimum
coverage required under subsection (a).
(d) Notice.--A health plan shall provide notice to each enrollee
under such plan regarding the coverage required by this section in
accordance with regulations promulgated by the Secretary of Health and
Human Services, in consultation with the National Association of
Insurance Commissioners. Such notice shall be in writing and
prominently positioned in any literature or correspondence made
available or distributed by the health plan and shall be transmitted--
(1) in the next mailing of general information made by the
plan to the enrollee,
(2) as part of the yearly informational packet sent to the
enrollee, or
(3) not later than January 1, 1996,
whichever is earliest.
(e) Enforcement.--
(1) Failure to provide coverage.--Any health plan that
violates the provisions of this section (other than subsection
(d)) shall be subject to a civil money penalty in an amount
determined by the Secretary of Health and Human Services.
(2) Failure to provide notice.--Any health plan that
violates the provisions of subsection (d) shall be subject to a
civil money penalty in an amount determined by the Secretary of
Health and Human Services.
(3) Process.--The provisions of section 1128A of the Social
Security Act (other than subsections (a) and (b)) shall apply
to civil money penalties under this subsection in the same
manner as they apply to a penalty or proceeding under section
1128A(a) of such Act.
(f) Health Plan.--
(1) In general.--As used in this section, the term ``health
plan'' means any plan or arrangement which provides, or pays
the cost of, health benefits.
(2) Exclusions.--Such term does not include the following,
or any combination thereof:
(A) Coverage only for accidental death or
dismemberment.
(B) Coverage providing wages or payments in lieu of
wages for any period during which the employee is
absent from work on account of sickness or injury.
(C) A medicare supplemental policy (as defined in
section 1882(g)(1) of the Social Security Act).
(D) Coverage issued as a supplement to liability
insurance.
(E) Worker's compensation or similar insurance.
(F) Automobile medical-payment insurance.
(G) A long-term care policy, including a nursing
home fixed indemnity policy (unless the Secretary
determines that such a policy provides sufficiently
comprehensive coverage of a benefit so that it should
be treated as a health plan).
(H) Such other plan or arrangement as the Secretary
of Health and Human Services determines is not a health
plan.
(3) Certain plans included.--Such term includes any plan or
arrangement not described in any subparagraph of paragraph (2)
which provides for benefit payments, on a periodic basis, for--
(A) a specified disease or illness, or
(B) period of hospitalization,
without regard to the costs incurred or services rendered
during the period to which the payments relate.
SEC. 3. EFFECTIVE DATE.
The provisions of section 2 shall apply to all health plans
offered, sold, issued, or renewed after the date of the enactment of
this Act. | Mothers' and Infants' Good Health Act of 1995 - Requires a health plan that provides maternity benefits that include benefits for child birth to provide coverage for a minimum amount of time following delivery in: (1) a health care facility; and (2) the home or other outpatient setting. Prohibits a health plan from modifying the terms and conditions of coverage, if an enrollee requests less than the minimum coverage required in this Act.
Requires a health plan to provide notice, as specified, to each enrollee regarding the coverage required in this Act.
Establishes civil penalties for failure to provide coverage and failure to provide notice. |
hashimoto encephalopathy ( he ) is known as a steroid- responsive encephalopathy associated with autoimmune thyroiditis or nonvascular inflammation - related autoimmune meningoencephalitis . the average age of onset of he is approximately 50 years ; and it is more common in women . the onset of he may be acute or subacute .
the course of most he cases is relapsing and remitting , which is similar to that of vasculitis and stroke .
in this article , we present a previously healthy 32 years old;veterinarian male with palatal myoclonus , as a rare presentation of this disorder , and review the neurologic aspects of hashimoto encephalitis .
the clinical presentation of he is characterized by progressive cognitive decline tremor , transient aphasia , seizures , abnormal gait , sleep disorder and stroke - like episodes .
myoclonus , either generalized or multifocal , and tremor , often of the bilateral upper extremities , is the most frequently observed involuntary movements in he .
a previously healthy 32 years old ; veterinarian male , referred to the emergency department complaining about 2 episodes of generalized tonic clonic seizure within the past 24 hours .
according to his wife , he had depressed mood and psychomotor slowing during the past 3 weeks .
he also had episodes of confusion , agitation , visual hallucinations , decrement of interpersonal relationship , generalized purities and flushing .
three days before admission , he had abnormal movements of the palate and tongue . on physical examination , the patient was ill and lethargic .
there was a low grade fever ( temp : 37.4 auxiliary ) , but other vital signs were normal .
on general examination , there were itching excoriations on his skin , but other systemic examinations were normal .
neurologic examination was normal , apart from mild confusion and myorrhythmic movements of tongue and soft palate .
the patients mri showed abnormal symmetric hyper signality in both caudate nuclei and putamens on t2 and flair .
2 ) flair sequence mri were shown symmetric abnormal hypersignality in bilateral caudate and putamen t2 mri of medulla shows no abnormality in inferior olive the csf was clear with normal level of protein and glucose .
antinuclear antibodies , anti - ds - dna , anti ss - a , anti ss - b , lupus anticoagulant , anti phospholipid ab and rf were normal .
thyroid function tests were within normal limits , but the thyroid thyroglobulin antibody ( tgha ) titer was 120 iu / ml ( normal < 22 iu / ml ) and the thyroid peroxidase antibody ( anti - tpo ) titer was 356u / ml ( normal < 60 iu / ml ) .
a diagnosis of he was made , and the patient was treated with oral prednisolone 1 mg / kg / d , levothyroxin and anticonvulsants . before starting treatment with prednisolone , the patient had 3 - 4 episodes of simple focal seizures per day which were not controlled with antiepileptic drugs .
less than 24 hours after the initiation of prednisolone , the palatal myorrhythmic movements , itching , and flushing were subsided and focal seizures never repeated .
we did not do needle biopsy of thyroid gland . on the follow - up ,
at days 10 and 40 , the patient had no seizures and the palatal myorrhythmic movements disappeared ; and eeg was normal at 40 . the anti- tpo level was decreased to 73 iu / ml after 6 months .
as our findings , we excluded our differential diagnoses such as cns infection , acute disseminated encephalomyelitis , primary hypoxic injury , prolonged hypoglycemia , degenerative diseases , toxic encephalopathies and lymphoma . also , we confirmed our diagnosis , hashimoto encephalopathy , with elevated serum levels of anti - tpo and tgha and the response of the patient to our treatment .
he is known as steroid - responsive encephalopathy associated with autoimmune thyroiditis ( 13 ) .
the first set of criteria for the diagnosis of he was published by peschen - rosin et al . in 1999
these criteria encompassed unexplained occurrence of relapsing myoclonus , generalized seizures , psychiatric disorders or focal neurological deficits and conditions among which are : abnormal eeg , elevated thyroid antibodies , elevated csf protein , excellent response to steroids and unrevealing cerebral mri .
the average age of onset , is approximately 50 years ( range , 9 to 84 y ) , and he is more common in women.(2 , 6 ) the onset of he may be acute or subacute .
the course of most he cases is relapsing and remitting , which is similar to that of vasculitis and stroke ( 13 , 7 ) .
the clinical presentation of he is characterized by progressive cognitive decline , behavioral change , tremor , transient aphasia , seizures , abnormal gait , sleep disorder , stroke - like episodes , generalized hyper- reflexia and other signs of pyramidal tract involvement , psychosis ( visual hallucinations and paranoid delusions ) ( 13 ) .
myoclonus and tremor , often of the bilateral upper extremities and palatal myorrhytmia , are the most frequently observed involuntary movements in he ( 8) .
our case illustrates the importance of considering rare but treatable causes of encephalopathy in a patient presenting with subacute cognitive decline , seizure and palatal myorrhythmia .
however , a recent report has shown that they are capable of binding cerebellar astrocytes suggesting a pathogenic role .
focal spikes , sharp waves and transient epileptic activity may be seen ( 9 ) .
approximately 50% of cases with he show brain- imaging abnormalities ; cerebral atrophy is the most common alteration . diffuse abnormalities in white matter and meningeal enhancement or nonspecific t2 signal abnormalities in subcortical white matter have been reported ( 1 , 2 ) . as he usually responds to corticosteroid therapy well , corticosteroids are the preferred drugs for its treatment , whereas other immunosuppressants have also been reported to treat he successfully ( 6 , 10 ) .
most patients have a good prognosis unless there is a delay in diagnosis and treatment .
we suggest that both thyroid function and thyroid antibody assessment be included in the assessment of patients with rapidly progressive cognitive dysfunction and encephalopathies . | objectivehashimoto encephalopathy ( he ) is known as a steroid- responsive encephalopathy associated with autoimmune thyroiditis or nonvascular inflammation - related autoimmune meningoencephalitis . the average age of onset of he is approximately 50 years ; and it is more common in women . the onset of he may be acute or subacute .
the course of most he cases is relapsing and remitting , which is similar to that of vasculitis and stroke.methodsin this article , we present a previously healthy 32 years old;veterinarian male with palatal myoclonus , as a rare presentation of this disorder , and review the neurologic aspects of hashimoto encephalitis.resultsthe clinical presentation of he is characterized by progressive cognitive decline tremor , transient aphasia , seizures , abnormal gait , sleep disorder and stroke - like episodes.myoclonus , either generalized or multifocal , and tremor , often of the bilateral upper extremities , is the most frequently observed involuntary movements in he.conclusionthe rapidly progressive cognitive dysfunction and encephalopathies observed . |
By Ken Lemon
A teenager, who police said was killed when he was pulled feet first into a wood chipper in Kings Mountain, has been identified.
Emergency crews responded Saturday to Hawthorne Road for the accident.
Man pulled into a wood chipper and killed at a Kings Mountain home. Police say the death is accidental. No foul play. Details on @wsoctv — Ken (@kenlemonWSOC9) December 7, 2015
The victim has been identified as Mason Cox, 19, from Gastonia.
Channel 9 learned Cox had just started working for Crawford's Tree and Stump Grinding Service, and Saturday was his first day on the job.
Photos of Mason Cox
Investigators said no one witnessed Cox get pulled into the wood chipper.
Jon Crawford, the owner of the business, suffered a heart attack at the scene and had to be rushed to the hospital, police said.
Alice Neal has been haunted by the disturbing thought of her grandson being dragged into the wood chopper.
"How could this happen to such a vibrant, young gentleman?" Neal asked.
Officers determined the incident was accidental, and no foul play was suspected.
Cox was putting tree limbs into the wood chipper when Crawford heard the machine get bogged down. Crawford quickly hit the kill switch and put the machine in reverse, but he could not save Cox from getting pulled into the machine.
Coworkers who saw Cox's body became emotional. They started running around, ripping off their gloves and hats. Neighbors, who did not know what had happened, thought the crew was being attacked by bees.
Cox's family was stunned. They have received constant calls of support since his death.
OSHA is investigating the incident.
Be sure to download the WSOC-TV Wake Up app to get the latest breaking news, weather and traffic on your phone first thing in the mornings.
Read more top trending stories on wsoctv.com:
||||| A Gastonia man was pulled into a wood chipper and killed over the weekend, police say.
Officials believe 19-year-old Mason Scott Cox was attempting to kick a limb into the chipper when he got pulled in. The incident happened around 12:37 p.m. Saturday on Hawthorne Road in Kings Mountain.
The company, Crawford Tree Service out of Belmont, was cutting down trees in a yard. The Department of Labor and Kings Mountain Police are investigating. They say the death was accidental and no foul play is believed to be involved.
Cox was found inside the wood chipper and pronounced dead on scene, officials say.
Cox's family spoke to WBTV in an interview Monday morning. Cox's mother, Debra Sisk, said the teen had very limited experience in the tree removal industry, but had worked on cell towers before. She questions whether he was being supervised when the accident happened.
"It was his first day on this job. He was trying to find work and he had been putting in applications," Sisk explained.
She said she got the phone call about the accident Saturday afternoon and said it was horrifying to learn how her son had died.
"I just started screaming when I found out how he died. It's bad enough that's he's gone," she said.
Family members said they currently have no plans to contact the company Cox was working for. They said they aren't angry over the incident, but they would like to know how the accident happened.
"I loved him very much and I'm going to miss him very much," said Cox's mother.
Jon Crawford, owner of Crawford Tree Service, spoke to WBTV about the incident in an interview over the phone. He said Cox was working for him as a subcontractor Saturday, He said he still isn't sure how the accident happened.
"The limb must have grabbed a piece of his clothing and took him into the chipper," said Crawford.
The business owner said that the work site was safe and Cox wasn't performing any tasks too difficult for a beginner.
"I've been in the business for 26 years. I've had one other accident where a person was injured. Mason Cox was working side by side with two experienced employees," Crawford said.
He said the incident has left him filled with grief.
"I have not slept. I am sick from it," Crawford said. "I would trade places with that child right now."
He said his business is going to temporarily close because of the incident.
Copyright 2015 WBTV. All rights reserved. | – A North Carolina teenager died one of the most horrific workplace deaths imaginable on his first day on the job. Mason Cox, 19, died on Saturday after being pulled feet-first into a wood chipper, police in Kings Mountain say. WSOC reports that co-workers who had been cutting down trees in a yard were so distressed by the sight of Cox's body that they ran around ripping off their gloves and hats, causing neighbors to think that they were being attacked by bees. Police say John Crawford (some sources have him listed as Jon Crawford), the owner of Crawford's Tree and Stump Grinding Service, was hospitalized after having a heart attack at the scene, the station reports. Officials tell WRAL that Cox apparently became caught in the machine when he tried to kick a tree limb inside and his clothing snagged. Crawford, who has temporarily shut down the business, says Cox had been assigned a task considered safe for a beginner. "I've been in the business for 26 years. I've had one other accident where a person was injured. Mason Cox was working side by side with two experienced employees," he tells WBTV, adding that he is grief-stricken over the incident. "I have not slept. I am sick from it," he says. "I would trade places with that child right now." Cox's mother says she started screaming when she discovered how he died. "I loved him very much and I'm going to miss him very much," she tells WBTV. (This state is the deadliest for US workers.) |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Global Investment in American Jobs
Act of 2012''.
SEC. 2. FINDINGS.
Congress finds the following:
(1) It remains an urgent national priority to improve
economic growth and create new jobs.
(2) National security requires economic strength and global
engagement.
(3) Businesses today have a wide array of choices when
considering where to invest, expand, or establish new
operations.
(4) Administrations of both parties have consistently
reaffirmed the need to maintain an open investment climate as a
key to domestic economic prosperity and security.
(5) The United States has historically been the largest
worldwide recipient of global investment but has seen its share
of inbound global investment decline relative to its gross
domestic product in recent years.
(6) Governors and mayors throughout the United States face
increasing competition from other countries as they work to
recruit investment from global companies.
(7) Foreign direct investment can benefit the economy and
workforce of every State and Commonwealth in the United States.
(8) According to the latest Federal statistics, the United
States subsidiaries of companies headquartered abroad
contribute to the United States economy in a variety of
important ways, including by--
(A) providing jobs for nearly 5,300,000 Americans
with average compensation that is approximately 33
percent higher than the national private-sector
average, as these jobs are often in high-skilled, high-
paying industries;
(B) strengthening the United States industrial base
and employing nearly 15 percent of the United States
manufacturing sector workforce;
(C) establishing operations in the United States
from which to sell goods and services around the world,
thereby producing nearly 18 percent of United States
exports;
(D) promoting innovation with more than
$41,000,000,000 in annual United States research and
development activities;
(E) paying nearly 17 percent of United States
corporate income taxes; and
(F) purchasing more than $1,800,000,000,000 in
domestic goods and services annually from local
suppliers and small businesses, amounting to 80 cents
for every dollar spent on input purchases.
(9) These companies account for 5.8 percent of United
States private sector Gross Domestic Product.
(10) The Secretary of Commerce and the Secretary of State
have declared increasing inbound global investment to be among
their top priorities.
(11) The President issued a statement in 2011 reaffirming
the longstanding open investment policy of the United States
and encouraged all countries to pursue such a policy.
(12) The President signed an Executive order in 2011 to
establish the SelectUSA initiative, aimed at promoting greater
levels of business investment in the United States.
(13) The President's Council on Jobs and Competitiveness in
2011 recommended the establishment of a National Investment
Initiative to attract $1,000,000,000,000 in new business
investment from abroad.
(14) The United States and the European Union recently
unveiled a set of principles aimed at promoting a more open
climate for international investment and intended as a model
for countries around the world.
(15) Maintaining the United States commitment to open
investment policy encourages other countries to do the same and
enables the United States to open new markets abroad for United
States companies and their products.
SEC. 3. SENSE OF CONGRESS.
It is the sense of Congress that--
(1) the ability of the United States to attract inbound
investment, particularly net new investment, is directly linked
to the long-term economic prosperity, competitiveness, and
security of the United States;
(2) in order to remain the most attractive location for
global investment, Congress and Federal departments and
agencies should be mindful of the potential impact upon the
ability of the United States to attract foreign direct
investment when evaluating proposed legislation or regulatory
policy;
(3) it is a top national priority to enhance the
competitiveness, prosperity, and security of the United States
by--
(A) removing unnecessary barriers to inward global
investment and the jobs that it creates throughout the
United States; and
(B) promoting policies to ensure the United States
remains the premier destination for global companies to
invest, hire, innovate, and manufacture their products;
and
(4) while foreign direct investment can enhance our
economic strength, policies regarding foreign direct investment
should reflect national security interests.
SEC. 4. AMENDMENT TO FOREIGN DIRECT INVESTMENT AND INTERNATIONAL
FINANCIAL DATA IMPROVEMENTS ACT OF 1990.
Section 3 of the Foreign Direct Investment and International
Financial Data Improvements Act of 1990 (22 U.S.C. 3142) is amended by
adding at the end the following:
``(d) Review of United States Laws and Policies on Foreign Direct
Investment in the United States.--
``(1) Review.--The Secretary of Commerce, in coordination
with the Federal Interagency Investment Working Group and the
heads of other relevant Federal departments and agencies, shall
conduct an interagency review of United States laws and
policies on foreign direct investment in the United States and
develop recommendations to make the United States more
competitive in attracting and retaining strong investment flows
from abroad.
``(2) Additional matters to be included.--The review
conducted pursuant to paragraph (1) shall include the
following:
``(A) A review of the current economic impact of
foreign direct investment in the United States and
broader trends in global cross-border investment flows,
including an assessment of the current United States
competitive position as an investment location for
companies headquartered abroad.
``(B) A review of United States laws and policies
that uniquely apply to foreign direct investment in the
United States, with particular focus on those laws and
policies that may have the effect of diminishing or
promoting the ability of the United States to attract
and retain foreign direct investment.
``(C) A review of ongoing Federal Government
efforts to improve the investment climate, reduce
investment barriers, and facilitate greater levels of
foreign direct investment in the United States.
``(D) Recommendations based on the review carried
out pursuant to subparagraph (B), including a
comparative analysis of efforts of other competing
countries, to make the United States more competitive
in attracting global investment.
``(E) The impact of foreign direct investment on
innovation and national economic competitiveness.
``(F) A review of State and local government
initiatives to attract foreign investment.
``(3) Comment period.--The review conducted under paragraph
(1) shall include an open comment period to solicit public
input on matters covered by the review.
``(4) Inclusion in report.--The Secretary of Commerce shall
include the results of the review conducted pursuant to
paragraph (1) in the first report prepared under subsection (a)
of this section on or after the date of the enactment of the
Global Investment in American Jobs Act of 2012.''.
Passed the House of Representatives September 19, 2012.
Attest:
KAREN L. HAAS,
Clerk. | Global Investment in American Jobs Act of 2012 - Expresses the sense of Congress that: (1) U.S. ability to attract inbound investment (particularly net new investment) is directly linked to U.S. long-term economic prosperity, competitiveness, and security; (2) Congress and federal departments and agencies should be mindful of the potential impact upon U.S. ability to attract foreign direct investment when evaluating proposed legislation or regulatory policy; (3) it is a top national priority to enhance U.S. competitiveness, prosperity, and security by removing unnecessary barriers to inward global investment and the U.S. jobs it creates and promoting policies to ensure the United States remains the premier destination for global companies to invest, hire, innovate, and manufacture their products; and (4) U.S. policies regarding foreign direct investment should reflect national security interests.
Amends the Foreign Direct Investment and International Financial Data Improvements Act of 1990 to direct the Secretary of Commerce to conduct an interagency review of U.S. laws and policies on foreign direct investment in the United States and develop recommendations to make the United States more competitive in attracting and retaining strong investment flows from abroad. |
on the number theoretical properties of the geometric structures arising from physics there has been growing interest . though perhaps relatively nascent a field in comparison to the tremendous cross - fertilization which algebraic and differential geometry have enjoyed with gauge and string theories , ever augmenting importance and ever increasing profundity of these number theoretic connections
compel us .
recent developments in investigating calabi - yau varieties over finite fields @xcite , modularity of zeta functions of calabi - yau manifolds @xcite , emergence of modular forms and moonshine behaviour in mirror maps , gromov - witten invariants and matrix models @xcite , and especially geometric perspectives on langlands duality via s - duality @xcite exemplify the incipience of arithmetic within a physical context , in particular with regard to the visions of the langlands programme .
our concern shall be supersymmetric gauge theory , the physics , the geometry , as well as the interplay thereof have established themselves as a canonical subject , of rich structure and fundamental importance .
the algebraic geometry of the theory has been crucial to such deep insight as the holographic principle . indeed , in the ads / cft correspondence , wherein the gauge theory arises from the world - volume dynamics of branes , the space of vacua parameterizes precisely the bulk geometry , typically calabi - yau .
this vacuum moduli space ( vms ) of gauge theories has itself been studied @xcite , and with the advances in computational commutative algebra , been subject to new scrutiny @xcite , uncovering perhaps unexpected signatures in such standard examples as the mssm @xcite or sqcd @xcite .
a programme of enumerating operators in a supersymmetric gauge theory has recently been constructed , the methodology , dubbed the `` plethystic programme '' , harnesses the algebraic geometry of the classical vms , determined from certain flatness conditions once the lagrangian is known @xcite . interpreting the vacuum as prescribed by an ideal in a , possibly complicated , polynomial ring , the hilbert series and its plethystic exponentiation
can then be regarded as grand canonical partition function which then encodes the chiral ring of operators of the gauge theory as a statistical - mechanical system .
we are therefore naturally endowed with two implements of which we feel obliged to take advantage : ( 1 ) a wealth of experimental data in the form of catalogues of supersymmetric gauge theories , each of which engendering an algebraic variety , realized as the vms , and ( 2 ) an algorithmic framework within which the geometry of the vms is exploited for the sake of enumeration of the spectrum of bps operators and in which a fruitful dialogue between combinatorics and gauge theory is engaged
. this concurrent inspiration , experimental and theoretical , in further accordance with the aforementioned skein of number theory already weaving herself into the tapestry of algebraic geometry arising from physics , shall suffice to serve as a beacon to our path . and
the path on which we are led will be as follows .
we commence with a brief review in [ s : rev ] , setting notation and laying the foundation , of the two chief protagonists .
first , we outline how to obtain the moduli space of vacua , given the ( @xmath0 superspace ) lagrangian of an arbitrary supersymmetric gauge theory , by algorithmically recasting the f- and d - flatness conditions as a quotient of the space of ( mesonic ) gauge invariant operators ( gio ) by the jacobian ideal of the superpotential .
the vms is then explicitly realized as an affine cone over a ( weighted ) projective variety .
the geometry , and in particular the hilbert series of the vms and combinatorial functionals thereof , is then utilized in the enumeration of the gios via the syzygies .
second , of the vast subject of algebraic varieties over finite number fields we touch upon some rudiments which will be of use .
we emphasize on the construction of the local zeta function and the beautiful restriction of its rational form by the weil conjectures .
then , forming the euler product over primes , we remind the reader of the arrival at the global hasse - weil zeta function and its dirichlet l - series expansion .
thus armed , we march through a multitude of gauge theories in
[ s : eg ] , many of which are well - known , such as the free theory and sqcd .
we will investigate these gauge theories under our new light , by finding the vms , which is then subject to plethystic analyses , some of which have already been investigated through the plethystic programme in the literature , but more importantly , to the reduction over finite fields .
a host of zeta functions is then constructed for these field theories , and various properties , observed .
fortified by our gaining experience on the two enumerative problems , one counting the syzygies and the other , zeros over number fields , one could not resist but to perceive them , both deeply rooted in gauge theory , in a unified outlook .
we attempt , in [ s : compare ] , to glimpse at this unifying principle , and show how one may proceed from one to the other , whereby establishing a curious duality between sets of gauge theories , with the geometric invariant properties of one controlling the arithmetic properties of another . in the case where the vms is dimension one and calabi - yau , _ viz .
_ , the elliptic curve , this correspondence is very much in the spirit of the modularity theorem of taniyama - shimura - weil - wiles .
we trudge on , in [ s : asym ] , towards the asymptotic behaviour of the operators in the gauge theory , already an integral component of the plethystic programme , but now accompanied by this duality , and see once more how the emergence of the dirichlet series in governing the large r - charge and large @xmath1 trends in the physics . finally
, we part with concluding remarks and prospects in [ s : conc ] .
let us begin with a rather pedagogical presentation of the two subjects which will be crucial to our ensuing investigations .
the contrast and parallels between them will constitute the comparative study in which we shall engage .
the first originates from supersymmetric gauge theories and the _ point dappui _ is the syzygies of the vacuum moduli space as an algebraic variety ; the second is key to arithmetical properties of algebraic varieties and whose foundations rest upon the hasse - weil zeta function . given a gauge theory , one of the most fundamental tasks is the construction of its gauge invariant operators . in the case of supersymmetric gauge theories , especially those arising in the context of string theory , exhibiting as quiver gauge theories living on the world - volume of branes , due to the intrinsically geometrical nature of the situation , these operators are inextricably linked to the vacuum geometry of the theory .
we shall restrict our attention to @xmath0 supersymmetric gauge theories in @xmath2-dimensions on whose vacuum geometry we now briefly expound ; the analysis extends itself readily to higher supersymmetries in other dimensions .
an @xmath0 ( global ) supersymmetric gauge theory is given by the action @xmath3 \ , \ ] ] with the @xmath4 variables parameterizing @xmath0 superspace over which we integrate .
the @xmath5 are chiral superfields transforming in some representation @xmath6 of the gauge group @xmath7 ; @xmath8 is a vector superfield transforming in the lie algebra @xmath9 ; @xmath10 , the gauge field strength , is a chiral spinor superfield ; and @xmath11 is the superpotential , which is a holomorphic and typically polynomial , function of the @xmath5 . upon integrating over superspace
, we obtain the scalar potential of the theory : @xmath12 where @xmath13 are the scalar components of the chiral fields @xmath5 , and with @xmath14 being their charges . when the gauge group is abelian , one could , in addition , allow a fayet - illiopoulos ( fi ) term to the lagrangian : @xmath15 with fi parametre @xmath16 .
the vacuum of the above theory is the minimum of the potential , which , being a sum of squares , occurs when each squared quantity vanishes : @xmath17 for supersymmetric theories , the ( classical ) vacuum , defined by the above flatness conditions for the f- and d - terms , is non - trivial , and is , in fact , an affine algebraic variety generically @xcite of greater than one complex dimension .
therefore , there is a continuous moduli of vacua and this variety is commonly called the * vacuum moduli space * ( vms ) , @xmath18 .
the solution space of the f - terms alone is also of significant interest and is known as the * master space * @xcite ( cf . review in @xcite ) . whereas gives the explicit defining equation of @xmath18 , the standard geometrical approach is to construe the d - terms as gauge invariants , subject to the vanishing of the f - terms .
more specifically , @xmath18 is a git quotient of d - terms by the f - terms @xcite .
calculationally , one can establish a convenient algorithm @xcite , using the techniques of computational algebraic geometry , to interpret the d - term invariants as a polynomial ring map from the ideal defined by the f - terms , with its image the ideal defining @xmath18 in a convenient grbner basis .
the procedure can be summarized succinctly as follows . 1 .
let there be @xmath19 ( scalar - components of super-)fields @xmath20 and start with polynomial ring @xmath21 $ ] ; 2 .
identify the obvious set of mesonic gios and find the generating set @xmath22 , consisting of @xmath23 gauge invariants ( the set of gios is always finitely generated ) ; this prescribes a ring map between two polynomial rings : @xmath21 \stackrel{d}{\longrightarrow } { \mathbb{c}}[d_1 , \ldots , d_k]$ ] ; 3 . now incorporate superpotential @xmath24 , generically a polynomial in the fields @xmath13 and find its jacobian ideal of partial derivatives ( f - flatness ) : @xmath25 ; 4 .
the vms is then explicitly the image of the ring map @xmath26 } { \ { f = \langle f_1 , \ldots , f_m \rangle \ } } \stackrel{d = gio}{\longrightarrow } { \mathbb{c}}[d_1 , \ldots , d_k ] , \quad { { \cal m}}\simeq { \rm im}(d ) \ .\ ] ] the algebro - geometric nature of the vms is especially pronounced in the context of string theory .
when a single brane is placed transversely to a non - trivial back - ground , as in the ads / cft correspondence , a duality is established between the world - volume physics and the bulk supergravity . in particular , if a d3-brane is placed transverse to a local , affine calabi - yau three - fold singularity @xmath18 , filling the 10-dimensions of type iib , the world - volume is precisely a @xmath2-dimensional gauge theory with @xmath0 supersymmetry , product gauge group and bi - fundamental matter , encoded conveniently into a quiver . by construction , the mesonic ( _ i.e. _ , operators composed of direct contraction , involving no more than the kronecker delta tensor , of the chiral fields ) vms of this gauge theory , computed from , is exactly the calabi - yau three - fold @xmath18 .
when @xmath1 parallel coincident d3-branes are present , the vms , due to the permutation on the branes , simply becomes @xmath27 , the @xmath1-th symmetrized product of @xmath18 .
we are interested in the complete spectrum of bps mesonic operators in the gauge theory .
as mentioned above , the space of these objects , quotiented by the f - flat constraints , should give rise to the vms @xmath18 .
these mesonic gauge invariant operators fall into two categories : single- and multi - trace .
the former consists of words in the operators , with gauge - indices contracted but only a single overall trace and the latter , various products of the single - trace gauge invariants .
we shall denote the generating function of the single - trace gauge invariants at @xmath1 branes ( or , equivalently , for @xmath28 matrices in the gauge theory ) as @xmath29 and that of the multi - trace invariants , @xmath30 ; then , the @xmath31-th coefficient in the series expansion would enumerate the corresponding gauge invariants , where @xmath31 is a natural level corresponding to , for example , the total r - charge of the gauge theory . using the algebraic geometry of @xmath18 to construct @xmath32 and @xmath33 , and hence to address
the counting problem is the purpose of the so - called * plethystic programme * , developed in @xcite and furthered in @xcite . without much ado , let us briefly summarize the key points of this programme , referring the reader to details to _ loc .
cit_. * the quantity @xmath34 , counting the single - trace gauge invariants at large @xmath1 is equal to @xmath35 ; this is the _ point dappui _ of our construction .
the level ( r - charge ) @xmath31 imposes a natural grading on the polynomial ring in which @xmath18 is an ideal and hence the generating function is the hilbert series of @xmath18 in the suitable affine cordinates embedded by the f- and d - terms : @xmath36 here , the coefficient @xmath37 is simultaneously the number of single - trace gauge invariants at total r - charge @xmath31 and the complex dimension of the @xmath31-graded piece of the cordinate ring prescribed by @xmath18 ; * for arbitrary @xmath1 , the relation between the single- and multi - trace gios are related by @xmath38 , \quad g_{\infty}(t ) = pe[g_1(t ) ] ; \qquad g_{n}(t ) = pe[f_n(t)]\ ] ] where @xmath39 $ ] is the * plethystic exponential * functional defined as @xmath40 = \exp\left ( \sum_{n=1}^\infty \frac{f(t^n ) - f(0)}{n } \right ) = \frac{1}{\prod\limits_{n=1}^\infty ( 1-t^n)^{a_n } } \ ; \ ] ] the structure of the infinite - product incarnation of this function should be reminiscent of the bosonic oscillator partition function ; * the plethystic exponentiation has an analytic inverse , called the plethystic logarithm and is given in terms of the number - theoretical mbius function @xmath41 : @xmath42 * the defining equation , or syzygy , of @xmath18 is given by @xmath43 , which can be readily obtained from the plethystic logarithm of the hilbert series : @xmath44 = \mbox { defining equation of $ { { \cal m}}$}.\ ] ] when , in particular , @xmath18 is a complete intersection variety , @xmath45 is a terminating polynomial . * to obtain the counting for arbitrary @xmath1 , we promote @xmath39 $ ] to a parametre - inserted version and define the function @xmath46 dependent on the fugacity parametre @xmath47 .
the series expansion of @xmath48 in @xmath47 gives @xmath49 , the multi - trace generating function at given @xmath1 , as its coefficients .
the single - trace generating function @xmath50 is then retrieved as @xmath51 $ ] .
we see , therefore , that the hilbert series , through the plethystic functions , links the algebraic geometry of @xmath18 and the enumeration of the gios , single- and multi - traced , of the @xmath0 gauge theory whose vms is @xmath18 .
it is thus expedient to quickly remind the reader some key features of @xmath52 .
it is important that the hilbert series is a _ rational function _ in @xmath53 and can be expressed in two ways : @xmath54 where @xmath23 is the dimension of the ambient affine space in which @xmath18 embeds . in either guise , the numerators @xmath55 and @xmath56 are polynomials with _ integer _ coefficients and
@xmath57 is the degree of @xmath18 .
the powers of the denominators are such that the leading pole captures the dimension of the embedding space and the manifold , respectively . when expanding the hilbert series into a taylor series , then , the coefficients have polynomial growth and is called the hilbert polynomial .
we remark that for _ non - commutative _ graded rings and associated spaces , it is not necessary that the hilbert series be rational @xcite ; it would indeed be interesting to investigate such circumstances , especially since to d - brane gauge theories one should associate a non - commutative algebra , whose centre is the classical vms @xcite . in this section ,
we remind the reader of some well - known results on algebraic varieties defined over finite fields . in particular
, we shall address some basic principles of local zeta functions and the weil conjectures as well as global zeta function and their manifestation as l - functions .
in due course , we will see expressions reminiscent of our plethystic functions discussed in the previous section .
first , by a finite field we mean a number field with a finite number of elements ( cf .
we are acquainted with @xmath58 ; this is simply the cyclic group of @xmath59 elements for some prime number @xmath59 ( called the * characteristic * of the field ) , with members represented by @xmath60 and the field axioms for addition , multiplication and division being the usual arithmetic modolo @xmath59 .
less familiar are perhaps the finite ( galois ) extensions of this field , these are @xmath61 , consisting of @xmath62 elements for some positive integer @xmath63 .
these elements can be explicitly constructed as follows .
take the polynomial ring @xmath64 $ ] with coefficients in the field @xmath58 , and consider a monic irreducible polynomial @xmath65 of degree @xmath63 ; then the quotient ring , by the principal ideal @xmath66 @xmath64 / ( f(t))$ ] , is a field of @xmath62 elements .
it is well - known that @xmath61 for various primes @xmath59 and positive integers @xmath63 are all the finite number fields .
our main purpose is to consider an algebraic variety @xmath67 , defined not over the field @xmath68 of complex numbers , but , rather , over @xmath61 , _
i.e. _ , all indeterminates are to take values in these finite fields ( _ cf .
e.g. _ @xcite ) . as such ,
our usual notion of a variety now simply becomes a discrete set of points .
an exponentiated generating function , can be formed for the number of points @xmath69 of @xmath67 over @xmath62 : @xmath70 this is dubbed the * local zeta function * of the variety @xmath67 for the prime @xmath59 because it is localized at a fixed prime .
we can delocalize by taking the product of the above over all primes ( we will encounter so - called primes of good versus bad reduction later ) giving us the so - called * global * , or * hasse - weil * , zeta function : @xmath71 it is customary to apply the substitution @xmath72 to the above , for reasons which will soon become apparent in the ensuing examples , to which we now turn . [ [ a - point ] ] a point : + + + + + + + + + the simplest variety is a single point . in this case ,
@xmath73 for all @xmath59 and all @xmath63 .
whence , @xmath74 where , in the second line , we have used the standard euler product for the riemann zeta function .
this illustrative example indeed should clarify the various names and substitutions stated above .
[ [ the - projective - space - mathbbpk ] ] the projective space @xmath75 : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + for the case of the affine line @xmath76 over @xmath61 , there are clearly @xmath62 points ; the projectivization introduces a point at infinity , and hence @xmath77 , giving us @xmath78 the affine line itself would have simply given @xmath79 and @xmath80 .
the generalization to @xmath75 over @xmath81 is straight - forward .
recall that @xmath82 where @xmath83 are the non - zero elements in the field , totalling @xmath84 in number .
thus , the number of points in @xmath75 is @xmath85 quotiented by @xmath84 , giving us @xmath86 .
therefore , @xmath87 similarly , we have that , for @xmath88 , @xmath89 , giving us @xmath90 the euler product in , a key property for the riemann zeta function , is a general feature of the global zeta functions of our concern .
indeed , one can develop an expansion of such products , into what is known as an * dirichlet series * ( sometimes called l - series for reasons which shall become clear later ) : @xmath91 where the product over primes is naturally converted to a sum over the integers .
for the above example of a single point , the coefficients @xmath92 are simply all unity , the famous representation of @xmath93 . some standard identities in the theory of dirichlet series ( cf .
@xcite ) will be pertinent to us .
the first is that , for @xmath94 , @xmath95 where we recall that @xmath96 is the sum over the @xmath97-th power of the divisors of @xmath31 .
this is a special case of the so - called convolution property of dirichlet series , that @xmath98 with the convolution defined as @xmath99 in general , the coefficients of the l - series can be obtained by transform of mellin - type .
this inversion is the so - called perron s formula and states that for @xmath100 , convergent when @xmath101 , @xmath102 for positive integer @xmath19 , @xmath103 an arbitrary real number such that @xmath104 .
these partial sums can then be listed to iteratively obtain the individual terms desired .
we also have a direct , though less computationally straight - forward inversion formula that @xmath105 finally , one could use an even more direct method of taking limits , wherever possible . indeed , writing , by setting @xmath106 so that as @xmath107 tends to 0 , @xmath108 tends to infinity , @xmath109 we have that @xmath110 , whence @xmath111 , and so on , successively , until order by order all the coefficients are obtained .
the general structure of the local zeta function of the algebraic variety @xmath67 reflects , in a remarkably elegant fashion , the geometrical nature of @xmath67 .
these are captured by what historically have come to be known as the * weil conjectures * ( 1940 s ) and proved by deligne in 1974 , using the @xmath112-adic cohomological techniques envisioned by grothendieck . in summary ,
the statement is that for @xmath67 a ( non - singular ) @xmath19-dimensional complex projective algebraic variety , * the local zeta function @xmath113 is a rational function which can be more precisely written as alternating products in numerator and denominator : @xmath114 where @xmath115 , @xmath116 and @xmath117 are all polynomials with integer coefficients , admitting factorization @xmath118 with @xmath119 being complex numbers with modulus @xmath120 .
when @xmath121 , this means that all zeros of @xmath122 are at @xmath123 , an analogue of the riemann hypothesis .
* a functional equation @xmath124 , where @xmath125 is the euler number of @xmath67 , is obeyed . * for primes @xmath59 of good reduction ( that is , when the variety remains non - singular over @xmath81 , a point which we discuss in appendix [ a : reduction ] ) , the degree of @xmath126 is the @xmath127-th betti number of @xmath67 as a complex variety .
having given a brief account of our two protagonists , it is now expedient to present , in relation thereto , some illustrative examples of gauge theories , their moduli spaces and associated arithmetic as well as geometric properties , as much as a warm - up , as a provision of a small catalogue against which one could initiate some systematic checks and experiments ( note that our approach is different from _
e.g._@xcite to whose penetrating insights the reader is highly encouraged to refer ) .
the simplest gauge theory is undoubtedly that of @xmath28 with a single free field @xmath67 charged therein , embodied as @xmath128 matrices .
there is no superpotential and the gauge invariants are simply @xmath129 for @xmath130 , with any power @xmath131 re - writable , in terms of newton polynomials , in this fundamental generating set .
when @xmath132 where no such matrix relations occur , we have that the moduli space is simply the affine complex line @xmath68 , generated by @xmath133 and the full specturm of operators are @xmath134 thus , the fundamental generating function is the hilbert series for @xmath68 ( cf .
7.1 of @xcite ) : @xmath135 the plethystic logarithm gives @xmath136 = f_1(t;{\mathbb{c } } ) = t$ ] , signifying precisely the above : that the chiral ring is freely generated by a single element .
the plethystic exponential is the euler eta - function @xmath137 , whose expansion encodes the ( free ) partition of integers and corresponds to the various ways the above single - trace operators can be multiplied . finally , the @xmath47-inserted plethystic exponential gives @xmath138 = \frac{1-t^{n+1}}{1-t } \ .\ ] ] therefore , at fixed @xmath1 , the vms becomes the symmetric product @xmath139 , and the corresponding single- and multi - trace spectra are counted , respectively , by @xmath140 and @xmath141 .
strictly speaking , one should think of the vms as being the hilbert scheme of @xmath1-points on @xmath68 ( q. v. @xcite ) and plethystics for these are discussed in @xcite .
the arithmetic properties of the above vmss are also readily computed .
for @xmath68 , the local and global zeta functions were given in : @xmath142 for @xmath143 , the spaces become more involved , even though their hilbert series are neatly compacted into @xmath144 .
let us begin with @xmath145 .
here we have the affine variety described by @xmath146 acting on @xmath147 $ ] .
the hilbert series is given by @xmath148^{-1}$ ] , signifying a freely generated algebra by two elements , of degrees 1 and 2 , respectively : these we see clearly as the invariants @xmath149 and @xmath150 under the exchange .
the vms is therefore an affine cone over the weighted projective space @xmath151}$ ] .
thus , other than the weighting of the cordinates , the variety is simply @xmath152 and no extra syzygies exist for our particular embedding .
hence , the zeta functions are simply @xmath153 and @xmath154 .
this treatment generalizes to arbitrary @xmath1 , giving the vms as the affine cone over @xmath155}$ ] , isomorphic to @xmath156 , and having zeta functions as given in .
parenthetically , the projectivization of the above is also interesting . adding a point at infinity gives @xmath157 , and the global zeta function , from , is the product @xmath158 .
consequently , the l - series is @xmath159 where we have used .
if we were to develop the power series with the l - series coefficients @xmath160 , we would have @xmath161 .
this can be re - written @xcite as a so - called * lambert summation * , @xmath162 where the number theoretic divisor function becomes implicit .
one of the most studied gauge theory in recent times is unquestionably the world - volume theory of @xmath1 parallel coincident d3-branes , especially in the context of holography and maldacena s ads / cft correspondence .
the simplest setup is that of the d3-brane transverse to flat @xmath163 , considered as a real cone over @xmath164 , with near - horizon geometry of @xmath165 .
the world - volume theory is @xmath166 , @xmath167 super - yang - mills theory in 4-dimensions with three adjoint fields , say @xmath168 , charged under the @xmath167 .
there is a simple cubic superpotential @xmath169)$ ] and the matter content can be easily represented by the clover quiver : @xmath170{c3 } \end{array } \qquad \qquad w = { \mathop{\rm tr}}(x[y , z ] ) \ , \ ] ] where the node corresponds to the @xmath167 gauge group and the three arrows , the three ( adjoint ) fields .
the vms , by construction , is parameterized by the transverse motion of the branes and subsequently is @xmath163 for a single d3-brane and the @xmath1-th symmetrized product thereof for arbitrary @xmath1 .
the f - terms , from the jacobian of @xmath24 , demand that @xmath168 mutually commute and we have the symmetric commutative algebra generated by three elements .
the plethystics were computed in @xcite and , with the standard binomial symbol @xmath171 we have @xmath172 \ .\end{aligned}\ ] ] now , for @xmath173 , we have @xmath163 and the zeta functions are back to . at @xmath145 ,
expanding the @xmath47-inserted plethystic exponential gives us @xmath174 the non - terminating syzygies in @xmath175 signifies that we have a vms which is non - complete intersection , whose hilbert series is given by @xmath176 .
luckily , because of the relative simplicity of the space , we can readily write down the invariants . let @xmath168 be the cordinates of @xmath163 ( this is not an abuse of notation , the three fields , after imposing the commuting f - terms , should correspond precisely to these affine cordinates ) , then our @xmath177 action takes these to , say @xmath178 , and we have the full 6 cordinates of @xmath179 . in degree one , the invariants are clearly @xmath180 , @xmath181 and @xmath182 . in degree two , the invariants are the obvious @xmath183 , @xmath184 and @xmath185 , as well as @xmath186 , @xmath187 and @xmath188 . since @xmath177 is a group of order 2 , by nther s theorem on invariants ,
we need not look for higher invariants .
we can then calculate , facilitated by the aid of @xcite , that there are non - trivial syzygies amongst these invariants : we obtain the non - complete intersection which is an affine complex cone over 6 quartics in @xmath189}$ ] .
explicitly , the equations are @xmath190 given this algebraic variety , we can proceed to compute its zeta function .
the base of the cone is a complex 5-dimensional projective variety , therefore the local zeta function , by , should be of the form @xmath191 , where @xmath192 , for @xmath193 , is a polynomial of degree @xmath194 , the @xmath127-th betti number of the 10 real - dimensional base manifold .
now , the cone has one more point than the base , _ viz .
_ the tip at , say , the origin , which is removed when projectivizing .
thus , this addition of unity to @xmath69 , upon exponentiating according to the definition , gives a trivial factor of @xmath195 .
hence , the total affine variety has zeta - function @xmath196 the coefficients of these polynomials can be fixed by tabulating the explicit number of solutions for some low values of @xmath62 .
we find , for example , that @xmath197 for the first few primes , a pattern which we speculate will persist to hold .
for now , let us not belabour the point and turn to demonstrate the determination of such coefficients for some simpler examples . a relatively simple gauge theory , canonical in the string theory literature @xcite , is the theory of d3-branes on a conifold @xmath198 , _ i.e. _ , the quadric in @xmath199 or @xmath200 $ ] .
note that this is a toric variety and enumeration of gauge invariants are greatly facilitated thereby ; we include the toric diagram below , drawn in a plane due to the calabi - yau nature , for reference .
the world - volume theory has @xmath0 supersymmetry , @xmath201 gauge group , with four bi - fundamental fields as well as a quartic superpotential : @xmath202{conifold } \end{array } & { \small \begin{array}{l } \begin{array}{ccc } & su(n ) & su(n ) \\ a_{i=1,2 } & { \raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt } } } } & { \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}}}\\ b_{j=1,2 } & { \overline{{\raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt } } } } } } & { \raisebox{-.5pt}{{\hbox{\rule{0.4pt}{6.5pt}\hskip-0.4pt\rule{6.5pt}{0.4pt}\hskip-6.5pt\rule[6.5pt]{6.5pt}{0.4pt}}\rule[6.5pt]{0.4pt}{0.4pt}\hskip-0.4pt\rule{0.4pt}{6.5pt}}}}\end{array}\\ w = { \mathop{\rm tr}}(\epsilon_{il } \epsilon_{jk } a_i
b_j a_l b_k ) \end{array } } \end{array}\ ] ] the counting of the gauge invariants can be done explicitly @xcite .
we have four fundamental invariants , corresponding to the four euler cycles in the quiver @xcite , @xmath203 , subjecting to the f - term relation obtained from the quartic superpotential : @xmath204 .
diagrammatically , we can then see the lattice points in the toric cone corresponding to the gauge invariants ( cf .
@xcite ) : @xmath205{conigio } \end{array}\ ] ] subsequently , the vms is by construction the cone over the said quadric hypersurface for a single d - brane and for arbitrary @xmath1 , plethystic analysis gives us : @xmath206 we see that the @xmath207 indeed captures the lattice cone counting above .
now , we have a rather simple projective variety , a single hyper - surface , call it @xmath208 , of degree 2 in @xmath209 , over which @xmath198 is an affine complex cone .
this base surface @xmath208 is clearly a khler manifold and the hodge diamond is @xmath210 , @xmath211 , @xmath212 , @xmath213 and @xmath214 .
whence , the betti numbers .
here , however , we are considering it as a complex cone over the quadric surface and will study this compact base surface here . ] are @xmath215 , @xmath216 , @xmath217 .
again , because @xmath198 has one more point , at the tip of the cone , than @xmath208 , the local zeta function is as dictated by , together with an additional factor of @xmath218 : @xmath219 in the denominator , the only non - trivial factor would have been @xmath220 , a quadratic form which we have spelt out , wherein a single indeterminate , _ viz . _
, @xmath221 is to be fixed .
it therefore suffices to enumerate at @xmath222 to determine @xmath221 and govern all the finite galois extensions thereof in a single sweep . comparing with the definition for @xmath223 and factorizing @xmath224
, we find that @xmath225 \ . \end{aligned}\ ] ] whence , we can determine the coefficient @xmath221 as @xmath226 we can readily find the first values of @xmath227 on the computer : @xmath228 interestingly , these are all square - free integers : @xmath229 from these we can determine the global zeta function , and thence its l - series development : @xmath230 what is perhaps more interesting is , upon seeing no immediate pattern to the above , when one desingularizes the cone by a standard deformation of complex structure . in particular , let us consider the variety @xmath231 , which we shall denote @xmath232 .
we have chosen the complex parametre to be 1 to avoid it being reduced back to 0 for some prime factor , constituting an obviously bad reduction . in this case , we find that @xmath233 or , as one could emperically convince oneself , @xmath234 .
this gives us the form of the local zeta function , using , as @xmath235 and subsequently the global zeta function as @xmath236 the function in the form of the infinite product can be thought of as an l - function for this variety ; we shall return to this type of function for a more canonical example , involving the elliptic curve , later on in
[ s : e ] and appendix [ a : reduction ] . using the form of
, we can also perform a dirichlet expansion to obtain : @xmath237 now , for higher @xmath1 , the space becomes more involved .
take @xmath145 , for a brief example .
we have a @xmath177 action on @xmath238 $ ] , exchanging the primed and unprimed cordinates , and in addition we have two copies of the defining quadric equations .
the invariants are @xmath239 , @xmath240 , @xmath241 and @xmath242 at degree 1 , @xmath243 , @xmath244 , @xmath245 , @xmath246 , as well as the combinations @xmath247 , @xmath248 , @xmath249 , @xmath250 , @xmath251 and @xmath252 at degree 2 , which should be subject to @xmath253 and @xmath254 .
this is subsequently gives a non - complete - intersection , of complex dimension 6 , defined by four cubics and twenty quartics , embedded in @xmath255}$ ] .
the hilbert series can be computed , either from @xcite , or from , to be @xmath256 .
of parenthetical interest is perhaps the master space in the toric , or @xmath173 , case .
this space is the solution set to the f - terms alone and controls , in the sense of git quotient , the final vms ; it has been extensively studied for gauge theories in @xcite . for the present case of the conifold ,
the space is simply @xmath199 and the zeta functions once more return to the simple form in . as a further digressive remark , we know that the gauge theories for the so - called generalized conifold @xmath257 and orbifolded conifold @xmath258 have been extensively studied ( cf .
@xcite ) . reducing these varieties over some low primes
, however , produced the same enumeration as of points as did the above for the conifold itself .
this should be due to the frobenius automorphism from points to its power , reduced over characteristic @xmath59 and hence produce no further points .
it was shown in @xcite that since any toric calabi - yau threefold singularity can be obtained from partial resolutions of @xmath259 for sufficiently large @xmath23 , all toric gauge theories on d3-branes can be algorithmically obtained by higgsing the theory obtained from the orbifold projection .
it is thus illustrative for us to present an analysis for these parent orbifold theories .
the toric diagram is an @xmath260 right isosceles triangle of lattice points and the matter content is captured by a periodic quiver with @xmath261 nodes and the superpotential is comprised of the closed triangles in the quiver ( cf .
@xcite which obtained the first results for these @xmath0 gauge theories ) : @xmath262{znzn}\ ] ] the plethystic programme was carried out for these spaces in @xcite and the vms was found to be complete intersection ; in particular , the hilbert series and syzygies are presented in eqs ( 4.4 - 4.5 ) in _ cit
_ : @xmath263 at @xmath264 , we are of course back to the case of @xmath163 . for @xmath265 , we have the cone over a single sextic in @xmath266}$ ] from the above expression for @xmath267 .
writing the cordinates of the weighted projective space ( in the order of the prescribed weights ) as @xmath268 , we have the sextic as @xmath269 .
hence , @xmath270 for the weighted projective variety we find that @xmath271 .
hence the zeta function is actually quite simple , because the base space is homologically rather trivial .
the counting for the affine cone thus proceeds as though it were @xmath163 and we have that @xmath272 indeed , explicitly counting over the first 20 primes on the computer confirms the @xmath273 solution .
we remark that had we desingularized the origin to @xmath274 and set @xmath275 to avoid primes of bad reduction , the solutions are drastically different : @xmath276 as our last remark , the ( irreducible top - dimensional component of the ) master space of this example was studied in detail in @xcite and we recall , from eq ( 2.11 ) therein , that it is a calabi - yau variety of dimension 6 , degree 14 and comprised of the incomplete intersection of 15rics in 12 variables , with the hilbert is given by @xmath277 . reducing over the first primes we obtain @xmath278 .
the next simplest case is the hypersurface @xmath279 corresponding to @xmath280 ( which partially resolves to all the toric del pezzo cones , to which we shall shortly return ) .
this is an affine cone over the cubic in @xmath209 and we can rescale weights to obtain @xmath281 now , the cubic surface in @xmath209 is the well - known del pezzo surface which is @xmath282 blown up at 6 generic points and whose betti numbers are standard : @xmath283 .
this is confirmed by the toric diagram , which captures a special point in the moduli space of this del pezzo surface ( after all , only up three blow - ups can be accommodated by a toric description ) .
therefore , the zeta function has the form , following the argument above for the conifold , _ mutatis mutandis _ : @xmath284 where @xmath285 is a polynomial of degree 7 with integer coefficients and unit constant term .
we may then use the values of @xmath286 for @xmath287 to fix the indeterminate coefficients in @xmath285 much like what we did for the conifold , an intense computation into which we shall not presently delve . suffice
it to say that , trying out the first number of primes gives us @xmath288 and the first few values of @xmath289 are @xmath290 indeed , as @xmath23 grows , the degree of the indeterminate factors too will grow , and whence the number of coefficients to fix . for now , we shall not occupy ourselves with the higher cases , though it is certainly interesting to find out what the growth rates of the coefficients in the zeta function are with respect to @xmath23 .
the importance of del pezzo surfaces , in their ubiquitous appearances in algebraic geometry , representation theory as well as gauge theory , can hardly be over - stated . in the framework of d3-brane probes , they provide a marvellously rich class of stringy background by being the base surfaces over which cones are affine calabi - yau threefolds .
the world - volume gauge theories for the toric members ( _ viz .
_ @xmath282 blown up at @xmath291 points , as well as @xmath292 ) were first presented in @xcite while the higher ones ( @xmath293 ) were given in @xcite .
it is irresistible that we at least mention these gauge theories . in @xcite
, we found that for the cone over the @xmath19-th del pezzo surface ( and hence of degree @xmath294 ) , the fundamental generating function is @xmath295 the case of @xmath296 , _
i.e. _ , the cubic surface , we have already probed in our aforementioned study of the @xmath297 orbifold , as a special point in the complex structure moduli space , so here let us move onto another simple example , say , @xmath298 .
this is simply the total space of the @xmath299 anti - canonical bundle over @xmath282 , resolving the gorenstein singularity @xmath300 . as an affine embedding ,
this is given by the non - complete intersection of 27 quadrics in @xmath301 , explicitly presented in eq ( 5.14 ) of @xcite .
because the betti numbers of the base are @xmath302 and that we are adding the origin as the tip of the cone , we have , as before , that @xmath303 , being fixed by after we projectivize back to @xmath282 . therefore , the global zeta function is @xmath304 . as a first non - trivial example , let us consider the next del pezzo cone , of @xmath121 . here , we have @xmath305 and @xmath306 = 9 t - 20 t^2 + 64 t^3 - 280 t^4 + 1344 t5 + { { \cal o}}(t^6 ) \ , \ ] ] signifying a non - complete intersection .
the gauge theory can be found in section 4 of @xcite , with the adjacency matrix @xmath307 of the quiver and the superpotential @xmath24 given by @xmath308 where we have used the standard notation that @xmath309 is the @xmath23-th arrow from nodes @xmath127 to @xmath310 .
the vms is readily found by the methods outlined in [ s : vms ] and comprises of 20 quadrics in @xmath311 : @xmath312 one can also check @xcite that the hilbert series for this embedding is as stated .
now , the base surface is a projective variety in @xmath313 and has betti numbers @xmath314 , thus the local zeta function should be @xmath315}\ ] ] where @xmath316 and @xmath317 are constants to be determined .
proceeding as in , we in fact find the same number of zeros as and whence the same form of the local and global zeta functions as the conifold .
having indulged ourselves with a plethora of examples , many from the context of d - branes and calabi - yau spaces in string theory , let us , as our final set of illustrations , take a complete departure and study perhaps the most canonical field theory of them all , _ viz .
_ , supersymmetric qcd .
the geometry of this was the theme of @xcite , whose intent was to provide an algebro - geometric and plethystic aperu on this old subject .
the explicit vms as an affine variety was computed and some first examples , presented in eq ( 3.25 ) therein .
let us denote the vms of sqcd with @xmath318 flavours and @xmath319 colours as @xmath320 .
then for @xmath321 , @xmath322 , the flat affine space . for @xmath323 , @xmath320 has complex dimension @xmath324 as an affine variety embedded in @xmath325 . in the particular case
when @xmath326 , @xmath327 is a single hypersurface of degree @xmath328 .
for some first few values , the defining equations of the vms and the associated hilbert series are : @xmath329 now , @xmath330 is just the flat space @xmath68 and needs no further comment .
@xmath331 is a dimension 4 , degree 6 affine variety .
counting the number of points , reducing over the first few primes , shows that here @xmath332 .
going with this pattern easily gives us that @xmath333 as though we have the counting for @xmath199 .
@xmath334 is more complicated ; this is a degree 2 , dimension 5 variety as a cone over a quadric 4-fold .
the betti numbers are easily determined to be @xmath335 , for an euler number of 6 .
therefore , the local zeta function , by and adding the tip of the affine cone , is @xmath336 we have indeterminate coefficients @xmath337 which we can fix by observing some values .
as was in the case of the conifold , we expand the above expression to relate the coefficient @xmath337 with @xmath338 , the latter of which we can list the first few values : @xmath339 hence , the global hasse - weil zeta function becomes @xmath340 where the l - function is @xmath341 with the first few values of @xmath337 being @xmath342 .
developing @xmath343 into a dirichlet series gives the first few coefficients as @xmath344 .
we have thus performed extensive experimentation , in studying the gauge invariant as well as the arithmetic properties of a host of supersymmetric field theories .
the data presented are perhaps of interest _
ipso facto_. however , contented with our catalogue , we could forge ahead with some further calculations . that two enumeration problems , as seen from the proceeding discussions , should each be governed by a rational function as a generating function naturally lends itself to an instant speculation .
could the zeta function of the vms of one gauge theory , encoding its zeros over finite fields , be related to the hilbert series of the vms of another gauge theory ?
this comparative study , relating one generation to another , would engender quite a peculiar relationship , wherein the bps mesonic spectrum of a gauge theory should correlate to the arithmetic of another vacuum geometry .
two immediate hurdles , however , quickly present themselves were we to make a nave identification .
first , the ( local ) zeta function , which is a rational function according to weil - deligne , is defined with respect to a given prime number @xmath59 ; the straight - forward analogue of this parametre in the case of the hilbert series is unclear .
it seems unnatural that the bps spectrum should be at all particular to any fixed prime number .
second , and perhaps more seriously , is the difference in the growth rate of @xmath37 , the number of gauge invariant operators versus that of @xmath345 , the number of zeros over @xmath346 .
the former , being the hilbert series of an algebraic variety , usually tends polynomially in @xmath31 ( and indeed , governed by the so - called hilbert polynomial in the degree @xmath31 ) .
the latter , however , grows rather much faster , and is in fact exponential in @xmath31 , say @xmath347 .
this is not only seen in the examples presented in
[ s : zeta ] , but is , in fact , compelled to be thus by , so as to ensure that the generating zeta function can have the exponent behaving logarithmically , and consequently cancelling the exponential to give a rational function .
for example , @xmath348 is a perfectly acceptable growth for a gauge theory .
in fact , the mesonic spectrum of the d - brane theory on the flat - space @xmath152 , or equivalently , the hilbert series of the bi - variate polynomial ring @xmath147 $ ] , is simply @xmath349 ; whence @xmath350 .
however , having @xmath351 would force the zeta function to be non - rational ; signifying that no algebraic variety over any number field could possibly have such a behaviour for its zeros .
parenthetically , we point out that in an interesting paper @xcite , the authors find a fascinating relation between the hilbert series of a variety and the zeta function of another @xcite . there , the veronese curve @xmath67 prescribed by the embedding of @xmath157 by the very ample line bundle @xmath352 for some @xmath353 is considered .
the dimension at degree @xmath31 is therefore @xmath354 , giving us the hilbert series : @xmath355 on the other hand , we recall that the zeta function for @xmath356 , given momentarily in the discussion on that of @xmath75 , is @xmath357 . we thus see that the numerator of the hilbert series of the veronese curve , evaluated at the negative of its argument , identifies with the denominator of the weil zeta function of the affine line , a seemingly different geometry . in this example , the aforementioned first objection was circumvented by the choice of the line bundle in embedding @xmath157 , whereby inherently introducing a parametre @xmath358 , which is then associated with some prime @xmath59 .
similarly , one could consider the @xmath47-inserted plethytics for @xmath359 . here , as was computed in @xcite , @xmath360 , giving @xmath361 , and whence @xmath362 , with @xmath363 .
this , with a simple re - definition , is of the form for the zeta function for @xmath75 in .
these above digressions are , of course , merely formal resemblances .
what we wish for is a systematic correspondence ; this is certainly encouraged by the similarity between the definitions of the zeta function and the plethystic exponential , a similarity whose discrepancies , however , are of sufficient significance that a direct identification is not pronouncedly manifest .
nevertheless we are inspired by the following diagram : @xmath364 the diagram is self - suggestive and let us make a few remarks .
the geometric object of concern is @xmath67 , the classical vms of a gauge theory .
the syzygies @xmath365 , or defining equations of @xmath67 , is a polynomial in @xmath53 when @xmath67 is complete intersection , otherwise , it will be some power series .
the plethystic exponential takes @xmath365 to the hilbert series @xmath366 , which counts the single - trace ( mesonic ) bps spectrum of the gauge theory and is a rational function by hilbert s theorem on algebraic varieties .
the full ( mesonic ) spectrum is obtained by a second plethystic exponentiation , in the spirit of a bosonic oscillator partition function and recast as a product over the vibration modes , from @xmath366 .
these multi - trace operators constitute the `` global '' , or complete , set of objects in the gauge theory , and is obtainable from two plethystic substitutions from the intrinsic geometric property @xmath365 of @xmath67 . in a parallel vein
, we can consider the arithmetic properties of @xmath67 and enumerate the number of solutions @xmath69 over finite fields .
an exponential generating function gives the zeta function , which is rational by .
this is made global by a product over primes and gives a hasse - weil zeta function , which can then be expanded into a dirichlet series .
the plethystics have analytic inverses involving the mbius function while the inverse procedure to forming the zeta functions is quite difficult .
nevertheless , the similarities of proceeding from intrinsic geometric ( or arithmetic ) properties of @xmath67 , via a rational function , to a global enumerative problem associated with the gauge theory , through two exponential ( infinite product ) substitutions in generating functions , is tantalizing indeed .
let us commence again with examples .
since the zeta function is severely restricted in form , it is perhaps expedient to start therewith .
so our strategy will be to begin with a gauge theory whose vms is @xmath67 , we then compute the arithmetical properties of @xmath67 , starting from the bottom left box in the diagram in , trace the arrows , via rationality and globality , to the right and then go upwards , trace the arrows backwards , via locality and syzygy , to the geometrical properties of a possibly different vms @xmath367 of another gauge theory .
let @xmath67 be a single point .
we recall from that here the local zeta function is @xmath218 and the global zeta function is the riemann zeta function .
the l - series coefficients @xmath92 are thus all unity .
we then identify @xmath92 with the coefficients @xmath37 in the plethystic exponential , and can therefore form the power series @xmath368 , where we have added 1 as the zeroth term for normalization in order to take care of the @xmath369 term in the plethystic exponent .
we have arrived , of course , at the hilbert series for @xmath68 , and subsequently the mesonic bps operators of d - branes probing this trivial calabi - yau 1-fold .
the gauge theory corresponding to this vms , as we recall from [ s:1field ] , is a free theory of a single field .
thus , in our trivial warm - up example , we have gone from a point to @xmath68 , which can be thought of as a cone over a point .
next , let us study the family of affine space @xmath88 ; this can be thought of as the vms of @xmath23 mutually commuting @xmath28 fields at large @xmath1 . from , we recall that @xmath370
. therefore the dirichlet coefficients are @xmath371 .
were this the enumerations of a hilbert series , we would have that ( again normalizing with 1 for the @xmath372 term ) : @xmath373 where @xmath374 is the standard ( de jonquire s ) poly - logarithm function . note the nomenclature here : we have used @xmath375 because the convention in the preceding discussion was that @xmath376 refers to the hilbert series of the algebraic variety @xmath67 whereas here we are formally constructing a power - series , the space for which @xmath377 may be a hilbert series is yet to be determined .
now , for integral parametres @xmath23 , @xmath378 are all rational functions , which is re - assuring as the corresponding hilbert series should be so as is required by an algebraic variety .
specifically , let us recall some of the first few values : @xmath379 indeed , for @xmath380 , this gives us @xmath381 , in accord with the aforementioned case of the single point .
subsequently , we have that : @xmath382 that these functions are in the form of hilbert series of either the first or second kind is pleasing .
note that the numerators for @xmath374 are all palindromic ; for a hilbert series , this would imply that the corresponding algebraic variety be calabi - yau by stanley s theorem @xcite ( cf .
@xcite for its implication in d - brane gauge theories ) .
however , we see that the full hilbert series is palindromic only for odd @xmath23 .
this can be seen from the following argument .
first , we have the so - called inverse formula @xcite , that for all @xmath383 , @xmath384 \\ \zeta(1-s , \frac12 - \frac{\log(-1/z)}{2 \pi i } ) \ , & z \notin ( 1,\infty ) \end{array } \right .
\ , \ ] ] where @xmath385 is the standard hurwitz zeta function .
because of the pole of the gamma function at negative integer values , this implies that @xmath386 now , because each of our polylogarithmic function with negative integral parametre is a rational function with equal degree of numerator and denominator , with the latter being trivially @xmath387 , palindromicity of the numerator simply means that @xmath377 should equal @xmath388 , which is indeed guaranteed by for odd @xmath23 .
returning to our list in , the first case of @xmath380 is simply the point .
next , with the case of @xmath264 and hence @xmath389 we also have some familiarity .
let us take the plethystic logarithm to yield @xmath390 = t + t^2 + t^3 - t^6 \ .\ ] ] according to the rules prescribed in @xcite and some discussions on a similar circumstance in @xcite , if we were to construe the above as a projective variety , then the terminating plethystic logarithm , signifying the syzygies , should be interpreted as follows : we have three generators , in degrees 1,2 and 3 respectively , obeying a single relation in degree 6 .
that is , we have a sextic hypersurface in weighted projective space @xmath391}$ ] .
this , of course , is none other than an elliptic curve . in light of our present discussion ,
that we are dealing with affine spaces and that our gauge theory vmss are naturally _ affine _ varieties , it is perhaps more expedient of interpret the hilbert series as that of an affine variety .
thus , we think of the geometry above as that of an affine cone over ( _ i.e. _ , the dehomogenization of ) the said elliptic curve . the gauge theory is not immediately reconstructible .
indeed , were the moduli space simply @xmath152 , then we would have , much in analogy with [ s:1field ] , an @xmath28 theory with two adjoint fields at large @xmath1 , say @xmath392 and @xmath393 , such that the f - terms from the superpotential force them to commute and all the mesonic bps operators would be in the form @xmath394 with @xmath395 . however , the hilbert series would simply be @xmath396 , with trivial numerator .
nevertheless , we see that @xmath389 is written in the form of a hilbert series of second kind .
thus , the associated affine variety is of complex dimension 2 and of degree @xmath397 where @xmath398 is the numerator .
this can geometrically be realized as a line in @xmath163 .
interestingly , the multi - trace operators are counted by @xmath399 = \prod\limits_{n=1}^\infty \frac{1}{(1-t^n)^n } : = mac(t ) \ , \ ] ] the macmahon function , which is crucial to the crystal melting picture of a - type topological strings @xcite .
it is curious that so rich a structure can be encoded in the zeta function of so simple a geometry as the affine complex line .
moving on to higher @xmath23 gives more involved results : indeed , one can check that the plethystic logarithm of @xmath400 in are _ non - terminating_. this means that the corresponding algebraic varieties are not obviously complete intersections and there exist non - trivial higher syzygies _
ad infinitum_. again , we can interpret the hilbert series as being of the second kind since the numerator and denominator have been cleared maximally .
hence , @xmath23 corresponds to a variety of dimension @xmath401 and degree @xmath402 , following readily from the asymptotic expansion of the poly - logarithm , that @xmath403 where @xmath404 are the bernoulli numbers and the limit @xmath405 should be taken .
let us focus , as inspired by string theory , on cases of @xmath406 , these being potentially theories on the d3 and m2-branes @xcite .
taking the plethystic logarithm of the @xmath265 case gives @xmath407 = t+3 t^2 + 5 t^3+t^4 - 6 t^5 - 17 t^6 - 4 t^7 + 29 t^8 + 56 t^9 + 7 t^{10 } + { { \cal o}}(t^{11 } ) \ .\ ] ] indeed , as much as @xmath389 , whose expansion coefficients are @xmath31 , needs to be compared to @xmath152 , whose coefficients are @xmath408 , the present example , whose expansion coefficients are @xmath409 , needs to be compared to the _ conifold _ ( quadric hypersurface defined in @xmath199 ) , which has coefficients @xmath207 as was seen in .
both latter cases are simple geometries whereas the former , by a seemingly trivial shift of 1 , already becomes quite involved . moreover , since the numerator is not palindromic , the space needs not even be calabi - yau . in any event , we know this to be a 3-dimensional variety of degree 2 .
similarly , for @xmath280 , we have that @xmath410 = t+7 t^2 + 19 t^3 + 9 t^4 - 72 t^5 - 246 t^6 - 72 t^7 + 1422 t^8+{{\cal o}}\left(t^{9}\right ) \ , \ ] ] a non - complete intersection space of dimension 4 and degree 6 .
therefore , in each case of @xmath23 , we could indeed find a vms of a rather non - trivial gauge theory whose hilbert series coincides with the zeta function of @xmath88 .
the astute reader may have asked why , in the above example , in identifying the dirichlet coefficients from the euler product with plethystic product , we have set @xmath92 equal to @xmath37 , rather than @xmath411 ( adhering to the nomenclature of ) .
the reason , of course , is that we wish to readily guarantee that we could arrive at an obvious rational function upon taking the plethystic logarithm . indeed , as we shall discuss in further detail in
[ s : asym ] , we need to be mindful of the growth rate of these coefficients . begotten from a hilbert series of commutative variety , @xmath37 are approximately polynomial growth , and whence , by plethystic exponentiation , @xmath411 grow as a polynomial multiplied by an exponential . on the other hand , due to the work of schnee , landau and ramanujan on the general theories of dirichlet series ( cf .
@xcite ) , @xmath92 is usually taken to be of polynomial growth in order to allow absolute convergence of the dirichlet series in the upper half - plane and its subsequent analytic continuation - crucial , of course , for any statements pertaining to the generalized riemann hypothesis
. therefore , identification of @xmath92 with @xmath37 is the more natural choice for now , as was seen above . indeed , for algebraic schemes more miscellaneous
, the hilbert series can be arbitrary and whence more general identifications could be permissible .
let us illustrate with the example of the conifold on which we expounded to some length above .
we recall the dirichlet coefficients @xmath92 from and redevelop this as a power series ( without troubling ourselves too much with convergence presently ) . setting these to be the @xmath37 coefficients in a power series
, we can then take the plethystic logarithm , at least order by order , to find that @xmath412 & = & 7 t-3 t^2 - 31 t^3 + 209 t^4 - 744 t^5 + 1431 t^6 + 2194 t^7 - 35726 t^8+\\ & & + 186120t^9 - 573070 t^{10}+{{\cal o}}\left(t^{11}\right)\end{aligned}\ ] ] according to the rules , this would describe a non - complete - intersection manifold , generated by 7 linear forms , obeying 3 quadratic , 31 cubic relations , together with non - terminating higher syzygies .
of course , nothing prevents us from going in direction converse to the above .
we can compute the hilbert series for the geometry of a vms of a gauge theory whose syzygies encode the mesonic bps spectrum and then attempt to find another gauge theory whose zeta function has the same enumeration . in other words , we start from the upper left corner of the diagram in , trace to the right via plethystics , and then proceed contrariwise to the arrows in the bottom row , via localization to primes , and attempt to arrive at the vms of another gauge theory . in principle , we can proceed thence , forming another hilbert series and another vms , potentially _ ad nauseam_. this latter direction of reconstructing the zeta function , at least computationally , is more difficult than the one reconstructing the hilbert series , because whereas plethystic exponentiation has an analytic inverse in terms of the mbius function , finding the factors in an euler product is not so immediate .
first , one may ask why the above examples of elliptic curves and affine spaces worked so nicely .
a key is the multiplicativity . in order that a dirichlet expansion be allowable in being developed into an euler product , as was hinted in
[ lseries ] , its coefficients @xmath92 in the series @xmath413 must be multiplicative ; that is , @xmath414 whenever @xmath19 and @xmath31 are coprime .
this can be seen by explicitly writing out the euler product .
note that this is a weaker condition from complete multiplicativity where this relation holds for all positive integers @xmath19 and @xmath31 ( cf .
@xcite for multiplicativity in the context of enumerating d - brane orbifold theories ) . in the case of affine space , the coefficients @xmath415 for some non - negative integer power @xmath23 , which is certainly completely multiplicative and whence we were able to expand @xmath416 .
subsequently , this allows for the euler product over primes as @xmath417 , so that each of the factors is a rational function which can be then be interpreted as the zeta function of an algebraic variety . of course , in order that @xmath92 also be conceivable as the dimensions of the graded pieces in a commutative ring in accord with the hilbert series and in addition to it being multiplicative , @xmath92 can only be such a pure monomial power . in other words , for example , the dirichlet series of @xmath418 for some integer @xmath419 can be performed without difficulty , even though the coefficients @xmath420 will not be multiplicative , whereby prohibiting an euler product with rational factors , and seems not amenable to an immediate arithmetic perspective .
this rather severe restriction , that the coefficients be both polynomial , in accord with hilbert , and multiplicative , in accord with hasse - weil - dirichlet , should not discourage us .
after all , for any gauge theory , especially those arising form branes at calabi - yau singularities , the entropy ( asymptotic growth rate ) of the bps operators is entirely determined by the leading behaviour of the hilbert polynomial which governs the hilbert series - a point to which we will return in the section on asymptotics . nevertheless , examples still abound and let us continue with the train of thought prescribed above .
we have found , in , that the zeta function for @xmath68 , or the affine cone over a single point , gave rise to a mysterious elliptic curve ( the cone over which is the vms of a gauge theory with two fields and constraints ) .
thus , our starting point is the sextic curve at the upper left corner , giving us @xmath421 .
we computed the plethystics in , but now let us compute the zeta function instead .
the arithmetic of an elliptic curve @xmath422 is a vast subject .
luckily , we only require some rudiments . first , from , the local zeta function is of simple rational form : @xmath423 with a single parametre @xmath424 depending on the complex structure of the specific curve and on the prime @xmath59 .
the global zeta function is therefore @xmath425 in forming this product we run into the issue of so - called good and bad reduction , as well as the concept of the * hasse - weil l - function * , formed by a product over primes dividing the * conductor * of @xmath422 . for a more detailed discussion
we leave the reader to appendix [ a : reduction ] .
our elliptic curve is a sextic and using @xmath426 as the weighted projective cordinates of @xmath391}$ ] in the given order , let us , for now , fix it to be @xmath427 .
the l - function here is simply @xmath428 .
the coefficient @xmath424 is determined only by @xmath59 , _
i.e. _ , knowing the number of points of @xmath422 for @xmath222 determines the number for all @xmath62 . on equating with the definition of the local zeta function gives such a relation ( cf .
@xcite ) : @xmath429 where @xmath316 is the root for the numerator : @xmath430 . in particular ,
@xmath431 , giving us , upon explicit enumeration of points , these following beginning values for @xmath432 : @xmath433 subsequently , we form the product over the local zeta function and apply the dirichlet expansion , the first terms are : @xmath434 having recoursed to elliptic curves , one could not possibly resist the opportunity to digress to modular forms . the celebrated * taniyama - shimura - weil * conjecture , now known as the modularity theorem by the works of wiles et al .
, can be stated in explicit analytic form within our context .
let the l - series of an elliptic curve over @xmath435 , developed into a dirichlet expansion @xmath436 , be recast into a generating function @xmath437 , then this function is in fact a cusp form of weight 2 and level @xmath1 , which is the conductor for the elliptic curve .
we shall leave some more details explaining this correspondence to appendix [ a : ts ] . generalizing this modularity arising from the global zeta function for not just the calabi - yau one - fold , _ viz .
_ , the elliptic curve , but to higher dimensions , has been a growing field @xcite . in a parallel spirit , that the mirror map , encoding the gromov - witten invariants for certain calabi - yau manifolds , especially non - compact toric calabi - yau threefolds exemplified in [ s : eg ] , ( _ q.v .
@xcite ) , should be a ( quasi- ) modular form , has also attained interest .
indeed , our substitution , in accordance with the schematic diagram in the beginning of this section , of the l - series coefficients into the generating hilbert series of the variety is very much in the spirit of this correspondence of taniyama - shimura et al . and
fall under the special situation when the growth rate of these coefficients be polynomial .
in fact , interpreting the plethystic exponential as a grand canonical partition function , one , as to which was earlier alluded , should call @xmath438 , @xmath439 the * fugacity * and @xmath440 , @xmath441 , the * chemical potential * associated with the r - charge and number of colours of the susy gauge theory ( q.v .
@xcite ) . in any saddle point analysis in extracting asymptotics , for example ,
as will be done in the ensuing section , contour integrals are to be performed with respect to these exponents . in other words , in light of both modularity and the casting thereof as a fugacity when considering the theory as statistical - mechanical , the `` dummy variable '' @xmath53 in the hilbert series of the vacuum variety of our gauge theory
should be substituted exponentially , and a fourier @xmath419-expansion , be afforded .
when the situation permits , then , the plethystic exponential of the hilbert series , therefore becomes a modular form .
of course , the modularity theorem is established only for elliptic curves and with some evidence compiling for higher dimension , so in our present context , it is expedient to re - consider our above example of the sextic elliptic curve in
[ s : e ] . to facilitate the usage of @xcite ,
let us de - homogenize @xmath427 and work with the 3 affine patches of the projective space @xmath391}$ ] .
first , in the patch @xmath442 , we trivially have the quadric ( defining @xmath443 ) parabola @xmath444 and the number of zeros over @xmath445 can be tabulated as @xmath446 .
similarly , in the patch @xmath447 , we have the cubic ( defining @xmath448 ) @xmath449 , and we have @xmath450 . in the patch @xmath451 , however , we have the standard weierstra representation of the elliptic curve @xmath452 and that @xmath453 . now , the conductor of the curve is found to be @xmath454 , thus the zeta function can be written as @xmath455 .
correspondingly , using the dirichlet coefficients of the l - function part of the above , and summing over the fourier expansion , we find @xmath456 this is a cusp form of weight 2 and level 144 , belonging to a vector space of dimension 59 . were these to be interpreted as not fourier coefficients but , rather , power series coefficients encoding the non - terminating syzygies , we would be tempted to perform the plethystic exponentiation , formally with the variable @xmath53 , and arrive at @xmath457 as we saw in the case of the conifold , choice of complex structure of course sensitively affects the zeros . experimenting with some values , we find that @xmath458 has the particularly small conductor of @xmath459 , whereupon the associated l - series , and by taniyama - shimura - wiles , the @xmath419-series of the associated cusp form , of weight 2 and level 27 , is @xmath460 luckily , the space of cusp forms of @xmath461 at weight 2 is of dimension 1 and so is spanned by a single function @xcite , thus we can actually write down the analytic form for @xmath462 , in terms of the dedekind eta function ( the reciprocal of which , of course , without the prefactor , gives the standard partition of integers ) : @xmath463
to the growth rate of the various coefficients relevant in our analyses we have alluded a number of times in our proceeding discussions , on account of summability , rationality as well as multiplicativity . in this section ,
we embark on the examination of the asymptotics of the series central to our exposition .
the partition of integers is encoded by the eta function , or in our language , by the hilbert series for @xmath68 and the plethystics for the single - field free theory .
the asymptotic behaviour , _
i.e. _ , the growth rate of the number of partitions for large integers , was determined by the celebrated result of hardy and ramanujan .
the generalization of this problem for weighted partitions was solved by meinardus @xcite and states that for the expansion @xmath464 = \prod\limits_{n=1}^\infty ( 1-t^n)^{-a_n } \ , \qquad \mbox { with } \qquad f(t ) = \sum\limits_{n=0}^\infty a_n t^n \ , \ ] ] the asymptotic behaviour of @xmath411 is : @xmath465 ( 1 + { { \cal o}}(n^{-c_3 } ) ) \ .\ ] ] the constants , or critical exponents , in the above expression are determined as follows .
if the dirichlet series for the coefficients @xmath37 of @xmath32 , _ viz_. , @xmath466 with @xmath467 , converges and is analytically continuable into the strip @xmath468 for some real constant @xmath469 and such that in this strip , @xmath470 has only 1 simple pole at @xmath471 with residue @xmath472 .
the constants in are , explicitly , @xmath473 and @xmath474 some positive constant with which we here need not contend
. indeed , as mentioned in , the expansion coefficients @xmath37 of the hilbert series grows polynomially and so asymptotically is governed by the leading term , which is essentially @xmath475 where @xmath476 is the dimension of the vms and @xmath477 is a constant coarsely depending on the geometry .
for example , for affine space , @xmath478 , and for orbifolds thereof , @xmath477 is some fraction depending on the order of the group .
we are thus led back to a situation very much akin to our example in [ s : cn ] . in this case
, we have that @xmath479 , @xmath480 , @xmath481 , and @xmath482 \ .\ ] ] though standard to the plethystic programme , the above results can now be re - examined under our new light .
indeed , dictates that the asymptotica of the total spectrum of ( mesonic ) bps operators of a gauge theory is governed by the analytic characteristics - _ viz .
_ , the placement of the pole and the residue thereon - of the dirichlet series constructed from the coefficients of the hilbert series of its vms . however , this is precisely the duality substitution outlined in diagram and on which we dwelled in [ s : compare ] .
carrying on with this train of thought , we should ascribe a geometry to @xmath470 ; this , of course , is one for which the global zeta function is @xmath483 .
the local zeta function is thus @xmath484 , which , normalizing the @xmath485 constant term , gives @xmath486 .
therefore , recalling the origin of our coefficients @xmath37 , asymptotically then , we have that this @xmath487-dimensional gauge theory arising from arithmetic is dual `` holographically '' to the @xmath476 dimensional gauge theory emerging from geometry .
having entered the vast realm of analytic and asymptotic properties of zeta functions , one could hardly contain oneself , as a parting speculation , from remarking on the rle of its zeros and poles .
the celebrated zeros of the riemann zeta function aside , it being the analytic continuation of the hasse - weil zeta function for a single point , more contiguous to our present theme is perhaps the conjecture of * birch and swinnerton - dyer * ( cf .
it states that for an elliptic curve ( and possibly generalizing to higher abelian varieties ) of rank of an elliptic curve @xmath422 over @xmath435 form a group which decomposes as @xmath488 where @xmath489 is the torsion part , constituted by some finite group and @xmath63 , called the rank , governs the number of copies of @xmath490 .
hence @xmath491 means that there are , in particular , infinite rational points on @xmath422 . ]
@xmath63 , the l - function tends as @xmath492 for some constant @xmath103 and near @xmath493 .
thus , if the l - function vanishes at 1 , then there is an infinite number of rational points .
now , we have argued above that the asymptotic growth rate of the bps spectrum of a gauge theory is controlled by the pole and residue of the dirichlet series arising from a `` holographic '' dual , or equivalently , by the order of the zero of the reciprocal of the dirichlet series .
the reciprocal of the hasse - weil zeta function clearly inverts each local zeta factor .
this , as was pointed out in @xcite , is an interesting action : it exchanges even and odd cohomology according to the weil conjectures . for calabi - yau spaces , or any generalization thereof , this is actually * mirror symmetry*. eq ( 10.6 ) in _ ibid .
_ proposes a `` quantum zeta function '' @xmath494 for a calabi - yau manifold @xmath18 whose mirror is @xmath495 such that the numerator of @xmath494 is that of the numerator of the ordinary @xmath496 and the denominator is the numerator of @xmath497 . therefore , since the delocalization to the global zeta function is via a product , the zero of the hasse - weil zeta function of one manifold is the pole of that of its mirror .
now , the order of the zero at 1 , at least for abelian varieties , determines the rank of its group of rational points by ( generalizations of ) birch - swinnerton - dyer .
this then , should in turn be ascertained by the order of the pole at 1 for the mirror variety . however , by our correspondences in the preceding discussions in
[ s : compare ] , the pole of the dirichlet series representation of the global zeta function determines the asymptotic growth , in the manner of a critical exponent , of a gauge theory whose vms possesses a hilbert series which can be identified formally with the coefficients in the dirichlet expansion . in this fashion , the asymptotics of one gauge theory , whose vms is @xmath18 , via the pole structure of the plethystic exponential of the fundamental generating function of its bps spectrum , would control the zeroes of the zeta function of another theory whose vms is the mirror @xmath495 of @xmath18 , and thence , the rank of the rational points on @xmath495 .
it is of course interesting to pursue this line of thought , however , for now , let us content ourselves with leaving this to future work .
we have embarked on a somewhat length journey through the expansive landscape of supersymmetric gauge theories , treading along a selected path which is guided by two principles , the first geometric , hinging upon the established plethystic programme for the counting of the bps spectrum of the operators , and the second arithmetic , founded on the zeros of the vacuum moduli space over number fields of finite characteristic .
drawing from the observations over a plenitude of examples , we have attempted to regard the two parallel enumerative problems under the same light , as outlined by the diagram in .
both proceed from an intrinsic property , exponentiated to arrive at a fundamental rational generating function , and then exponentiated again in order to be delocalized to an infinite product : the former , originates from the syzygies and ends with a canonical partition function and the latter , begins with the zeroes over finite fields and arrives at an euler product over primes . by explicitly constructing pairs of gauge theories , where the vacuum of one governs the other by having their generating functions
exchanged , we have observed an interesting duality wherein the geometry of one and the arithmetic of another inter - mingle .
asymptotic analyses on the growth rates of the coefficients in the generating functions , by construction constituting the enumerations , suggest a curiously `` holographic '' nature of this duality , which holds for arbitrary gauge theories , as coursely controlled asymptotically by the dimension of the vacuum moduli space . in due course , we have been inevitably led to the study of l - functions , dirichlet series , analytic behaviour of the zeroes and poles of hasse - weil zeta functions , as well as the modularity theorem , all of which tremendous subjects in themselves ; we pray that the patient reader has as much forgiven our inexpertise as he or she has indulged in our long exposition , especially in the drudgery of our examples and experimentation .
it is hoped that we have only skimmed over the surface of a deeper subject . to mention but a few prospects in this brief epilogue , we should , for instance , explore the full quantum moduli space , which in the geometry often materializes as deformations in complex structure .
we have seen how such deformations could drastically alter , if not the chiral ring , at least the arithmetic .
moreover , the vacuum moduli space of gauge theories , especially in the context of d - brane world - volume physics , should be comprehended scheme - theoretically , with the classical abelian case being the centre of some non - commutative algebra .
we have placed rational restrictions on the hilbert series and the local zeta functions because of commutative algebraic geometry , however , the realm of non - commutativity would significantly relax such constraints and would , naturally , lead to further correspondences . for now , let us repose awhile from our excursions onto this territory of physics , geometry and number theory , and regain our strength by further reflections , before voyaging further on such fertile ground .
1 _ pro commentariis amicorum carissimorum suorum , philippi candelas , xeniae de la ossa , amihayi hanany , vishnuus jejjala , iacobi moxness et georgii minic , y .- h.h . gratias plurimas agit , dum debet animam suam scientiae et technologiae concilio anglicae , et ricardo fitzjames , episcopo londiniensis , ceterisque omnibus benefactoribus collegii mertonensis oxoniensis , universitate urbis londiniensis , et cathedrae professoris chang - jiangiensis universitatis nan - kai .
+ bibet pro salutatem dominae iessicae rawson , custodis mertonensis , salutem dicetque domino martino taylor , custodi novi .
stet fortuna domus !
+ sed super omnes , domino illuminatione mea , pro amore catharinae sanctae alexandriae , lacrimarum mariae semper virginis , et ad maiorem dei gloriam hoc opusculum dedicat . _
in performing the product over all the prime in obtaining the global zeta function from the local , we encounter situations of primes of bad - reduction where the variety may become singular .
we illustrate this , in a pedagogical manner , using an explicit example explained lucidly by @xcite whose excellent presentation we will attempt to follow here .
take the elliptic curve @xmath498 $ ] , with @xmath31 some integer parametre , and denote it as @xmath499 .
indeed , the curve , together with its jacobian , prescribe the simultaneous system : @xmath500 . working over a field of characteristic @xmath62 ,
this has non - trivial solutions if @xmath501 ( for @xmath502 , @xmath503 and for @xmath504 , @xmath505 ) , whereby making the point corresponding to the solution singular and the elliptic curve , degenerate .
such a prime @xmath59 is called one of * bad reduction*. over these primes , there are always @xmath77 points .
for instance , when @xmath506 , the curve degenerates to a complex line @xmath507 , over which , we recall , there are @xmath508 points over @xmath61 . over the remaining primes , of good reduction ,
the weil conjectures give us the rational form in .
note that the bad reduction primes is always a finite set , determined as those divisible by some parametre . here
@xmath509 is this governing parametre and gives rise to the so - called * conductor * for the given elliptic curve . in general , the conductor @xmath1 is a single integer whose prime factors are precisely those of bad reduction . in summary , @xmath510 so that the global zeta function , upon substituting @xmath511 , should be @xmath512 where @xmath513 is dubbed the * hasse - weil l - function*. the relation between the parametre @xmath514 and the number of points over @xmath222 is as in : @xmath515
the particular case of taniyama - shimura , now called the modularity theorem by the work of wiles et al .
special case of the langlands programme , which has of late become important in string theory due to witten - upon which we here briefly touch is the hasse - weil conjecture for elliptic curves . of course ,
all these impinge on an enormous subject , for which we have neither the qualifications nor the space to expound in any depth .
we shall concentrate on the analytics of the dirichlet expansion @xmath516 for the l - function of a given elliptic curve @xmath422 . to set notation , by a modular of weight @xmath23 and level @xmath1 we mean an analytic function @xmath517 defined on the complex upper - half plane @xmath518 such that @xmath519 under @xmath520 , a particular congruence subgroup of the modular group @xmath521 where @xmath103 divides @xmath1 .
furthermore , a cusp form is one for which the zeroth coefficient @xmath522 of its @xmath419-expansion @xmath523 ( where @xmath524 ) vanishes .
now , the @xmath499 in appendix [ a : reduction ] have rather complicated conductors , so let us use a simpler example . consider the elliptic curve @xmath525 , one could find @xcite that the conductor is 11 .
we can tabulate , for some first primes , some leading values of @xmath227 ( which we can readily find on the computer ) and the coefficient @xmath424 in the local zeta function , related thereto by a relation in analogy to : @xmath526 : @xmath527 forming the l - function and expanding into dirichlet series gives : @xmath528 on the other hand , the space of modular forms at each weight is a finitely generated vector space .
in particular , cusp forms of weight 2 and level 17 is generated by a single function , given as a plethystic type product , with @xmath529 the standard dedekind eta - function : @xmath530 as one can see , the coincidence of the two sets of expansion coefficients is highly non - trivial and constitutes one of the highlights of twentieth century mathematics .
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a. okounkov , n. reshetikhin and c. vafa , `` quantum calabi - yau and classical crystals , '' arxiv : hep - th/0309208 . n. koblitz , `` introduction to elliptic curves and modular forms , '' , gtm , 1993 . | we investigate certain arithmetic properties of field theories . in particular , we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic .
parallel to the plethystic programme of counting the spectrum of operators from the syzygies of the complex geometry , we construct , based on the zeros of the vacuum moduli space over finite fields , the local and global hasse - weil zeta functions , as well as develop the associated dirichlet expansions .
we find curious dualities wherein the geometrical properties and asymptotic behaviour of one gauge theory is governed by the number theoretic nature of another . 0.25 in on fields over fields + yang - hui he + [ cols= " < , < " , ] + + |
in qcd an important role is played by topological properties . by the axial anomaly ,
matrix elements or correlation functions involving the topological charge density operator @xmath2 can be related to relevant quantities of hadronic phenomenology .
we mention the topological susceptibility @xmath3 , which is determinant in the explanation of the @xmath4 problem @xcite , and the on - shell nucleon matrix element of @xmath2 , which can be related to the so - called spin content of the nucleon @xcite .
lattice techniques represent our best source of non - perturbative calculations , however investigating the topological properties of qcd on the lattice is a non - trivial task . in a lattice theory
the field is defined on a discretized set and therefore the associated topological properties are strictly trivial .
one relies on the fact that the physical continuum topological properties should be recovered in the continuum limit . from a field
theoretical point of view , i.e. considering the lattice as a regulator , difficulties may come from unphysical divergences proportional to powers of the cut - off , which must be removed and therefore make the extraction of the physical signal hard . in order to get reliable quantitative estimates of physical quantities , one should control the unphysical cut - off dependent corrections even when they disappear in the continuum limit , given that numerical simulations are performed at finite lattice spacings , i.e. at finite values of the cut - off .
such corrections may be relevant , in that the typical values of the bare coupling @xmath5 where simulations are usually performed are actually not small , but @xmath6 , thus few terms in perturbation theory are not always reliable . considering a lattice version of @xmath2 , @xmath7 ,
the classical continuum limit must be in general corrected by including a renormalization function . in pure qcd , where @xmath2 is renormalization group invariant , @xcite @xmath8 where @xmath9 is a finite function of the bare coupling @xmath5 going to one in the limit @xmath10 , but at @xmath6 it may be very different from one .
the finite renormalization of the widely used lattice operator @xcite @xmath11\;\ , \label{stop}\ ] ] ( @xmath12 is the product of link variables @xmath13 around a @xmath14 plaquette ) is quite nonnegligible : for @xmath15 @xmath16 @xcite . the relation of the zero - momentum correlation of two @xmath7 operators @xmath17 with the topological susceptibility @xmath3 is further complicated by an unphysical background term , which eventually becomes dominant in the continuum limit .
( we recall that the definition of @xmath3 requires also a prescription to define the product of operators @xcite . )
indeed @xmath18 neglecting terms @xmath19 , the background term @xmath20 can be written in terms of mixings with the unity operator ( so - called perturbative tail scaling as @xmath21 ) and with the trace of the energy - momentum ( scaling as @xmath22 ) . in the case of the operator ( [ stop ] ) and for @xmath15 , @xmath20 is already dominant at @xmath6 : it is about 85% of @xmath23 at @xmath24 @xcite . as a consequence the uncertainty on @xmath3 can be hardly made smaller than @xmath25 by using the operator ( [ stop ] ) and the heating method to evaluate @xmath9 and @xmath20 @xcite .
another problem , which has come up in some studies concerning the lattice determination of the on - shell proton matrix element of @xmath2 @xcite , is that the lattice operator ( [ stop ] ) is very noisy , requiring very accurate statistics and therefore expensive simulations in order to get a reasonable uncertainty on the final result . in view of a full qcd lattice calculation
the search for a better estimator appears a necessary step .
we study , within the field theoretical approach , the possibility of improving the lattice estimator of @xmath2 with respect to all the problems listed above , that is we look for local versions of @xmath2 which are less noisy , have a multiplicative renormalization closer to one , and whose corresponding @xmath23 is not dominated by the unphysical backgroung signal @xmath20 in the region @xmath6 .
( any @xmath23 defined from a local @xmath7 will eventually be dominated by its perturbative tail in the continuum limit . for the purpose of evaluating @xmath3 it would suffice to have a small tail at @xmath6 , which should be already in the scaling region . )
inspired by the widely used smearing techniques , we consider the following set of operators defined in terms of smeared links @xmath26 : @xmath27 , \label{impop}\ ] ] where @xmath28 is the product of smeared links @xmath26 around a @xmath14 plaquette .
such smeared links are constructed by the following procedure : @xmath29^{1/2 } } \label{imppr}\end{aligned}\ ] ] where @xmath30 .
@xmath31 and therefore @xmath32 depend on the parameter @xmath33 , which can be tuned to optimize the properties of @xmath32 .
all these operators have the correct classical continuum limit , i.e. for @xmath34 , @xmath35 .
notice that the size of @xmath32 increases with increasing the integer parameter @xmath36 .
nevertheless @xmath32 can be still considered as local operators when keeping @xmath36 fixed while approaching the continuum limit .
also , as we shall see , by optimizing the choice of the parameter @xmath33 , a good improvement with respect to @xmath37 is already achieved for small values of @xmath36 .
for @xmath38 the procedure ( [ imppr ] ) keeps the smeared links @xmath31 belonging to the @xmath38 group , and it is equivalent to the smearing procedures proposed in ref . @xcite . for @xmath39
the smeared links no longer belong to the @xmath40 group .
the procedure ( [ imppr ] ) may be used to improve any local operator involving link variables .
smearing methods to improve lattice estimators have been already widely employed in the study of long distance correlations , such as large wilson loops and hadron source operators .
one often adopts an equivalent `` schrdinger picture '' of smearing , whereby lattice operators retain their original definition , while all links in the configuration undergo transformation ( [ imppr ] )
. full consistency of this picture would then require that @xmath31 be unitary .
( as it stands , @xmath31 is only unitary in the case of @xmath38 . )
projecting a matrix v onto @xmath40 amounts to finding @xmath41 which minimizes @xmath42 , or equivalently maximizes @xmath43 .
the solution is given by : @xmath44 where @xmath45 is the real root of the equation : @xmath46 and @xmath47 are the eigenvalues of @xmath48 .
it can be verified that the lower loop results for @xmath9 and the perturbative tail @xmath49 ( see sec .
[ pertan ] ) are not modified by rendering @xmath31 unitary as above .
it is worth mentioning at this point that abrupt cooling leads to exactly the same unitary links @xmath50 , for @xmath51 . indeed
, cooling reassigns to each link a new value , @xmath52 in a way as to minimize the action , i.e. maximize : @xmath53 at @xmath51 , which coincides with eq.([unitary ] ) . for @xmath39 , instead of projecting back onto the @xmath40 group
we propose last step of the procedure ( [ imppr ] ) , which is simpler and should retain most of the advantages of the standard smearing procedure .
we have calculated @xmath54 to one loop for the once - smeared operator @xmath55 with the wilson action . to carry out this calculation ,
@xmath56 is expanded in a taylor series in the gauge field @xmath57 , where @xmath58 . in fig .
[ fig1 ] we show the three diagrams contributing to @xmath59 .
we find @xmath60 \ ; , \label{mr}\end{aligned}\ ] ] where @xmath61 .
at @xmath62 we recover the non - smeared results @xcite : @xmath63 which do not lead to a reliable estimate of @xmath64 . as @xmath33 varies , the following extreme values of @xmath65 are obtained : @xmath66 in both cases , @xmath65 is quite close to unity for typical values of @xmath5 , making the one loop estimate more reliable .
it is noteworthy that the last step in the smearing procedure ( [ imppr ] ) turns out to be essential to make @xmath65 approach one for @xmath67 . for @xmath55
, we have also calculated the lowest perturbative contribution to the mixing with the unity operator @xmath49 , which is the dominant part of the background term @xmath20 in the continuum limit .
the corresponding diagram is shown in fig .
[ fig2 ] and leads to the result : @xmath68 the minimum of this everywhere - concave polynomial is @xmath69 .
thus , for all @xmath70 , the leading order of @xmath49 diminishes by more than two orders of magnitude compared to its non - smeared value ( @xmath62 ) . in the presence of dynamical fermions
one should take into account the fact that , unlike pure gauge theory , the topological charge density mixes under renormalization with @xmath71 , where @xmath72 is the singlet axial current .
the nonrenormalizability property of the anomaly in the @xmath73 scheme means that the anomaly equation should take exactly the same form in terms of bare or renormalized quantities
. however the renormalization of @xmath74 and @xmath2 is nontrivial @xcite .
a renormalization group analysis leads to the following relation valid for all matrix elements of a lattice version @xmath7 of @xmath2 in the chiral limit @xcite : @xmath75 where @xmath76 is a finite function of @xmath5 , and @xmath77 is a renormalization group invariant quantity ; @xmath78 indicates the operator @xmath79 renormalized in the @xmath73 scheme , and the function @xmath80 is related to the anomalous dimension of the continuum operators @xmath2 , @xmath81 in the @xmath73 scheme : @xmath82 . notice that @xmath83 is what can be naturally extracted also from experimental data . in perturbation theory one finds @xmath84 , where @xmath85 is the coefficient of the @xmath86 term of the finite renormalization of @xmath87 in the pure gauge theory ( cfr .
( [ mr ] ) ) , and @xmath88 turns out to be a small number : @xmath89 for @xmath90 and @xmath91 @xcite .
estimates of the multiplicative renormalizations of the operators @xmath32 and of the background term in the corresponding @xmath23 can be obtained using the numerical heating method @xcite , without any recourse to perturbation theory .
this method relies on the idea that the multiplicative renormalization @xmath9 and the background term @xmath20 is produced by short ranged fluctuations at the scale of the cut - off @xmath92 .
therefore , when using a standard local algorithm ( for example metropolis or heat bath ) to reach statistical equilibrium , the modes contributing to @xmath65 and @xmath93 should not suffer from critical slowing down , unlike global quantities , such as the topological charge , which should experience a severe form of critical slowing @xcite .
we applied the heating method to the operators @xmath32 for @xmath94 and for a number of values of @xmath33 in the region @xmath95 .
we restricted our analysis to the @xmath38 pure gauge theory , expecting no substantial differences for @xmath90 .
the measurements were performed at @xmath96 ( @xmath97 ) , which is a typical value for the @xmath38 simulations with the wilson action .
the local updating was performed using the heat - bath algorithm .
an estimate of @xmath65 can be obtained by heating a configuration @xmath98 which is an approximate minimum of the lattice action and carries a definite topological charge @xmath99 .
such a configuration has been constructed by discretizing an instanton solution in the singular gauge @xmath100 where @xmath101 and @xmath102 , and exponentiating it to define link variables @xmath103 . then a few cooling steps ( about 5 )
were performed to make the configuration smoother . on a lattice @xmath104 and choosing @xmath105 we obtained an instanton - like configuration carrying a topological charge @xmath106 ( all improved operators we considered gave approximately the same value for @xmath98 ) .
one then constructs ensembles @xmath107 of many independent configurations obtained by heating @xmath98 for the same number @xmath108 of updating steps , averaging @xmath109 over @xmath110 at fixed @xmath108 .
let us define @xmath111 , i.e. the average on the ensemble @xmath107 .
fluctuations of length @xmath112 contributing to @xmath65 should rapidly thermalize , while the topological structure of the initial configuration is left ( approximately ) unchanged for a long time .
after a few heating steps where the short ranged modes contributing to @xmath65 get thermalized , @xmath113 should show a plateau approximately at @xmath114 .
the estimates of @xmath115 from the plateaux observed in the heating procedure are reported in table [ tab1 ] , and should be compared with the value @xmath116 for the standard operator ( [ stop ] ) @xcite .
the plateaux formed by the ratios @xmath117 starting from @xmath118 are clearly observed in fig .
[ zeta ] , where data for @xmath94 and @xmath119 are plotted versus @xmath108 .
checks of the stability of the background topological structure of the initial configuration were performed at @xmath120 by cooling back the configurations ( locally minimizing the action ) finding @xmath121 after few cooling steps .
this analysis confirms the one - loop perturbative calculations , that is the improved operators we considered have a multiplicative renormalization closer to one than that of the initial operator @xmath7 . from @xmath122 of @xmath7 ,
we pass , by roughly optimizing with respect to the parameter @xmath33 , to @xmath123 by one improving step , and @xmath124 by two improving steps . for larger @xmath36
we expect to get @xmath125 closer and closer to one , as also suggested from the results of the cooling method @xcite . on the other hand
, we should not forget that increasing the number of improving steps the size of the operator @xmath32 increases .
one should find a reasonable compromise taking into account the size of the lattice one can afford in the simulations .
a comparison of the above results for @xmath126 with the one - loop calculation ( [ mr ] ) shows that the contribution of the higher perturbative orders is still non - negligible , but not so relevant as in the case of the operator without improving .
another important property of the improved operators we can infer from the heating method results is that they are much less noisy than @xmath7 at fixed background . in other words , in the monte carlo determinations of the matrix elements of @xmath2 the contribution of short ranged fluctuations to the error is largely suppressed . a quantitative idea of
this fact may come from the quantity @xmath127 , where @xmath128 is the typical error of the data in the plateau during the heating procedure described above .
we indeed found for @xmath129 and for an equal number of measurements @xmath130 an estimate of the background signal @xmath20 can be obtained by measuring @xmath131 on ensembles of configurations @xmath132 constructed by heating the flat configuration for the same number @xmath108 of updating steps @xcite .
measurements were performed on a @xmath133 lattice .
the plateau showed after few heating steps ( @xmath134 in this case ) by the data of @xmath135 should be placed approximately at the value of @xmath136 , since no topological activity is detected there , i.e. the background is still flat ( this is checked by cooling back the heated configurations ) , while the other modes contributing to @xmath20 should be already approximately thermalized ( for a discussion of this issue see @xcite ) .
the estimates of @xmath137 from the plateaux observed during heating are given in table [ tab2 ] , and should be compared with the value @xmath138 relative to the standard operator ( [ stop ] ) . in fig .
[ tail ] we plot @xmath139 for @xmath94 and @xmath140 as a function of the heating step @xmath108 , and compare with the corresponding data for the standard operator .
the expected plateaux are observed from @xmath134 .
notice the strong suppression of the background term in the improved operators . for @xmath141
the reduction is about a factor 8 when performing one improving step , and about a factor 30 by two improving steps . for a larger number of improving steps
, the suppression is expected to be larger . the suppression of the background term in eq .
( [ chileq ] ) together with the relevant increase of @xmath65 should drastically change the relative weights of the contributions to @xmath23 in the relevant region for monte carlo simulations . by a standard monte carlo simulation at @xmath96 on a @xmath142 lattice , we measured @xmath143 for @xmath94 and @xmath144 .
we performed 15000 sweeps using an overrelaxed algorithm ; this sample size is already sufficient to show the better properties of the operators @xmath32 .
data for @xmath145 are given in table [ tab3 ] .
for comparison we also calculated @xmath146 by cooling @xcite .
for the standard operator we found @xmath147 , which , due to the large corresponding background term @xmath148 , does not allow one to determine @xmath146 at this value of @xmath149 .
instead the improved operators @xmath32 provide , using eq .
( [ chileq ] ) , reliable estimates of @xmath146 having about 10% of uncertainty , which are consistent with each other and are also consistent with the determination from cooling : @xmath150 , although the latter seems to be systematically lower .
this fact may be explained taking into account that @xmath151 , which is used to estimate the topological charge of cooled configurations , underestimates the topological charge content ( for the lattice size we are working with ) , as we found out explicitly when we constructed an instanton configuration on the lattice .
the determinations of @xmath65 and @xmath93 should not be subject to relevant finite size scaling effects ( as explictly checked in ref .
@xcite ) , since they have their origin in short ranged fluctuations .
thus finite size corrections to our estimates of @xmath65 and @xmath93 should be negligible .
larger finite size effects are expected on the topological modes , as can be argued from numerical studies available in the literature .
for this reason the measurement of @xmath23 , which receives contributions also from topological modes , was performed on a larger lattice .
we should say that we did not perform a complete analysis of the finite size corrections to @xmath23 , since our purpose was just to show the better behavior of the improved operators @xmath32 and not the determination of @xmath3 for the @xmath38 gauge model .
so we limited ourselves to a numerical study not requiring a super - computer .
if the improvement for @xmath15 is similar to that achieved for @xmath38 , using the optimal operator for @xmath152 at @xmath24 the unphysical term in eq .
( [ chileq ] ) is expected to become a small part of the total signal , allowing a precise determination of @xmath3 by the field theoretical method .
we have analyzed the properties of a class of improved lattice topological charge density operators constructed by a smearing - like procedure .
such operators look promising for the lattice calculation of the on - shell proton matrix element of the topological charge density operator in full qcd , which is related to the so - called proton spin content .
indeed their use should overcome the difficulty due to the large noise observed in preliminary quenched studies @xcite , and they have a multiplicative renormalization much closer to one .
improved operators are also expected to provide a much better determination of the topological susceptibility by the field theoretical method in the @xmath15 gauge theory , by strongly reducing the unphysical background term while enhancing the term containing @xmath3 with larger values of the multiplicative renormalization .
this should allow a precise and independent check of the alternative cooling method determinations ( see e.g. refs .
@xcite ) , whose systematic errors are not completely controlled .
furthermore the improved operators may also open the road to a more reliable lattice investigation of the behavior of the topological susceptibility at the deconfinement transition , where cooling does not give satisfactory results @xcite . the smearing - like procedure ( [ imppr ] )
may be used to improve any local operator involving link variables , and a renormalization study would again be called for in all cases .
we hope to return to this issue in the future .
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j. r. sanford , and references therein .
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laursen , m. mller - preussker , g. schierholz and h. shiller , nucl . phys . *
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present @xmath115 for @xmath94 and various values of @xmath33 , as obtained by the heating method for a number of @xmath153 trajectories .
the errors diplayed include both a statistical error ( determined by the typical errors of data in the plateau ) and a systematic error related to the stability of the background configuration .
the numbers in this table should be compared with the value @xmath116 for the standard operator ( [ stop ] ) @xcite . [ cols= "
> , > , < , > , < , > , < " , ] | we analyze the properties of a class of improved lattice topological charge density operators , constructed by a smearing - like procedure . by optimizing the choice of the parameters introduced in their definition , we find operators having ( i ) a better statistical behavior as estimators of the topological charge density on the lattice , i.e. less noisy ; ( ii ) a multiplicative renormalization much closer to one ; ( iii ) a large suppression of the perturbative tail ( and other unphysical mixings ) in the corresponding lattice topological susceptibility .
# 1currentlabel@secnum>0 .[#1 ] improved lattice operators : the case of the topological charge density .
@xmath0 department of natural sciences , university of cyprus , nicosia @xmath1 dipartimento di fisica delluniversit and i.n.f.n . ,
pisa , italy . |
the derivation of the the closed set of coupled equations of motion for correlation functions for two - level laser systems is given in ref .
@xcite . for our qd model ( shown in fig .
[ fig2 ] ) a more complicated but similar analysis can be performed . to simplify the discussion ,
we assume that @xmath59 , which does not affect the underlying physics ( in real systems , @xmath124 , whose effect could be effectively incorporated by introducing an additional shift in @xmath125 . )
the correlation functions that we need to consider are @xmath126 for @xmath127 . equations ( [ eq : bxk ] ) ,
( [ eq : dxk ] ) , ( [ eq : txk ] ) , ( [ eq : txxk ] ) , and ( [ eq : bx12k ] ) , are reformed based the spin inversion symmetry in the system . for the @xmath128-th photon correlation function ,
the following relationship is fulfilled : @xmath129 the relationship is used to obtain the second order coherence at zero time delay , @xmath130 .
derivation of the equation of motion for the correlation function is straightforward using @xmath131 with the qme , @xmath60+\mathcal{l } \rho$ ] .
their explicit form is as follows : where we define the exciton spin relaxation rate @xmath133 and the decay coefficients are given by @xmath134 in the steady state ( @xmath135 ) , a balance relation is obtained for @xmath136 , @xmath137 for @xmath138 , the physical meaning is clearly the balance equation between `` loss ( l.h.s . ) '' and `` gain ( r.h.s . ) '' .
the first and second terms on the r.h.s .
correspond to the optical gain contributions from the exciton ( bx1/bx2 @xmath139 g ) and biexciton ( xx @xmath139 bx1/bx2 ) transitions .
the coupled equations of motion in eqs .
( [ eq : eom1])-([eq : eom8 ] ) produce an infinite series of equations from @xmath140 to @xmath141 .
these equations can be solved numerically if the high - order correlation functions are ignored by introducing a photon - number cutoff @xmath142 i.e. by putting @xmath143 for @xmath144 . however , this is unreasonable for the evaluation of the first ( @xmath138 ) and second order ( @xmath145 ) correlation functions in the linear regime at weak pumping . here
, we give a brief introduction to the perturbative treatment which we perform to evaluate the second - order coherence .
this treatment allows us to calculate analytic expressions and provides more insight into the physics , and the dependence of qd populations , mean photon number , and @xmath0 on numbers of parameters ( @xmath77 ) . by assuming the following pump rate dependence , ( for the linear regime ) : @xmath146 we are able to obtain these correlation functions perturbatively in powers of small @xmath8 .
hereafter , the perturbation series of the @xmath128-th order correlation function @xmath147 is defined as @xmath148 where the @xmath149-th component is proportional to @xmath150 . in the zeroth order , @xmath151 , and all other quantities
are of higher order in @xmath8 .
for the first order , the resulting closed coupled equation of motions are @xmath152 with the first - order normalization condition @xmath153 which reads @xmath154 since @xmath155 irrespective of the stationary conditions ( from eq .
( [ eq : nomalization1 ] ) ) , there are only two independent equations among eqs .
( [ eq : perturb1ste1])-([eq : perturb1ste3 ] ) .
the first - order equations are written in matrix form as @xmath156 where the coefficient @xmath157 given by @xmath158 now seen in an explicit form , the correlation function to first - order in @xmath8 is given by the source term of the zeroth order , @xmath159 , and we find @xmath160 being similar to the result for qd sp emitters without cavities in eqs .
( [ eq : rhoxx])-([eq : rhodx ] ) , we found that only the dark state population @xmath162 ( and also @xmath163 from eq .
( [ eq : nomalization1 ] ) ) is divergent at @xmath164 .
of course , this perturbation analysis applies only in the weak pumping limit , and the low - order perturbation treatment becomes unreliable if the contribution becomes of order unity .
however , the ratio @xmath165 can be arbitrarily large for small @xmath2 even in the linear regime . in a similar manner
, a strong enhancement also occurs in @xmath0 as seen below . where the decay coefficients are @xmath168 a matrix inversion of eq .
( [ eq:2ndperturbation ] ) yields the second - order perturbation series with the first - order ones as source terms .
since the first - order source terms contain @xmath162 and @xmath163 @xmath1 , the second - order correlation functions relevant to @xmath169 ( @xmath170 from eq .
( [ eq : balance ] ) ) also contain the divergent factor @xmath1 .
the second - order normalization condition @xmath171 reads @xmath172 by repeating the same steps , it is in principle possible to obtain higher order correlation functions analytically in the liner weak - pump limit .
however , third- and higher - order analysis requires much more laborious calculations , so we limit our calculation to the the second order . in order to check the validity of the perturbation result , in fig .
[ fig : suppleb ] we compare the analytic results for the mean photon number @xmath173 and @xmath174 with the numerical qme results obtained after time evolutions until the system had reached the steady state . in the figure , we clearly see that the two methods give the same result , and the perturbation result is correct in the linear regime for weak pumping rate .
second - order coherence @xmath0 ( blue ) and mean cavity photon number @xmath175 ( red ) are shown as a function of pumping rate @xmath176 .
the results evaluated by two different approaches , a perturbation analysis to their lowest order , @xmath177 and @xmath178 ( solid ) , and a direct numerical simulation of the qme ( points ) , are compared .
the dashed lines are guide for eye .
we set @xmath179 in @xmath180ev .
the vertical grey line marks the definition of @xmath181 we now briefly note how we determined the crossover photon emission rate @xmath78 in the main text and in fig .
[ fig2 ] and fig .
[ fig3 ] . as seen from the qme result in fig .
[ fig : suppleb ] , @xmath0 increases with @xmath8 while it is constant in the linear regime .
this is natural since the increase in the cavity photon number directly leads to the increase in multiple photon emission events .
therefore , real sp emitting devices should work in the linear regime to maintain a small value @xmath0 .
the crossover photon emission rate @xmath182 is the maximum cavity photon number for a pump rate at the crossover between the linear and non - linear regimes ( @xmath183 ) .
this is defined more rigorously in our simulation as the condition where second order corrections amount to fifty percent of the first order corrections with respect to @xmath175 and @xmath184 .
if @xmath185 and @xmath186 , the smaller pump rate between @xmath187 and @xmath188 , at which the nonlinear @xmath8-dependence becomes apparent in @xmath0 , corresponds to @xmath189 : @xmath190 the evaluation of this is possible within the second order perturbation analysis presented here , and we mark @xmath183 obtained by eq . ( [ eq : pmax ] ) in fig . [
fig : suppleb ] .
we find that the calculated @xmath189 agreemees well with the numerical qme result , where the nonlinear @xmath191dependence in @xmath192 and a deviation from the weak pump limit of @xmath0 are found .
@xmath78 evaluated in this way therefore gives a good estimate for a maximum available sp emission rate , above which the qd emitters have a degraded single photon purity .
finally , we give analytic expressions for the correlation functions for a system without dx states , dx1 and dx2 , and the dark pumping path via the dx states .
comparison between the results obtained with and without the dark path can be used to evaluate the increase in @xmath0 due to the path . in the no dark path case , the first - order normalization condition in eq .
( [ eq : nomalization1 ] ) is replaced by @xmath193 the first - order equation in eq .
( [ eq : nomalization1 ] ) by @xmath194 and the second - order equation in eq .
( [ eq:2ndperturbation ] ) by [ [ supplec - rate - equation - analysis - for - sp - emitters - with - cavities - the - existence - of - an - optimal - cavity - loss - kappa ] ] [ supplec ] rate equation analysis for sp emitters with cavities : the existence of an optimal cavity loss @xmath66 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ as referred to in the main text , for good cavities with small @xmath66 , photons accumulating in cavity increase the multi - photon probability and hence @xmath0 .
therefore , @xmath0 decreases with increasing @xmath66 .
this is similar to cavity qed of two - level systems ( cavity loss @xmath66 , spontaneous emission @xmath197 , coupling @xmath198 ) .
an expression for @xmath0 is given by @xmath199 in @xcite , for which one finds @xmath200 as @xmath201 .
hereafter , we will focus on bad cavities in the weak coupling limit @xmath202 to show the existence of the optimal @xmath66 .
a rate equation analysis is presented by using the simplified qd model as shown in fig .
[ fig : supplec ] ( a ) for a qualitative discussion .
the cavity mode is assumed to be in resonance with the exciton transition ( bx @xmath203 g ) .
we denote the rates of the radiative transitions into the cavity mode by @xmath204 for the exciton transition and @xmath205 for the biexciton transition .
since we are focusing on the weak pump regime , we take into account only the density matrix elements limited to those for a biexciton state with no photons , @xmath206 , bright exciton states with zero and one photons , @xmath207 and @xmath208 , empty states with zero , one , two photons , @xmath209 , @xmath210 , and @xmath211 , and a dark exciton state with no photons @xmath212 . from the probability flows in fig . [
fig : supplec ] ( b ) , we obtain the following set of rate equations : the rate equations is solved with the normalization condition , @xmath214 . for large @xmath66 where @xmath215 , we have for the steady state , @xmath216 to the lowest order in @xmath217 .
here we have taken the limit @xmath218 after taking @xmath219 .
we find again the same enhancement factor of @xmath220 in the expression ( see eq .
( [ eq : g2simple ] ) in the main text . )
the prefactor is determined by the ratio of the transition rates @xmath221 which depends on @xmath66 as we shall see below . if @xmath66 is larger than @xmath65 , @xmath2 , and @xmath198 , but @xmath222 as shown in fig .
[ fig : supplec2](a ) , the transition probabilities are given by @xmath223 and @xmath224 .
in this case , the prefactor @xmath225 is small . for large @xmath226
, @xmath0 vanishes , being analogous to the result in eq .
( [ eq : g2simple ] ) in the main text .
on the other hand , if @xmath66 is larger than @xmath65 , @xmath2 , and @xmath198 and @xmath98 as shown in fig .
[ fig : supplec2](b ) , we find @xmath227 and the prefactor equals two . according to this result , for bad cavities @xmath228 , @xmath0 increases with @xmath66 until @xmath229 , where it begins to saturate at a value of @xmath230 .
now it is clear that there should be a minimum in @xmath0 as a function of @xmath66 , from the 2 results : ( i ) @xmath0 decreases with increasing @xmath66 for small @xmath66 , and ( ii ) increases with @xmath66 for large @xmath66 .
the optimal value of @xmath231 is found in a range @xmath232 . | incoherent pumping in quantum dots ( qds ) can create a biexciton state through two paths : via the formation of bright or dark exciton states .
the latter , dark - pumping , path is shown to enhance the probability of two - photon simultaneous emission , and hence increase @xmath0 by a factor @xmath1 , due to the slow spin relaxation rate @xmath2 in qds .
the existence of the dark path is shown to impose a limitation on the single photon ( sp ) emission process , especially in nanocavities which exhibit a large exciton - cavity coupling and a purcell enhancement for fast quantum telecommunications . _
introduction _ a high quality single photon ( sp ) source is essential for the realization of secure telecommunications based on the principles of quantum mechanics , such as quantum key distribution ( qkd ) @xcite .
semiconductor quantum dots ( qds ) are promising candidates for solid - state single photon emitters , because of their well - defined atom - like quantized states @xcite , and a high controllability of their emission wavelength @xcite , by means of applied electric and magnetic fields .
it is also possible to populate the states of qds via both current injection and optical excitation .
interactions between qd excitons and photons are also controllable by embedding qds in optical microcavities such as photonic crystal ( ph - c ) nanocavities @xcite , in which cavity quantum electrodynamics ( cavity qed ) effects have been observed @xcite . the quality of a sp emitter is quantified by measuring the conditional probability to observe photons at a delay time @xmath3 after a photon counting event , @xmath4 @xcite .
the value of @xmath4 at zero time delay , @xmath0 , should be or be as close as possible to zero to obtain good sp emitters .
this is equivalent to minimizing the probability of finding multiple - photon simultaneous emissions . for application in qkd , a high emission rate
is also desired , which can be attained if qds are combined with optical microcavities @xcite . in this brief report , we investigate incoherent pumping processes in a qd sp emitter to find a `` dark path'' a pumping path from ground to biexciton states via a dark exciton state that can strongly increase @xmath0 , thus imposing a limit on the available single photon purity , especially in small cavities with a small mode volume , @xmath5 , and a large exciton - cavity coupling , @xmath6 . several ways to reduce the effect of the dark path are also mentioned . in the following analysis , we define @xmath7 for simplicity . _ impact of the dark path in qd sp emitters without cavities _ in order to see how the dark path increases the multiple photon emission probability , we first study a simple phenomenological model for a qd sp emitter without cavity coupling . here , an undoped qd is pumped incoherently and continuously under a charge - neutral condition .
the qd states relevant to our study are restricted to the neutral states with up to two electron - hole pairs as shown in fig .
[ fig1 ] ( a ) .
excited carriers injected at high energy levels become trapped in the lowest qd level after fast relaxation from a continuum above the band gap and excited trapped states ( which are truncated in our model ) .
the whole process of injection and relaxation of the carriers ( electron - hole pairs ) to the lowest qd level is described by a single pumping rate @xmath8 .
depending on the spins of carriers , the bright and dark exciton states ( bx / dx ) are randomly generated from the initial empty state ( g ) with the same rate @xmath8 .
successive creations of two electron - hole pairs further excite the system to the biexciton state , xx .
the single photon emission process is mainly governed by the recombination transition from bx to g with a spontaneous emission rate @xmath9 , and the two photon emission process by the cascaded emission from xx to g via bx ( the energy difference between biexciton and single - exciton emissions is the binding energy @xmath10 ) . in qds ,
spin relaxation processes between bx and dx ( the rate @xmath2 ) are usually slow and often neglected compared to the other dynamics @xcite , however they must be considered carefully to evaluate @xmath0 as shown below .
( a ) ground , exciton , and biexciton states ( g , bx , dx , and xx ) , pumping ( @xmath8 ) and relaxation processes ( @xmath11 , and @xmath2 ) in an undoped qd described in the text .
( b ) emission spectral profiles of the biexciton and exciton recombination transitions .
the spectral filter used for the photodetection ( with a detection window @xmath12 ) is also shown . ]
the rate equations for the populations at each qd levels are @xmath13 , @xmath14 , @xmath15 , and @xmath16 , for which the steady state satisfies @xmath17 in the linear regime at weak pumping . from this result , neglecting a factor of order unity related to the emission profiles , the normalized second order correlation function is given by @xmath18 @xcite . here , @xmath19 is the probability of finding a photon emitted from @xmath20 within the spectral range of the detector window @xmath21 as shown in fig .
[ fig1](b ) . upon making the assumptions that @xmath22 , @xmath23 and @xmath24 ,
@xmath25 can be expressed as @xmath26 and hence , in the linear regime @xmath27 the expression for @xmath0 contains a factor @xmath28 that becomes large when the spin relaxation is very slow @xmath29 @xcite .
the enhancement of @xmath0 occurs due to an unwanted excitation of state xx through a `` dark path''a path via the excitation of dx .
this can can be verified by testing using another model without the dark path : we find that @xmath30 if the dx state and the `` dark '' pumping path are not present ( this result is also obtained when @xmath31 in eq .
( [ eq : g2simple ] ) . )
the above scenario can also be verified by considering the steady state population in eq .
( [ eq : rhobx ] ) and eq .
( [ eq : rhodx ] ) : the dark state population @xmath32 and the ratio @xmath33 diverge as @xmath34 so that the production rate of @xmath35 is largely enhanced when the dark pumping path is present .
following the simple discussion above , we find that the dark path can act as a bottleneck when trying to purify the single photon generation in qds , since the spin relaxation process is usually slower ( typically 1 - 10 ns timescale ) than the other processes @xcite : radiative recombination and dephasing , in qd systems . the strong impact of a dark pumping path on @xmath0 has been shown for many two - level atoms or many qds by temnov _
et al . _
@xcite , where the connection with cooperative spontaneous emission and superradiance are also discussed . even though the system considered here is a single emitter , similar physics does exist and can reduce the quality of a sp emitter .
the interpretation of the other parts in eq .
( [ eq : g2simple ] ) , @xmath36 , is physically clear ; @xmath0 can be made small if the biexciton and exciton emissions are energetically separated ( large @xmath37 ) @xcite and the detector window @xmath38 is small , by which the probability of counting unwanted photons fed by xx state into the window can be reduced . _
impact of the dark path on high - speed sp emitters with cavities _ we next shift our discussion to how the use an optical microcavity @xcite ( which increases the sp emission rate by purcell effect ) affects the single photon purity . the realization of high - quality sp sources in microcavities is an important issue , and a number of experiments have been reported on the fabrication and evaluation of such devices ( for a recent review , see @xcite ) .
hence , it is important to understand what affect such a dark path may have on qds in microcavities . from the result obtained in the previous section , ( eq .
( [ eq : g2simple ] ) ) , one may guess that the purcell enhancement in @xmath39 would result in the increase in @xmath0 , and hence that the `` dark path '' pumping might be more troublesome than in a system without a cavity .
however , the discussion without cavity can not be applied directly to this case . here
we investigate the effect of a microcavity within the cavity qed framework with quantum master equations ( qme ) @xcite , treating the dynamics of cavity mode photons as well .
we consider a system that consists of carriers inside a qd and photons interacting inside a cavity .
six electronic configurations of the qd are considered @xcite : an empty state , @xmath40 , two bright exciton states , @xmath41 and @xmath42 , two dark exciton states , @xmath43 and @xmath44 , and a biexciton state , @xmath45 , where @xmath46 and @xmath47 ( @xmath48 and @xmath49 ) are annihilation ( creation ) operators of electrons and holes with spin @xmath50 in their respective lowest energy levels of the qd .
the number of cavity photons is given by @xmath51 , where @xmath52 and @xmath53 are the photon annihilation and creation operators , respectively .
assuming the frequencies of the cavity ( @xmath54 ) and exciton ( @xmath55 ) are tuned to resonance , @xmath56 , the hamiltonian of the coupled qd - cavity system @xcite can be written as @xmath57 where @xmath58 is the total excitation number , and we put @xmath59 for simplicity in the simulations . assuming the dynamics in the environment ( pump and decay baths outside the coupled qd - cavity system ) are fast and uncorrelated , the time evolution of the system density matrix is given by markovian qme , @xmath60+\mathcal{l } \rho$ ] @xcite , where @xmath61 using the standard notation for superoperators , @xmath62 , we consider the following situation ; the decay of the injected electron - hole pairs is dominated by the spontaneous emission into the cavity mode ( whose couplings are @xmath63 and @xmath64 ) and free space ( with a rate @xmath65 ) @xcite ; photons decay out of the cavity with rate @xmath66 ; the polarizations suffers dephasing with rate @xmath67 ; the spin flip of electrons and holes ( with the rates @xmath68 and @xmath69 ) results in the transitions between dark and bright exciton states with a rate @xmath70 .
one could determine the non - equilibrium steady state numerically by a long - time evolution of the system , @xmath71 , from an initial vacuum state @xmath72 after the pumping is switched on @xmath73 at @xmath74 .
the obtained density matrix , @xmath71 , can then be used to determine the photon number @xmath75 and @xmath76 .
however , we choose an alternative analytic approach to find the photon correlation functions , which is allowed in a linear regime at weak pump rate , and can be performed by a perturbation method @xcite .
this analytic approach brings clear insights of the physics and greatly reduces the calculation time to obtain the properties of photons as a function of numbers of parameters ( @xmath77 ) .
see the supplementary material for details of the calculation @xcite .
figures [ fig2 ] ( b , c ) and ( d , e ) show the calculated @xmath0 and the crossover photon emission rate @xmath78 ( defined as the photon emission rate @xmath79 at the crossover pump rate @xmath8 between the linear and nonlinear regime @xcite ) as a function of @xmath66 for a microcavity and a nanocavity , respectively .
@xmath78 indicates the maximum available photon emission rate with @xmath0 being kept low when @xmath0 is less than unity in the weak pump limit .
figures [ fig2 ] ( b , d ) are the calculation results for a microcavity structure as in @xcite with @xmath80 and @xmath81
. figures [ fig2 ] ( c , e ) show the results for an ultrasmall nanocavity structure , e.g. a ph - c nanocavity as in @xcite , with @xmath82 and @xmath83 . in each plot , three spin relaxation rates , @xmath84 , and @xmath85 ghz , are examined .
the spontaneous emission rate @xmath86 , dephasing rate @xmath87 , and the biexciton binding energy @xmath88 mev used in all calculations are typical values for inas qds .
interestingly , the figures exhibit an optimal @xmath89 minimizing @xmath0 ( @xmath90ev for both cavities with @xmath91 . )
they also exhibit an optimal @xmath66 ( @xmath92 ) , which maximizes @xmath78 .
this is in a remarkable contrast to cavity qed with a two - level atom @xcite , in which @xmath0 decreases from two down to zero as @xmath66 increases from the good - cavitiy to bad - cavity limits .
thus , we understand that the existence of optimal cavity losses arises due to the existence of the biexciton ( multiple exciton ) state . the optimal loss is found in a range @xmath93 .
this is explained by connecting the two limits : ( i ) for good cavities with @xmath94 , photons accumulate in the cavity resulting in the non - negligible multiple - photon probability resulting in a decreasing @xmath0 with increasing @xmath66 .
( ii ) in the weak coupling regime @xmath95 , the rate of exciton and biexciton transitions into the cavity mode ( @xmath96 , @xmath97 become of similar order for @xmath98 , leading to increased cascaded two - photon emission , and an increasing @xmath0 with @xmath66 ( see sec .
[ supplec ] of the supplements @xcite . )
second - order coherence @xmath0 ( thick ) and a crossover photon emission rate @xmath78 ( thin ) as a function of spin relaxation rate @xmath2 for a microcavity ( red dashed ) and a nanocavity ( black solid ) with @xmath99 .
other parameters for the microcavity and nanocavity are the same as in fig .
[ fig2 ] .
dot - dashed lines : guides for the eye on @xmath100 .
the pale part of the @xmath78 plot for the nanocavity corresponds to the region where @xmath101 .
the green shaded area indicates a typical parameter range for inas qds ( @xmath102 ) . ]
an important finding is that for the larger microcavity in fig .
[ fig2 ] ( b , d ) , the values of @xmath0 at the minima do not change so much as the spin relaxation rate changes ( @xmath103 ghz ) . on the other hand , for the smaller nanocavity in fig .
[ fig2 ] ( c , e ) , one finds a large enhancement in @xmath0 for the slow spin relaxation rate ( @xmath104 ghz ) .
qds in a nanocavity with @xmath104 ghz can not be considered as a sp emitters since @xmath0 never falls below 0.5 ( unless some means were taken as mentioned below ) !
therefore , the impact of the `` dark path '' on the sp emission is stronger in smaller cavities , which agrees with the simple intuitive guess made at the beginning of this section . for comparison , we also show calculated results for the qd model without the dark states and dark paths @xcite ( solid black curves in fig .
[ fig2 ] ( b)-(e ) . )
an increase in @xmath0 at @xmath105 as @xmath2 changes from @xmath106 to @xmath107 ghz is clear in fig .
[ fig2 ] ( c ) . a reduction of @xmath78 due to the dark path , claimed by strauf _ et al . _
@xcite , is also found in fig .
[ fig2 ] ( d , e ) , and the reduction is much more pronounced for the nanocavity in fig . [ fig2 ] ( e ) ( the nano cavity exhibits a more than 10-fold decrease at @xmath108 for @xmath109 ghz . ) figure [ fig3 ] shows the @xmath2-dependence of @xmath0 and @xmath78 for a cavity loss @xmath99 ( chosen around @xmath110 ) . for both cavities
, @xmath0 is proportional to @xmath111 at small @xmath2 due to the enhanced dark path effect .
the @xmath111-dependency and an observation that the dark pumping path reduces the quality of qd sp emissions for slow spin relaxations originate from the same physics explained above .
however , for the case of the microcavity , the @xmath111-dependency is not found in the typical parameter regime ( @xmath102 : the shaded region in fig .
[ fig3 ] ) , meaning the dark path rarely causes the unwanted effect of multiple photon emission . on the other hand
, this effect is always important in the small ph - c nanocavity , since the @xmath111-dependency is found in the typical regime . _
summary _ the strong impact of the `` dark path'' a pumping path via dark exciton states to biexciton states on the quality of sp emitters has been shown to exist in qd systems .
the observed increase in the value of @xmath0 indicates the dark path can reduce quality of qd sp emitters , especially those situated in small cavities like nanocavities .
the effects of the dark path were investigated under cw excitation conditions , but will also manifest themselves under long - pulse excitation . the effect of short - pulse excitation will be discussed elsewhere .
finally , we mention several ways to reduce the impact of the dark path for an application purpose .
( i ) the use of a charged exciton state @xmath112 where there is no dark path @xcite .
( ii ) the use of resonant and coherent laser excitation @xcite which automatically selects to create bright states not the dark states . (
iii ) enhancement of the spin relaxation rate @xcite to suppress the unwanted multiple photon emission .
( iv ) selection of qds with a large biexciton binding energy @xcite in order to limit the spectral overlap of cascaded photons .
( v ) the use of a spectral filter to further reduce the unwanted output from xx emission can partly reduce the impact of the dark path if the filter bandwidth were optimally selected @xcite . _
acknowledgements _ we thank y. ota , m. holmes , and s. kako for useful comments and discussions .
this work is supported by the project for developing innovation systems of mext .
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_ lisa_pathfinder ( _ _ ) is an _ esa_mission , whose main objective is to put to test critical parts of _ lisa_(laser interferometer space antenna ) , the first space borne gravitational wave ( gw ) observatory @xcite .
the science module on board _ _ is the _ lisa_test - flight package ( _ ltp _ ) @xcite , which basically consists in two test masses in nominally perfect geodesic motion ( free fall ) , and a laser metrology system , which reports on _ residual deviations _ of the test masses actual motion from the ideal free fall , to a given level of accuracy @xcite . in order to ensure that the test masses are not deviated from their geodesic trajectories by external ( non - gravitational ) agents , a so called gravitational reference system ( grs )
is used @xcite .
this consists in position sensors for the masses which send signals to a set of micro - thrusters ; the latter take care of correcting as necessary the spacecraft trajectory , so that at least one of the test masses remains centred relative to the spacecraft at all times .
the combination of the grs plus the actuators is known as _ drag - free _ subsystem .
the _ drag - free _ is of course a central component of _ lisa _ , and needs to be operated at extremely demanding levels of accuracy .
the laser metrology system should then be sufficiently precise to measure relative test mass deviations .
the overall level of noise acceptable for _ lisa_is defined in terms of rms acceleration spectral density , and has been set to @xmath0\ , { \rm m}\,{\rm s}^{-2}/\sqrt{\rm hz } \label{eq.1}\ ] ] in the frequency range @xmath1 .
this is equivalent to @xmath2@xmath34@xmath410@xmath5 hz@xmath6 , with the same frequency dependence . because _ _ is a _ technological mission _ , aimed to assess the feasibility of _ lisa _
, its ultimate goal has been relaxed to @xcite @xmath7\ , { \rm m}\,{\rm s}^{-2}/\sqrt{\rm hz } \label{eq.2}\ ] ] in the frequency range @xmath8 , i.e. , one order of magnitude less demanding , both in noise amplitude and in frequency band .
equation ( [ eq.2 ] ) gives the _ global _ noise budget .
this is naturally made up of contributions from different perturbative agents , such as temperature and magnetic field fluctuations , grs and interferometer noise , etc . as a general rule , a requirement on the magnitude of each of the various perturbing factors
is set at a 10% fraction of the total . in the case of temperature fluctuations , this is equivalent to @xmath9 because temperature stability is important , a decision has been taken to place high precision thermometers in several strategic spots across the _
ltp_as part of what is called _ diagnostics subsystem _
such high precision temperature measurements will be useful to identify the fraction of the total system noise which is due to thermal fluctuations only , and this will in turn provide important debugging information to assess the performance of the _ ltp_. if the temperature gauges are to be sensitive to fluctuations at the level given by ( [ eq.3 ] ) then clearly the entire measuring device should be less noisy , typically by a factor of 10 .
this means that such device , which includes both the sensors _ and _ the associated electronics , can generate a maximum level of noise of @xmath10 research work is currently being conducted at _
ieec_(barcelona , spain ) to identify the appropriate sensors and design the better suited front end electronics . but
the prototype system needs of course to be tested for compliance with equation ( [ eq.4 ] ) .
thus , in order to do a meaningful test , the system must be sufficiently thermally isolated that the observed fluctuations in the readout data can be attributed _ solely _ to sensor noise , rather than to a combination of it with real ambient temperature fluctuations .
this means temperature fluctiations in the thermomters placements should again be at least one order of magnitude below the target sensitivity , equation ( [ eq.4 ] ) , or @xmath11 it turns out that 10@xmath12 is a truly demanding temperature stability , orders of magnitude beyond the capabilities of normal thermally regulated rooms .
we thus need to design a specific thermal insulator to shield the sensors from ambient temperature fluctuations during the test process . in the ensuing pages
we describe in detail the insulator design .
it is extremely important to stress at this point that the performance of the insulator , i.e. , its ability to screen out ambient temperature fluctuations , _ can not be checked _ experimentally , at least under working thermal conditions in the laboratory .
this is because , by definition , the insulator is the tool to check the sensing instruments , _ not viceversa _ : we need to rely on the results of theoretical argumentation to make a decission on which is the appropriate thermal insulator for our purposes .
an experimental verification of the model is only thinkable under much more extreme conditions , where external temperature fluctuations are orders of magnitude higher than the ones which will be met during the test .
the idea of the insulator design is displayed in figure [ fig.1 ] : an interior metal core of good thermal conductivity is surrounded by a thick layer of a poorly conductive material .
the inner block ensures thermal stability of the sensors attached to it , while the surrounding substrate efficiently shields it from external temperature fluctuations in the laboratory ambient .
we propose a spherical shape for the sake of simplicity of the mathematical analysis , even though this will be eventually changed to cubic in the actual experimental device due to practical feasibility issues . ,
title="fig:",width=230 ] , title="fig:",width=185 ] the basic assumption of the mathematical analysis we shall present is that heat flows from the interior of the insulator to the air outside , and from the latter to the interior of the insulator , only by thermal _
conduction_. this is a very realistic hypothesis in the context of the experiment , as radiation mechanisms are certainly negligible and convection should not play any significant role , either , since the entire body is solid , and temperature fluctuations will be small at all times anyway .
let then @xmath13 be the temperature at time @xmath14 of a point positioned at vector * x * relative to the centre of the sphere . @xmath13 thus satisfies fourier s partial differential equation @xcite @xmath15 \label{eq.6}\ ] ] where @xmath16 , @xmath17 and @xmath18 are the density , specific heat and thermal conductivity , respectively , of the substrate .
we shall assume these are uniform values within each of the two materials making up the insulating body , with abrupt changes in the interface .
we can thus represent them as discontinuous functions of the radial coordinate , as follows : @xmath19 with @xmath20@xmath21@xmath22 .
initial and boundary conditions are the following : @xmath23 where @xmath24 and @xmath25 are spherical angles which define positions on the sphere s surface .
the boundary temperature can be expediently expressed as a multipole expansion : @xmath26 where @xmath27 are spherical harmonics , and @xmath28 are boundary multipole temperature components . in practice
, the boundary temperature will be _ randomly fluctuating _ , therefore @xmath28 will be considered _
stochastic _ functions of time .
we shall also reasonably assume them to be _ stationary gaussian _
noise processes with known spectral densities , @xmath29 .
as shown in the appendix , the frequency analysis of this problem leads to a _ transfer function _ expression of the temperature inside the body : @xmath30 where _ tildes _ ( @xmath31 ) stand for fourier transforms , e.g. , @xmath32 etc . if we make the further assumption that different multipole temperature fluctuations at the boundary are _ uncorrelated _ , i.e. , @xmath33 then the spectral density of fluctuations at any given point inside the insulating body is given by @xmath34 it is ultimately the spectral density @xmath35 which has to comply with the requirement expressed by equation ( [ eq.4 ] ) .
based on knowledge ( by direct measurement ) of ambient laboratory temperature fluctuations , equation ( [ eq.12 ] ) will provide the guidelines , as regards materials and dimensions , for the actual design of a suitable insulator jig .
thermal conditions in the laboratory are rather _
this means that the boundary temperature fluctuations will be in practice essentially independent of the angles @xmath24 and @xmath36 , i.e. , @xmath37 and consequently the generic expansion equation ( [ eq.9 ] ) includes only the _ monopole _
term , hence @xmath38 the temperature @xmath39 in this case will only depend on radial depth , @xmath40 , therefore , @xmath41 with @xmath42@xmath21@xmath43 . according to equation ( [ eq.a13 ] ) of the appendix ,
this is @xmath44 \eta_0(\omega)\,j_0(\gamma_2r ) + \zeta_0(\omega)\,y_0(\gamma_2r)\ , & a_1\leq
r \leq a_2 \end{array}\right . \label{eq.16}\ ] ] = 0 ) of a spherical thermal insulator as given in equation ( [ eq.16]) , along with the frequency response of a low - pass filter of order one and same frequency cut - off , @xmath45=@xmath46 .
[ fig.2],width=294 ] this is a low - pass filter transfer function even though the cumbersome frequency dependencies involved in the expressions above do not make it immediately obvious . a plot of the square modulus of @xmath42 is shown in figure [ fig.2 ] for @xmath20=0 ( red curve ) .
the figure also shows a low - pass filter of the first order with the same frequency cut - off , @xmath47=@xmath48 , for conceptual comparison ( blue curve ) .
the most salient feature emerging out of the plot is the stronger drop in @xmath42 at the high frequency tails .
the latter can be easily assessed in quantitative detail , and the result is @xmath49 where @xmath50 is the filter s time constant a complicated function of the insulator s physical and geometric properties , to be discussed below . as already mentioned in the introduction section , to test the temperature sensors and electronics we need a very strong noise suppression factor in the _ ltp_frequency band .
a look at figure [ fig.2 ] readily shows that high damping factors require such frequency band to lie in the filter s tails .
the thermal insulator should therefore be designed in such a way that its time constant @xmath51 be sufficiently large to ensure that the _ ltp_frequencies are high enough compared to 1/@xmath51 .
the exponential drop in the transfer function shown by equation ( [ eq.19 ] ) makes the filter actually feasible with reasonable dimensions .
in this section we consider the application of the above formalism to obtain practically useful numbers for the actual implementation of a real insulator device which complies with the needs of our experiment .
first of all , a selection of an _ aluminum _ core surrounded by a layer of _ polyurethane _ was made .
aluminum is a good heat conductor and is easy to work with in the laboratory ; polyurethane is a good insulator and is also convenient to handle , as it can be foamed to any desired shape from canned liquid .
other alternatives are certainly possible , but this appears sufficiently good and we shall therefore only make reference to this specific one . the relevant physical properties of aluminium and polyurethane are specified in table [ tab.1 ] .
.density , specific heat and thermal conductivity of aluminium and polyurethane .
units are given in the international system .
[ tab.1 ] [ cols="<,^,^,^ " , ] figure [ fig.3 ] plots the _ amplitude damping coefficient _ of the insulator block , @xmath52 , at the lower end of the _ ltp_frequency band , i.e. , 1 mhz , and at the interface position , @xmath20=@xmath53 .
each of the curves corresponds to a fixed value of the latter , and is represented as a function of the outer radius of the insulator .
this choice is useful because the sensors are implanted for test on the surface of the aluminium core , and also because at higher frequencies thermal damping is stronger .
so in practice the actual damping power of the device will be the one plotted , and better at the higher frequencies in the measuring bandwidth .
the figure clearly shows that the assymptotic regime of equation ( [ eq.19 ] ) is quite early established .
, width=366 ] the choice of dimensions for the insulating body must of course ensure that the minimum requirement , equation ( [ eq.5 ] ) is met . for this
, a primary consideration is the size of the ambient temperature fluctuations in the site where the experiment is made .
dedicated measurements in our laboratory showed that @xmath54 we therefore need to implement a device such that @xmath55@xmath5610@xmath57 throughout the measuring bandwidth ( mbw ) .
suitable dimensions can then be readily read off figure [ fig.3 ] , and various alternatives are possible , as seen . before making a decission , however , we need to make an additional estimate of the heat leakage down the electric wires which connect the temperature sensors with the elctronics , which lies of course outside the insulator .
we come to this next .
we use a simple model , consisting in assuming the connecting wires behave as straight metallic rods which connect the central aluminum core with the electronics , placed in the external laboratory ambient . because the polyurethane provides a very stable insulation
, we can neglect the lateral flux , hence only a unidimensional heat flow needs to be considered .
for this , the following equation relates the heat flux to the temperature difference between the two wires edges : @xmath58 \label{eq.21}\ ] ] where @xmath59 is the thermal conductivity of the wire , @xmath60 its transverse radius , and @xmath61 its length _ inside _ the polyurethane layer . on the other hand , the heat flux results in temperature variations in the metal core , given by @xmath62 where @xmath63=@xmath64 is the volume of the metal core . equating the above expressions we find @xmath65 = \rho_1c_{{\rm p}1}v_1\ , \frac{\partial t}{\partial t}(a_1,t ) \label{eq.23}\ ] ] for fluctuating temperatures
, we can now obtain the relationship between the spectral density at the aluminium core and the ambient , due to heat conduction along the wire : @xmath66 where @xmath67 and where the approximation has been made that the temperature fluctuations at the inner end of the wire are much smaller than those at the outer end , due to the presence of the polyurethane layer . in practice
, there will be several sensors for test inside the insulator . under
the hypothesis made that no lateral heat flux is relevant , the transfer function for a bundle of @xmath68 of wires is , at most , @xmath68 times that of a single wire .
thus , @xmath69 let us consider numerical values in this expression .
we use thin copper wires ( @xmath70=401wm@xmath71k@xmath71 ) of radius @xmath60=0.1 mm , and assume some fiducial parameters for the size of the aluminium core , @xmath53 , the wire length , @xmath61 , the number of connecting wires , @xmath72 , and the frequency , @xmath73 .
the following obtains : @xmath74 this result indicates that , for laboratory fluctuations in the level of equation ( [ eq.20 ] ) , leakage through wiring causes fluctuations in the temperature sensors of about 10@xmath75k/@xmath76 , equation , which is compliant with the requirement of stability of equation .
the most sensitive parameter in the above expression is the size of the metal core , and this determines the need to make it somewhat large .
the length of the wires has been taken to be 25 cm , but this does not necessarily mean we need @xmath77=38 cm ( assuming the radius of the aluminum core is @xmath53=13 cm ) , because the wires can be partly wound inside the polyurethane layer to further protect the system against leakage .
in fact , this wire lengthening is an easy way to improve attenuation .
as regards frequency dependence , compliance is guaranteed in the entire mbw if it is at its lower end : indeed , not only @xmath78 decreases as @xmath79 , also ambient noise fluctuations drop below 10@xmath71k/@xmath76 at higher frequencies .
temperature fluctuation measurement is very demanding in the _ ltp _ , and subsequently _ lisa _ , as reflected by equation . accordingly
, very delicate sensor and associated electronics must be designed , and of course tested in ground before boarding .
however , even the best laboratory conditions are orders of magnitude worse than the above requirement , so meaningful tests of the temperature sensing system can not be tested without suitably screening the sensors from ambient temperature fluctuations .
we have addressed how this can be accomplished by means of an insulating system consisting of a central metallic core surrounded by a thick layer of a very poorly conducting material .
the latter provides good thermal insulation , while the central core , having a large thermal inertia , ensures stability of the sensors environemnt .
the choice of materials is flexible , so aluminium and polyurethane , which are easily available in the market , has been adopted .
thereafter , the dimensions need to be fixed . the appropriate sensors for the needs are temperature sensitive resistors , more specifically thermistors also known as ntcs .
it appears that , because these sensors need to be wired to external electronics , heat leakage through such wires is an effect which needs to be quantitatively assessed to prevent losses .
we have analysed this problem , and concluded that it strongly depends on the central metallic core size , and imposes that it be somewhat large .
laboratory ambient temperature fluctuations , determined by dedicated _ in situ _
measurements , are of the order of 10@xmath71k/@xmath76 at 1 mhz , and dropping at higher frequencies within the mbw . the required stability conditions at the sensors , attached at the core s surface , thus need an attenuation factor of 10@xmath57 , or better .
our analysis determines that a central aluminium core of 13 cm of radius , surrounded by a concentric layer of polyurethane 1520 cm thick , comfortably provides the needed thermal screening which guarantees a meaningful test of the sensors performance .
the results of this paper are based on modelling .
because our aim is to produce a very stable thermal environment for the temperature sensors , we can not check _ experimentally _ the correctness of our conclusions .
we must instead rely on the validity of the hypotheses made essentially that heat only flows by thermal conduction and on the underlying physical laws which govern heat conduction . even though there is good reason to believe that both are sufficiently accurate , unexpected behaviour e.g. at the interface between the metal core and the insulator , may partly distort the results .
direct measurements with very large temperature gradients applied across the insulating device are envisaged , and will be reported elsewhere as an auxiliary independent test of the model .
we want to thank albert toms , from _ nte _ , for discussions on the subject of this paper .
support for this work came from project esp2004 - 01647 of plan
nacional del espacio of the spanish ministry of education and science ( mec ) .
mn acknowledges a grant from generalitat de catalunya , and js a grant from mec .
here we present some mathematical details of the solution to the fourier problem , equations ( [ eq.6])-([eq.9 ] ) .
we first of all fourier transform equations ( [ eq.6 ] ) and ( [ eq.9 ] ) : @xmath80 \label{eq.a1}\ ] ] @xmath81 equation ( [ eq.a1 ] ) can be recast in the form @xmath82
@xmath83 where @xmath20@xmath21@xmath22 , and @xmath84 to these , matching conditions at the interface and boundary conditions must be added : @xmath85 @xmath86 @xmath87 equations ( [ eq.a3a ] ) and ( [ eq.a3b ] ) are of the helmholtz kind .
their solutions are thus respectively given by @xmath88 \displaystyle \sum_{lm}\,\left[c_{lm}(\omega)\,j_l(\gamma_2r ) + d_{lm}(\omega)\,y_l(\gamma_2r)\,\right]\ , y_{lm}(\theta,\varphi)\ , & a_1\leq r \leq a_2 \end{array}\right . \label{eq.a5}\ ] ] where @xmath89 and @xmath90 are spherical bessel functions @xcite , @xmath91 and the coefficients @xmath92 , @xmath93 and @xmath94 are to be determined by equations ( [ eq.a7a])([eq.a7c ] ) .
these can be expanded as follows , respectively : @xmath95\ , y_{lm}(\theta,\varphi ) & & \label{eq.a8a}\end{aligned}\ ] ] @xmath96\ , y_{lm}(\theta,\varphi ) \label{eq.a8b}\end{aligned}\ ] ] @xmath97\ , y_{lm}(\theta,\varphi)\ = & & \nonumber \\ \
\sum_{lm}\,\tilde b_{lm}(\omega)\,y_{lm}(\theta,\varphi ) \label{eq.a8c}\end{aligned}\ ] ] because of the completeness property of the spherical harmonics , the above equations completely determine the coefficients @xmath92 , @xmath93 and @xmath94 .
the result is @xmath98 with @xmath99 \label{eq.a9a}\ ] ] @xmath100 \label{eq.a9b}\ ] ] @xmath101 \label{eq.a9c}\ ] ] and @xmath102\ + \nonumber \\ & + & \ \kappa_2\gamma_2\,j_l(\gamma_1a_1)\,\left [ j_l(\gamma_2a_2)\,y'_l(\gamma_2a_1 ) - j'_l(\gamma_2a_1)\,y_l(\gamma_2a_2)\right ] \label{eq.a10}\end{aligned}\ ] ] when the above results , equations ( [ eq.a9a ] ) through ( [ eq.a10 ] ) , are inserted back into equation ( [ eq.a5 ] ) the result stated in equation ( [ eq.10 ] ) in the main text obtains , i.e. , @xmath103 where @xmath104 \left[\eta_l(\omega)\,j_l(\gamma_2r ) + \zeta_l(\omega)\,y_l(\gamma_2r)\,\right]\ , y_{lm}(\theta,\varphi)\ , & a_1\leq r \leq a_2 \end{array}\right . \label{eq.a12}\ ] ] for monopole only boundary conditions , equation ( [ eq.15 ] ) , the transfer function is @xmath44 \eta_0(\omega)\,j_0(\gamma_2r ) + \zeta_0(\omega)\,y_0(\gamma_2r)\ , & a_1\leq r \leq a_2 \end{array}\right . \label{eq.a13}\ ] ] | this paper reports on the methods and results of a theoretical analysis to design an insulator which must provide a thermally quiet environment to test on ground delicate temperature sensors and associated electronics .
these will fly on board _ esa _ s _ lisa_pathfinder ( _ _ ) mission as part of the thermal diagnostics subsystem of the _ lisa_test - flight package ( _ ltp _ ) .
we evaluate the heat transfer function ( in frequency domain ) of a central body of good thermal conductivity surrounded by a layer of a very poorly conducting substrate .
this is applied to assess the materials and dimensions necessary to meet temperature stability requirements in the metal core , where sensors will be implanted for test .
the analysis is extended to evaluate the losses caused by heat leakage through connecting wires , linking the sensors with the electronics in a box outside the insulator .
the results indicate that , in spite of the very demanding stability conditions , a sphere of outer diameter of the order one metre is sufficient . |
An infant blinded by a hunter's stray bullet that came through his living room window has returned to his Pennsylvania home after more than two months in the hospital.
Shayne Iverson's homecoming near Saltsburg on Wednesday was just in time for his mother's 31st birthday, the Pittsburgh Tribune-Review reported.
"It was a pretty emotional night," Shayne's father, Jeremie Iverson, told the newspaper.
The 42-year-old Iverson was cuddling the boy, just 6 days old at time, on their couch on Sept. 25. Shayne was in Children's Hospital of Pittsburgh ever since.
"I know he's a little baby, but to me, I think he knows he's home," Iverson said.
Doctors have said the boy likely survived because the bullet that hit his head exited through his eye socket rather than hitting his brain.
Indiana County District Attorney Pat Dougherty has said the hunter had an agricultural deer control permit.
No charges have been filed, though investigators were reviewing whether game regulations or other laws were violated.
Although he's home, Shayne still faces more surgeries.
"We're taking it one day at a time," Jeremie Iverson said. ||||| The family of a 6-day-old Pennsylvania boy who was wounded by a hunter's stray bullet says the infant is expected to survive, but will be blind.
Stefanie Iverson says her son Shayne's life was spared when the bullet exited through the orbital area -- or eye socket -- of his skull rather than hitting his brain.
The boy's father, Jeremie, was holding the baby on Sept. 25 when the bullet came through a window of the family's home near Saltsburg, about 35 miles east of Pittsburgh, and struck the baby's skull.
Indiana County District Attorney Pat Dougherty says the hunter had an agricultural deer control permit when he fired the shot that wounded the boy about 7 p.m. that day.
The shooting was likely accidental, but questions remain about whether the hunter followed state regulations. | – Jeremie Iverson was sitting on the couch inside his family's Pittsburgh-area home Thursday, holding his 6-day-old son Shayne, when a bullet came through the window and hit the baby in the head. Authorities say the stray bullet came from a hunter's gun; the hunter had a permit, but authorities are still investigating whether state regulations were followed, WTAE reports; a decision on charges is expected this week. The baby's mother, Stefanie, says Shayne will survive, but was left blind by the accident, NBC Philadelphia reports. "He lost his vision, but that’s what probably saved his life," she tells the Indiana Gazette. "The bullet came out his orbital [eye socket] instead of going into his brain." |
coronary artery disease ( cad ) including myocardial infarction ( mi ) is a leading cause of death worldwide [ 1 , 2 ] .
the well - known conventional coronary risk factors include age , male sex , hypertension , diabetes mellitus , hypercholesterolemia , smoking and family history , which have been repeatedly demonstrated in multiple epidemiological studies [ 35 ] .
lifestyle and environmental factors play an important role in the pathogenesis ; however , genetic predisposition is also thought to contribute to cad / mi since these diseases cluster in families . in the epidemiological studies using twins ,
the relative hazard of death among men from cad when one 's twin died of cad before the age of 55 years , as compared with the hazard when one 's twin did not die before 55 , was 8.1 for monozygotic twins and 3.8 for dizygotic twins .
the recent epidemiological survey in the framingham study showed that parental cardiovascular disease independently predicted future offspring events . in this survey , participants with at least one parent with premature cad had greater risk for events with age - adjusted odds ratios ( ors ) of 2.6 for men and 2.3 for women compared with those with no parental cad .
elucidating the genetic determinants would improve risk assessment and provide better measures for prevention and treatment .
as the molecular biology and genetics had progressed , the genetic backgrounds were explored in the several genes which were thought to contribute to the pathogenesis of atherosclerosis and conventional coronary risk factors .
candidate gene studies tested the hypothesis that proteins known to be involved in the pathogenesis of atherosclerosis carry variants that affect their protein functions and the risk of developing cad . in 1992 , cambien et al . explored a possible association between cad and a variation found in the gene encoding angiotensin - converting enzyme ( ace )
the polymorphism ace / insertion / deletion ( ace / id ) is strongly associated with the level of the circulating enzyme .
they reported that the deletion homozygote ( dd genotype ) , which was associated with higher levels of circulating ace , is significantly more frequent in patients with mi than in controls .
the representative variants associated with cad / mi found by candidate gene approach are listed in table 1 .
one of the reasons for poor reproducibility is that many of the study samples were not large enough with some exceptions to identify disease - associated genetic variants with odds ratio < 2.0 .
in addition , candidate gene studies only tested a single to few variants for association with cad and these approaches can not discover unknown novel variants and also can not evaluate how strong each variant contribute to the susceptibility to cad .
therefore , the candidate gene approach resulted in only limited success in the elucidation of genetic risks for cad . in parallel with candidate gene studies , other strategies were carried out to interrogate the entire human genome without hypotheses on which genes may be responsible for disease risk .
one of the strategies is genome - wide linkage analysis and it is based on the mendelian cosegregation of a genetic marker within a family . however , great efforts had to be made in order to collect sufficient numbers of affected sibling pairs .
only a small number of studies were successfully performed and few genetic loci ( 2q21 - 22 , xq23 - 26 , myocyte enhancer factor-2 ( mef2a ) , arachidonate 5-lipoxygenase - activating protein ( alox5ap ) , leukotriene a4 hydrolase ( lta4h ) ) were detected to be associated with cad ( table 2 ) .
these genes had never been suggested as causative genes before these family - based studies , suggesting the effectiveness of this approach in detection of novel genetic determinants .
such a family - based study has been frequently used to identify new loci in monogenic diseases , but the application of this strategy to multifactorial diseases is relatively limited . in this situation ,
whole genome analysis in a case - control study design had gradually emerged around the beginning of the 21st century .
resources including the single nucleotide polymorphism ( snp ) databases , major technological advances in high - throughput genotyping , and methods of data processing and statistical analysis allow researchers to confront limitations in previous approaches . here ,
we introduce the representative genome - wide case - control association studies in the next two sections .
beginning in 2000 , the prime minister 's millennium project ( j - snp ) was launched in japan and about hundred thousand snps located in genes or in adjacent regions that might influence the coding sequence of the genes were identified in japanese population .
j - snp established a web - based database and allowed researchers access to high quality snp data .
genome - wide association studies using this snp database were performed in our country in many important clinical fields including cardiovascular diseases , diabetes , renal dysfunction and autoimmune collagen diseases . as the first genome - wide case - control association study in the world , ozaki et al . used 92,788 gene - based snp markers and identified that the homozygosity in two snps in lymphotoxin a ( lta ) at 6p21 was significantly associated with increased risk for mi in japanese ( odds ratio ( or ) = 1.78 ) . in vitro analyses showed that one functional snp ( thr26asn ) caused a twofold increase in induction of several inflammation - related cell - adhesion molecules including vascular cell adhesion molecule 1 ( vcam1 ) in vascular smooth - muscle cells .
moreover , the snp located in intron 1 of lta enhanced the transcriptional level of lta .
these results indicated the variants in the lta are risk factors for mi and implicated lta as a novel pathogenic factor for mi . in the same year , lta knockout mouse was shown to be resistant to atherosclerosis .
double knockout mice of apolipoprotein e ( apoe ) and lta ( apoe/lta/ mice ) showed less extent of atherosclerosis than apoe/lta+/+ mice , indicating lta deteriorates atherosclerosis in vivo , consistent with the result of the genetic association study of lta as a genetic risk for atherosclerotic disease .
subsequently , they identified snps that were significantly associated with mi in lectin , galactoside - binding , soluble , 2 gene ( lgals2 ) , proteasome subunit alpha type 6 gene ( psma6 ) , myocardial infarction associated transcript ( miat ) , inter - alpha ( globulin ) inhibitor 3 gene ( itih3 ) and brca1-associated protein gene ( brap ) mainly by functional approaches .
all the six causative genetic regions are related to inflammatory process in vasculature and are thought to contribute to the process in atherosclerotic changes through its inflammatory functions and thus increase the risk of mi .
genome - wide association studies based on the j - snp database ( approximately 100,000 snps ) have detected several snps which had significant association with myocardial infarction .
however , the j - snp database does not cover snps in intergene regions . in the meantime ,
the international hapmap project was conducted to create a public genome - wide database of common snps and enable systematic studies of common snps for their potential role in human disease [ 22 , 23 ] .
the project analyzed dna samples from 90 people with european ancestry , 90 yoruba people in nigeria , 44 japanese and 45 han chinese and has now genotyped over 3.1 million snps in each of these populations
. however , testing all of these snps in a person 's chromosomes would be extremely expensive .
adjacent snps across the genome are correlated each other , a phenomenon known as linkage disequilibrium and snps that are inherited together were compiled into
a haplotype block may contain many snps , but only a few tag snps can provide most of the information on the pattern of genetic variation in the block . the hapmap project identified these tag snps within haplotypes that uniquely identify these haplotypes .
the hapmap data allowed efficient design of chip - based genome association studies and allowed investigators to genotype far fewer snps while still retaining statistical power to find genetic variants related to common illness .
the development of dense genotyping chips enables genotyping up to 1 million snps on a single small chip .
this chip technology allowed genome - wide association studies ( gwas ) to be performed on a large numbers of subjects .
chip - based gwas typically involves genotyping approximately a few thousands cases with a disease and a few thousands of controls for about 500,000 tag snps .
since there are 500,000 comparisons per study , there is a high potential for false positive results .
the proposed solution for that is applying the stringent p value using the bonferroni correction for multiple tests . in that case , p value will be 0.05 divided by 500,000 and that is 0.0000001 ( 10 ) and this stringent p value is often termed as genome - wide significance ' .
the most statistically significant variants identified in the initial case - control analysis are tested for replication in subsequent case - control studies . in gwas method ,
associations between snps and the diseases are made free of bias of particular candidate genes .
this makes the possibility of obtaining novel and unbiased information and provides the important direction to better understand the pathophysiology of the disease . for cad ,
three chip - based gwas were simultaneously reported in 2007 and all of them showed the significant association between cad and snps on chromosome 9p21 .
enrolled a total of 4587 mi cases and 12,767 controls and genotyped total 305953 snps using illumina hap300chip ( illumina ) ( table 3 ) .
they identified disease association variant located in 9p21 , adjacent to the tumor suppressor genes cyclin - dependent kinase inhibitor 2a ( cdkn2a ) and cyclin - dependent kinase inhibitor 2b ( cdkn2b ) with great statistical significance .
they showed the allele g of the snp rs10757278 ( figure 1 ) showed the strongest association with mi .
the ors for heterozygous and homozygous carriers of the risk allele g were 1.26 and 1.64 , respectively .
the ors for early - onset mi ( mi before the age of 50 for males and before the age of 60 for females ) are 1.49 and 2.02 for heterozygous and homozygous carriers of the risk allele , respectively .
they estimated the population attributable risk is 21% for mi in general and 31% for early - onset cases .
the snps on chromosome 9p21 associated with mi are located in the same disequilibrium block of the one which contains cdkn2a and cdkn2b .
these genes encode two members of the inhibitors of cdk4 ( ink4 ) family of cyclin - dependent kinase inhibitors , p16 and p15 , and a completely unrelated protein called arf .
the p16 and p15 which activates retinoblastoma ( rb ) family members and arf which activates p53 were shown to be upregulated in cancer cells .
they play a critical role in cell proliferation and aging , senescence and apoptosis [ 25 , 26 ] .
however , sequencing 93 early - onset mi patients across these genes did not reveal obvious causal functional variants or variants that could account for the correlation of rs10757278 to mi .
the linkage disequilibrium block also contains two exons of the transcript hypothetical methylthioadenosine phosphorylase fusion protein mrna , however the functional significance of the variants in this region remains to be elucidated .
mcpherson et al . also identified a 58-kilobase region on chromosome 9p21 that was consistently associated with cad in six independent samples consisted of 4306 cases and 20119 controls from four caucasian populations .
they identified two snps rs10757274 and rs2383206 on 9p21 that are significantly associated with incident of cad .
the risk allele was associated with and ~15 to 20% increase risk of cad in the 50% individuals who are heterozygous and ~30 to 40% increase in the 25% who are homozygous for the allele .
they further genotyped surrounding region of these snps in detail and found that eight additional snps at the locus spanning a 58-kb region were significantly associated with cad . again
however , the region overlaps a newly annotated noncoding rna called noncoding rna in the ink locus ( anril ) .
the whole blood rna expression levels of short variants of anril are increased and the expression levels of the long variant are decreased in subjects homozygous for the risk alleles .
there is also a positive correlation between transcript levels of the long variant of anril and cdkn2b .
the study using genetically engineered mice showed that the deletion of orthologous 70-kb non - coding interval on mouse chromosome 4 ( chr4mice ) highly reduced cardiac expression of two neighboring genes cdkn2a and cdkn2b .
primary culture of smooth muscle cells from chr4mice showed increased proliferation and diminished senescence , the features relevant to atherosclerosis .
these findings indicated the noncoding interval is involved in the disease process via gene - regulatory effects on cdkn2a and cdkn2b .
the wellcome trust case control consortium ( wtccc ) study which enrolled 1926 case subjects with cad and 2938 controls also reported the powerful association between the snps on chromosome 9p21 and cad .
the strongest signal was seen at rs1333049 , however the associations were seen for snps across > 100 kb .
then , they further looked for replication in the german mi family study which involved 875 mi cases and 1644 controls using the genechip human mapping 500k array set ( affymetrix ) .
the same locus on chromosome 9p21 ( rs1333049 ) had the strongest association with cad in both studies with the risk increased by 36% per copy of the c allele .
of the nine loci which were shown to be strongly associated with cad , two of these loci were able to replicate in the german mi study : chromosome 6q25.1 ( rs6922269 ) and chromosome 2q36.3 ( rs2943634 ) .
further , the combined analysis of the two studies revealed four additional loci significantly associated with cad : chromosome 1p13.3 ( rs599839 ) , 1q41 ( rs17465637 ) , 10q11.21 ( rs501120 ) and 15q22.33 ( rs17228212 ) . in 2009
, they performed another replication study with 11550 cases with cad and 11205 controls from 9 european studies .
other than the 9p21 locus , they confirmed significant association at 1p13.3 ( rs599839 ) , 1q41 ( rs3008621 ) and 10q11.21 ( rs501120 ) .
they were not able to show the significant association with 6q25.1 and 2q36.3 and there was no evidence for association with the locus at 15q22.33 .
the four loci ( 9p21 , 1p13.3 , 1q41 and 10q11.21 ) act independently and cumulatively increased the risk for cad by 15% per additional risk allele .
the genes located within or adjacent to the these four loci are listed in table 4 .
the locus at chromosome 1p13.3 has been shown to be associated with increased plasma ldl cholesterol , and thus may contribute to cad development [ 3437 ] .
the locus at 10q11.21 lies adjacent to the chemokine ( c - x - c motif ) ligand 12 gene ( cxcl12 ) which encodes stromal cell - derived factor-1 , a chemokine which plays a important role in stem - cell homing and regeneration of myocardial tissue in ischemic cardiomypopathy and in promoting angiogenesis by recruiting endothelial progenitor cells from the bone marrow .
the snps at 1q41 locates within the melanoma inhibitory activity family , member 3 ( mia3 ) gene .
underlying mechanism how these genetic loci affect the pathogenesis of cad need to be further investigated . the meta - analysis of aforementioned three studies [ 24 , 27 , 32 ] and 7 additional case - control studies successfully replicated the significant association between the risk allele ( c ) of the lead snp , rs1333049 at chromosome 9p21 and risk of cad ( or= 1.29 ) .
these study have analyzed primarily on european descent , however , since the allele frequency differs among the different ethnic groups , the risk of cad related to the snps at 9p21 may differ among each ethnic group . since then , the replicated results in other ethnics such as chinese , japanese and pakistanis are published and the association of the snps at 9p21 with cad seems to be consistent among various ethic groups [ 4245 ] . it is noteworthy that the snps in 9p21 region are also found to be associated with variety of diseases such as ischemic stroke ( or = 1.011.21 ) [ 46 , 47 ] , abdominal aortic aneurysm ( or = 1.31 ) , intracranial aneurysm ( or = 1.29 ) , peripheral artery disease ( or = 1.29 ) , incident heart failure ( or = 1.17 ) , perioperative myocardial injury after coronary artery bypass graft surgery , type 2 diabetes ( or = 1.20 ) [ 52 , 53 ] .
more recently , the loci other than 9p21 have been shown to be associated with cad or mi .
applied less stringent statistical thresholds on their gwas for cad to identify any dismissed snps with modest effects or low allele frequencies and they found one new locus on 3q22.3 in muscle ras oncogene homolog ( mras ) ( or = 1.15 ) , the gene thought to play an important role in inflammation [ 54 , 55 ] .
there is another gwas which identified the snps in the gene related to inflammation to be associated with mi .
they found five snps which affect eosinophil counts in blood in icelandic population and reported that a nonsynonymous snp at 12q24 in sh2b adaptor protein gene ( 3sh2b3 ) was associated with mi significantly ( or = 1.13 ) .
three of them were newly identified in the study : ( i ) an intergenic region between mrps6 ( mitochondrial ribosomal protein s6 ) , slc5a3 ( solute carrier family 5 ( sodium / myo - inositol cotransporter ) , member 3 ) and kcne2 ( potassium voltage - gated channel , isk - related family , member 2 ) on chromosome 21q22 ( or = 1.19 ) , 6p24 in phactr1 ( phosphatase and actin regulator 1 ) ( or = 1.13 ) and 2q33 in wdr12 ( wd repeat domain 12 ) ( or = 1.17 ) .
the mechanism by which genes at these three regions increases the risk of mi needs to be elucidated .
in addition to the common variant , copy number variations can be analyzed by snp chip and there were no common or rare copy number variations associated with risk of early - onset mi in this study .
the group from the wtccc / german mi study further conducted a genome - wide haplotype association study for the first time and identified the slc22a3-lpal2-lpa gene cluster on 6q26 - 27 as a strong susceptibility locus for cad ( or = 1.8 ) .
clarke et al . identified three chromosomal regions ( 6q26 - 27 , 9p21 and 1p13 ) were strongly associated with the risk of cad using the human cvd bead chip which included 48742 markers relevant to cardiovascular disease on 6500 subjects . among them , the lpa locus on 6q26 - 27 encoding lp(a ) lipoprotein had the strongest association .
they identified two lpa variants that were strongly associated with both an increased level of lp(a ) lipoprotein and an increased risk of cad ( or = 1.70 and 1.92 ) .
both variants were strongly associated with a reduced copy number in lpa kringle iv - type 2 repeats and an increased level of lp(a ) lipoprotein .
after adjustment for the lp(a ) lipoprotein level , the association between the lpa genotype score and the risk of cad was abolished .
initially , gwas have been primarily assessed only on european descent and the results of these gwas may not be applicable to other ethnics due to wide difference of distribution of snps and allele frequency .
further studies for various ethnicity need to be done with use of newer chips which contains 1 million snps to increase coverage .
the cad associated loci have been found in regions without known gene - encoding loci .
therefore , further studies will be required to elucidate the exact functional mechanism by which these loci modulate cad risk .
the odds ratios for cad risk in each selected snps are small ( around 1.2 ) and explain only a small proportion of the heritable , genetic component of susceptibility to the disease .
newer susceptibility loci for cad need to be validated with replication studies and in the future , we should evaluate the genetic risks by combining multiple independent common variants susceptible for cad .
the gwas method is supported by the common disease - common variant hypothesis , which predicts that genetic variants causing common disease exist frequently , but each variant only have a small effect on disease susceptibility .
the rare variant hypothesis postulates that common disease is caused by multiple rare variants which have a strong causative effect on disease and this hypothesis was confirmed in colorectal adenomas [ 63 , 64 ] .
rare variants can not be captured by gwas and requires whole genome sequencing using next generation sequencing system .
in addition , other types of variants , such as insertion - deletion variant , block substitution and inversion variant , so called structural variants may account for important contributors to the diseases and are also hard to detect by the chip - based method .
the snps data from the hapmap project and development of new chip technology enabled genotyping large amount of common variants simultaneously and contributed to efficiently identify gene loci affecting susceptibility to common diseases including cad .
the region at 9p21 was shown to be significantly associated with cad in 2007 and comprehensive replication across multiple studies provides unequivocal evidence that this locus is associated with cad in european descent .
this region is also associated with abdominal aneurysm , intracranial aneurysm and type 2 diabetes , and seems to be a very important region for various diseases .
since the odds ratios of the risk allele at 9p21 for cad are small , screening for this risk allele probably affects little , if any , to the each individual 's risk prediction .
using genomic tests to improve existing risk models would likely require combining the effects of multiple common genetic variants .
rare variants and structural variants which can not be captured by gwas need to be searched by whole genome sequencing .
gwas approach has identified novel and unbiased genetic contributors to cad and these insights provide the important direction to better understand the pathogenesis of cad and to develop new and improved preventive measures and treatments for cad . | coronary artery disease ( cad ) is a multifactorial disease with environmental and genetic determinants .
the genetic determinants of cad have previously been explored by the candidate gene approach .
recently , the data from the international hapmap project and the development of dense genotyping chips have enabled us to perform genome - wide association studies ( gwas ) on a large number of subjects without bias towards any particular candidate genes . in 2007 ,
three chip - based gwas simultaneously revealed the significant association between common variants on chromosome 9p21 and cad .
this association was replicated among other ethnic groups and also in a meta - analysis .
further investigations have detected several other candidate loci associated with cad .
the chip - based gwas approach has identified novel and unbiased genetic determinants of cad and these insights provide the important direction to better understand the pathogenesis of cad and to develop new and improved preventive measures and treatments for cad . |
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Email notifications are only sent once a day, and only if there are new matching items. ||||| The Maryland couple behind the viral YouTube "prank" channel DaddyOFive were sentenced to five years of probation on charges of child neglect on Monday. Michael and Heather Martin had been charged with two counts each of child neglect after their "kids prank" videos sparked outrage and allegations of child abuse. Some of the videos depicted the Martins yelling at their children until they cried, screaming obscenities at their children, and — in one instance — shoving a child who then got a bloody nose. According to a negotiated plea agreement between the couple's defense attorney and the Frederick County State's Attorney, the Martins entered Alford pleas — a special kind of guilty plea that means that while they are not necessarily admitting what they did was legally wrong, they agreed that the state has enough evidence to prove guilt going forward. The Frederick County Sheriff's Office and Child Protective Services began investigating the Martins after several citizen complaints about the couple's YouTube videos that appeared to show their children in emotional distress. After the Martins and their five children underwent psychological evaluations, it was found that two of the children, 10-year-old Cody and 11-year-old Emma, suffered "mental injury" as a result of the videos, Frederick County Assistant State's Attorney Lindy Angel told BuzzFeed News on Monday.
In May, the couple lost custody of Cody and Emma, who are Michael Martin's biological children and Heather Martin's stepchildren. Under the terms of their probation, the Martins are not allowed to have contact with Cody and Emma, unless dictated by a judge in their ongoing custody case. They are also not allowed to post videos featuring Cody and Emma on social media. Cody, the youngest child in the family, was a frequent target of his parents' recorded pranks and appeared to be the most resistant to them, according to popular YouTube commentator Philip DeFranco, who was among the first to suggest that DaddyOFive's videos amounted to possible child abuse. In a now-deleted video, Cody was seen crying hysterically after Heather Martin falsely accused him of pouring ink on his bedroom carpet, called him a liar, and hurled obscenities at the 10-year-old. In another video, Cody got a bloody nose after Michael Martin shoved him into a bookcase. The three other children, who are Heather Martin's biological sons, were not subjects of the criminal case as the psychological evaluations found that they did not suffer from "mental injury" associated with the videos, Angel said.
Angel said that while she first thought the videos were "horrendous," she believed the sentence was in "the best interest of the children."
She said that the couple's psychological evaluations indicated they had "an extreme lapse in judgment," but that there was "no intention to injure the children."
"It was insensitive, cruel, bad decision-making," Angel said. "But there was no real intention behind it."
She said that since the allegations came to light, the Martins had complied with authorities by taking counseling and refraining from making and posting videos.
"The Martins are taking this very seriously," Angel said, adding that the prosecution did not want the children to go through a trial.
She said the probation sentence "serves everyone's interest."
Stephen Tully, lawyer for the Martins, told BuzzFeed News they were "fully satisfied" with the outcome of the case as it was a negotiated agreement.
In terms of learning a lesson from this, he said the Martins were "concerned about what took place and what effect it had on the children that they did not foresee."
He said that while the couple had agreed not to post social media videos with Cody and Emma, it was a "possibility" that they would continue to post videos of themselves and their three other children. "Just not in the same fashion as before," Tully said. ||||| - A Maryland couple behind prank videos involving their young children that were posted on their YouTube channel has pleaded guilty to child neglect as part of a plea agreement that will have them avoid serving time in prison.
Mike and Heather Martin gained national attention for their controversial videos on the DaddyOFive YouTube page. The parents received heavy backlash after a video titled “Invisible Ink Prank” posted earlier this year showed them pranking their son in a profanity-filled tilled tirade that left him hysterically in tears.
Following the criticism, the family said their videos were fake, over-exaggerated or scripted and would later pull all of their videos off of the YouTube channel. They also issued a video apology.
“There was no doubt that there was mental abuse occurring, so we had child protective services do some evaluations,” said Frederick County State’s Attorney J. Charles Smith. “It was clear from those evaluations that these kids were emotionally traumatized, so we felt child neglect charges were appropriate.”
On Monday, the Martins pleaded guilty to two counts of child neglect. Under the plea agreement, they received a 10-year suspended prison sentence and five-year supervised probation.
“We were outraged, the public was outraged,” Smith said. “We received numerous complaints on these two, especially the fact that they were profiting from abusing these kids was just outrageous. Obviously there was moral outcry. We had to take a look at it from a legal perspective. We had to make sure there was a crime occurring.”
The Martins lost custody of two of their children following the investigation. As part of the plea agreement, they are not allowed to contact them unless it is approved by a judge. Their probation also restricts them from posting any videos or images of their children on social media unless it is for family use.
“They are very happy to get the matter resolved and over with,” said Stephen Tully, the Martins’ attorney. “This has been a tremendously stressful experience for them.” | – A Maryland couple whose YouTube prank videos garnered them accusations of child abuse were sentenced to five years probation on child neglect charges Monday, BuzzFeed reports. Michael and Heather Martin entered a plea to avoid jail time, admitting the state had enough to convict them without actually admitting guilt. The Martins' YouTube channel, DaddyOFive, featured hundreds of videos of them "pranking" their five children, according to the Frederick News-Post. Prosecutors singled out one video showing Heather screaming obscenities at a crying 10-year-old Cody—their youngest child—after falsely accusing him of pouring ink on the carpet and another video where Cody is falsely told he is no longer going to live with them. Psychological evaluations found Cody and 11-year-old Emma suffered "mental injury" from the videos. The Martins lost custody of Cody and Emma in May. Under the terms of their probation, they aren't allowed to have any contact with the two children or post any videos featuring them. "It was clear from those evaluations that these kids were emotionally traumatized, so we felt child neglect charges were appropriate," State's Attorney J. Charles Smith tells Fox 5. Assistant State's Attorney Lindy Angel says the Martins showed "an extreme lapse in judgement" but didn't mean to harm their children. Heather and Michael are still posting prank videos that don't feature their children to their MommyOFive channel. Their lawyer says they may return to posting videos featuring their other three children "just not in the same fashion as before." (It's not the only YouTube video to end horribly.) |
Story highlights Archaeologists believe they've discovered Aristotle's tomb
Aristotle is regarded as one of history's greatest philosophers
(CNN) A Greek archaeologist believes he has discovered the tomb of Aristotle.
Konstantinos Sismanidis, who has been painstakingly excavating the ruins of Stagira since 1990, told CNN his team has very strong evidence the 2,400-year-old tomb belongs to the great philosopher.
Sismanidis said the structure, about 40 miles east of Thessaloniki, was built to honor Aristotle's death in 322 B.C.
"It was constructed very rapidly," he said. "It was in the center of the ancient city Agora."
Aristotle died in Chalcis on the island of Euboea.
"We know that Aristotle died in Chalcis on the island of Euboea," he explained. "But after some years, they took his ashes and placed them in a bronze vessel."
Read More |||||
Greek archaeologists at Ancient Stagira, Central Macedonia, say they have found Aristotle’s tomb. Addressing the Aristotle 2400 Years World Congress, they point to the 2,400-year-old tomb as the most important finding from the 20-year excavation.
The discovery of the tomb of Aristotle was announced by archaeologist Kostas Sismanidis, according to whom the findings from the 1996 excavation lead to the conclusion that the tomb belongs to Aristotle.
Aristotle was born in Stagira in 384 BC and died in Chalcis, Evia, at 322 BC. The great philosopher was originally believed to have been buried at Chalcis, however, archaeologists are now certain that the tomb they have found belongs to Aristotle. Two literary sources indicate that the people of Stagira may have transferred his ashes to his birthplace.
The mounded domed tomb has a marble floor dated to the Hellenistic period. It is located in the center of Stagira, near the Agora, with 360-degree views. The public character of the tomb is evident by its location alone, however archaeologists also point to a hurried construction that was later topped with quality materials. There is an altar outside the tomb and a square-shaped floor.
The top of the dome is at 10 meters and there is a square floor surrounding a Byzantine tower. A semi-circle wall stands at two-meters in height. A pathway leads to the tomb’s entrance for those that wished to pay their respects. Other findings included ceramics from the royal pottery workshops and fifty coins dated to the time of Alexander the Great.
The tomb structure was destroyed by the Byzantines, who built a square tower on top of it.
(Photo credit : Kostas Sismanidis)
||||| Bust of Aristotle. Marble, Roman copy after a Greek bronze original by Lysippos from 330 BC
Archaeologists believe they’ve found Aristotle’s tomb in central Macedonia.
A team of researchers say the 2,400-year-old tomb was excavated as part of a 20-year exploration of ancient Stagira, where the great philosopher was born in 384 BC, reported the Greek newspaper Kathimerini.
The discovery will be formally announced Thursday at an international conference, the “Aristotle 2400 Years” World Congress, held in Thessaloniki.
READ MORE: Here’s how Medieval Christians twisted Aristotle’s philosophy so they could justify persecuting ‘witches’
Aristotle, who is regarded as the one of the most important thinkers in the history of Western Civilization, died in 322 BC at Chalcis, Evia, and was long believed to have been buried there.
However, archaeologists who are excavating Stagira are now certain the tomb they have found belonged to Aristotle, who ashes may have been transferred there, according to two literary sources.
The tomb is a mounded dome about 32 feet high, with a marble floor dated to the Hellenistic period, reported the Greek Reporter website — which published several photos taken at the site.
It’s located in the center of Stagira, with sweeping 360-degree views, which signifies its importance.
But archaeologists say evidence suggests the tomb was hastily constructed and later finished with higher quality materials.
A pathway leads to the entrance of the tomb, which was destroyed by the Byzantines — who built a square tower on top of it.
Aristotle, who studied under the great philosopher Plato, is regarded as the first genuine scientist in human history.
He made significant and seminal contributions to biology, physics and zoology, and he also influenced thousands of years of thought in aesthetics, metaphysics, linguistics, government and poetry.
He tutored Alexander the Great, who spread Greek philosophy to Africa and the Middle East.
READ MORE: How Aristotle’s ancient teachings can help you live the good life ||||| The 2,400-year-old tomb of the great Greek philosopher Aristotle has been found in the ancient city of Stagira, Greek media reported Thursday. The discovery is the result of 20 years of digging in Aristotle’s birthplace in northern Greece.
“I have no hard proof, but strong indications lead me to almost certainty,” archaeologist Kostas Sismanidis told Sigmalive of the discovery.
Aristotle was born in Stagira in 384 B.C. on the coast of Greece and died in 322 B.C. of a digestive problem in Chalcis, about 50 miles north of Athens. His burial site has been disputed for years, and some literary sources have cited Stagira as the place where Aristotle’s ashes may have ended up.
The domed tomb includes an altar and a short tower. It was eventually destroyed by the Byzantines. Images of what the tomb might have looked like in its prime were published by the Greek Reporter. An official announcement explaining the origins of the tomb was expected to be made Saturday at the Aristotle 2400 Years World Congress hosted by the Aristotle University of Thessaloniki in Greece.
Aristotle famously studied philosophy under Plato and went on to teach Alexander the Great. His musings on natural sciences, metaphysics, ethics, government and the arts continue to shape global politics and debate. In Arabic philosophy, he was known as “the First Teacher” while in the West, he has been called “the Philosopher.” He is believed to have written more than 200 works, of which only 31 survive. They include, “Art of Rhetoric and Poetics” and “Metaphysics.”
Photo: Reuters
Academics and researchers around the world have planned celebrations of Aristotle’s life this year to mark the 2,400-year anniversary of his teachings. The small town of Stari Grad, Croatia, plans this summer to hold a sea and seamen festival with lectures, workshops, food festivals, concerts, biking events and exhibitions. In the U.S., Rice University in Texas hosted “An Aristotle Birthday Party” in February with experts from across the United States, Canada and England.
“We put 24 candles on the cake [one for each century], lit the candles, turned out the lights and sang ‘Happy Birthday’ to Aristotle. Two scholars then sang ‘Happy Birthday’ in modern Greek,” conference organizer Don Morrison, professor of philosophy and classical studies at Rice, said in a press release. ||||| Aristotle. (Photo: Ludovisi Collection/Public Domain)
A group of archaeologists in Greece say they have found the lost tomb of Aristotle, the Greek philosopher and likely world’s first true scientist.
The Greek newspaper Ekathimerini reported Thursday that the finding will be announced at a press conference, as a capstone to a Aristotle-themed conference in Thessaloniki.
The archaeologists had been digging for 20 years at a site in the ancient northern Greece city of Stageira, where Aristotle was born in 384 B.C. Aristotle died 62 years later in Chalcis, about 50 miles north of Athens.
Ahead of the official announcement, the Greek Reporter has some more details on the tomb, saying that “literary sources” say that Aristotle’s ashes were transferred there after his death. It is located near the ancient city’s agora, apparently intended to be viewed by the public.
From the Greek Reporter:
The top of the dome is at 10 meters and there is a square floor surrounding a Byzantine tower. A semi-circle wall stands at two-meters in height. A pathway leads to the tomb’s entrance for those that wished to pay their respects. Other findings included ceramics from the royal pottery workshops and fifty coins dated to the time of Alexander the Great.
Not much is known about Aristotle’s life, aside from what he left in his own writings. It took over 2,300 years, but at least we’re starting to learn more about his death. | – Nearly 2,400 years after his death, archaeologists believe they've finally found the tomb of Aristotle. Researchers made the discovery during a 20-year dig in the ancient Greek city of Stagira, reports Atlas Obscura. Aristotle was born there in 384 BC, but he died in a different city, Chalcis, about 50 miles north of Athens. Literary sources mention that Aristotle's remains were moved to Stagira after his death, but his burial site has been a topic of debate for many years, the International Business Times reports. The tomb in Stagira believed to be the philosopher's is a 32-foot-tall dome with a marble floor and views of the entire city. "The thing is, the archaeologist data is in fine accordance with historical sources," archaeologist Konstantinos Sismanidis tells CNN. The tomb appears to have been built quickly and later fancied up, reports the Greek Reporter, which has photos. The structure was destroyed in later years by the Byzantines, who built a tower on top of it. Aristotle is seen as “the first genuine scientist in human history," as Raw Story puts it, studying under Plato and tutoring Alexander the Great. And he's believed to be the author of more than 200 works. (Historians say they've found Leonardo da Vinci's relatives.) |
multicomponent systems often exhibit unusual behavior and transport effects @xcite .
many of these effects are caused by the additional correlations which are associated with particle distinguishability .
the short - range `` back correlations '' ( memory effect ) @xcite in the classical two - component lattice gas with excluded volume constraint may serve as an example . at the macroscopic level the particle distinguishability manifests itself as the additional nonlinear flux which is responsible for the mixing of different species of a lattice gas .
this flux leads to the array of anomalous diffusive transport effects , e.g. , the drag effect , formation of the drifting spatial structures @xcite , effects of `` negative '' mass transport @xcite .
when the difference between the values of the component mobility is significant , the nonlinear flux can lead to indirect correlations in the slow subsystem .
these correlations are induced by the light component that plays the role of interaction mediator for the particles of the slow subsystem .
such a phenomenon is similar to the hydrodynamic interactions between colloidal particles @xcite .
one of the intriguing effects observed in these suspensions is the presence of long - time correlations between liquid - embedded particles when the velocity correlation function of a particle pair is characterized by the long - time negative tail @xcite . in this paper
we are aimed to show the possibility of similar long - time correlations for the slow component of a lattice gas . for this purpose ,
we consider the simplest case of a two - component lattice gas by using the adiabatic and the uniform clusters approximations .
we consider the simplest two - component lattice gas model subject to an excluded volume constraint .
the kinetics is defined by the jumps of particles to the neighboring vacant sites .
the variation of the @xmath0-th site occupancy by the particles of sort @xmath1 during the time interval @xmath2 , @xmath3 ( @xmath4 is the duration of a particle jump to a neighboring site , @xmath5 being the life time of a particle on a site ) , is described by the standard continuity equation ( see , e.g. , @xcite ) @xmath6 where @xmath7 are the local occupation numbers of particles @xmath1 at the @xmath0-th site , @xmath8 gives the mean number of jumps ( of particles @xmath1 from site @xmath0 to a neighboring site @xmath9 per time @xmath2 ) , @xmath10 is the frequency of these jumps , @xmath11 is the occupation number of the @xmath9th site vacancies .
the term @xmath12 stands for the langevin source of the @xmath0th site occupation number fluctuations .
equations for the average local occupation numbers may be obtained from eqs .
( [ balance+ ] ) , using the local equilibrium approximation ( zubarev approach ) @xcite , which in our case coincides with the mean field approximation @xcite . in the case of two components , introducing time derivatives in eqs .
( [ balance+ ] ) , see @xcite , the macroscopic equations take the form @xcite [ 3 ] @xmath13 @xmath14 where @xmath15 and @xmath16 are the average occupation numbers of the two components at the point @xmath17 , @xmath18 and @xmath19 are the jump frequencies of particles @xmath15 and @xmath16 , correspondingly .
these equations are obtained in the long - wavelength approximation assuming that the characteristic scale of the gas inhomogeneity is much grater than the lattice constant @xmath20 .
the dimensionless spatial coordinate @xmath21 is introduced .
distinguishability of the particles in the noninteracting lattice gas leads to the additional nonlinear flow @xmath22 in the macroscopic eqs .
( [ 3 ] ) that is absent in the case of a one - component gas .
an important condition for the onset of this additional term is the excluded volume constraint , i.e. , when a site may be occupied by one particle only .
this flow is responsible for the mixing of different particle species and leads to additional correlations in the system . in the case of considerable difference between the species mobilities , @xmath23
, the indirect correlations can occur in the slow subsystem @xmath16 .
these correlations are induced by the fast component that plays the role of the `` interaction mediator '' .
such correlations are similar to the hydrodynamic correlations between colloidal particles @xcite and may have the long - time character . in order to show the presence of the long - time correlations in the heavy subsystem of the lattice gas we consider the fluctuations of the heavy particles drift caused by an external field .
they manifest itself as the fluctuations of hydrodynamic velocity field @xmath24 . in what follows , we assume that the characteristic time - scale @xmath25 of the fluctuations @xmath24 satisfies the condition @xmath26 and restrict ourselves to the adiabatic approximation , @xmath27 .
it means that the distribution of the fast component instantly gets into the stationary one with the momentary distribution of the slow component .
then , kinetic equations take form [ adiabat ] @xmath28 the light component @xmath29 depends on a `` slow '' time @xmath30 as on a parameter .
it should be noted , that the fluctuations of drift are associated with the fluctuations of the particle jump probability @xmath31 between the neighboring lattice sites @xmath0 , @xmath32 and in general case this term may have a more complicated form .
for example , in the case of the asymmetric jumps of the lattice gas particles , @xmath33 , @xmath34 , the drift term reads @xmath35 .
however , here we restrict ourselves to the case given by eqs .
( [ adiabat ] ) and , similarly to @xcite , consider a quasi - one - dimensional situation when interparticle correlations become most significant . in this case
, one can easily eliminate the fast variable @xmath15 from eqs .
( [ adiabat ] ) , see @xcite , and obtain the self - consistent equation for the heavy component @xmath16 @xmath36 ^ 2}\right)\frac{\partial^2n(x,\tau)}{\partial x^2 } + \nu_n^{-1}u(x,\tau)\frac{\partial n(x,\tau)}{\partial x } , \label{nonlocal}\ ] ] @xmath37 ^ 2}\right)^{-1}. \label{j}\ ] ] here we introduced the dimensionless time @xmath38 . the quantity @xmath39 [ eq . ( [ j ] ) ] corresponds to the average macroscopic flow of the light component @xmath40 passing through the system @xcite ; @xmath41 , @xmath42 , and @xmath43 being the values of the mean occupation numbers @xmath15 and @xmath16 at the system boundaries @xmath44
it follows from eq .
( [ nonlocal ] ) that the correlations in the slow subsystem appear only in the nonequilibrium case with the nonzero flow @xmath39 that is responsible for the nonlinear and nonlocal character of the diffusion process .
next we make use of the uniform density cluster approximation that is often exploited , e.g. , for the description of coulomb explosions of deuterium clusters @xcite . under this approximation ,
the density distribution @xmath45 is considered as a system of uniform one - dimensional clusters .
it is justified when the cluster size is much smaller than that of the system .
each such cluster is characterized by its `` center of mass '' @xmath46 and width @xmath47 , so that the distribution of the slow component can be written as @xmath48 where @xmath49 is the number of the particles contained by the @xmath50th cluster .
further , we assume the characteristic spatial scale @xmath51 of the fluctuations @xmath52 to be much grater than the typical cluster size but less than the distance between them , @xmath53 .
then , evaluating the moments of distribution ( [ napprox ] ) from eq .
( [ nonlocal ] ) one can obtain the equations for @xmath46 and @xmath47 [ apro2 ] @xmath54-\nu_n^{-1}u_k(\tau),\ ] ] @xmath55+j(\tau)\left(\sum_{l
< k}q_lg[n_l(\tau)]-\sum_{l > k}q_lg[n_l(\tau)]\right).\ ] ] the first equation ( [ apro2_a ] ) describes the drift velocity @xmath56 of the @xmath50th cluster .
the motion of the cluster as a whole is induced by the fluctuations of the external field @xmath57 and by the flow @xmath58\}^{-1}$ ] of the fast component ( the drag effect ) .
the function @xmath59\!=\![1-n_k(\tau)]^{-1}+[1-n_k(\tau)]^{-2}$ ] describes the drag velocity slowdown caused by the cluster expansion .
the second equation ( [ apro2_c ] ) describes the rate of the cluster expansion that is defined by the diffusion coefficient @xmath60=1-(m_1+m_2)/2+j(\tau)r_k(\tau)$ ] to be cluster position dependent and by the drag velocities @xmath61 of other clusters , see ( [ apro2_a ] ) .
note that the quantity @xmath62 is a natural small parameter since @xmath63 .
in fact eqs .
( [ nonlocal ] ) describe the brownian - like dynamics of the penetrable , expanding clusters embedded into the flow of the fast component . for simplicity ,
next we consider the system of the two initially identical clusters , @xmath64 , @xmath65 , with the @xmath66-correlated fluctuations , @xmath67 .
we are interested in the response of one cluster caused by the initial velocity perturbation of another cluster . for this purpose , we consider the pair correlation function of velocity fluctuations @xmath68[\dot r_2(0)-\bar v_2(0)]\rangle$ ] , @xmath69 , where @xmath70 satisfies unperturbed eqs .
( [ apro2 ] ) ( i.e. , eqs .
( [ apro2 ] ) provided @xmath71 ) . supposing that the fluctuations @xmath72 are small , @xmath73 , and using the perturbation theory in @xmath74 and @xmath9 ( we assume , that @xmath75 ) , one can get @xmath76 ^ 4}+\frac{2qr(\tau)}{[r(\tau)-q]^5}-\frac{c_0r(\tau)}{[r(\tau)-q]^3}\right),\ ] ] where @xmath77^{1/2}$ ] , @xmath78 and @xmath79/[r(0)-q]^2 $ ] . the correlation function ( [ correlator_full ] ) , fig . ( [ fig:1 ] ) , velocity cross - correlation function of a cluster pair as a function of time [ @xmath80 , @xmath81 , @xmath82 , @xmath83
. the inset shows the long - time asymptotic behavior , the dashed line indicates a slope of 1 . ]
has the long - time negative tail with the asymptotic behavior @xmath84 .
the long - time correlations between the two diffusive clusters are similar to hydrodynamic ones appearing between colloidal particles confined in a liquid - filled linear channel @xcite .
the significant difference of particle mobilities in a two - component lattice gas leads to the induced correlations in the slow subsystem mediated by the fast one . they manifest itself as a negative long - time tail in the behavior of the pair correlation function and are similar to the well - known long - time correlations between colloidal particles @xcite .
note that there is no additional interparticle interaction introduced in the lattice gas except that due to hard - core exclusion . in order to demonstrate this phenomenon
we have considered the one - dimensional case and used the simplest , somewhat rough , approximations . in particular , we have used the adiabatic one and neglected the retardation effects . as a result
, the correlations instantly spread all over the system and the averaged flow of the fast component does not depend on the distance between the clusters of the slow one .
it give rise to the weak dependence of the correlation function on the inter - cluster distance that make itself evident in the higher orders of the perturbation theory expansion .
considered correlations may be associated with the `` elastic - type interactions '' , similar to the case of the liquid - embedded particles @xcite .
however , another type of the induced correlations in the slow component may be caused by the equilibrium fluctuations in the fast one and associated with so - called casimir - like forces @xcite , that is beyond the scope of this paper .
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b * 16 * , 1393 ( 1977 ) j. zweiback , r. a. smith , t. e. cowan , g. hays , k. b. wharton , v. p. yanovsky , t. ditmire , phys .
lett . * 84 * , 2634 ( 2000 ) | the distinguishability of at least two species of particles in the classical lattice gas with no interactions except hard - core exclusion entails additional interparticle correlations .
a nonlinear mixing flow appears and manifests itself most pronounced in the case of significant difference between mobilities of species .
it may result in the induced correlations for the slow component mediated by the fast one . in the quasi - one - dimensional case ,
the long - time correlations are demonstrated to take place in the slow component , that is similar to the hydrodynamic correlations between colloidal particles . in the adiabatic approximation
, these correlations may come into play only in the non - equilibrium case with the flow of the fast component present in the system . |
The December solstice happens at the same instant for all of us, everywhere on Earth. This year the solstice occurs on Tuesday December 22nd at 04:49 GMT (Universal time) with the sun rising over Stonehenge in Wiltshire at 08:04.
The winter solstice happens every year when the Sun reaches its most southerly declination of -23.5 degrees. In other words, when the North Pole is tilted furthest – 23.5 degrees – away from the Sun, delivering the fewest hours of sunlight of the year.
The Sun is directly overhead of the Tropic of Capricorn in the Southern Hemisphere during the December solstice and is closer to the horizon than at any other time in the year, meaning shorter days and longer nights.
The day after the winter solstice marks the beginning of lengthening days, leading up to the summer solstice in June.
In the Southern Hemisphere, it's opposite. Dawn comes early, and dusk comes late. The sun is high and the shortest noontime shadow of the year happens there. In the Southern Hemisphere, people will experience their longest day and shortest night.
Shouldn't it be on December 21st?
While it more often than not falls on December 21st, the exact time of the solstice varies each year.
Sunrise between the stones at Stonehenge on the Winter Solstice in 1985 Photo: Mark Grant
In the Northern hemisphere the winter solstice is the shortest day of the year, because it is tilted away from the sun, and receives the least amount of sunlight on that day.
However, the earliest sunset does not occur on the solstice, because of the slight discrepancy between 'solar time' and the clocks we use.
The shortest day of the year often falls on December 21st, but the modern calendar of 365 days a year - with an extra day every four years - does not correspond exactly to the solar year of 365.2422 days.
The solstice can happen on December 20, 21, 22 or 23, though December 20 or 23 solstices are rare.
The last December 23 solstice was in 1903 and will not happen again until 2303.
Why isn’t the earliest sunset on the year’s shortest day?
Solar noon - the time midway between sunrise and sunset is when the sun reaches its highest point for the day, but the exact time of solar noon, as measured by Earth’s spin, shifts.
A clock ticks off exactly 24 hours from one noon to the next but actual days – as measured by the spin of the Earth – are rarely exactly 24 hours long.
Winter Solstice by Barbara Hepworth (1970)
If the Earth’s spin is measured from one solar noon to the next, then one finds that around the time of the December solstice, the time period between consecutive solar noons is actually 30 seconds longer than 24 hours.
Therefore two weeks before the solstice, for example – the sun reaches its 'noontime' position at 11:52 a.m. local standard time.
Two weeks later - on the winter solstice – the sun reached that noontime position at 11:59 a.m. - seven minutes later.
The later clock time for solar noon also means a later clock time for sunrise and sunset. The result? Earlier sunsets before the winter solstice and increasingly later sunrises for a few weeks after the winter solstice.
The exact date of earliest sunset varies with latitude but the sequence is always the same.
For the Northern Hemisphere the earliest sunset occurs in early December and the latest sunrise in happens in early January.
What does 'solstice' mean?
The term 'solstice' derives from the Latin word 'solstitium', meaning 'Sun standing still'.
On this day the Sun seems to stand still at the Tropic of Capricorn and then reverses its direction as it reaches its southernmost position as seen from the Earth.
Some prefer the more teutonic term 'sunturn' to descibe the event.
Why is Stonehenge important?
Stonehenge, the prehistoric monument located in Wiltshire, is carefully aligned on a sight-line that points to the winter solstice sunset (opposed to New Grange, which points to the winter solstice sunrise, and the Goseck circle, which is aligned to both the sunset and sunrise).
Archaeologists believe it was constructed from 3000 BC to 2000 BC and it is thought that the winter solstice was actually more important to the people who constructed Stonehenge than the Summer solstice.
The winter solstice was a time when cattle was slaughtered (so the animals would not have to be fed during the winter) and the majority of wine and beer was finally fermented.
Entrance to the stones is free on December 22nd and will be available from about 7.45am until 10am, when the site will close before re-opening as normal.
The sun rises over Salisbury Plain as light illuminates the mist shrouding Stonehenge (Getty)
The only other megalithic monuments in the British Isles to contain a clear, compelling solar alignment are Newgrange in County Meath, Ireland and Maeshowe situated on Mainland, Orkney, Scotland.
Both famously face the winter solstice sunrise.
Keep up, Druids...
In 2009, a crowd wearing traditional costume, met at Stonehenge on December 21st morning to mark the rising of the sun on the shortest day of the year.
But unfortunately their calculations were slightly out meaning they had in fact arrived 24 hours prematurely.
• Revellers celebrate the 2014 winter solstice at Stonehenge
The '09 solstice fell at exactly 5.47pm that day, and because the sun had already set, the official celebrations should have taken place at sunrise the next day.
Arthur Pendragon during the winter solstice at Stonehenge in Wiltshire Photo: PA
English Heritage, who manage the ancient site in Wiltshire, decided to open the gates anyway and welcome those who had made a miscalculation.
A spokesman for English Heritage said at the time: "About 300 people turned up a day early. We took pity on them and opened the stone circle so they could celebrate anyway. They were a day early but no doubt had a wonderful time as well.
"People always assume that because the Summer solstice is the June 21st, the winter solstice will be the 21st December. They should always check because it does change."
Pagan leader Arthur Pendragon said: "It is the most important day of the year for us because it welcomes in the new sun.
"There were hundreds of people there. If we'd celebrated on the 21st it would have been the right day but the wrong sun – when the whole point of the occasion is about welcoming in the new sun."
What's Google's Doodle about?
To mark the day, Google has done a special Doodle of ice skaters in a snow globe that can be viewed by several countries, including most of Europe, Canada, Mexico, Colombia and Japan.
How can I best watch the solstice where I live?
There's no need to travel out of town to see the sunrise.
Photo: http://sztanko.github.io/
This handy website shows the streets in cities around the world where you can get a clear view of the sun rising on the morning of the solstice.
How was/is the solstice celebrated around the world?
The December solstice marks the 'turning of the Sun' as the days slowly get longer. Celebrations of the lighter days to come have been common throughout history with feasts, festivals and holidays around the December solstice celebrated by cultures across the globe.
Saturnalia
Ther winter solstice festival Saturnalia began on December 17 and lasted for seven days in In Ancient Rome.
These Saturnalian banquets were held from as far back as around 217 BCE to honor Saturn, the father of the gods.
The holiday was celebrated with a sacrifice at the Temple of Saturn, in the Roman Forum, and a public banquet, followed by private gift-giving, continual partying, and a carnival atmosphere that overturned Roman social norms.
The festival was characterised as a free-for-all when all discipline and orderly behaviour was ignored.
Wars were interrupted or postponed, gambling was permitted, slaves were served by their masters and all grudges and quarrels were forgotten.
Saturnalia by Antoine-Francois Callet (1741-1823) Photo: Oil on canvas. Musée du Louvre
It was traditional to offer gifts of imitation fruit (a symbol of fertility), dolls (symbolic of the custom of human sacrifice), and candles (reminiscent of the bonfires traditionally associated with pagan solstice celebrations).
The Saturnalia would degenerate into a week-long orgy of debauchery and crime – giving rise to the modern use of the term 'saturnalia', meaning a period of unrestrained license and revelry. A mock 'king' was even chosen from a group of slaves or convicts and was allowed to behave as he pleased for seven days (until his eventual ritual execution).
The poet Catullus considered it to be "the best of days."
Feast of Juul
The Feast of Juul (where we get the term 'Yule' from at this time of year) was a pre-Christian festival observed in Scandinavia at the time of the December solstice.
People would light fires to symbolise the heat and light of the returning sun and a Juul (or Yule) log was brought in and dropped in the hearth as a tribute the Norse god Thor.
The Yule Log often was an entire tree, carefully chosen and brought into the house with great ceremony and sometimes, the largest end of the log would be placed into the fire hearth, while the rest of the tree stuck out into the room.
The Yule log is introduced to the proceedings
The log would be lit from the remains of the previous year's log which had been carefully stored away and often slowly fed into the fire through the Twelve Days of Christmas. Tradition dictated that the re-lighting process was carried out by someone with clean hands.
The log was burned until nothing but ash remained. The ashes were then collected and either strewn on the fields as fertilizer every night until Twelfth Night or kept as a charm and or as medicine.
A piece of the log was kept as both a token of good luck and as kindling for the following year’s log.
French peasants believed that if the ashes were kept under the bed, they would protect the house against thunder and lightning. The present-day custom of lighting a Yule log at Christmas is believed to have originated in the bonfires associated with the feast of Juul.
Yalda
Yalda or Shab-e Chelleh ('night of forty') is an Iranian festival celebrated on the "longest and darkest night of the year," i.e. the night of the Northern Hemisphere's winter solstice.
Every year, on December 21st, Iranians celebrate the arrival of winter, the renewal of the sun and the victory of light over darkness on Yalda Night.
Ancient Iranians believed that the dawning of each year is marked with the re-emergence or rebirth of the sun, an event which falls on the first day of the month of Dey in the Iranian calendar (December 21).
On this day, the sun was salvaged from the claws of the devil, which is represented by darkness, and gradually spread its rays all over the world to symbolize the triumph of good over evil.Family members get together (most often in the house of the eldest member) and stay awake all night long in Yalda.
Photo: Saman Aghvami
Pomegranate, watermelon and dried nuts are served as a tradition and classic poetry and old mythologies are read in the gathering.
It is believed that eating watermelons on the night of Chelleh will ensure the health and well-being of the individual during the months of summer by protecting him from falling victim to excessive heat or disease.
In Khorasan, there is a belief that whoever eats carrots, pears, pomegranates, and green olives will be protected against the harmful bite of insects, especially scorpions. Eating garlic on this night protects one against pains in the joints.
Getting a ‘Hafez reading’ from the book of great Persian poet Shamsu d-Din Muhammad Hafez-e Shirazi is also practiced.
Another custom performed in certain parts of Iran on the night of Chelleh involves young engaged couples. The men send an edible arrangement containing seven kinds of fruits and a variety of gifts to their fiancees on this night. In some areas, the girl and her family return the favour by sending gifts back for the young man.
Central Asian countries such as Afghanistan, Tajikistan, Uzbekistan, Turkmenistan and some Caucasian states such as Azerbaijan and Armenia share the same tradition as well and celebrate Yalda Night annually at this time of the year.
Santo Tomas in Guatemala
December 21 in St Thomas's Day in the Christian calendar. In Guatemala on this day, Mayan Indians indulge in the ritual known as the Palo Volador, or “flying pole dance”.
Three men climb on top of a 50-foot pole as one of them beats a drum and plays a flute. The other two men wind a rope attached to the pole around one foot and jump.
Mayan Indians take part in the Palo Volador in Guatemala Photo: Alamy
If they land on their feet, it is believed that the sun god will be pleased and that the days will start getting longer.
The ancient Incas celebrated a special festival to honour the sun god at the time of the December solstice.
In the 16th century ceremonies were banned by the Roman Catholics in their bid to convert the Inca people to Christianity.
A local group of Quecia Indians in Cusco, Peru, revived the festival in the 1950s. It is now a major festival that begins in Cusco and proceeds to an ancient amphitheatre a few miles away. ||||| CLOSE For many of us, winter has made itself known for a few weeks now. But according to astronomers, December 21st marks the start of winter. USA TODAY
Hundreds of druids and pagans celebrate the winter solstice at Stonehenge on December 22, 2009 in Wiltshire, England. Hundreds of people gathered at the famous stone circle to celebrate the sunrise closest to the Winter Solstice, the shortest day of the year. (Photo: Getty Images)
Here comes the dark. The winter solstice — marking the longest night and shortest day of the year — is Monday night.
The solstice occurs at the same instant everywhere on Earth. In the United States, it happens at 11:48 p.m. ET Monday (or 10:48 p.m. CT, 9:48 p.m. MT and 8:48 p.m. PT).
In Europe, Africa, Asia and Australia, that means the solstice actually comes on Tuesday.
The winter solstice is the precise moment the Northern Hemisphere is tilted its farthest from the sun all year, and usually occurs near the day when there is the least amount of daylight and the most darkness.
One of the most famous solstice celebrations occurs at the ancient Stonehenge ruins in Wiltshire, England, where druids, pagans and other revelers gather each year to celebrate the event.
The solstice is the astronomical beginning of winter — the start of the coldest three months in the Northern Hemisphere — even though meteorologists view winter as starting Dec. 1. After the solstice, the days slowly start to get longer again.
It's the opposite in the Southern Hemisphere, where Dec. 21 marks the longest day of the year and the beginning of astronomical summer.
Winter's shortest day, however, is typically not the coldest day of the year. There is a lag between the shortest day of the year and the coldest average temperatures for most spots in the USA.
This lag in temperature occurs because even though the amount of daylight is increasing, the Earth's surface continues to lose more heat than it receives from the sun. In most locations across the country, the minimum daily temperature occurs around two or three weeks later, in early to mid-January.
For example, the coldest days in Boston, on average, are Jan. 17-26. In Chicago, it's Jan. 17-20, and in Miami, it's Jan. 2-22. At the end of January, more heat finally begins arriving than leaving, and days slowly start to warm up.
The Earth's tilted axis causes the seasons. During the Northern Hemisphere's winter, the land north of the equator is tilted away from the sun, which lowers the amount of the sun's energy warming the Northern Hemisphere.
And why is the Earth tilted? It's probably the result of collisions with various proto-planets and other massive objects during the formation of the solar system billions of years ago, according to NASA. Just a bit unsettling to realize that the reason the Earth has the perfect temperature for life to form is a few random collisions with other space rocks a few eons ago.
In the meantime, happy solstice!
Read or Share this story: http://usat.ly/1YuscGF ||||| The December solstice happens at the same instant for everyone, everywhere on Earth – and this year the winter solstice occurs today, Friday December 21st 22:23 GMT in the Northern Hemisphere.
The winter solstice happens every year when the Sun reaches its most southerly declination of -23.5 degrees. In other words, it is when the North Pole is tilted farthest away from the Sun, delivering the fewest hours of sunlight of the year.
The Sun is directly overhead of the Tropic of Capricorn in the Southern Hemisphere during the December solstice and is closer to the horizon than at any other time in the year, meaning shorter days and longer nights.
The shortest day of the year lasts for 7 hours 49... |||||
The winter solstice will fall in the early morning hours of Dec. 22, marking the first day of winter and the shortest day of the year in the Northern Hemisphere.
The astronomical event also means it’ll be the longest day of the year for those who live south of the equator. The solstice starts at 4:48 a.m. UTC on Dec. 22 (which is 11:48 p.m. ET on Dec. 21), the moment when the Northern Hemisphere is pointed at its farthest distance from the sun.
READ MORE: 5 Things to Know About the Winter Solstice
During the solstice, those on the East Coast of the U.S. will only see nine hours and 15 minutes of daylight.
Christmas has become associated with winter solstice, which serves as a turning point in the year in many cultures. | – Mondays always feel longer, but that's not the only reason today may be dragging. Yes, it's the winter solstice, meaning Northern Hemisphere residents will be tilted as far from the sun as they will be all year—so it's also the shortest day and the longest night, USA Today reports. Just how short a day? Nine hours and 15 minutes of daylight on the East Coast, per Time. The solstice, which happens everywhere on Earth at the same instant, will take place at 11:48pm EST, meaning some parts of the world—including Stonehenge, where there are usually wild solstice celebrations—will experience the solstice on Tuesday. In fact, due to the imprecise syncing of the solar year with the modern calendar, the winter solstice can actually take place anywhere between Dec. 20 and Dec. 23 (though those two dates are rare), the Telegraph reports. That said, this kickoff of the North's astronomical winter (and the Southern Hemisphere's summer) isn't necessarily the coldest part of the year for those above the equator—as we learned when weather forecasters said this could be one of the warmest Christmas weeks on record. Days will once again grow longer starting Dec. 22, but Earth will still lag behind and continue to lose heat at a faster rate than it's taking it in from the sun; cities in the US typically don't start to warm up on average until at least the end of January, per USA Today. (Check out the Telegraph for some neat history on winter solstice celebrations.) |
the moderate to high redshift universe has been probed at unparallelled depth with the most sensitive observations performed at x - ray wavelengths in the _ chandra _ deep fields .
the _ chandra _
2ms observations ( alexander et al . 2003 , luo et al . 2008 ) resolved about 80 per cent of the extragalactic x - ray light in the hard 2 - 10 kev band ( see brandt & hasinger 2005 for a review ) .
these deep surveys find a sky density of 5000 sources per square degree , the vast majority of which are found to be agn through optical spectroscopy ( e.g. barger et al . 2003 ) .
in contrast , the optical surveys for qsos ( e.g. the combo-17 survey ) reach only a surface density about an order of magnitude lower ( e.g. wolf et al . 2003 ) .
this clearly demonstrates the power of x - ray surveys for detecting agn .
this is because hard x - rays can penetrate large amounts of gas without suffering from significant absorption .
indeed detailed spectral analysis on x - ray selected agn reveals large amount of obscuration ( e.g. akylas et al .
2006 , tozzi et al .
2006 , georgantopoulos et al .
in particular , about two thirds of the x - ray sources , over all luminosities , present column densities higher than @xmath11 .
these high absorbing columns are believed to originate in a molecular torus surrounding the nucleus .
however , even the efficient 2 - 10 kev x - ray surveys may be missing a fraction of highly obscured sources .
this is because at very high obscuring column densities ( @xmath12 , corresponding to an optical reddening of @xmath13 ) , the x - ray photons with energies between 2 and 10 kev are absorbed .
these are the compton - thick agn ( see comastri 2004 for a review ) where the compton scattering on the bound electrons becomes significant . despite the fact that compton - thick agn are abundant in our vicinity ( e.g. ngc1068 , circinus ) , only a few tens of compton - thick sources have been identified from x - ray data ( comastri 2004 ) .
although the population of compton - thick sources remains elusive there is concrete evidence for its presence .
the x - ray background synthesis models can explain the peak of the x - ray background at 30 - 40 kev , where most of its energy density lies , ( frontera et al .
2007 , churazov et al .
2007 ) only by invoking a large number of compton - thick agn ( gilli , comastri & hasinger 2007 ) .
additional evidence for the presence of a compton - thick population comes from the directly measured space density of black holes in the local universe .
it is found that this space density is a factor of two higher than that predicted from the x - ray luminosity function ( marconi et al .
this immediately suggests that the x - ray luminosity function is missing an appreciable number of obscured agn . in recent years
there have been many efforts to uncover heavily obscured and in particular compton - thick agn in the local universe by examining ir or optically selected , [ oiii ] , agn samples .
this is because both the ir and the narrow - line region originate beyond the obscuring region and thus represent an isotropic property of the agn .
risaliti et al . ( 1999 ) examine the x - ray properties of a large sample of [ oiii ] selected seyfert-2 galaxies whose x - ray spectra were available in the literature .
they find a large fraction of compton - thick sources ( over half of their sample ) .
their estimates are complemented by more recent _ _ observations of local agn samples ( cappi et al .
2006 , panessa et al .
2006 , guainazzi et al .
all these authors also claim a large compton - thick agn fraction exceeding 30 per cent of the seyfert-2 population . the advent of the _ swift _ and _ integral _ missions which carry x - ray detectors with imaging capabilities ( e.g. barthelmy et al . 2005 , ubertini et al . 2003 ) in ultra - hard x - rays ( 15 - 200 kev ) try to shed new light on the absorption properties of agn in the local universe . in principle , at these ultra - hard x - rays obscuration should play a negligible role , at least up to column densities as high as @xmath14 .
however , because of the limited effective area the above surveys can provide x - ray samples , down to very bright fluxes @xmath15 , with limited quality spectra . again observations are often required to determine the column density in each source .
interestingly , these surveys find only a limited number of compton - thick sources ( markwardt et al .
2005 , bassani et al .
2006 , malizia et al .
2007 , ajello 2008 , winter et al .
2008 , tueller et al .
2008 , sazonov et al .
2008 ) . here , we present observations of _ all _ 38 seyfert galaxies in the palomar spectroscopic sample of nearby galaxies ( ho et al .
this is the largest complete optically selected agn sample in the local universe analyzed so far .
23 of the seyfert galaxies presented here have already been discussed in previous works ( e.g. cappi et al .
2006 ) . for 5 of them newer observations
are available and are presented here .
the current work should provide the most unbiased census of the agn column density distribution at low redshifts and luminosities .
[ thesample ] the seyfert sample used in this study is derived from the palomar optical spectroscopic survey of nearby galaxies ( ho , fillipenko , & sargent 1995 ) .
this survey has taken high quality spectra of 486 bright ( @xmath16 mag ) , northern ( @xmath17 ) galaxies selected from the revised shapley - ames catalogue of bright galaxies ( rsac , sandage & tammann 1979 ) and produced a comprehensive and homogeneous catalogue of nearby seyfert galaxies .
the catalogue is 100% complete to @xmath18 mag and 80% complete to @xmath16 mag ( sandage , temmann & yahil 1981 ) . for the purpose of this work
we consider all the seyfert galaxies from the palomar survey .
sources lying in - between the seyfert - liner or the seyfert - transient boundary have been excluded .
furthermore seven seyfert galaxies ( i.e. ngc1068 , ngc1358 , ngc1667 , ngc2639 , ngc3185 , ngc4235 , ngc5548 ) , which have been included in the palomar survey for various reasons ( see ho et al .
1995 ) , even though they did not satisfy the survey selection criteria , are also excluded .
there are 40 seyfert galaxies comprising the optical sample .
9 sources are classified as type-1 ( contains types 1 , 1.2 , 1.5 ) and 31 as type-2 ( contains types 1.8,1.9,2 ) seyfert galaxies .
however ngc4051 , ngc4395 and ngc4639 which have been initially classified as seyfert 1.2 , 1.8 and 1 by ho et al .
( 1997 ) has been re - classified as type-1.5 , 1 and 1.5 respectively ( see cappi et al .
2006 , panessa et al .
2006 , baskin & laor 2008 ) .
moreover ngc185 which is classified as a seyfert-2 may not contain an active nucleus since it presents line intensity ratios possibly produced by stellar processes ( ho & ulvestad 2001 ) .
the main characteristics of these sources , taken from ho et al .
( 1997 ) , are listed in table [ optical ] .
some galaxies listed here present @xmath19 fainter than the formal limit of the palomar survey . according to ho et al .
( 1995 ) this discrepancy can be attributed to errors in the apparent magnitudes given in the rsac . [ cols="^,^,^,^,^,^ " , ] column 1 : name column 2 : black hole mass in units of solar masses column 3 : bolometric luminosity in units of ergs s@xmath20 column 4 : accretion rate @xmath21
in this work we present observations of all the seyfert galaxies from the palomar survey ( ho et al . 1995 ) . we find that @xmath2250 per cent of the seyfert population is absorbed by @xmath23 @xmath24 . in this sample
we have identified 3 compton - thick sources which translates to a fraction of @xmath228 per cent .
five more sources possibly host a highly absorbed or a compton thick nucleus . in the very extreme , and rather unlikely case were all these candidates are true compton - thick sources their fraction reaches 20 per cent of the total population .
cappi et al .
( 2006 ) and pannesa et al .
( 2006 ) , also using data from the palomar survey , provide estimates for the fraction of obscured agn in the local universe .
these authors find that about 50% of their sources are obscured ( @xmath5 ) .
their estimates on the fraction of compton thick sources suggest an absolute minimum of 20 per cent of the total population .
this result comes in contradiction with our findings .
however their sample includes 2 objects not fulfilling the palomar survey selection criteria ( see also section [ thesample ] ) .
these are the 2 compton - thick agn ngc1068 and ngc3185 .
when we exclude these an agreement is found .
risaliti et al .
( 1999 ) study the x - ray absorption in a sample of 45 seyfert-2 galaxies finding that a considerable fraction of these are associated with compton - thick nuclei .
a direct comparison with our results is not straightforward since these authors exclude all the sources with @xmath25}>4\times 10^{-13}$ ] .
however we think that only a luminosity cutoff could reveal column density distribution of the population that contributes to the xrb ( see section 5.2 ) .
the xrb synthesis models can provide tight constraints on the number density of compton - thick sources .
these models attempt to fit the spectrum of the x - ray background roughly in the 1 - 100 kev range .
it is well established that a large number of compton - thick sources is needed ( gilli et al .
2007 ) to reproduce the hump of the x - ray background spectrum at 30 - 40 kev where most of its energy density lies ( churazov et al .
2007 , frontera et al . 2007 ) . here
, we compare the fraction of the compton - thick sources predicted by the model of gilli et al .
2007 with our results .
we use the publicly available pompa software.gilli/counts.html ] this predicts the number counts at a given redshift , flux and luminosity range using the best - fit results for the fraction of obscured , compton - thick sources , of the x - ray background synthesis model of gilli et al .
( 2007 ) .
we restrict the comparison to low redshifts @xmath26 and x - ray luminosities in the bin @xmath27 .
as our sample is not flux limited in the x - rays , we have to choose a flux limit deep enough to ensure that all sources in this luminosity and redshift bin are detected .
a flux limit of @xmath28 satisfies this constraint .
the x - ray background synthesis models predict a fraction of compton - thick sources of about 40 % which is higher compared with our results @xmath29% .
only if all the low @xmath30}$ ] seyfert-2 galaxies are associated with a compton - thick nuclei the discrepancy would become less pronounced .
optically selected samples can still miss a fraction of compton - thick agn .
for example , ngc6240 is classified as a liner in the optical while _ bepposax _
observations show the presence of a compton - thick nucleus ( vignati et al .
moreover _ suzaku _ observations ( ueda et al . 2007 and comastri et al . 2007 ) have demonstrated that a small fraction of agn may have a 4@xmath31 coverage , instead of the usually assumed toroidal structure .
these sources will not exhibit the usual high excitation narrow emission lines and therefore will not be classified as agn on the basis of their optical spectrum .
recent results based on _ integral _ and _ swift _ observations reveal a small fraction of compton - thick sources ( e.g. sazonov et al .
2008 , sazonov et al .
2007 , ajello et al . 2008 ) .
in particular at the flux limit of @xmath32 in the 17 - 60 kev energy band , observations find @xmath33 compton - thick sources .
swift_/bat hard x - ray survey failed to identify any compton - thick agn .
this non detection discards the hypothesis that their fraction accounts for the 20 per cent of the total agn at @xmath34 confidence level .
it is true however that some heavily obscured compton - thick sources with @xmath35 would be missed even by these ultra hard x - ray surveys . in the low - luminosity sub - sample ( intrinsic @xmath36 erg s@xmath20 ) the fraction of obscured sources diminishes to 30% .
this result comes in apparent contradiction with recent findings suggesting an increasing fraction of obscuration with decreasing luminosity ( e.g. akylas et al .
2006 , la franca et al . 2005 ) .
this behaviour may reflect a physical dependence of the column density with intrinsic luminosity as suggested by elitzur & shlosman ( 2006 ) .
these authors present a model where the torus and the blr disappear when the bolometric luminosity decreases below @xmath37 ergs s@xmath20 because the accretion onto the central black hole can no longer sustain the required cloud outflow rate .
it is interesting to note that the corresponding luminosity in the 2 - 10 kev band is about several @xmath38 , assuming the spectral energy distribution of elvis et al .
interestingly , almost all of our seyfert-2 sources with no absorption present luminosities below this limit ( with the exception of ngc3147 ) .
we note however , there are sources ( ngc3486 , ngc3982 ) with low luminosity , which present column densities around @xmath11-@xmath39 @xmath24 .
alternatively , it is possible that at least in a few cases , the large xmm - newton point spread function results in contamination by nearby sources
. thus the nuclear x - ray emission could be out - shined giving the impression that there is no obscuration ( e.g. brightman & nandra 2008 ) .
however , both the inspection of the images as well as the stacked spectrum of the unabsorbed sources do not favour such a scenario .
observations are available for all 38 seyfert galaxies from the palomar spectroscopic sample of galaxies of ho et al .
( 1995 , 1997 ) .
our goal is to determine the distribution of the x - ray absorption in the local universe through x - ray spectroscopy .
our sample consists of 30 seyfert-2 and 8 seyfert-1 galaxies .
the results can be summarised as follows : * we find a high fraction of obscured sources ( @xmath5 ) of about 50 % . * a number of sources present low @xmath30}$ ] ratio .
their individual spectra show no evidence of high absorbing column densities .
however , their stacked spectrum shows significant amount of absorption ( @xmath40 ) * considering only the bright sub - sample ( @xmath41 ) , i.e. only these sources which contribute a significant amount to the x - ray background flux , we find that 75 % of our sources are obscured . * in the bright sub - sample
there are at least 3 compton - thick agn translating to a fraction of 15% which is lower than the predictions of the x - ray background synthesis models at this luminosity and redshift range . only if we consider , the rather unlikely scenario , where all seyfert-2 galaxies with a low @xmath30}$ ] ratio are associated with compton - thick sources we would alleviate this discrepancy . * we find a large number of unobscured seyfert-2 galaxies .
all these have low luminosities @xmath42 .
inspection of the images , where available , demonstrates that in most cases these are not contaminated by nearby sources .
furthermore , their stacked spectrum reveals no absorption .
it is most likely that these are genuinely unobscured sources in accordance with the predictions of the models of elitzur & sloshman ( 2006 ) .
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a&a , 411 , l131 ueda y. , eguchi s. , terashima y. , et al .
, 2007 , apj , 664 , 79 vignati p. , molendi s. , matt , g. , et al . , 1999 , a&a , 349 , 57 weaver k. a. , nousek j. , yaqoob t. , mushotzky r. f. , makino f. , & otani c. 1996 , apj , 458 , 160 winter l. m. , mushotzky r. f. , tueller j. , markwardt c. , 2008 , apj , 674 , 686 wolf c. , wisotzki l. , borch a. , dye s. , kleinheinrich m. , meisenheimer k.,2003 , a&a , 408 , 499 | we present _ xmm - newton _ spectral analysis of all 38 seyfert galaxies from the palomar spectroscopic sample of galaxies . these are found at distances of up to 67 mpc and
cover the absorbed 2 - 10 kev luminosity range @xmath0 .
our aim is to determine the distribution of the x - ray absorption in the local universe .
three of these are compton - thick with column densities just above @xmath1 and high equivalent width fek@xmath2 lines ( @xmath3 ev ) .
five more sources have low values of the x - ray to [ oiii ] flux ratio suggesting that they could be associated with obscured nuclei .
their individual spectra show neither high absorbing columns nor flat spectral indices .
however , their stacked spectrum reveals an absorbing column density of @xmath4 .
therefore the fraction of absorbed sources ( @xmath5 ) could be as high as @xmath6 % .
a number of seyfert-2 appear to host unabsorbed nuclei .
these are associated with low - luminosity sources @xmath7 .
their stacked spectrum again shows no absorption while inspection of the images , where available , shows that contamination from nearby sources does not affect the _ xmm - newton _ spectra in most cases .
nevertheless , such low luminosity sources are not contributing significantly to the x - ray background flux .
when we consider only the brighter , @xmath8 , 21 sources , we find that the fraction of absorbed nuclei rises to @xmath9 % while that of compton - thick sources to 15 - 20% . the fraction of compton - thick agn is lower than that predicted by the x - ray background synthesis model in the same luminosity and redshift range
. 2@xmath10 |
accurate photometry is one of the key tools of astronomy , yet ground - base astronomy continues to suffer the traditional challenge of accurate photometric calibration . careful analysis of standard ground - based ccd imaging data can yield relative photometry of objects in a small field with accuracy of 1% or better , and exotic techniques can produce much higher accuracy in special cases ( e.g. , * ? ? ?
* ; * ? ? ?
the remaining challenge for the generic astronomer is that of calibration of the photometry of a given field into one of the standard systems .
part of the difficulty comes from the various effective bandpasses due to the different telescopes and cameras used by observers .
critical attention must be paid to the bandpass defined by the choice of filter , detector , etc ( see , * ? ? ?
however , for main sequence stars of spectral types earlier than @xmath6 k0 , these bandpass effects can be dealt with through measured color transformations .
the larger challenge comes from the calibration of the images with respect to a well - defined reference .
calibration of images obtained from the ground is naturally difficult due to the large area of the sky and the small sizes of detectors , even modern large mosaic cameras .
calibration of most individual images still ultimately relies on observations of objects in reference fields outside of the field of view of interest .
since there is currently no all - sky network of calibrated references with sufficiently dense spacing , the calibration observations invariably do not overlap the science fields .
photometric calibration is thus sensitive to the systematic impact of changes in the atmosphere or the instrument between the observation of the science field and the reference field .
ground - based optical astronomy is on the verge of escaping this traditional problem several projects are now ( or will soon be ) able to define dense large - area networks of reference photometry with accuracies at or below the 1% level .
the sloan digital sky survey @xcite , for example , provides good photometry across the @xmath7 steradians covered by that survey ( up through dr9 ) , with reported systematic errors of @xmath8 millimagnitudes for the @xmath9 filters @xcite .
lsst will eventually provide the same or better for the @xmath10 steradians of the portion of the sky covered by that survey .
the project is surveying the @xmath0 steradians north of @xmath11 deg declination @xcite .
a major goal of this survey project is the construction of a precision photometry reference catalog covering the entire @xmath0 region .
the design of the survey and the careful attention to calibration concerns place it in an excellent position to provide a photometric ( and astrometric ) reference for this entire @xmath0 region .
the survey is continuing , and final calibration will not be complete for @xmath6 6 months after the survey completion , roughly mid 2014 . at this point in time , however , interest in the community has grown strong in a preliminary data release to demonstrate the progress at precision photometric calibration , and to potentially provide reference data in the ps1 photometry system , and in regions not currently served by the sdss survey .
@xmath0 survey coverage statistics[table : coverage ] [ cols= " < , > , > , > ,
< , > , > " , ] over the next 1.5 - 2 years , pan - starrs 1 will finish the initial basic survey , completing coverage of the full @xmath0 region .
one of our major eventual goals is the production of a high - quality astrometric and photometric reference catalogs which can be used by observers to calibrate data with in - field references .
the full survey dataset is necessary to pin down all regions at the highest possible precision .
the vagaries of weather means that some substantial patches have not yet been observed in photometric conditions , and are only currently tied via relative photometry to the rest of the survey . in this initial public release
, we are providing the ps1 reference photometry ladder as a sample of future photometric calibration data .
the ladder consists of 4 strips in right ascension , 1 degree high , at declinations of ( -25 , 0 , + 25 , + 50 ) , and 24 strips in declination , 1 ra degree wide centered on ra hours ( see figure [ fig : ladder ] ) .
we have selected a subset of bright ( @xmath12 ) , well - measured ( @xmath13 observations total ) objects in these regions .
the brightness limit was chosen to be equivalent to an instrumental magnitude of -9.5 , or roughly 2% statistical errors .
this brightness cut not only restricts the sample to objects with high signal - to - noise , it also avoids the stars affected by inconsistencies for faint stars .
the inconsistencies we have observed take the form of variations in the measured flux for faint stars , relative to bright stars in the same images , as a function of seeing .
we have also limited the density to @xmath1 objects for each 1 square degree patch . to choose a high - quality sample at this limited density , we used the mean @xmath14 value for the , , and mean magnitudes to select the high - quality measurements .
we then selected the 1000 objects for a given patch in ascending order of @xmath14 so that objects with consistent photometry are preferred .
we provide two sets of photometry tables : `` ubercal '' and `` relphot '' .
the ubercal tables only include objects for which all 5 filters have measurements calibrated directly in the ubercal analysis .
the relphot tables accept objects for which some filters have been tied to the ubercal data via relative photometry .
as discussed above , the relphot values have lower confidence and should not be used for precision photometry .
however , the relphot tables provide additional sky coverage . in most of these areas , a subset of the filters
have ubercal photometry .
careful use of the per - filter flags is advised !
the tables are provided as fits and comma - separated value tables .
table [ table : example ] defines the columns available in the tables .
there are 27 separate tables , 1 for each of the ladder rungs in dec and 1 for each of the rungs in ra .
note that there are duplicate entries between files where the rungs overlap .
table [ table : example ] describes the fields provided for each object .
data for each of the five filters ( ) are given in blocks , with 6 parameters provided for each filter .
the magnitude provided is the mean psf magnitude calibrated as described above .
the error is the formal error determined by accepting the reported error from the photometric analysis for each separate measurement .
@xmath15 represents the number of measurements actually used to determine the mean magnitude .
because of outlier clipping , this number may be smaller than the number of separate epochs available for a given object .
the standard deviation of the mean magnitude is reported _ after _ clipping has been applied . the mean magnitude calculated for each filter
is coupled to a set of bit - flags which describe the averaging process ( table [ table : flags ] ) .
this value is reported as a 32-bit integer , but only the following 8 bits are used for each filter ( see the discussion in section [ sec.relphot ] ) . to assess the extendedness of an object , we use the difference between the psf and aperture magnitudes . if this difference is larger than 0.1 added in quadrature to 2.5 times the statistical error , then the measurement is considered extended .
this measurement shows the presence of additional light in the aperture beyond the core consistent with the psf model .
the flag noting a possible extended object is raised if more than 50% of the measurements in a given band are observed to be extended based on this test .
the survey has been made possible through contributions of the institute for astronomy , the university of hawaii , the pan - starrs project office , the max - planck society and its participating institutes , the max planck institute for astronomy , heidelberg and the max planck institute for extraterrestrial physics , garching , the johns hopkins university , durham university , the university of edinburgh , queen s university belfast , the harvard - smithsonian center for astrophysics , and the las cumbres observatory global telescope network , incorporated , the national central university of taiwan , and the national aeronautics and space administration under grant no .
nnx08ar22 g issued through the planetary science division of the nasa science mission directorate .
partial support for this work was provided by national science foundation grants ast-1009749 & ast-1238877 .
hsieh , h. h. , yang , b. , haghighipour , n. , kaluna , h. m. , fitzsimmons , a. , _ et al .
_ , 2012 , asteroids , comets , meteors 2012 , proceedings of the conference held may 16 - 20 , 2012 in niigata , japan .
lpi contribution no .
1667 , id.6313 .
tonry , j. , & onaka , p. 2009
, advanced maui optical and space surveillance technologies conference , proceedings of the advanced maui optical and space surveillance technologies conference , ed . :
s. ryan , p.e40 .
tonry , j. l. , stubbs , c. w. , lykke , k. r. , doherty , p. , shivvers , i. s. , burgett , w. s. , chambers , k. c. , hodapp , k. w. , kaiser , n. , kudritzki , r .-
, magnier , e. a. , morgan , j. s. , price , p. a. , wainscoat , r. j. 2012 , schlafly , e. f. , finkbeiner , d. p. , juri , m. , magnier , e. a. , burgett , w. s. , chambers , k. c. , grav , t. , hodapp , k. w. , kaiser , n. , kudritzki , r .-
p . , martin , n. f. , morgan j. s. , price , p. a. , stubbs , c. w. , tonry , j. l. , wainscoat , r. j. 2012 , . | as of 2012 jan 21 , the pan - starrs1 @xmath0 survey has observed the 3/4 of the sky visible from hawaii with a minimum of 2 and mean of 7.6 observations in 5 filters , .
now at the end of the second year of the mission , we are in a position to make an initial public release of a portion of this unprecedented dataset .
this article describes the ps1 photometric ladder , release 12.01 this is the first of a series of data releases to be generated as the survey coverage increases and the data analysis improves .
the photometric ladder has rungs every hour in ra and at 4 intervals in declination .
we will release updates with increased area coverage ( more rungs ) from the latest dataset until the ps1 survey and the final re - reduction are completed .
the currently released catalog presents photometry of @xmath1 objects per square degree in the rungs of the ladder .
saturation occurs at @xmath2 ; @xmath3 ; and @xmath4 .
photometry is provided for stars down to @xmath5 in the ab system .
this data release depends on the rigid ` ubercal ' photometric calibration using only the photometric nights , with systematic uncertainties of ( 8.0 , 7.0 , 9.0 , 10.7 , 12.4 ) millimags in ( ) .
areas covered only with lower quality nights are also included , and have been tied to the ubercal solution via relative photometry ; photometric accuracy of the non - photometric regions is lower and should be used with caution . |
A senior prank in which 72,000 ladybugs were released in a public high school has several youths and adults facing criminal charges.
Early Wednesday, five people forced open a door at Chopticon High School in Morganza, Maryland, according to the St. Mary's County's Sheriff's Office.
Wearing masks and hoodies, they released the ladybugs throughout the school while two others waited in a car, deputies said.
Four male juveniles and three men were identified as suspects, investigators said. One of the suspects ordered the ladybugs online, deputies said.
Weird News Photos: Man Shoves Snake in Pants
The four juveniles are charged with burglary, property destruction and disruption of school activities. They were released to their parents.
The three men will be charged by criminal summons, deputies said.
Copyright Associated Press ||||| Many celebrities are willing to pose for PETA in various stages of dress and undress. Check out the photos here.
Many celebrities are willing to pose for PETA in various stages of dress and undress. Check out the photos here.
Many celebrities are willing to pose for PETA in various stages of dress and undress. Check out the photos here.
Many celebrities are willing to pose for PETA in various stages of dress and undress. Check out the photos here.
Guilty or not, these strange mug shots are worth a look. This information was supplied by law enforcement and describes recent arrests and charges. All defendants are presumed innocent.
Guilty or not, these strange mug shots are worth a look. This information was supplied by law enforcement and describes recent arrests and charges. All defendants are presumed innocent.
Guilty or not, these strange mug shots are worth a look. This information was supplied by law enforcement and describes recent arrests and charges. All defendants are presumed innocent.
Guilty or not, these strange mug shots are worth a look. This information was supplied by law enforcement and describes recent arrests and charges. All defendants are presumed innocent.
People are always trying to sneak things into the country through area airports. Here are some of the items they were caught with.
People are always trying to sneak things into the country through area airports. Here are some of the items they were caught with.
People are always trying to sneak things into the country through area airports. Here are some of the items they were caught with.
People are always trying to sneak things into the country through area airports. Here are some of the items they were caught with.
For the second time in three years, fishermen in southern Maryland have pulled in a shark from the most unlikely place -- the Potomac River. Actually they caught two sharks.
For the second time in three years, fishermen in southern Maryland have pulled in a shark from the most unlikely place -- the Potomac River. Actually they caught two sharks.
Here are the latest additions to the FOX 5 mugshot photo gallery. These mugshots were provided to us by law enforcement based on recent arrests and charges. All defendants are presumed innocent.
Here are the latest additions to the FOX 5 mugshot photo gallery. These mugshots were provided to us by law enforcement based on recent arrests and charges. All defendants are presumed innocent.
Here are the latest additions to the FOX 5 mugshot photo gallery. These mugshots were provided to us by law enforcement based on recent arrests and charges. All defendants are presumed innocent.
Here are the latest additions to the FOX 5 mugshot photo gallery. These mugshots were provided to us by law enforcement based on recent arrests and charges. All defendants are presumed innocent.
A Los Angeles woman says she is tired of Hollywood's obsession with perfection. So, she's doing something drastic right in the middle of Hollywood on Hollywood boulevard to show other women.
A Los Angeles woman says she is tired of Hollywood's obsession with perfection. So, she's doing something drastic right in the middle of Hollywood on Hollywood boulevard to show other women.
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Students protested Tuesday after learning some of their classmates will face discipline following a school prank at their St. Mary's County high school.
Pranks committed by graduating seniors are nothing new. But at Chopticon High School, the prank was certainly original and involved tens of thousands of lady bugs.
The students released 72,000 lady bugs inside the school building last Wednesday night as their senior prank. However, school officials and police are not laughing and some of the kids are in legal trouble.
“Please let me walk,” said Brian Reminga. “It was a harmless prank.”
That is the message Reminga has for school administrators as he will not be allowed to walk at Chopticon's graduation because of the prank.
Six Chopticon senior students and one alumnus broke into the school at around 3:30 a.m. Wednesday and released the lady bugs inside.
Now they are facing criminal charges. Four minors were charged with fourth-degree burglary, property destruction and disruption of school activities. The other three will be charged as adults by criminal summons.
Sgt. Cara Grimbles, a spokesperson with the St. Mary's County Sheriff's Office, explained why.
“They set the burglary alarm off and the police did respond and we arrived there,” Grimbles said. “Then it takes it to a different level and we certainly don't want to see anybody get hurt.”
Mike Wyant, director of safety and security for St. Mary's County Schools, told FOX 5 that the school followed protocol with regard to the decision to notify police. Wyant told parents that their primary concern was the level of potential danger the students put themselves in by breaking into the school.
Friends are outraged that Reminga will not be able to walk at his graduation and the class president will not be able give a speech at the ceremony either. This after they say another one of the students involved was allowed to play in the baseball state championship game after the prank, which the school won.
“Somebody just ordered bugs on Amazon and we decided to do it,” Reminga said. “I wasn't really part of much of the planning.”
“You work four years for something and that is to walk across the stage, and then a little thing like that shouldn't ruin that much,” said one of Reminga's friends.
“I don't think that they should go straight out of high school with these criminal records that's going to make them not get a job, get into college,” said Trinity Alexander.
Both the school and district offices were closed on Monday because of Memorial Day. We emailed the principal for a comment, but have not heard back.
Chopticon's graduation is on Wednesday. ||||| Students released hundreds of thousands of lady bugs at Chopticon High School as a senior prank. (Photo: Stephanie Ramirez, WUSA9)
MORGANZA, Md. (WUSA9) -- "You turn around the corner and all you see is ladybugs on the lights and a bunch of lady bugs on the lights," described Jerod Gaines, a Junior at Chopticon High School.
"Walking in, seeing a bunch of lady bugs squished and lying around," said Nick Hughes.
It sounds like a movie scene but the students are describing a high school senior prank, where 72,000 ladybugs were let loose into Chopticon High School in St. Mary's County, Maryland.
Police said five of the students forced their way into the high school while another two waited in a car in the early hours of May 20, 2015. The ladybugs were apparently purchased online.
Students and school staff discovered the swarming senior prank later that morning.
"Everybody got a good laugh out of it, I don't really see what the big deal is about it," Kyle Fisher a student at the school said.
However, school officials did not find it as amusing. The seven students involved are facing charges and two of them were banned from walking at graduation according to other students at the school, who decided to protest early Tuesday.
"A lot of us thought it was unfair how they weren't allowed to walk after they worked so hard all of high school and just to have it taken away because of a harmless senior prank," said Fisher.
School officials don't see the prank as harmless. St. Mary's County Public Schools Director of Safety and Security, Mike Wyant told WUSA they expect senior pranks and measure the severity of the prank based on certain criteria, including whether there was any damage to property.
"This is moderately serious," said Wyant, "the biggest thing for me is, 3 o'clock in the morning, forcible entry into a school building …"
Officials also weigh each student's participation individually, Wyant said.
"I think it broke the AC unit, so I know about that … janitors had to come from other schools," said Hughes.
Wyant could not confirm the air conditioner but did say they had to pay for staff members to remove the bugs.
By the afternoon, Wyant confirmed only one senior will be banned from graduation. He does not think the school will budge and allow this senior to participate despite the student protest.
"Just be careful about making your decisions," he said of those looking to pull a senior prank in the future.
Four of the alleged pranksters are juveniles. Police charged them with 4th Degree Burglary, Property Destruction Under $1,000, and Disruption of School Activities. The four suspects were released to the custody of their parents after being processed.
The three remaining alleged pranksters are adult males. Police said they will be charged by criminal summons.
Students plan to protest again Tuesday night at the Board of Education meeting. They still say it is unfair only one senior is not allowed to walk.
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Read or Share this story: http://on.wusa9.com/1HHbWi1 | – A new entry in the senior-prank-gone-awry category: A number of Maryland high school students found themselves on the wrong side of the law after allegedly breaking into their high school at 3:40am Wednesday and dispersing 72,000 ladybugs. The St. Mary's County Sheriff's Office has identified seven suspects: Police say five mask- and hoodie-clad males broke into Chopticon High School by busting in a door, triggering an alarm; two others remained in the car. My Fox DC reports six were seniors at the school and one was an alumnus. NBC Washington reports the ladybugs were purchased online. Four are juveniles and have been hit with fourth-degree burglary, property destruction under $1,000, and disruption of school activities charges, reports WUSA-TV; the other three will be charged as adults by criminal summons. There also have been consequences at the school, consequences some students are protesting as unfair: They say one male who was involved got the green light to play in the baseball state championship game post-prank, but that the class president is being barred from giving a speech at tomorrow's graduation. (An entire Ohio school district was forced to cancel school this month over a prank.) |
tori are nodular protuberances of mature bone , the exact designation of which depends on anatomic region.1 torus palatinus ( tp ) is an exostosis of the hard palate localized along the median palatine suture , involving both the processi palatini and the os palatinum .
it contains compact and cancellous bone and is formed by the hypertrophy of the spongy and oral compact layers , the nasal compact layer remain unchanged.2 it is generally accepted as an anatomical variation rather than a pathological condition.3 tp forms different shapes as flat , nodular , spindle and lobular ( figure 1)4,5 and is often detected in young adults and middle - aged people.68 tp is asymptomatic , grows slowly during the second and third decades of life and often goes unnoticed until middle age.911 although , tp is not pathologically significant , surgical removal is required if it causes chronic trauma or interfere with oral function or with the replacement of a denture base or framework.3 although a large number of researches have tried to clarify the influence of genetic,8,9 environmental,7,12 nutritional , and climatologic factors , there is still no consensus on the etiology of tp .
the prevalence of tp ranges from 1.4 to 66.0% in different populations ( table 1),24,69,1326 and it was reported between 20.945.4% in turkish populations.19,22,26 it was also found that females have a higher prevalence of tp.3,4,6,7,9,1315,18,19,21,23,26,27 the aims of this study were to determine the prevalence , size , shape and location of tp and to investigate the relationship between the findings in relation to age and gender in cappadocia region population .
a total of 2660 dental patients admitted to the faculty of dentistry , erciyes university from cappadocia region of turkey .
the subjects were stratified into six age groups : 1319 , 20 29 , 30 39 , 40 49 , 50 59 and 60 years and older .
the examination of the tp was assessed by clinical inspection and palpation , performed by the same author .
for the diagnosis , tp was defined as a raised bony exostosis in the midline of the hard palate .
the maximum elevation of the outgrowth of tp , usually in consistent with width and length,3 was applied for the measurement of the size of tp and graded according to previous description21,26 as more or less than 2 cm .
the shape of tp was classified as flat , nodular , spindle and lobular according to jainkittivong et al.4 the locations of tp were classified as incisors , incisors - premolars , premolars - molars , molars , and incisors - premolars molars .
the observed results were analyzed with spss 11.0 ( statistical package for social science inc . ,
the observed results were analyzed with spss 11.0 ( statistical package for social science inc . ,
the mean age was 33.015.1 years with the ages ranging from 13 to 85 years .
there were 591 ( 22.2% ) subjects in the 1319 year , 693 ( 26.0% ) subjects in the 2029 year , 508 ( 19.1% ) subjects in the 3039 year , 437 ( 16.4% ) subjects in the 40 49 year , 277 ( 10.4% ) subjects in the 50 59 year and 154 ( 5.8% ) subjects in the 60 years and older groups ( table 2 ) .
it was found to be significantly higher ( p<.001 ) in females ( 5.7% ) than in males ( 1.8% ) . the highest tp prevalence ( 7.1% )
the prevalence of tp in females was higher than in males in terms of all age groups ( except 1319 years age group ) .
the distribution of tp size according to gender and age is shown in table 3 .
of the 110 tp cases the mostly ( 75.4% ) were smaller than 2 cm .
the age and gender differences in the distribution pattern of tp according to size were not statistically significant ( p>.05 ) .
table 4 shows the location of tp on the hard palate in 110 subjects in relation to age .
the most common tp was found at the premolar - molar region ( 66.4% ) , followed by molars ( 15.4% ) and premolars regions ( 13.6% ) .
the less common locations were at incisor premolar and incisor - premolar - molar regions ( 4.5% ) .
other less common shapes of tp were spindle ( 36.3% ) , nodular ( 0.9% ) and lobular ( 0.0% ) .
there was no significant difference found in tp shape between females and males ( p>.05 ) .
there are many studies showing the tp prevalence ranges from 1.4 to 66.0% in different populations.24,69,1326 a turkish study22 was performed in 80 dry skulls , reported a high prevalence ( 45.4% ) of tp . in other study,26
the prevalence of tp was 30.9% in 1943 school children ( 515 years old ) .
cagirankaya et al19 pointed out that the prevalence of tp was 20.9% in consecutive 253 subjects ( 1749 years old ) . according to our knowledge ,
this is the most detailed study in terms of the subject number ( n=2660 ) and the age range ( 1385 years old ) investigating tp prevalence in turkish population .
the tp prevalence in this study ( 4.1% ) was lower in comparison to most of the other studies.24,69,1317,1924,26 the same low prevalence ( 3.9% ) was found by bruce et al18 in 926 dental patients in the ghanaian community .
however , it was showed that there is a high prevalence of tp in other studies such as 21.0% in the young and adult population of israelis,21 and in 20.9% of the united states population24 and in the norway study ( 32.7%).6 it was thought that environmental , genetic and functional factors are important for these prevalences .
a less tp prevalence was found at gizan region , saudi arabia ( 1.4%).25 this study may reveal that racial differences are much more important for the prevalence . in turkish population , yildiz et al26 investigated tp prevalence in 1943 school children and showed a higher prevalence ( 30.9% ) in comparison to the present study .
all the school children were 515 years old , but our patients were 1385 years old .
the number of our subjects ( 2660 ) is higher than that study . in the other study,19
it was showed that the prevalence of tp was 20.9% in consecutive 253 subjects ( 1749 years old ) .
all these reports including our study were performed in the different regions and populations of turkey .
it may suggest that these prevalence differences may be due to age , regional and dietary factors .
it was reported that among similar ethnic groups living in different areas,6,16 or different ethnic groups living in same areas21,28 have various prevalences of tp .
a huge number of investigators have evaluated the effects of environmental,7,12 and genetic factors8,9 including masticatory stress,7,8,23 and nutritional6 factors .
the prevalence of tp within the same race reported by different authors varies greatly ( table 1 ) .
the inconsistent results of various authors possibly are due to the difference of the number of subjects , different geographic location , and standards .
it was suggested that saltwater fish consumption in norway possibly supplies higher levels of polyunsaturated fatty acids and vitamin d which is involved in bone growth and this may increase the prevalence of tori .
belsky et al30 showed that the presence and especially the size of tp is correlated with increased bone mineral density .
genetic factors may be the probable causes of the low tp prevalence in turkish population .
seafood consumption is not as common in the cappadocia region population as in the other parts of the world having water sources .
the tp prevalence obtained from dry skulls was always higher than those from living subjects.3,22 woo3 studied five series of adult skulls and reported the tp prevalence ranging 38 to 66.5% .
gzil et al22 investigated 80 dry skulls , and reported a high prevalence ( 45.4% ) of tp in turkish population .
this high prevalence may be due to a detailed and easy examination of dry skulls in terms of tp .
in the present study , the tp prevalence was significantly higher in females ( 5.7% ) than in males ( 1.8% ) ( p<.001 ) .
singaporean study is the only study that shows the same frequency of tp in both sexes.20 the findings of our study that the prevalence of tp was higher in females than in males is consistent with other studies.3,4,6,7,9,11,1315,18,19,21,23,26,27 there is no certain explanation for this difference , but genetics may be suggested as a major factor .
earlier studies3,7,13,17 revealed higher tp prevalences during the second and third decades of life , whereas in our present study , it was higher during the sixth decade .
the high prevalence of tp among the 60 years and older age group in our study should not be taken into consideration as an important finding because the sample of that age group is not large and might not reflect the true prevalence . in our study ,
most of tp was smaller than 2 cm ( 75.4% ) , and located in premolar - molar area ( 66.4% ) .
yildiz et al26 reported that 91.5% of tp smaller than 2 cm , and 62% located in molar area in 515 age group .
king and more31 who studied 400 individuals from the united states and united kingdom reported that 67% of tp smaller than 2 cm .
hashim et al32 revealed that the prevalence of tp larger than 2 cm was much greater than that of smaller .
as hashim et al32 studied groups from the malaysian ethnic group ; it is possible that size may be associated with ethnicity .
most of the studies,2,17,24,33,34 in agreement with the present study , showed that flat tp is the most common type , but reichart et al8 and jainkittivong et als4 studies reported spindle tp .
it may suggest that ethnic differences in terms of tp shape do exist or not need further investigations .
the prevalence of tp in our sample was low in comparison to other turkish population .
most tp were found in flat shape ( 62.7% ) , smaller than 2 cm ( 75.4% ) and located at premolar - molar region ( 66.4% ) . according to the literature
, it was firstly showed that flat tp was the most common type in our large population .
the present study supports that the etiology of tp are a combination of multifactorial genetic and environmental factors . | objectivesthe objectives of this study were to determine the prevalence , size , shape and location of the torus palatinus ( tp ) in dental outpatients in cappadocia region of turkey and to investigate the relationship between the findings in relation to age and gender.methodsthe present study included 2660 patients , who attended the department of oral diagnosis and radiology in the faculty of dentistry at erciyes university for their dental problems between december 2005 and may 2007 . the presence or absence of tp
was examined by clinical inspection and palpation.resultsthe prevalence of tp in our large sample was low ( 4.1% ) in comparison to other turkish population .
it was found to be significantly higher ( p<.001 ) in females ( 5.7% ) than in males ( 1.8% ) .
most tp were found in flat shape ( 62.7% ) , smaller than 2 cm ( 75.4% ) and located at premolar - molar region ( 66.4%).conclusionsthis study indicated that the prevalence of tp in turkish population was low .
our results showed a significant relationship between the occurrence of tp and gender . according to the literature
, it was firstly showed that flat tp was the most common type in our large population . |
The man arrested in connection with the deaths of seven women whose bodies were found over the weekend across northwest Indiana was charged Monday in one of the cases.
Darren Deon Vann, 43, of Gary, was charged with one count of murder, as well as murder in the perpetration of a robbery and robbery resulting in serious bodily harm, all related to the death of 19-year-old Afrikka Hardy.
Though Vann hasn't yet been charged in the deaths of the other six women, Mayor Thomas McDermott Jr. told reporters Vann is "what I would label a serial killer."
Hammond Police Chief John Doughty said Vann met Hardy last Friday in a room at a Motel 6 on the 3800 block of 179th Street in Hammond after arranging a sexual encounter online. Hardy had been strangled, and Hammond Police Lt. Richard Hoyda said Sunday that as part of the investigation into her death, police served a search warrant on a home on 49th Avenue in Gary, where Vann was taken into custody.
According to a probable cause affidavit, Hardy's naked body was found in a bathtub with what appeared to be a black piece of clothing covering her arms and around her neck.
While being questioned, Doughty said Vann came forward with information about six other dead women, all in Gary. Aside from Hardy, three of the victims were publicly identified by midday Monday: 35-year-old Anith Jones, 28-year-old Teairra Batey, and 36-year-old Christine Williams.
"During his initial arrest in the city of Gary, Mr. Vann told Hammond police officers at the scene that he had 'messed up' by committing the crime in Hammond and was surprised at how quickly he was located after the incident," Doughty said.
Doughty said Vann has been a registered sex offender in Texas since a September 2009 conviction.
He did not rule out the possibility that the ongoing investigation would reveal more victims.
"It could go back as far as 20 years, based on some statements we have," Doughty said.
Police discovered Jones' body at around 11:20 p.m. Saturday. Her family had recently reported her missing, and a group of about 30 Gary police officers searched the 4900 block of Louisiana Street, where her car was found sitting in a driveway of an abandoned house, looking for her. She had been missing since Oct. 8.
Jones’ sister, Yolanda Nowell, did not wish to speak Sunday afternoon, but said last week that her sister was "very street savvy."
Jones had a stand at the 41st Avenue and Calumet Street flea market, Nowell said, and had moved from Chicago to Northwest Indiana about 10 years ago. She was one of seven siblings.
Police then discovered Batey's body at around 1 a.m. Sunday in the 1800 block of E. 19th Avenue. She was found wearing a green hooded sweatshirt and blue jeans.
A third body was found in the 2200 block of Massachusetts Street at 1:50 a.m. Sunday. The woman was found wearing a pair of blue jeans and white Nike shoes.
Late Sunday, the coroner’s office confirmed the discovery of three additional women.
Williams was found at about 7:50 p.m. in the 4300 block of Massachusetts Street in Gary, according to the coroner’s office. Hours later, at 10:05 p.m., two additional female bodies were discovered in the 400 block of East 43rd Avenue in Gary.
Two of the areas in which police found bodies were similar in that they contained blocks comprised of badly blighted, sometimes fire-damaged abandoned houses. The house near where Jones was found is the only one in a thriving neighborhood, although the exact house is camouflaged behind grass and weeds at least 5-feet tall.
Hammond Mayor Thomas McDermott Jr. said in two Facebook posts Sunday afternoon that the man, who he called a serial killer, has “admitted to a couple of homicides in Hammond,” some of which date back 20 years. He also said in his posts that the man is a convicted sex offender.
Gary Cpl. Gabrielle King tried to defuse concerns among citizens, noting that the man is in custody and that Gary and Hammond police are working together to bring charges.
“We would like to dispel the rumor that there is a serial killer on the loose. There is a 43-year-old man in the custody of The Hammond Police Department, who led officials to 3 deceased female victims who has claimed responsibility for their demise. Gary Police are closely working with Hammond Police to assist in covering every area of the investigation needed to pursue charges as expeditiously as possible,” the statement read.
In a joint statement, Gary Mayor Karen Freeman-Wilson and Gary Chief Larry McKinley asked for calm and patience.
“We commend the officers for their work thus far and ask the citizens to remain calm and patient as our teams work this investigation and do what they do best,” their statement said.
On two Facebook posts, McDermott praised the Hammond Police Department’s investigation in the case, especially as it comes soon after a lawsuit filed against the department claiming several officers used excessive force and falsely arrested a man during a traffic stop.
“As you hear the details of this grisly murder in a Hammond motel room and discover how this murder was solved by our police, it will make you proud of the Hammond PD,” McDermott wrote. “...Hammond, and NWI, are safer today because this murder case was solved. Our condolences and prayers go out to the victims, and to the families of the victims.”
Copyright SunTimes / NBC Chicago ||||| GARY, Ind. (AP) — The bodies of seven women have now been found in northwestern Indiana after a man confessed to killing one woman who was found strangled at a motel and leading investigators to least three other bodies, authorities said Monday.
The Lake County coroner's office said three of the bodies were found Sunday night at two locations in Gary, in addition to the four bodies found earlier over the weekend. The coroner's office called the new deaths homicides, with one victim strangled and unspecified injuries for the other two women.
It wasn't immediately clear Monday whether the man directed police to the three bodies Sunday night. Phone and email messages seeking comment from Gary police spokeswoman Cpl. Gabrielle King weren't immediately returned.
Police said Sunday that a 43-year-old man confessed to killing a woman whose body was found in a Motel 6 in the neighboring city of Hammond and told investigators where the bodies of three other women could be found in Gary. Those women were found late Saturday and early Sunday.
Gary police found the bodies of three women at different locations in Gary late Saturday and early Sunday, following up on information the man provided during questioning, Hammond police Lt. Rich Hoyda said Sunday. The county coroner's office on Sunday identified the victim found in Hammond as 19-year-old Afrika Hardy and ruled she had been strangled.
The coroner's office said a second victim had been identified by family members as 35-year-old Anith Jones of Merrillville. Autopsies had not yet been completed on her or the other two women, who have not yet been identified. Jones had been missing since Oct. 8, and Gary police had recently searched a block looking for her, the Post-Tribune of Merrillville reported.
Police discovered Hardy's body about 9:30 p.m. Friday at a Motel 6.
"A friend of the deceased called us, and she was concerned when she didn't respond to her calling," Hoyda said. "We were sent there and found that person dead."
Police investigating her death obtained a search warrant for a home and vehicle in Gary. Police conducted the search Saturday afternoon and took the man into custody. Hoyda said the man confessed during questioning and then told investigators "where several other female victims of possible homicide were located."
Hoyda wouldn't comment on how the man knew the women, on a possible motive or on whether the man confessed to killing any of the other women.
Hoyda said the man's name wasn't being released because he had not yet been formally charged. He would not say when charges will be filed. He was being held in the Hammond City Jail. ||||| Murder and robbery charges filed against suspect in NW Indiana slayings Sun-Times Media
Darren Deon Vann | Lake County, Indiana, sheriff's office
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HAMMOND, Ind. — Police believe a suspect in seven murders in Northwest Indiana used an online prostitution service to lure some of those women to several locations in Hammond and Gary — typically abandoned buildings — before they were killed.
Murder and robbery charges were filed Monday afternoon against Darren Deon Vann, 43, in the death of 19-year-old Afrika Hardy, who was found strangled to death on Friday night at a Motel 6 at 3840 179th St. in Hammond.
Detectives from Hammond and Gary are still gathering evidence to charge him in six other killings. Vann was convicted of sexual assault in Texas in September 2009, and is listed on the Indiana sex offender registry.
At a Monday news conference, Hammond Police said Vann apparently solicited prostitution services on Chicagobackpage.com and arranged a meeting at the motel. The female facilitator of the transaction tried to contact Hardy on Friday night, but she received suspicious text responses she believed were from Vann. She sent a man to see what was wrong and he found Hardy dead, police said.
The facilitator provided police with Vann’s phone number and that’s how police were able to locate him. Police executed a search warrant in Gary on Saturday and arrested Vann, police said.
Vann was charged in Lake Superior Court with murder, murder in perpetration of a robbery and robbery resulting in serious bodily injury after he admitted he met Afrika Hardy for sex at the Hammond Motel 6, where her body was found in the bathtub at about 9:27 p.m. Friday.
Vann had sought the services of the escort “Octavia,” who was Hardy, the night before her death, but he’d contacted her and said he couldn’t get a babysitter. The witness told police Hardy the same man who used the name “Big Boy Appetite,” called Friday to meet her, the probable cause affidavit states. He arrived at about 5:13 p.m. The witness told police she’d tried to call Hardy five to eight times afterward, but got no response, so she went to the motel with a friend and discovered Hardy dead. Her cell phone, which had a pink cover, was missing.
Surveillance footage showed a man later identified as Vann arriving at the motel and later running from the room to a 2013 blue Jeep, which drove away. The SUV was registered to Vann’s sister in the 600 block of West 49th Avenue in Gary, where police set up surveillance, the probable cause affidavit states.
Inside the room was a broken finger nail, a light-colored shirt button and torn condom wrapper.|
A search warrant at his sister’s residence, where Vann was arrested, netted a white glove, key to the Jeep, an Indiana Sex Registry sheet with Vann’s name on it, listing him as a sex offender through Lake County, and a gray puffy jacket and dark-colored hooded sweatshirt that looked similar to the man in the motel surveillance footage. Inside the hoodie was a pack of condoms that were the same brand and style as a wrapper found in the motel room. Police also found a cell phone in a pink case similar to the one described by the witness, and a shirt with a missing button that matched the button from the motel floor, records state.
In a statement to police, Vann admitted he met “Octavia” at the motel where her body was found after driving his sister’s Jeep there. They had sex, which got rough, and Hardy began to fight with him. Vann told police he strangled the woman with his hands and then an extension cord before placing her in the bathtub and leaving in his sister’s Jeep. He admitted he used white gloves during the killing and that the brown extension cord was used to kill Hardy, court records state.
Upon his arrest, Vann told police he had “messed up” and was surprised he was located so quickly.
Hardy turned out to be the first of seven women who would be found dead this weekend across northwest Indiana.
Once in custody, officials said, Vann provided information on where police could find three more bodies.
Hammond Chief John Doughty told reporters that Vann is cooperating with police and that Hammond authorities are pursuing charges against him in the death of Afrika Hardy, 19, whose body was found Friday.
But with the identities of most of the bodies not yet released, the Lake County Coroner’s office has received about 15 calls from family members of missing persons, a spokesman for the office said.
“We’ve got a pretty good idea of who these people are from all the work that detectives have done, but there will probably have to be some DNA testing done because several of the bodies are severely decomposed,” said a source at the office.
Vann was taken into custody after Hardy was found fatally strangled Friday night at a Motel 6 in the neighboring city of Hammond.
Vann was released from a Texas prison in July last year, after serving a 5-year sentence for sexually assaulting an Austin woman in his apartment, according to Texas Department of Criminal Justice spokesman Jason Clark.
Vann tried to strangle the woman, who was Hispanic, and struck her several times during the assault, Clark said. He served the full five years of his sentence.
Federal court records indicate Vann was denied time off for good behavior after a confrontation at a prison in Marlin, Texas. Vann sued prison officials for allegedly mishandling the incident, but the case was tossed out by a judge.
He remains on the Texas Department of Public Safety’s sex offender registry, but is described as a “low” risk on the department’s website.
Vann’s ex-wife was stunned Monday to learn he might be connected to a string of homicides.
“Oh my gosh, it would shock me,” said the woman, who said she was married to the suspect from 1995 to 2011 and didn’t want her name used. “I can’t see him doing that.”
The woman said she first met Vann in Hammond and married him in Texas. At the time, the suspect had recently been discharged from the U.S. Marines, she said, and had no criminal history that she knew about. The couple lived together in Indiana, she said.
“He always took care of me,” she said. “I never had any problems with him. He was never a violent person to me. He was sweet to me.”
Gary Mayor Karen Freeman-Wilson said authorities aren’t certain how long Vann has been in northwestern Indiana, although he does have a conviction for residential entry in the area. The mayor said she doesn’t know whether more bodies might be found.
The Lake County Coroner is expected to finish her examinations of the last of the seven bodies Monday afternoon.
A cousin of Hardy’s said the teen, who spelled her first name “Afrikka” on some social media sites, originally was from the Chicago area but had grown up in the Denver area, graduating from high school there. She recently had moved back to Chicago, the cousin said.
Police discovered the body of Anith Jones, 35, of Merrillville, at 413 E. 43rd Ave., around 11:20 p.m. Saturday. Jones’ family had recently reported her missing, and a group of about 30 Gary police officers searched the 4900 block of Louisiana Street, where her car was found sitting in a driveway of an abandoned house. She had been missing since Oct. 8.
Monday, one of Jones’ sisters, Yolanda Nowell, said she’s glad to hear police have someone in custody and said she wanted to be “left alone to grieve.”
“She was a kind, loving woman,” Nowell said of her sister. “She was my favorite sister. She was everybody’s favorite aunt.”
Jones had a stand at the 41st Avenue and Calumet Street flea market, Nowell said, and had moved from Chicago to Northwest Indiana about 10 years ago. She was one of seven siblings.
Police then discovered the third body around 1 a.m. Sunday in the 1800 block of East 19th Avenue. The woman was found wearing a green hooded sweatshirt and blue jeans.
She has since been identified as Teaira Batey, 28, of the 700 block of Martin Luther King Drive in Gary, the Lake County Coroner’s office said Monday.
A fourth body was found in the 2200 block of Massachusetts Street at 1:50 a.m. Sunday. The woman was found wearing a pair of blue jeans and white Nike shoes.
Late Sunday, the coroner’s office confirmed the discovery of three additional Jane Does.
At 7:50 p.m., a female body was discovered in the 4300 block of Massachusetts Street in Gary, according to the coroner’s office.
Hours later, at 10:05 p.m., two additional female bodies were discovered in the 400 block of East 43rd Avenue in Gary.
-Contributing: Teresa Auch Schultz, Christin Nance Lazerus, Michelle L. Quinn, Lori Caldwell, Carole Carlson, Mitch Dudek and Stefano Esposito | – After Afrika Hardy, 19, was found strangled to death in a motel room in Hammond, Indiana, on Friday night, police took a man into custody. The 43-year-old admitted to the killing, then provided information that led police to the bodies of three more women in separate locations in nearby Gary, reports NBC Chicago. Two of the bodies were found in areas full of abandoned, fire-damaged houses, while a third was found in a "thriving" neighborhood in a house that was obscured by 5-foot-tall grass and weeds, reports the Chicago Sun-Times. And the count didn't stop at three new bodies: Police last night found three more in abandoned homes in Gary, though it's not clear if the man directed police to them, the AP notes. The suspect is from Gary but is a convicted sex offender in Austin, Texas, reports WGN. Gary Mayor Karen Freeman-Wilson says several law enforcement agencies are now investigating the case. "We have evidence that he was in Texas and all over the United States," she says. "I would like them to complete the investigation, and I don't want to taint it with the prospect of calling this person a serial killer." Hammond's mayor was a little looser on Facebook, calling the suspect "an admitted serial killer" who "also admitted to a couple of homicides in Hammond back in '94 or '95." The man is still being questioned by police, who are expected to formally charge him and release his name later today. |
SECTION 1. SHORT TITLE.
This Act may be cited as the ``Railroad Antitrust Enforcement Act
of 2006''.
SEC. 2. INJUNCTIONS AGAINST RAILROAD COMMON CARRIERS.
The proviso in section 16 of the Clayton Act (15 U.S.C. 26) ending
with ``Code.'' is amended to read as follows: ``Provided, That nothing
herein contained shall be construed to entitle any person, firm,
corporation, or association, except the United States, to bring suit
for injunctive relief against any common carrier that is not a railroad
subject to the jurisdiction of the Surface Transportation Board under
subtitle IV of title 49, United States Code.''.
SEC. 3. MERGERS AND ACQUISITIONS OF RAILROADS.
The sixth undesignated paragraph of section 7 of the Clayton Act
(15 U.S.C. 18) is amended to read as follows:
``Nothing contained in this section shall apply to transactions
duly consummated pursuant to authority given by the Secretary of
Transportation, Federal Power Commission, Surface Transportation Board
(except for agreements described in section 10706 of title 49, United
States Code, and transactions described in section 11321 of that
title), the Securities and Exchange Commission in the exercise of its
jurisdiction under section 10 (of the Public Utility Holding Company
Act of 1935), the United States Maritime Commission, or the Secretary
of Agriculture under any statutory provision vesting such power in the
Commission, Board, or Secretary.''.
SEC. 4. LIMITATION OF PRIMARY JURISDICTION.
The Clayton Act is amended by adding at the end thereof the
following:
``Sec. 29. In any civil action against a common carrier railroad
under section 4, 4C, 15, or 16 of this Act, the district court shall
not be required to defer to the primary jurisdiction of the Surface
Transportation Board.''.
SEC. 5. FEDERAL TRADE COMMISSION ENFORCEMENT.
(a) Clayton Act.--Section 11(a) of the Clayton Act (15 U.S.C.
21(a)) is amended by striking ``subject to jurisdiction'' and all that
follows through the first semicolon and inserting ``subject to
jurisdiction under subtitle IV of title 49, United States Code (except
for agreements described in section 10706 of that title and
transactions described in section 11321 of that title);''.
(b) FTC Act.--Section 5(a)(2) of the Federal Trade Commission Act
(15 U.S.C. 44(a)(1)) is amended by striking ``common carriers subject''
and inserting ``common carriers, except for railroads, subject''.
SEC. 6. EXPANSION OF TREBLE DAMAGES TO RAIL COMMON CARRIERS.
Section 4 of the Clayton Act (15 U.S.C. 15) is amended by--
(1) redesignating subsections (b) and (c) as subsections
(c) and (d), respectively; and
(2) inserting after subsection (a) the following:
``(b) Subsection (a) shall apply to common carriers by rail subject
to the jurisdiction of the Surface Transportation Board under subtitle
IV of title 49, United States Code, without regard to whether such
railroads have filed rates or whether a complaint challenging a rate
has been filed.''.
SEC. 7. TERMINATION OF EXEMPTIONS IN TITLE 49.
(a) In General.--Section 10706 of title 49, United States Code, is
amended--
(1) in subsection (a)--
(A) in paragraph (2)(A), by striking ``, and the
Sherman Act (15 U.S.C. 1 et seq.),'' and all that
follows through ``or carrying out the agreement'' in
the third sentence;
(B) in paragraph (4)--
(i) by striking the second sentence; and
(ii) by striking ``However, the'' in the
third sentence and inserting ``The''; and
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and
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``(e) Application of Antitrust Laws.--
``(1) In general.--Nothing in this section exempts a
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(A) by striking ``The authority'' in the first
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inserting ``is exempt from all other law (except the
antitrust laws referred to in subsection (c)),''; and
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``(c) Application of Antitrust Laws.--
``(1) In general.--Nothing in this section exempts a
transaction described in subsection (a) from the application of
the Sherman Act (15 U.S.C. 1 et seq.), the Clayton Act (15
U.S.C. 12, 14 et seq.), the Federal Trade Commission Act (15
U.S.C. 41 et seq.), section 73 or 74 of the Wilson Tariff Act
(15 U.S.C. 8-9), or the Act of June 19, 1936 (15 U.S.C. 13,
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any such transaction for the purpose of any provision of law
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agency shall take into account, among any other considerations,
the impact of the transaction on shippers and on affected
communities.''.
(c) Conforming Amendments.--
(1) The heading for section 10706 of title 49, United
States Code, is amended to read as follows: ``Rate
agreements''.
(2) The item relating to such section in the chapter
analysis at the beginning of chapter 107 of such title is
amended to read as follows:
``10706. Rate agreements.''. | Railroad Antitrust Enforcement Act of 2006 - Amends the Clayton Act to grant the United States exclusive authority to bring suit for injunctive relief against a common carrier that is not a rail common carrier subject to the jurisdiction the Surface Transportation Board (STB).
Revises the declaration that prohibitions against mergers and acquisitions that tend to create monopolies shall not apply to certain transactions duly consummated pursuant to specified federal authority. Excepts specified rate agreements between two or more rail carriers (collective rate agreements) and certain transactions, including railroad mergers and acquisitions, from specified antitrust exemptions.
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Empowers the Federal Trade Commission to regulate, and engage in antitrust enforcement regarding, collective rate agreements and certain transactions, including railroad mergers and acquisitions.
Applies to rail common carriers subject to STB jurisdiction requirements governing the amount of recovery or prejudgment interest (treble damages) by injured persons, without regard to whether: (1) such railroads have filed rates; or (2) a complaint has been filed that challenges a rate.
Amends federal transportation law to terminate the exemptions from antitrust laws for collective ratemaking agreements.
Requires the STB, and other reviewing agencies, when reviewing a proposed agreement, to take into account its impact upon shippers, consumers, and affected communities.
Revises STB authority to provide that a rail carrier, corporation, or a person participating in an approved transaction is not exempt from specified antitrust laws. |
sec : intro changes are inevitable in nature , and those that are most dramatic with often drastic consequences are the ones that occur _ all of a sudden_. a particular class of such changes comprises those in which the system during its temporal evolution makes a sudden jump ( a reset " ) to a fixed state or configuration .
many nonequilibrium processes are encountered across disciplines , e.g. , in physics , biology , and information processing , which involve sudden transitions between different states or configurations .
the erasure of a bit of information @xcite by mesoscopic machines may be thought of as a physical process in which a memory device that is strongly affected by thermal fluctuations resets its state ( 0 or 1 ) to a prescribed erasure state @xcite . in biology
, resetting plays an important role inter alia in sensing of extracellular ligands by single cells @xcite , and in transcription of genetic information by macromolecular enzymes called rna polymerases @xcite . during rna transcription ,
the recovery of rna polymerases from inactive transcriptional pauses is a result of a kinetic competition between diffusion and resetting of the polymerase to an active state via rna cleavage @xcite , as has been recently tested in high - resolution single - molecule experiments @xcite .
also , there are ample examples of biochemical processes that initiate ( i.e. , reset ) at random so - called _ stopping _ times @xcite , with the initiation at each instance occurring in different regions of space @xcite . in addition , interactions play a key role in determining when and where a chemical reaction occurs @xcite , a fact that affects the statistics of the resetting process . for instance , in the above mentioned example of recovery of rna polymerase by the process of resetting , the interaction of the hybrid dna - rna may alter the time that a polymerase takes to recover from its inactive state @xcite .
it is therefore quite pertinent and timely to study resetting of mesoscopic systems that evolve under the influence of external or conservative force fields .
simple diffusion subject to resetting to a given location at random times has emerged in recent years as a convenient theoretical framework to discuss the phenomenon of stochastic resetting @xcite .
the framework has later been generalized to consider different choices of the resetting position @xcite , resetting of continuous - time random walks @xcite , lvy @xcite and exponential constant - speed flights @xcite , time - dependent resetting of a brownian particle @xcite , and in discussing memory effects @xcite and phase transitions in reset processes @xcite .
stochastic resetting has also been invoked in the context of many - body dynamics , e.g. , in reaction - diffusion models @xcite , fluctuating interfaces @xcite , interacting brownian motion @xcite , and in discussing optimal search times in a crowded environment @xcite . however , little is known about the statistics of stochastic resetting of brownian particles that diffuse under the influence of force fields @xcite , and that too in presence of a rate of resetting that varies in space . in this paper
, we study the dynamics of overdamped brownian particles immersed in a thermal environment , which diffuse under the influence of a force field , and whose position may be stochastically reset to a given spatial location with a rate of resetting that has an essential dependence on space . we propose a novel technique that allows to obtain exact expressions for the transition probability prior to the first reset , the first reset - time distribution , and , most importantly , the stationary spatial distribution of the particle . our technique is based on the feynman - kac formalism of treating stochastic processes @xcite , and consists in a mapping of the dynamics of the brownian resetting problem to a suitable quantum mechanical evolution in imaginary time . to demonstrate the potential of our technique , we consider several different stochastic resetting problems , see fig .
[ fig : fig1 ] : i ) free brownian particles subject to a space - independent rate of resetting ( fig .
[ fig : fig1]a ) ) ; ii ) free brownian particles subject to resetting with a rate that depends quadratically on the distance to the origin ( fig . [
fig : fig1]b ) ) ; and iii ) brownian particles trapped in a harmonic potential and undergoing reset events with a rate that depends on the energy of the particle ( fig .
[ fig : fig1]c ) ) . in this paper
, we consider for purposes of illustration the corresponding scenarios in one dimension , although our general technique of analysis may be extended to higher dimensions .
remarkably , our method provides exact expressions in all cases , and , notably , in cases ii ) and iii ) , where a standard treatment of analytic solution by using the fokker - planck approach seems daunting , and whose relevance in physics may be further explored in the context of , e.g. , optically - trapped colloidal particles and hopping processes in glasses and gels . in presence of a conservative potential @xmath0 .
the particle traces a stochastic trajectory ( black curve ) in the two - dimensional space until its position is reset at a random instant of time to its initial value ( orange arrow ) ; subsequent to the reset , the particle resumes its stochastic motion until the next reset happens . the rate of resetting @xmath1 ( left colorbar ) may depend on the position of the particle .
we study three different scenarios : * a ) * resetting of brownian particles under a space - independent rate of resetting ; * b ) * resetting of free brownian particles under a space - dependent rate of resetting ; * c ) * resetting of brownian particles moving in force fields under a space - dependent rate of resetting.,scaledwidth=110.0% ] fig : fig1
sec : general - formalism sec : model consider an overdamped brownian particle diffusing in one dimension @xmath2 in presence of a time - independent force field @xmath3 .
we consider a general scenario where the force may have both conservative and non - conservative components , @xmath4 , with @xmath5 denoting a potential energy landscape , and @xmath6 being an external non - conservative force .
the dynamics of the particle is described by a langevin equation of the form = f(x)+(t ) , eq : eom where @xmath7 is the mobility of the particle , defined as the velocity per unit force . in eq .
( [ eq : eom ] ) , @xmath8 is a gaussian white noise , with the properties ( t)=0 , ( t)(t)=2d(t - t ) , where @xmath9 denotes average over noise realizations , and @xmath10 is the diffusion coefficient of the particle , with the dimension of length - squared over time .
we assume that the einstein relation holds : @xmath11 , with @xmath12 being the temperature of the environment , and with @xmath13 being the boltzmann constant .
in addition to the dynamics ( [ eq : eom ] ) , the particle is subject to a stochastic resetting dynamics with a space - dependent resetting rate @xmath14 , whereby , while at position @xmath2 at time @xmath15 , the particle in the ensuing infinitesimal time interval @xmath16 either follows the dynamics ( [ eq : eom ] ) with probability @xmath17 , or resets to a given reset destination @xmath18 with probability @xmath19 .
our analysis holds for any arbitrary reset function @xmath14 , with the only obvious constraint @xmath20 ; moreover , the formalism may be generalized to higher dimensions . in the following , we consider the reset location to be the same as the initial location @xmath21 of the particle , that is , @xmath22 .
a quantity of obvious interest and relevance is the spatial distribution of the particle : what is the probability @xmath23 that the particle is at position @xmath2 at time @xmath15 , given that its initial location is @xmath21 ? from the dynamics given in the preceding paragraph , it is straightforward to write the time evolution equation of @xmath23 : & & = -+d + & & -r(x)p(x , t|x_0,0)+y r(y)p(y , t|x_0,0)(x - x_0 ) , eq : timevolution where the first two terms on the right hand side account for the contribution from the diffusion of the particle in the force field @xmath3 , while the last two terms stand for the contribution owing to the resetting of the particle : the third term represents the loss in probability arising from the resetting of the particle to @xmath21 , while the fourth term denotes the gain in probability at the location @xmath21 owing to resetting from all locations @xmath24 . when exists , the stationary distribution @xmath25 satisfies & & 0=-+d + & & -r(x)p_st(x|x_0)+y r(y)p_st(y|x_0)(x - x_0 ) .
eq : stationary it is evident that solving for either the time - dependent distribution @xmath23 or the stationary distribution @xmath25 from eqs .
( [ eq : timevolution ] ) and ( [ eq : stationary ] ) , respectively , is a formidable task even with @xmath26 , unless the function @xmath14 has simple forms . for example , in ref .
@xcite , the authors considered a solvable example with @xmath27 , where the function @xmath14 is zero in a window around @xmath21 and is constant outside the window . in this work ,
we develop an alternative powerful approach to solve for both the time - dependent and the stationary spatial distribution , by invoking the path integral formalism of quantum mechanics .
as we will demonstrate below , the method allows to obtain exact expressions even in cases with nontrivial forms of @xmath3 and @xmath14 .
sec : quantities - of - interest here , we develop a hitherto unexplored quantum mechanical approach to discuss stochastic resetting . to proceed , let us first consider a representation of the dynamics in discrete times @xmath28 , with @xmath29 , and @xmath30 being a small time step .
the dynamics in discrete times involves the particle at position @xmath31 at time @xmath32 to either reset and be at @xmath18 at the next time step @xmath33 with probability @xmath34 or follow the dynamics given by eq .
( [ eq : eom ] ) with probability @xmath35 .
the position of the particle at time @xmath32 is thus given by x_i & = \
{ ll x_i-1+t(|f(x_i)+_i ) & with probability1-r(x_i-1)t , + x^(r ) & with probabilityr(x_i-1)t , + .
eq : dynamics where we have defined @xmath36 , and have used the stratonovich rule in discretizing the dynamics ( [ eq : eom ] ) , and where the time - discretized gaussian , white noise @xmath37 satisfies _ i_j=2d_ij , with @xmath38 a positive constant with the dimension of length - squared over time - squared . in particular , the joint probability distribution of occurrence of a given realization @xmath39 of the noise , with @xmath40 being a positive integer , is given by p[\{_i}]=()^n/2(-_i=1^n_i^2 ) .
eq : joint - distribution in the absence of any resetting and forces , the displacement of the particle at time @xmath41 from the initial location is given by @xmath42 , so that the mean - squared displacement is @xmath43 .
in the continuous - time limit , @xmath44 , keeping the product @xmath45 fixed and finite and equal to @xmath15 , the mean - squared displacement becomes @xmath46 , with @xmath47 .
sec : propagator what is the probability of occurrence of particle trajectories that start at position @xmath21 and end at a given location @xmath2 at time @xmath48 without having undergone any reset event ? from the discrete - time dynamics given by eq .
( [ eq : dynamics ] ) and the joint distribution ( [ eq : joint - distribution ] ) , the probability of occurrence of a given particle trajectory @xmath49 is given by & & p_noreset[\{x_i}]=det(j)()^n/2_i=1^n(-)_i=0^n-1(1-r(x_i)t ) .
+ here , the factor @xmath50 enforces the condition that the particle has not reset at any of the instants @xmath51 , while @xmath52 is the jacobian matrix for the transformation @xmath53 , which is obtained from eq .
( [ eq : dynamics ] ) as ( ) _ 1i , j n= ( cccc - & 0 & 0 & + -- & - & 0 & + & & & ) _ nn , with primes denoting derivative with respect to @xmath2 .
one thus has ( j ) & = ( ) ^n _ i=1^n(1- ) + & ( ) ^n(-_i=1^n ) , where in obtaining the last step , we have used the smallness of @xmath54 .
thus , for small @xmath54 , we get & & p_noreset[\{x_i}]= ( ) ^n/2_i=1^n(-- ) + & & _
i=0^n-1(-r(x_i)t ) + & & = ( ) ^n/2(-t_i=1^n ) + & & ( t ) .
eq : path-0 from eq .
( [ eq : path-0 ] ) , it follows by considering all possible trajectories that the probability density that the particle while starting at position @xmath21 ends at a given location @xmath2 at time @xmath15 without having undergone any reset event is given by & & p_noreset(x , t = nt|x_0,0 ) + & & = ( ) ^n/2(t ) + & & _
i=1^n-1_-^dx_i(-t_i=1^n ) . in the limit of continuous time
, defining x(t)_n()^n/2_i=1^n-1_-^dx_i , one gets the exact expression for the corresponding probability density as p_noreset(x , t|x_0,0)= _
x(0)=x_0^x(t)=xdx(t)(-_0^tdt [ + + r(x ) ] ) .
eq : p - no - reset-0 : invoking the feynman - kac formalism , we identify the path integral on the right hand side of eq .
( [ eq : p - no - reset-0 ] ) with the propagator of a quantum mechanical evolution in ( negative ) imaginary time due to a quantum hamiltonian @xmath55 ( see appendix ) , to get p_noreset(x , t|x_0,0)= ( _ x_0^x f(x ) dx)g_q(x ,-
it|x_0,0 ) , eq : pnoresq with g_q(x ,- it|x_0,0)x|(-h_qt)|x_0 , eq : qma where the quantum hamiltonian is h_q-+v_q(x ) , eq : quantum - hamiltonian the mass in the equivalent quantum problem is m_q , and the quantum potential is given by v_q(x)++r(x ) .
eq : quantum - potential note that in the quantum propagator in eq .
( [ eq : qma ] ) , the planck s constant has been set to unity , @xmath56 , while the time @xmath57 of propagation is imaginary : @xmath58 @xcite .
since the hamiltonian contains no explicit time dependence , the propagator @xmath59 is effectively a function of the time @xmath15 to propagate from the initial location @xmath21 to the final location @xmath2 , and not individually of the initial and final times .
we also note that the integral @xmath60 in the prefactor in eq .
( [ eq : pnoresq ] ) has to be understood in the midpoint or stratonovich sense @xcite . in the absence of non - conservative forces , so that @xmath61 , on using @xmath11 , the prefactor equals @xmath62 , where @xmath63 is the heat absorbed by the particle from the environment @xcite .
sec : prob - first - reset let us now ask for the probability of occurrence of trajectories that start at position @xmath21 and reset for the first time at time @xmath15 . in terms of @xmath64 , one gets this probability density as p_reset(t|x_0)=_-^dy r(y)p_noreset(y , t|x_0,0 ) , eq : pt - final since by the very definition of @xmath65 , a reset has to happen only at the final time @xmath15 when the particle has reached the location @xmath66 , where @xmath66 may in principle take any value in the interval @xmath67 $ ] . the probability density @xmath65 is normalized as @xmath68 .
sec : prob - distr knowing @xmath69 and @xmath65 is sufficient to obtain the spatial distribution of the particle at any time @xmath15 , as we now demonstrate .
the probability density that the particle is at @xmath2 at time @xmath15 while starting from @xmath21 is given by p(x , t|x_0,0)&=&p_noreset(x , t|x_0,0)+_0^t d _
-^y r(y)p(y , t-|x_0,0)p_noreset(x , t|x_0,t- ) + & = & p_noreset(x , t|x_0,0)+_0^t d r(t-|x_0)p_noreset(x , t|x_0,t- ) , eq : pxt - final where we have defined the probability density to reset at time @xmath15 as r(t|x_0)_-^y r(y)p(y , t|x_0,0 ) .
eq : ft - definition one may easily understand eq .
( [ eq : pxt - final ] ) as follows . the particle while starting from @xmath21 may reach @xmath2 at time @xmath15 by experiencing not a single reset ; the corresponding contribution to the spatial distribution is given by the first term on the right hand side of eq .
( [ eq : pxt - final ] ) .
the particle may also reach @xmath2 at time @xmath15 by experiencing the last reset event at time instant @xmath70 , with @xmath71 $ ] , and then propagating from the reset location @xmath22 to @xmath2 without experiencing any further reset , where the last reset may take place with rate @xmath72 from any location @xmath73 $ ] where the particle happened to be at time @xmath70 ; such contributions are represented by the second term on the right hand side of eq .
( [ eq : pxt - final ] ) .
the spatial distribution is normalized as @xmath74 for all possible values of @xmath21 and @xmath15 . multiplying both sides of eq .
( [ eq : pxt - final ] ) by @xmath14 , and then integrating over @xmath2 , we get r(t|x_0)&=&_-^x r(x)p_noreset(x , t|x_0,0 ) + & + & _ 0^t d r(t-|x_0 ) .
the square - bracketed quantity on the right hand side is nothing but @xmath75 , so that we get r(t|x_0)=p_reset(t|x_0)+_0^t d p_reset(|x_0)r(t-|x_0 ) .
eq : rt - definition taking the laplace transform on both sides of eq .
( [ eq : rt - definition ] ) , we get ( s|x_0)=_reset(s|x_0)+_reset(s|x_0)(s|x_0 ) , eq : rs - equation where @xmath76 and @xmath77 are respectively the laplace transforms of @xmath78 and @xmath65 . solving for @xmath76 from eq .
( [ eq : rs - equation ] ) yields ( s|x_0)=. eq : rs next , taking the laplace transform with respect to time on both sides of eq .
( [ eq : pxt - final ] ) , we obtain ( x , s|x_0,0)=(1+(s|x_0))_noreset(x , s|x_0 ) = , eq : pxs where we have used eq .
( [ eq : rs ] ) to obtain the last equality .
an inverse laplace transform of eq .
( [ eq : pxs ] ) yields the time - dependent spatial distribution @xmath23 .
sec : stat - distr on applying the final value theorem , one may obtain the stationary spatial distribution as p_st(x|x_0)=_s0s(x , s|x_0,0)=_s0s , eq : pst-0 provided the stationary distribution ( i.e. , @xmath79 ) exists .
now , since @xmath65 is normalized to unity , @xmath80 , we may expand its laplace transform to leading orders in @xmath81 as @xmath82 , provided that the mean first - reset time @xmath83 , defined as t _ reset _ 0^t
tp_reset(t|x_0 ) , is finite .
similarly , we may expand @xmath84 to leading orders in @xmath81 as @xmath85 , provided that @xmath86 is finite . from eq .
( [ eq : pst-0 ] ) , we thus find the stationary spatial distribution to be given by the integral over all times of the propagator prior to first reset divided by the mean first - reset time : p_st(x|x_0)=_0^t p_noreset(x , t|x_0,0 ) .
eq : pxstat - final
sec : applications subsec : constant - resetting let us first consider the simplest case of free diffusion with a space - independent rate of resetting @xmath87 , with @xmath88 a positive constant having the dimension of inverse time . here , on using eq .
( [ eq : pnoresq ] ) with @xmath27 , we have p_noreset(x , t|x_0,0)&=&g_q(x ,- it|x_0,0)=x|(-h_qt)|x_0 , eq : pnoreset - free - parabola where the quantum hamiltonian is in this case , following eqs .
( [ eq : quantum - hamiltonian]-[eq : quantum - potential ] ) , given by h_q=- + r ; m_q= , = 1 . since in the present situation ,
the effective quantum potential @xmath89 is space independent , we may rewrite eq .
( [ eq : pnoreset - free - parabola ] ) as : p_noreset(x , t|x_0,0)&=&(-rt)g_q(x ,-
it|x_0,0 ) , eq : pnoreset - constant - resetting-0 with g_q(x ,-
it|x_0,0)x|(-h_qt)|x_0 , where the quantum hamiltonian is now that of a free particle : h_q- ; m_q= , = 1
. eq : hq - free therefore , the statistics of resetting of a free particle under a space - independent rate of resetting may be found from the quantum propagator of a free particle , which is given by @xcite g_q(x,|x_0,0)= ( - ) .
eq : g - free - parabola plugging in eq .
( [ eq : g - free - parabola ] ) the parameters in eq . ( [ eq : hq - free ] ) together with @xmath58 , we have g_q(x ,-
it|x_0,0)=(- ) . eq : g - free - parabola - final using eq . ( [ eq : g - free - parabola - final ] ) in eq . ( [ eq : pnoreset - constant - resetting-0 ] ) , we thus obtain p_noreset(x , t|x_0,0)=(- ) , eq : pnoreset - constant - resetting and hence , the distribution of the first - reset time may be found on using eq .
( [ eq : pt - final ] ) : p_reset(t|x_0)&= & r ( -rt)_-^dx ( - ) + & = & r(-rt ) , eq : pt - constant - resetting which is normalized to unity : @xmath90 , as expected . using eq .
( [ eq : pt - constant - resetting ] ) , we get @xmath91 , so that eq .
( [ eq : rs ] ) yields @xmath92 .
an inverse laplace transform yields @xmath93 , as also follows from eq .
( [ eq : ft - definition ] ) by substituting @xmath94 and noting that @xmath95 is normalized with respect to @xmath66 .
next , the probability density that the particle is at @xmath2 at time @xmath15 , while starting from @xmath21 , is obtained on using eq .
( [ eq : pxt - final ] ) as p(x , t|x_0,0)&=&(-(x - x_0)^2/(4dt ) ) + & & + r _ 0^t d ( -(x - x_0)^2/(4d ) ) .
eq : pxt - constant - resetting taking the limit @xmath96 , we obtain the stationary spatial distribution as p_st(x|x_0)&= & r _ 0^ ( -r ) ( -(x - y)^2/(4d ) ) , eq;pxstat - constant - resetting which may also be obtained by using eqs . ( [ eq : pxstat - final ] ) and ( [ eq : pnoreset - constant - resetting ] ) , and also eq . ( [ eq : pt - constant - resetting ] ) that implies that @xmath97 . from eq .
( [ eq : pxt - constant - resetting ] ) , we obtain an exact expression for the time - dependent spatial distribution as & & p(x , t|x_0,0)= + & & + , + while eq .
( [ eq;pxstat - constant - resetting ] ) yields the exact stationary distribution as p_st(x|x_0)=(- ) , eq : pxstat - constant - resetting - final where @xmath98 is the complementary error function . the stationary distribution ( [ eq : pxstat - constant - resetting - final ] ) may be put in the scaling form p_st(x|x_0)= ( ) , eq : pxstat - final - rconstant where the scaling function is given by @xmath99 . for the particular case @xmath100 , eq .
( [ eq : pxstat - constant - resetting - final ] ) matches with the result derived in ref .
note that the steady state distribution ( [ eq : pxstat - final - rconstant ] ) exhibits a cusp at the resetting location @xmath21 . since the resetting location is taken to be the same as the initial location , the particle visits repeatedly in time the initial location , thereby keeping a memory of the latter that makes an explicit appearance even in the long - time stationary state .
subsec : parabolic - resetting we now study the dynamics of a free brownian particle whose position is reset to the initial position @xmath21 with a rate of resetting that is proportional to the square of the current position of the particle . in this case , we have @xmath101 , with @xmath102 having the dimension of @xmath103 . from eqs .
( [ eq : pnoresq ] ) and ( [ eq : qma ] ) , and given that in this case @xmath27 , we get p_noreset(x , t|x_0,0)&=&g_q(x ,- it|x_0,0)=x|(-h_qt)|x_0 , eq : parabolic - resetting - pxt-0-x0 with the hamiltonian obtained from eq .
( [ eq : quantum - hamiltonian ] ) by setting @xmath104 : h_q= - + x^2 ; m_q= , = 1 .
eq : hq - free - parabola we thus see that the statistics of resetting of a free particle subject to a parabolic " rate of resetting may be found from the propagator of a quantum harmonic oscillator .
following schulman @xcite , a quantum harmonic oscillator with the hamiltonian given by h_q=- + m_q _
q^2 x^2 , with @xmath105 and @xmath106 being the mass and the frequency of the oscillator , has the quantum propagator & & g_q(x,|x_0,0)= ( [ ( x^2 + x_0 ^ 2)_q - 2 x x_0 ] ) .
eq : gq - free - parabola using the parameters given in eq .
( [ eq : hq - free - parabola ] ) , and substituting @xmath58 and @xmath107 in eq .
( [ eq : gq - free - parabola ] ) , we have & & g_q(x ,-
it|x_0,0 ) + & & = ( -[(x_0 ^ 2+y^2)(t)-2x x_0 ] ) .
eq : gq - free - parabola-1 we may now derive the statistics of resetting by using the propagator ( [ eq : gq - free - parabola-1 ] ) . equation ( [ eq : parabolic - resetting - pxt-0-x0 ] ) together with eq .
( [ eq : gq - free - parabola-1 ] ) imply & & p_noreset(x , t|x_0,0 ) + & & = ( -[(x_0 ^ 2+x^2)(t)-2x_0x ] ) .
eq : parabolic - resetting - pxt - x0 integrating eq .
( [ eq : parabolic - resetting - pxt - x0 ] ) over @xmath2 , we get the distribution of the first - reset time as & & p_reset(t|x_0 ) = _
-^dy r(y)p_noreset(y , t|x_0,0 ) + & & = ( -x_0 ^ 2(t ) ) + & & .
eq : parabolic - resetting - pt - x0 for the case @xmath100 , eqs .
( [ eq : parabolic - resetting - pxt - x0 ] ) and ( [ eq : parabolic - resetting - pt - x0 ] ) reduce to simpler expressions : & & p_noreset(x , t|x_0=0,0)=(- ) , + eq : parabolic - resetting - pxt - x00 + & & p_reset(t|x_0=0 ) = .
eq : parabolic - resetting - pt - x00 equation ( [ eq : parabolic - resetting - pt - x00 ] ) may be put in the scaling form p_reset(t|x_0=0)=g(t ) , with @xmath108 .
equation ( [ eq : parabolic - resetting - pt - x00 ] ) yields the mean first - reset time @xmath109 for @xmath100 to be given by t _
reset= , eq : tav - x00 where @xmath110 is the gamma function . equations ( [ eq : parabolic - resetting - pt - x00 ] ) and ( [ eq : tav - x00 ] ) yield the stationary spatial distribution on using eq .
( [ eq : pxstat - final ] ) : p_st(x|x_0=0)&=&_0^(- ) . + & = & ( ) ^1/4k_1/4 ( ) , eq : stationary - px - parabolic - resetting where @xmath111 is the @xmath112th order modified bessel function of the second kind
. equation ( [ eq : stationary - px - parabolic - resetting ] ) implies that the stationary distribution is symmetric around @xmath113 , which is expected since the resetting rate is symmetric around @xmath100 . the stationary distribution ( [ eq : stationary - px - parabolic - resetting ] )
may be put in the scaling form p_st(x|x_0=0)= ( ) , where the scaling function is given by @xmath114 .
using @xmath115 for @xmath116 @xcite , we find that @xmath117 given by eq .
( [ eq : stationary - px - parabolic - resetting ] ) is correctly normalized to unity .
moreover , using the results that as @xmath118 , we have @xmath119 for @xmath120 and that as @xmath121 , we have @xmath122 for real @xmath2 @xcite , we get p_st(x|x_0=0 ) ~\ { ll & for x0 , + ( -x^2/2 ) & for |x| . + .
eq : stationary - px - parabolic - resetting - limiting - forms thus , the steady state distribution ( [ eq : stationary - px - parabolic - resetting ] ) exhibits a cusp at the resetting location @xmath100 , a feature also seen in the stationary distribution ( [ eq : pxstat - constant - resetting - final ] ) and is a signature of the steady state being a nonequilibrium one @xcite .
note the existence of faster - than - exponential tails suggested by eq .
( [ eq : stationary - px - parabolic - resetting - limiting - forms ] ) in comparison to the exponential tails observed in the case of resetting at a constant rate , see eq .
( [ eq : pxstat - constant - resetting - final ] ) .
this is consistent with the fact that with respect to the case of resetting at a space - independent rate , a parabolic rate of resetting implies that the further the particle is from @xmath100 , the more enhanced is the probability that a resetting event takes place , and , hence , a smaller probability of finding the particle far away from the resetting location .
let us note that the stationary states ( [ eq : pxstat - constant - resetting - final ] ) and ( [ eq : stationary - px - parabolic - resetting ] ) are entirely induced by the dynamics of resetting .
indeed , in the absence of any resetting , the dynamics of a free diffusing particle does not allow for a long - time stationary state , since in the absence of a force , there is no way in which the motion of the particle can be bounded in space .
on the other hand , in presence of resetting , the dynamics of repeated relocation to a given position in space can effectively compete with the inherent tendency of the particle to spread out in space , leading to a bounded motion , and , hence , a relaxation to a stationary spatial distribution at long times . in the next section
, we consider the situation where the particle even in the absence of any resetting has a localized stationary spatial distribution , and investigate the change in the nature of the spatial distribution of the particle owing to the inclusion of resetting events .
subsec : parabolic - resetting - force we now introduce a resetting problem that is relevant in physics : an overdamped brownian particle immersed in a thermal bath at temperature @xmath12 and trapped with a harmonic potential centered at the origin : @xmath123 , where @xmath124 is the stiffness constant of the harmonic potential .
the particle , initially located at @xmath100 , may be reset at any time @xmath15 to the origin with a probability that depends on the energy of the particle at time @xmath15 .
the dynamics is shown schematically in fig .
[ fig : energy - resetting ] . for purposes of illustration of the nontrivial effects of resetting
, we consider the following space - dependent reseting rate : r(x)= = x^2 , eq : re1 where we use @xmath125 in obtaining the second equality .
note that the resetting rate is proportional to the energy of the particle ( in units of @xmath126 ) divided by the timescale @xmath127 that characterizes the relaxation of the particle in the harmonic potential in the absence of any resetting . in this way
, it is ensured that the rate of resetting ( [ eq : re1 ] ) has units of inverse time .
note also that in the absence of any resetting , the particle relaxes to an equilibrium stationary state with a spatial distribution given by the usual boltzmann - gibbs form : p_st^r=0(x)=(- ) .
eq : bgform - parabola - parabola moves with diffusion coefficient @xmath128 , with its motion being confined by a harmonic potential @xmath129 ( green ) , with @xmath130 being the stiffness constant .
here , @xmath2 is the position of the particle with respect to the center of the potential .
the particle , initially located in the trap center ( @xmath131 , left panel ) , diffuses at subsequent times in the energy landscape ( @xmath132 , middle panel ) , until a resetting event occurs at time @xmath133 ( right panel ) .
the black curve represents the history of the particle from @xmath131 up to the time corresponding to each snapshot .
the rate of resetting ( right colorbar ) is proportional to the instantaneous energy of the particle , and , therefore , a reset is more likely to take place as the particle climbs up the potential.,scaledwidth=72.0% ] fig : energy - resetting using @xmath134 and the expression ( [ eq : re1 ] ) for the resetting rate in eq .
( [ eq : quantum - potential ] ) , we find that the potential of the corresponding quantum mechanical problem is given by v_q(x)=++r(x ) = - , eq : vq - parabola - parabola where we have used @xmath135 . from eqs .
( [ eq : pnoresq ] ) and ( [ eq : qma ] ) , we obtain p_noreset(x , t|x_0=0,0)&= & ( _ x_0^x f(x ) dx)()x|(-h_qt)|x_0=0 + & = & ( -)()x|(-h_qt)|x_0=0 , eq : pnoreset - parabola - parabola-0 where the quantum hamiltonian is given by h_q= - + ; m_q= , = 1 .
eq : hq - parabola - parabola we thus find that the propagator @xmath136 is given by the propagator of a quantum harmonic oscillator , which has been calculated in sec . [ subsec : parabolic - resetting ] .
in fact , the hamiltonian given by eq .
( [ eq : hq - parabola - parabola ] ) is identical to that in eq .
( [ eq : hq - free - parabola ] ) with the identification @xmath137 , so that by substituting @xmath100 and @xmath138 in eq .
( [ eq : parabolic - resetting - pxt - x0 ] ) , we obtain x|(-h_qt)|x_0=0=(-(2t/_c ) ) .
eq : pnoreset - parabola - parabola-1 from eqs .
( [ eq : pnoreset - parabola - parabola-0 ] ) and ( [ eq : pnoreset - parabola - parabola-1 ] ) , we obtain p_noreset(x , t|x_0=0,0)=(- ) .
+ eq : pnoreset - parabola - parabola - final following eq .
( [ eq : pt - final ] ) , we may now calculate the probability of the first - reset time by using eq .
( [ eq : pnoreset - parabola - parabola - final ] ) to get p_reset(t|x_0=0)&=&_-^dx ( - ) + & = & , eq : preset - parabola - parabola - final which may be checked to be normalized : @xmath139 .
the first - reset time distribution ( [ eq : preset - parabola - parabola - final ] ) may be written in the scaling form p_reset(t|x_0=0)&= & ( ) , eq : preset - parabola - parabola - final2 with the scaling function given by @xmath140 .
the mean first - reset time , given by @xmath141 , equals & & t _ reset = _
2f_1(,;;- ) , eq : treset - parabola - parabola where @xmath142 is the generalized hypergeometric function . introducing the variable @xmath143 , and using eq . (
[ eq : pnoreset - parabola - parabola - final ] ) , we get & & p_st(x|x_0=0 ) + & & = ( -)_0^dz ( - ) + & & = ( - ) ( ) ^-1/4(1/8)w_1/8,1/4 ( ) , eq : pst - parabola - parabola where @xmath144 is whittaker s w function .
using eq .
( [ eq : treset - parabola - parabola ] ) in eq .
( [ eq : pst - parabola - parabola ] ) , we obtain & & p_st(x|x_0=0)= ( - ) ( ) ^1/4w_1/8,1/4 ( ) , + which may be checked to be normalized to unity .
we may write the stationary distribution in terms of a scaled position variable as p_st(x|x_0=0)= ( ) , with @xmath145 being the scaling function . using the results that as @xmath118 , we have @xmath146 for @xmath147 and that as @xmath121
, we have @xmath148 for real @xmath2 @xcite , we get the stationary spatial distribution p_st(x|x_0=0 ) ~\ { ll & for x0 , + ( - ) & for |x| . + .
eq : stationary - px - parabola - parabola - resetting - limiting - forms we see again the existence of a cusp at the resetting location @xmath100 , similar to all other cases we studied in this paper .
the results of this subsection could inspire future experimental studies using optical tweezers in which the resetting protocol could be effectively implemented by using feedback control @xcite .
interestingly , colloidal and molecular gelly and glassy systems show hopping motion of their constituent particles between potential traps or cages , " the latter originating from the interaction of the particles with their neighbors @xcite .
such a phenomenon is also exhibited by out - of - equilibrium glasses and gels during the process of aging @xcite .
our results in this section could provide valuable insights into the aforementioned dynamics , since the emergent potential cages may be well approximated by harmonic traps and the hopping process as a resetting event .
sec : conclusion in this paper , we addressed the fundamental question of what happens when a continuously evolving stochastic process is repeatedly interrupted at random times by a sudden reset of the state of the process to a given fixed state . to this end , we studied the dynamics of an overdamped brownian particle diffusing in force fields and resetting to a given spatial location with a rate that has an essential dependence on space , namely , the probability with which the particle resets is a function of the current location of the particle .
to address stochastic resetting in the aforementioned scenario , we developed a novel quantum mechanical approach , discussed in detail in eqs .
( [ eq : pnoresq])-([eq : quantum - potential ] ) in sec .
[ sec : propagator ] .
invoking the so - called feynman - kac framework of treating stochastic processes by exploiting the path integral formalism of quantum mechanics , we obtained a mathematical identity that relates the probability of transition between different spatial locations of the particle before it encounters any reset to the quantum propagator of a suitable quantum mechanical problem ( see sec .
[ sec : propagator ] ) .
the approach provides a powerful alternative to traditional methods of treating the dynamics analytically , and allows to obtain closed form analytical expressions for a number of statistics of the dynamics , e.g. , the probability distribution of the first - reset time ( sec .
[ sec : prob - first - reset ] ) , the time - dependent spatial distribution ( sec .
[ sec : prob - distr ] ) , and the stationary spatial distribution ( sec .
[ sec : stat - distr ] ) .
we applied the method to a number of representative examples , including in particular those involving nontrivial space dependence of the rate of resetting .
remarkably , we obtained the exact distributions of the aforementioned dynamical quantifiers for two non - trivial problems : the resetting of a free brownian particle under `` parabolic '' resetting ( sec .
[ subsec : parabolic - resetting ] ) and the resetting of a brownian particle moving in a harmonic potential with a resetting rate that depends on the energy of the particle ( sec .
[ subsec : parabolic - resetting - force ] ) .
our formalism may be extended to treat systems of interacting particles , with the advantage that the corresponding quantum mechanical system can be treated effectively by using tools of quantum physics and many - body quantum theory .
our theory also provides a viable method to calculate path probabilities of complex stochastic processes .
such calculations are of particular interest in many contexts , e.g. , in stochastic thermodynamics @xcite , and in the study of several biological systems such as molecular motors @xcite , active gels @xcite , genetic switches @xcite , etc . as a specific application in this direction ,
our approach allows to explore the physics of _ brownian tunnelling _
@xcite , an interesting stochastic resetting version of the well - known phenomenon of quantum tunneling , which serves to unveil the subtle effects resulting from stochastic resetting in , e.g. , transport through nanopores @xcite .
app : feynman - kac in this section , we provide a brief introduction to the path integral formalism , following the discussions in refs . @xcite .
consider a quantum particle of mass @xmath149 moving in one dimension @xmath2 in presence of a time - independent potential @xmath150 let @xmath151 denote the state of the particle at time @xmath57 , so that @xmath152 is the wave function , that is , @xmath153 gives the probability of finding the particle between @xmath2 and @xmath154 at time @xmath57 .
the time evolution of @xmath151 follows the schrdinger equation i = h| ( ) , where @xmath155 is the hamiltonian of the system . using @xmath156 the identity operator
, it then follows that i & = xx|h|x(x , ) + & = x(-+v(x))(x - x)(x , ) + & = ( -+v(x))(x , ) . here , we have used @xmath157 .
let @xmath158 denote the propagator or the transition probability amplitude for the particle to be at position @xmath2 at time @xmath159 given that the particle was at position @xmath21 at time @xmath160 thus , @xmath161 gives the probability for the particle to be between @xmath2 and @xmath154 at time @xmath159 given that the particle was at position @xmath21 at time @xmath162 . since the hamiltonian contains no explicit time - dependence , we may affect the relabeling @xmath163 , and work with the time elapsed since @xmath162 that we denote by @xmath57 .
correspondingly , let us denote the transition amplitude by @xmath164 according to the path integral formulation of feynman , the transition amplitude is obtained as g(x,;x_0)=_x(0)=x_0^x()=x[x()](is_cl[x()]/ ) , namely , an integral over all possible paths that propagate from @xmath21 to @xmath2 in time @xmath165 with every path @xmath166 $ ] weighted by the factor @xmath167/\hbar),$ ] where @xmath168 $ ] , a functional of the path @xmath166,$ ] is the classical action : @xmath169\equiv\int_0^{\tau}{\rm d}\tau'\,\mathcal{l}(x,\dot{x};~\tau').$ ] here , @xmath170 is the lagrangian , @xmath171 is the kinetic energy , and the dot denotes derivative with respect to @xmath57 .
thus , every possible path contributes with equal amplitude to the propagator , but has a different phase related to the classical action ; on summing over all possible trajectories , we obtain the propagator . differently from the path integral formalism ,
one has , by definition , g(x,;x_0)=x|(-ih/)|x_0 , where given that the particle is initially at position @xmath21 , we have the wave function at the initial instant given by @xmath172 .
we finally have & & x|(-ih/)|x_0=_x(0)=x_0^x()=x[x()](is_cl[x()]/ ) + & & = _
x(0)=x_0^x()=x[x( ) ] .
eq : propagator - quantum - mechanics discretizing times as @xmath173 with @xmath174 an integer and @xmath175 , and denoting by @xmath31 the position of the particle at the @xmath174-th time step , we get x|(-ih/)|x_0 & = _ nx_1dx_2 dx_n-1_i=1^nk(x_i,;x_i-1 ) ; x_n = x , where @xmath176 $ ] is the transition probability amplitude for the particle to be at position @xmath31 at time @xmath177 , given that the particle was at position @xmath178 at time @xmath179 requiring that @xmath180 yields @xmath181,$ ] so that we have & & x|(-ih/)|x_0 + & & = _ nx_1dx_2
dx_n-1()^n/2 + & & ; x_n = x . consider now imaginary time : @xmath182 then , using @xmath58 we get & & x|(-ht/)|x_0 + & & = _
nx_1dx_2 dx_n-1()^n/2e^-s_e[x()]/ ; + & & s_e[x(t)]=t_i=1^n(()^2+v(x_i ) ) + & & = _ x(0)=x_0^x(t)=x[x ( ) ] , eq : imaginary - time - propagator where @xmath183 is the so - called euclidean action .
er thanks ana lisica and stephan grill for initial discussions , and ken sekimoto for enlightening discussions on path probabilities .
er acknowledges funding from the spanish government , grant termic ( no .
fis2014 - 52486-r ) .
99 kac m 1951 on some connections between probability theory and differential and integral equations , in _ proc .
second berkeley symp . on math .
statist . and prob . _
( berkeley : university of california press ) perez - carrasco r , guerrero p , briscoe j , and page km 2016 intrinsic noise profoundly alters the dynamics and steady state of morphogen - controlled bistable genetic switches _
plos comput .
* 12 * e1005154 | we study the dynamics of overdamped brownian particles diffusing in force fields and undergoing stochastic resetting to a given location with a generic _ space - dependent _ rate of resetting .
we introduce a novel quantum mechanical approach that allows to calculate in a systematic way analytical expressions for a variety of statistics of the dynamics , such as ( i ) the propagator prior to first reset ; ( ii ) the distribution of the first - reset time , and , most interestingly , ( iii ) the spatial distribution of the particle at long times . a key to our accomplishment
is the derivation of an equality relating the transition probability prior to first reset with the propagator of a suitable quantum mechanical problem .
we apply our method to obtain _ exact _
results for a number of representative and hitherto unexplored examples of resetting dynamics , including a case of energy - dependent resetting , thereby unveiling the nontrivial effects of resetting .
keywords : random walks , stochastic processes , resetting , quantum mechanics |
kitaev s toric code @xcite serves as the simplest toy model of a quantum memory as well as being the archetypical example of a topological phase of matter .
topological protection of josephson junction qubits @xcite as well as topological error correction @xcite have already been experimentally demonstrated .
implementations of spin - lattice models with topologically ordered groundstates using polar molecules stored in optical lattices @xcite or laser - excited rydberg atoms @xcite have been proposed .
a challenge to any scalable implementation of topological protection of quantum information is the issue of thermal stability . in its standard form
, the toric code hamiltonian requires a set of local , commuting four - qubit stabilizer operators @xmath0 .
unfortunately , the `` bare '' toric code hamiltonian @xmath1 ( with @xmath2 ) does not allow for thermally stable storage of quantum information @xcite . while performing a bit- or phase - flip on a single qubit ( and thus creating two anyonics defects )
has an energy cost @xmath3 , these defects can then propagate without any further energy cost and thus destroy the stored quantum information . as a consequence ,
the lifetime of the quantum information is _ independent _ of the size of the memory .
furthermore , interactions in nature are usually two - body , such that the four - body operators @xmath4 can not be generated directly but have to emerge from an underlying structure of two - body interactions
. since @xmath4 will then appear in high - order perturbation theory @xcite , the energy penalty @xmath5 will naturally be weak .
these negative results on the bare toric code have motivated the study of long - range interactions between the stabilizer operators @xmath4 as a means to suppress the creation and/or diffusion of anyons and thereby increase the lifetime of the stored quantum information @xcite .
such long - range interactions can lead to quantum information lifetimes that grow polynomially or even exponentially with @xmath6 @xcite .
it has been suggested that such memories are compatible with a recent proposal for fault - tolerant holonomic quantum computation based on adiabatic deformation of the system hamiltonian @xcite . in order to mediate these interactions in a physically plausible way ,
all of these proposals require five - body operators of the form @xmath7 , where the operator @xmath8 allows to couple the stabilizer operator @xmath4 to an external field which mediates the interaction .
the external field can either be elementary ( e.g. photons as discussed in ref . ) or emerge from the energetically low - lying excitations of a many - body system ( e.g. phonons as discussed in ref . ) . in ref .
we have studied in detail the case of bosons hopping in a cubic lattice , leading to a parabolic dispersion near the center of the brillouin zone . in the present paper ,
we focus on the physical implementation of the quantum memory hamiltonian proposed in ref . .
we start from a spin hamiltonian involving only _ local two - body interactions _ and study its low - energy theory via a perturbative schrieffer - wolff transformation .
the bosonic field emerges from the energetically low - lying excitations of an ordered heisenberg ferromagnet ( magnons ) . for small wave - numbers ,
magnons indeed feature a parabolic dispersion .
furthermore , we present perturbative gadgets for generating the five - body operators @xmath7 , describing interactions between the four - qubit stabilizer operators @xmath4 of the toric code and a spin operator @xmath8 of the ferromagnet . since the quantum - memory hamiltonian of ref
. emerges as the effective low - energy / long - wavelength theory of our hamiltonian with only local two - spin interactions , this system is expected to exhibit self - correcting properties _ as long as this effective theory remains valid_. the rest of this paper is organized as follows .
we briefly review the main results of ref . in sec .
[ sec : previous ] and discuss the relation to the present work . in sec .
[ sec : gadgets ] , we present perturbative gadgets that allow effective five - body terms @xmath7 to be obtained from local two - body interactions only . in sec .
[ sec : fm ] , we show that using these five - body operators to couple the stabilizer operators @xmath4 to an ordered heisenberg ferromagnet leads to a low - energy effective theory which coincides with the quantum memory hamiltonian from ref . .
we can thus obtain an effective quantum memory hamiltonian from a system ( perturbative gadgets plus heisenberg ferromagnet ) with two - spin interactions only . in sec .
[ sec : validity ] we study the regime in which this effective description is expected to be valid . in sec .
[ sec : backaction ] we study the backaction of the coupling onto the ferromagnet and how to counteract it .
we conclude in sec .
[ sec : conclusions ] .
in ref . we have studied the following model @xmath9 for a self - correcting quantum memory . consider a bosonic hamiltonian @xmath10 with a dispersion , which in the low-@xmath11 limit is parabolic , @xmath12 .
the four - qubit stabilizer operators @xmath13 are arranged on a 2d array of size @xmath14 and locally couple to the bosonic field , @xmath15 where either @xmath16 or @xmath17 . here ,
@xmath18 and @xmath19 are fourier transforms of the bosonic operators @xmath20 and @xmath21 , @xmath22 , where @xmath23 is the spatial location of stabilizer @xmath13 and @xmath24 is the number of bosonic modes . in other words ,
the operator @xmath18 ( @xmath19 ) annihilates ( creates ) a boson at position @xmath23 . involve operators acting on the four qubits around a white or a dark plaquette .
operators acting on the four qubits around a white plaquette are of the form @xmath25 , while operators acting on the four qubits around a dark plaquette are of the form @xmath26 . ] the stabilizer operators ( or stabilizers for short ) @xmath13 are of the form @xmath25 or @xmath26 , see fig .
[ fig : code ] for an illustration .
all stabilizers commute with each other and have eigenvalues @xmath27 . under the assumption that the bosons are in thermal equilibrium , the bosonic field mediates long - ranged interactions between the stabilizer operators @xmath13 . technically speaking ,
it is possible to integrate out the bosonic field ( either exactly or perturbatively ) and derive an effective hamiltonian for the stabilizers .
this hamiltonian is of the form @xmath28 where @xmath29 describes a mediated attractive long - range interaction between the stabilizers .
more specifically , we have shown the following @xcite . for @xmath16
, we have @xmath30 , such that the energy cost for violating a stabilizer ( `` creating an anyon '' ) grows logarithmically with @xmath6 and the quantum memory lifetime grows polynomially with @xmath6 .
if , on the other hand , @xmath17 , we have @xmath31 , such that the energy cost for creating an anyon grows linearly with @xmath6 and the lifetime does so exponentially .
the goal of this work is to show that the hamiltonian @xmath32 can be obtained as an effective low - energy hamiltonian of a hamiltonian that involves only nearest - neighbor two - spin interactions .
this hamiltonian is then expected to exhibit self - correcting properties , given that the noise affecting the memory is such that the effective low - energy description remains valid .
we realize the bosonic field by a 3d ordered heisenberg ferromagnet ( fm ) to which the stabilizers of the toric code couple locally .
the long - range interactions @xmath29 in eq
. are then mediated by massless excitations of the fm ( goldstone modes ) , so - called magnons .
our model consists of a `` gadgetry '' and a `` ferromagnet '' part , @xmath33 where @xmath34 is a sum of identical gadget terms for each of the stabilizers .
the summands @xmath35 are sums of two - qubit terms , where one of the two qubits involved is part of the toric code and the other one is an auxiliary or `` mediator '' qubit . by integrating out all mediator qubits
, we obtain a first effective hamiltonian @xmath36 describing four - qubit stabilizer operators locally coupled to the fm . here
, @xmath37 is akin to @xmath38 in eq . .
the ordered heisenberg ferromagnet described by @xmath39 can be mapped to a bath of bosons ( magnons ) by means of the well - known holstein - primakoff transformation . even beyond the one - magnon approximation ( _ i.e. _ , taking magnon - magnon interaction into account ) , the interactions between the stabilizers mediated by the ferromagnet can be described by a final effective hamiltonian @xmath40 akin to @xmath32 in eq . .
the effective interactions @xmath29 are thereby given by the static susceptibility of the fm .
-plane , are sketched by red lines ) is embedded in a 3d heisenberg ferromagnet ( blue ) which is ordered in @xmath41-direction .
the stabilizer operators of the toric code @xmath13 ( illustrated in fig .
[ fig : code ] ) couple to the @xmath42-component of an adjacent spin @xmath43 of the ferromagnet .
the linear size of the planar toric code ( @xmath6 ) is assumed to be much smaller than the one of the ferromagnet ( @xmath44 ) , _ i.e. _ , @xmath45 . ]
\(b ) at ( 0,0 ) * b * ; ( d ) at ( 2,0 ) * d * ; ( a ) at ( 0,2 ) * a * ; ( c ) at ( 2,2 ) * c * ; ( f ) at ( 0.5,1 ) * f * ; ( g ) at ( 1.5,1 ) * g * ; ( u ) at ( 1,1.6 ) * u * ; ( p ) at ( 1,3.6 ) * p * ; \(a )
( f ) node [ midway , above ] @xmath46 ; ( b ) ( f ) node [ midway , below ] @xmath47 ; ( c ) ( g ) node [ midway , above ] @xmath47 ; ( d ) ( g ) node [ midway , above ] @xmath48 ; ( f ) ( u )
node [ midway , above ] @xmath49 ; ( g ) ( u ) node [ midway , above ] @xmath50 ; ( p )
( u ) node [ midway , right ] @xmath51 ; \(a ) ( b ) node [ midway , right ] @xmath52 ; ( c )
( d ) node [ midway , left ] @xmath52 ; ( f )
( g ) node [ midway , below ] @xmath53 ; ( f )
( p ) node [ midway , left ] @xmath54 ; ( g ) ( p ) node [ midway , right ] @xmath54 ;
given some hamiltonian with only local two - body interactions , one is often interested in an _ effective _ hamiltonian that describes the low - energy dynamics of the system .
this is achieved by `` integrating out '' the high - energy degrees of freedom .
the effective low - energy hamiltonian then often features a higher complexity than the original one .
this lead to the idea of _ perturbative gadgets _
@xcite , which allows one to systematically construct hamiltonians with local two - qubit interactions that yield some desired effective ( low - energy ) few - qubit hamiltonian . in particular , ref . showed that any local hamiltonian can be generated from some @xmath55-local hamiltonian .
the schrieffer - wolff ( sw ) transformation @xcite ( see appendix [ app : sw ] for a technical summary ) provides a natural framework for obtaining such effective terms .
ref . combined the gadgets of ref . with the sw method to discuss the simulation of local many - body hamiltonians by use of @xmath55-local interactions .
the schemes we propose in order to generate the five - body terms @xmath56 shall be analyzed by means of a sw transformation but are simpler than had they been constructed with the perturbative gadgets described in refs . .
note that while all of the proposals in refs .
require five - body terms of the form @xmath56 , other quantum memory proposals are not based on coupling stabilizer operators to external fields .
however , these alternate proposals in fact involve interactions between more than five qubits . specifically , the 3-dimensional toric code with `` welding '' @xcite requires six - qubit operators , while the 4-dimensional toric code @xcite and haah s cubic code @xcite require eight - qubit operators .
these models can thus only be realized with gadgets that are even more involved than the ones discussed in the following .
we introduce two sets of spins , namely @xmath57 for the spins of the 3d fm located at site @xmath58 of a cubic lattice and @xmath59 for the physical spins-@xmath60 ( qubits ) of the 2d toric code .
both spins satisfy the usual commutation relations .
the code qubits are arranged on a quadratic lattice with periodic boundary conditions .
the four - qubit stabilizer operators @xmath13 are of the form @xmath61 or @xmath62 , where the operators act on the four qubits around one plaquette of the lattice , as illustrated in fig .
[ fig : code ] .
we seek to construct effective terms of the form @xmath63 , where for the moment we consider @xmath64 . here , @xmath43 is the spin of the fm adjacent to the spins of the stabilizer @xmath13 , see fig . [
fig : fm ] .
let the summands in the gadget hamiltonian @xmath34 be given by @xmath65 with @xmath66 being larger than ( the absolute value of ) all other energies ( see fig .
( [ fig : gadget ] ) for an illustration ) .
we now apply the sw method to successively integrate out the mediator qubits @xmath67 , @xmath68 , and @xmath69 and calculate for each mediator qubit the resulting terms up to third order .
consider a mediator qubit @xmath70 with energy splitting @xmath66 , @xmath71 , and a perturbation @xmath72 . with @xmath73 , @xmath74 , and
@xmath75=0 $ ] , we obtain after integrating out the auxiliary qubit @xmath70 as described in appendix [ app : sw ] @xmath76 the unitaries applied during the sw procedure to integrate out qubits @xmath67 , @xmath68 , and @xmath69 ( cf . appendix [ app : sw ] ) do not commute and higher order terms will thus depend on the order in which this three qubits are integrated out . however , up to the orders stated below , the effective terms are independent of this ordering . for the sake of a shorter notation , let @xmath77 and @xmath78 .
we neglect terms in the interaction strengths which are smaller by at least a factor @xmath79 than the mentioned terms .
after straightforwardly applying eq . in appendix [ app : sw ] to the mediator
qubits @xmath67 , @xmath68 , and @xmath69 , we find @xmath80s_p^x - \xi^2\left[\tau - 8\frac{\alpha^2\gamma}{\delta^2}\right]r_p\otimes s_p^x { \nonumber}\\ & \quad + \left[\delta - \xi^2\left(\frac{\delta}{2 } -\beta + 4\frac{\alpha^2}{\delta}\right)\right]r_p + \xi^4\left[\beta-2\frac{\alpha^2}{\delta}\right]w_p { \nonumber}\\ & \quad - 4\xi^4\frac{\alpha^2\gamma}{\delta^2}w_p\otimes s_p^x + { \mathrm{const}}\ .\end{aligned}\ ] ] the parameter @xmath81 allows one to tune the strength of the plaquette term @xmath13 without affecting the strength of the five - body operator @xmath63 .
the interaction strength of the undesired operators @xmath82 and @xmath83 can be tuned to zero through appropriate choice of the parameters @xmath84 and @xmath85 , respectively .
we obtain an undesired one - body term @xmath86 which can be countered by an appropriate local field .
finally , the strength of our desired five - body term @xmath63 is to leading order given by @xmath87 .
if we use the operator @xmath63 to couple the plaquette @xmath13 to external fields , effective two - plaquette interactions mediated by the field will be of even order in @xmath5 .
the sign of @xmath88 , @xmath89 , and @xmath90 is thus irrelevant .
relabeling @xmath91 on all qubits , such that the commutation relations of the spin operators are preserved , we can obtain operators of the form @xmath92 rather than @xmath93 . in conclusion ,
integrating out the mediator qubits in each gadget leads to an effective coupling hamiltonian @xmath94 which is of the same form as eq . .
note that if we let @xmath95 in eq .
( [ eq : gadget ] ) , we find the simpler effective hamiltonian @xmath96r_p + 16\frac{\beta{\epsilon}^4}{\delta^4}w_p\ .\end{aligned}\ ] ] we can thus obtain stabilizer operators @xmath13 as they appear in kitaev s toric code @xcite as effective terms using only two auxiliary qubits , nearest neighbor ising interactions and single - qubit energy splittings .
this adds a particularly simple gadget to the list of proposals for perturbatively generating kitaev s toric code @xcite .
we have discussed how the strength of the undesired terms @xmath82 and @xmath97 can be tuned to zero by appropriate choice of the interaction strengths @xmath98 and @xmath99 .
of course , assuming that the strength of these interactions vanishes exactly is unphysical .
weak terms acting as @xmath82 are no threat to the toric code , as it is inherently stable against such local perturbations @xcite .
however , as the terms @xmath97 themselves couple to the gapless magnon field , one might fear that their combined non - local interaction may destabilize the toric code groundstate .
we have qualitatively discussed the effect of such non - locally coupled perturbations on the stability of the toric code in ref . and argued that they pose no threat to toric code stabilized by the fm as long as the strength of the accidental terms @xmath97 is sufficiently smaller than the engineered coupling strength @xmath5 .
after integrating out all mediator qubits in the perturbative gadgets , we arrived at a first effective hamiltonian @xmath100 describing four - qubit stabilizer operators of the toric code coupled to the fm .
let us now study the interactions between the effective stabilizer operators @xmath13 which are mediated by the ordered heisenberg fm @xmath39 , to which they are coupled over the operators @xmath101 .
the hamiltonian of the 3d heisenberg fm is given by @xmath102 , where @xmath103 is the exchange constant and the sum is restricted to nearest - neighbor lattice sites .
the fm is of linear size @xmath44 , which is much larger than the linear size of the toric code , @xmath104 .
the fm is assumed to be below the curie temperature and the spins ordered along the @xmath41-direction . to break the symmetry of the fm , a small magnetic field @xmath105 in @xmath41-direction
is applied .
this field also stabilizes the fm against the effective longitudinal magnetic field produced by coupling the stabilizer operators of the toric code to the @xmath42-component of adjacent fm spins ( see below ) . although @xmath39 is three - dimensional , we point out for the sake of clarity , that the actual quantum memory is the two - dimensional toric code .
the presence of the 3d system is necessary to mediate long - range interactions between the stabilizers .
however , the place where the logical qubits are stored is the two - dimensional toric code . for @xmath106 , we make use of a perturbative second - order schrieffer - wolff transformation @xcite to derive the effective plaquette - plaquette interaction ( see appendix [ app : swtransverse ] ) given by @xmath107 where the coupling is @xmath108 and @xmath109 is the static spin susceptibility of the fm .
this effective hamiltonian is of the same form as in eq . and , as we will discuss now , the mediated interaction strength @xmath29 , too , is of the same form .
the real space static susceptibility @xmath110 is defined as the fourier transform of @xmath111\right\rangle\ , \ ] ] for @xmath112 , where @xmath113 denotes thermal equilibrium expectation values of the @xmath114-spins at temperature @xmath115 .
the fourier components are defined as @xmath116 , where @xmath117 is the number of spins in the fm , and @xmath118 is a 3d vector pointing to the site of spin @xmath119 of the fm .
it is not necessary to explicitly calculate the spin susceptibility in the ferromagnetically ordered state to understand its general behavior at large distances ( or small @xmath120 ) @xcite .
indeed , for @xmath121 , the spontaneous @xmath122 symmetry breaking of the state with finite magnetization pointing along the @xmath41-axis , implies the presence of low - frequency goldstone modes ( called magnons in this context ) and long - range correlations , _
i.e. _ , the @xmath123- ( and @xmath124- ) susceptibility has to diverge for @xmath125 and takes the following generic form in the hydrodynamic regime ( low - energy and long wavelength regime ) @xcite @xmath126 here , @xmath127 is the stiffness constant of the fm and @xmath128 is the magnetization density with @xmath129 .
the divergence at @xmath130 in eq .
( [ eq : susceptibility ] ) is directly connected with the broken symmetry of the ground state : starting from a ferromagnetic state aligned along the @xmath41-direction , the slightest @xmath42-magnetic field is able to rotate and align all spins in @xmath42-direction and thus the response to an external magnetic field indeed diverges at @xmath130 .
( [ eq : susceptibility ] ) is the expression for the spin susceptibility in the continuum approximation ( lattice constant @xmath131 going formally to zero ) . to be valid
this approximation does not require that the number of spins goes to infinity , but rather that the distance between neighboring spins is much smaller than the distances we are interested in .
since we are concerned with the long - distance physics of our model on the scale of @xmath6 , this approximation is justified and simply requires @xmath132 . in this limit , both the lattice constants of the ferromagnet and of the toric code are taken to zero such that a single plaquette remains coupled to a single fm spin .
below we give an explicit expression for the stiffness @xmath133 in the one - magnon approximation . the presence of the symmetry - breaking magnetic field @xmath105 introduces a gap in the magnon spectrum and thus a mass term in the susceptibility , _
i.e. _ , @xmath134 .
the real space static susceptibility now follows by fourier transformation which leads to @xmath135 , with magnetic length @xmath136 .
consequently , eq . ( [ eq : effectivecoupling ] ) describes a stabilizer hamiltonian with plaquette - plaquette interactions given by a yukawa - like potential , @xmath137 since , again , @xmath127 ( see also below ) , the interaction between stabilizer operators @xmath138 is _
attractive_. for the sake of illustration
we calculate @xmath133 in the one - magnon ( harmonic ) approximation by making use of the holstein - primakoff transformation @xmath139 in the formal limit , where the occupation @xmath140 is much smaller than @xmath141 @xcite . here , @xmath142 and @xmath143 satisfy bosonic commutation relations and the associated quasi - particles are the well - known magnons ( or spin wave excitations ) . in fourier space
, we get @xmath144 , up to some irrelevant constant , with magnon dispersion @xmath145 $ ] , where @xmath146 , with @xmath147 the number of fm spins . inserting eq .
( [ eq : hp ] ) into eq .
( [ eq : susceptibility ] ) and using a small @xmath120 expansion leads to @xmath148 , which allows us to identify the stiffness in lowest order @xmath149 since here @xmath150 .
we thus obtain @xmath151 and from this the approximate plaquette coupling @xmath152 which is explicitly attractive since @xmath103 .
we emphasize that eq .
( [ eq : finalcoupling ] ) is the one - magnon approximation of eq .
( [ eq : coupling_stiffness ] ) .
the sole effect of both temperature and magnon - magnon interactions is to renormalize the coefficients of the interaction ( [ eq : finalcoupling ] ) , _ i.e. _ , @xmath153 @xcite , while the form of the potential is not affected .
note that the dimensionality of the 3d fm is critical since heisenberg fms in lower dimensions do not order at @xmath154 @xcite .
if @xmath155 is small enough such that @xmath156 , the transverse susceptibility of the fm and hence the mediated interaction @xmath29 in eq .
decay like @xmath157 on the length - scale @xmath6 of the toric code .
the same decay of @xmath29 was reported in sec .
[ sec : previous ] for the case of coupling to the bosonic operator @xmath158 .
this is of course no surprise , since the spin operator @xmath159 takes in the holstein - primakoff picture and in the limit @xmath160 indeed the form @xmath161 .
the external magnetic field @xmath105 is necessary for stabilizing the magnetization of the fm , keeping it along the @xmath41-direction .
indeed , the only condition which needs to be satisfied for the stability of the global magnetization of the fm is that the zeeman energy @xmath162 due to the @xmath105 field remains much larger than the zeeman energy @xmath163 due to the toric code . as a specific example
, one can make the following scaling choice satisfying all constraints : @xmath164 and @xmath165 , which satisfy @xmath166 and @xmath167 . under these conditions , it is clear that the total magnetization will not be affected by the presence of the memory and the fm spins will not rotate into the @xmath42-direction_on average_. this is in agreement with a metropolis simulation of the classical heisenberg fm , see fig .
[ fig : numerics ] .
however , we show below that backaction effects become eventually important for the fm spins _ close _ to the memory .
here we analyze in detail the conditions of validity of our effective theory . as we discussed in ref . , the thermal stability of the toric code protected by the effective hamiltonian @xmath40 in eq
is due to the fact that the cost for inverting a stabilizer @xmath13 ( creating an anyon ) grows without bounds as a function of @xmath6 .
indeed , assume that initially all stabilizers have a @xmath168 eigenvalue ( @xmath169 ) .
then , the energy cost for inverting one of them is given by @xmath170 where we used eq . and
the assumption @xmath171
. this seems to be in contradiction to the fact that our original hamiltonian @xmath172 is a sum of bounded local terms , such that the energy cost for a local change certainly is bounded and does not grow with system size .
however , in the case where the effective hamiltonian ( [ eq : effectivecoupling ] ) emerges from a system with two - body interactions , it describes the system correctly in the _ long - wavelength _ and _ low - energy limit _ only .
we first note that the schrieffer - wolff transformation employed in the derivation of @xmath40 , followed by tracing out the degrees of freedom of the mediator qubits and the ferromagnet is not a unitary operation .
hence , the spectra of @xmath173 and @xmath40 are , in general , not identical .
they match only in the low - energy sector where @xmath174 leads to bounded results .
indeed , when the quantum memory is in contact with a thermal heat bath at inverse temperature @xmath81 , the expected anyon density ( fraction of stabilizer operators @xmath13 with a @xmath175 value ) is approximately @xmath176 ( cf .
iv in ref . for a more careful discussion , taking inter - anyonic interactions into account ) .
the thermal energy of the code system is thus @xmath177 which vanishes exponentially as @xmath178 .
the thermal density of anyons is self - consistently suppressed by the effective anyon chemical potential @xmath179 .
the total thermal energy @xmath180 remains thus finite and small even for large @xmath6 .
the fact that @xmath179 diverges as a function of @xmath6 therefore does not invalidate our effective theory when its full effects are taken into account .
the effective description breaks down in the high - temperature limit , @xmath181 , which corresponds to populating high - energetic states with finite probability , _
i.e. _ , the anyon density becomes of order unity .
indeed , in this limit , we get @xmath182 , which is clearly in contradiction with a finite upper bound on the energy density @xmath183 .
this breakdown of the low - energy effective theory is of course not surprising , since in this regime the perturbative gadgets no longer work and the magnon expansion for the fm becomes invalid .
( for @xmath184 , the fraction of excited mediator qubits and the magnon occupation numbers become of order unity . )
thus , our effective long - wave length and low - energy description is self - consistent for sufficiently low temperatures @xmath115 and sufficiently large code sizes @xmath6 .
this is similar to e.g. the harmonic approximation of crystal vibrations described by phonons .
the hamiltonian @xmath185 is only valid in the low - energy regime , and high - energy ( large @xmath186 ) excitations are self - consistently suppressed by the bose - einstein factor @xmath187 .
the effective hamiltonian ( [ eq : effectivecoupling ] ) is not suited to describe the high - energy part of the spectrum , where the anyon density is of order unity .
high - energy excitations are produced when anyons are created non - adiabatically , forcing the mediator qubits and the fm to leave their local equilibrium .
in such a scenario the gadgets and the fm have no time to react and do not penalize the creation of anyons .
in fact , the energy cost to create an anyon `` instantaneously '' is bounded by a finite constant as argued above . the fast creation of an anyon produces a bunch of high - energy and short - wavelength excitations in the gadgets / fm and these kinds of processes are not described by our effective theory . in the following ,
we provide analytical expressions for the regime of validity of our effective theory . in the derivation of hamiltonian ( [ eq : effectivecoupling ] ) we explicitly assumed that mediator qubits reside in their groundstate and the fm
is locally aligned along @xmath41-direction .
this has to remain valid when thermal anyons are produced .
so besides the requirement that the coupling @xmath188 to the external bath is small ,
_ i.e. _ , @xmath189 , we work in the _ adiabatic regime _ where the external bath creates errors in the code on a timescale much longer than @xmath190 , or in other words , when the error rate is much smaller than @xmath5 . for instance , modeling the coupling between code and bath by a generic spin - boson model @xcite , the error rate @xmath191 describing processes in which an energy @xmath192 is transferred from a code qubit to the bath takes the following form @xcite @xmath193 where @xmath194 is an arbitrary cut - off and @xmath195 contains the coupling @xmath188 to the external bath ( in born approximation , @xmath196 ) . for @xmath197
the bath is called ohmic , while it is called super - ohmic for @xmath198 . the adiabaticity condition
then simply reads @xmath199 . in this case , the mediator qubits and the fm have enough time to adapt to the perturbation generated by an error and stay respectively in an unexcited state or locally aligned along @xmath41-direction . in this regime , trying to flip a single qubit of the code will `` drag along '' a large number of other spins , leading to a large effective energy penalty . to conclude , in such a scenario
the low - energy description @xmath40 of the two - spin hamiltonian @xmath173 , involving long - range interactions between four - qubit operators , remains valid .
( 1,1.2 ) ( -0.5,-0.05 ) ( 1.00,0.46)@xmath200 ( 0.75,1.05)@xmath201 ( 1.05,0.02)@xmath6 strictly speaking , our analysis of the toric code coupled to a fm ( by means of a perturbative schrieffer - wolff transformation ) is valid when the fm spins are aligned close to the @xmath41-direction .
this is the reason why we introduced the external field @xmath105 ; it stabilizes the fm against the transverse effective magnetic field induced by the toric code and forbids energetically the turning of the total magnetization . however , backaction effects are substantial for the fm spins close to the code and it is interesting to study the dynamics of the fm spins in contact to the toric code .
our study of backaction effects involve both analytical and numerical results and give a good picture of the dynamics of a heisenberg ferromagnet subject to transverse magnetic field that is localized in a given plane of the lattice .
let us consider the situation where the coupling of the surface code to the fm is turned on at @xmath202 and let us calculate the dynamics of the @xmath42-component of a fm spin @xmath203 assuming that @xmath204 . at time @xmath205 we have , @xmath206 , where @xmath207 and @xmath208 , with @xmath209 as in eq . . here
, @xmath210 in @xmath211 labels an arbitrary site @xmath212 of the fm .
the dynamics of @xmath213 can be calculated exactly as @xmath209 is exactly diagonalizable , see appendix [ app : dynamics ] .
we find that @xmath214 where @xmath215 and @xmath216 are the fresnel integrals .
this expression can be evaluated analytically in several limits ( see appendix [ app : dynamics ] for details ) .
let us first consider a spin at a fm site @xmath212 which is directly adjacent to the toric code .
for a small code ( @xmath217 ) we find the long - time limit @xmath218 .
we compare this result with a metropolis simulation of the classical heisenberg fm and obtain good agreement , see fig .
[ fig : numerics ] . on the other hand , consider a code which is assumed to be large enough such that it can be formally extended to infinity .
for this case , we find the finite - time behavior @xmath219 for spins adjacent to the toric code .
the fm spins next to the code adapt to the effective magnetic field in @xmath42-direction in a diffusive way with diffusion constant @xmath220 .
note that this expression diverges in the long - time limit , which is of course unphysical since @xmath221 is bounded by @xmath222 .
this divergence is an artefact of the harmonic ( one - magnon ) approximation .
we thus trust this approximation at most only for times which are such that @xmath223 .
the deviations @xmath213 in @xmath42-direction become comparable with @xmath222 after a time of order @xmath224 .
we refer to @xmath225 as the refreshing time : at this time , the backaction of the surface code on the fm has become substantial with the fm spins close to the code being tilted away from the magnetization direction of the fm ( along the @xmath41-axis ) and pointing now along the @xmath42-axis . to restore the full effect of the fm , we refresh the ferromagnetic state with , e.g. , a magnetic pulse , so that all spins point again along the @xmath41-axis .
this procedure has to be repeated periodically on a time scale @xmath225 , which , importantly , is independent of the code size @xmath6 .
this refreshing can be considered as part of a cooling cycle to get the heat generated by the surface code out of the system ( note that no measurements of stabilizers or entangling operations are involved ) .
this refreshing prevents the total system , fm plus surface code , to reach a new common equilibrium state , and instead ensures that the fm stays in its own equilibrium state .
finally , let us consider a spin at a fm site @xmath212 with a distance @xmath226 away from the toric code , which is again assumed to be very large .
for this case ,
. evaluates to @xmath227 the deviation of the fm spins from the ordering along @xmath41-direction decays quadratically with the distance from the code .
we note that the refreshing process represents a sufficent condition for maintaining an effective quantum memory hamiltonian .
however , it is not necessary .
indeed , let us consider the extreme case where all the spins of the fm tilt into @xmath42-direction ( possible if we allow @xmath228 to exceed @xmath229 by assuming e.g. @xmath230 ) . in this worst case scenario ,
the interaction between plaquettes is not given by the transverse susceptibility of the fm anymore but by the longitudinal one .
this fact is derived perturbatively in more detail in appendix [ app : swlongitudinal ] .
the longitudinal susceptibility of the fm has been studied in detail both with a spin wave analysis @xcite and with a decoupling method @xcite .
the small @xmath120 result reads @xmath231 .
this is valid when @xmath232 , which is the regime of interest here since we focus on distances smaller than @xmath233 .
we note that , contrary to the transverse susceptibility , @xmath234 vanishes at @xmath235 , since it corresponds to particle - hole excitations . here
@xmath236 points in longitudinal direction and is composed of an external magnetic field ( which , as above , is assumed to scale as @xmath237 ) and the magnetic field produced by the surface code . since the latter scales as @xmath238 , see appendix [ app : swlongitudinal ] , the longitudinal field produced by the memory can safely be ignored .
the magnetic length thus scales again as @xmath239 . in real space
we have @xmath240 .
this worst case is thus analogous to choosing @xmath16 in the hamiltonian discussed in sec .
[ sec : previous ] , for which the anyon chemical potential grows logarithmically with @xmath6 and the memory lifetime grows polynomially . again , this is what one would have expected , since in the holstein - primakoff picture the longitudinal spin component at @xmath23 is given by @xmath241 .
whether there is a physical hamiltonian that allows for thermally stable storage of quantum information is a big open question in theoretical physics .
the answer will depend on what properties are required for a hamiltonian to deserve the label `` physical '' . if one only requires bounded strength and locality of interactions , the answer is affirmative , as the 4d toric code shows @xcite .
the 4d toric code also constitutes the only known example of a quantum memory hamiltonian for which it is rigorously proven that the lifetime grows without bounds ( below a critical temperature ) and that it is stable against arbitrary ( local and weak enough ) perturbations .
requiring locality in at most three dimensions excludes the 4d toric code , but boson - mediated long - range interactions still can make the energetic penalty for creating an anyon arbitrarily high @xcite .
if one additionally requires that all operators be bounded ( and thereby excludes bosonic operators ) , the cubic code @xcite still exhibits self - correcting behavior .
finally , if one takes into account that interactions in nature are in fact two - body and thus requires that all terms in the hamiltonian involve at most two spins , one excludes all existing proposals . in this work
, we have shown that even under this most rigid understanding of what constitutes a `` physical '' hamiltonian , we can still expect to observe self - correcting behavior .
the quantum memory hamiltonian of ref . emerges as the low - energy effective theory of a 3d model with bounded - strength interactions between nearest - neighbor spins only .
this effective hamiltonian describes the low - energy , long - wavelength response of the system , and self - correcting behavior can only be observed if the noise affecting the memory is such that this description remains valid .
this work was supported by the swiss nf , nccr qsit , and iarpa .
is grateful for support from the alexander von humboldt foundation .
consider some hamiltonian @xmath242 with an energetic gap @xmath66 between a low- and a high - energy subspace . in the context of the perturbative gadgets in sec .
[ sec : gadgets ] , @xmath242 will simply describe the energy splitting @xmath66 of a _ mediator qubit _ , _
i.e. _ , an auxiliary qubit that mediates interactions between adjacent qubits . given some perturbation @xmath243 with @xmath244 , the modified hamiltonian @xmath245 will display a low - energy subspace of the same dimension as the one of @xmath242 , which is separated from the high - energy spetrum by a gap of at least @xmath246
. the sw transformation is then defined as a unitary operator @xmath247 ( with @xmath222 anti - hermitian ) , such that @xmath248 is block - diagonal with respect to the high- and low - energy subspaces of @xmath242 . together with the requirement that @xmath222 be block - off - diagonal with respect to the low- and high - energy subspaces of @xmath242 and that @xmath249 , this specifies @xmath222 uniquely @xcite .
let @xmath250 denote the projector onto the low - energy subspace of @xmath242 .
the _ effective low - energy hamiltonian _
@xmath251 can be expanded in a perturbative series @xmath252 , where explicit formulae for the low - order effective terms can be derived from ref . .
let @xmath253 , @xmath254 , and @xmath255 .
we have @xmath256 @xmath257 @xmath258p\,,\end{aligned}\ ] ] and @xmath259,{v_{{\mathrm{od}}}}\right]p\,.\end{aligned}\ ] ] in the last two expressions , @xmath260 is the liouvillian superoperator @xmath261 $ ] , whose inverse is given by @xmath262 for the second order effective hamiltonian , one finds the concise formula @xmath263p\,.\end{aligned}\ ] ] we note that with @xmath264 we have @xmath265 which leads to eq . .
we show here a detailed derivation of eq . of the main text with the use of a perturbative schrieffer - wolff transformation similar to ref .
we assume here that the fm is in broken - symmetry state with magnetization along @xmath41-direction and we couple the surface code to the transverse @xmath42 component of the fm spins : @xmath266 where @xmath267 is a general @xmath114-spin hamiltonian and @xmath268 arbitrary operators which commute with @xmath267 and with each other .
the fourier components are defined through @xmath269 and @xmath270 , where @xmath271 denotes the number of spins @xmath119 and @xmath272 their site . here
we identify the projector @xmath250 as the operator projecting onto the subspace with a fixed number of magnons @xmath273 . since @xmath274 does not conserve the number of magnons ,
it is clear that @xmath275 and @xmath276 .
note that we have absorbed the symmetry - breaking term @xmath277 into @xmath267 . up to second order
, we obtain from eq .
@xmath278\nonumber\\ & = -\frac{i}{2}\lim\limits_{\eta\rightarrow0^{+}}\sum_{{\bf q},{\bf q}'}\int_{0}^{\infty}{\mathrm{d}}t\,e^{-\eta t } \times{\nonumber}\\&\quad \left([s_{{\bf
q}}^{x}(t),s_{{\bf q}'}^{x}]a_{-{\bf q}'}a_{-{\bf q}}+s_{\bf q}^{x}(t)s_{{\bf q}'}^{x}\underbrace{[a_{-{\bf q}},a_{-{\bf q}'}]}_{=0}\right)\,.\nonumber\\\end{aligned}\ ] ] we assume that the @xmath114-spins are in thermal equilibrium , described by the canonical density matrix @xmath279 , where @xmath39 is the @xmath114-spin hamiltonian without the coupling to the plaquettes and corresponds to the main part of the hamiltonian in eq .
( [ eq : hamiltonian_supp ] ) , _ i.e. _ , @xmath280 . in doing so
, we neglect the backaction of the toric code on the ferromagnet .
this backaction will be addressed in appendix [ app : dynamics ] below where we show that it leads to a localized effect on the ferromagnet which becomes relevant when the size of the toric code increases ( see also sec . [ sec : backaction ] in the main text ) . here , we rely on a formal perturbation expansion in powers of @xmath281 . convergence of this formal expansion is an interesting question by itself and can be approached along the lines discussed in ref . .
however , such rigorous treatment is beyond the present scope .
still , in the one - magnon ( or harmonic ) approximation , the effective hamiltonian eq . in the main text is exact in all orders of @xmath282 , thus showing that all higher order contributions of the schrieffer - wolff expansion vanish exactly in the one - magnon regime .
the equilibrium expectation values are denoted by @xmath283 . since @xmath242 is translationally invariant , such that @xmath284 , we have @xmath285 , and thus @xmath286\right\rangle a_{{\bf q}}a_{-{\bf q}}{\nonumber}\\&=-\frac{1}{2}\sum_{\bf q}a_{-{\bf q}}\chi_{xx}({\bf q})a_{\bf q}\ , \end{aligned}\ ] ] where @xmath287 is the static spin susceptibility . we are now interested in the case where the surface code is coupled to the longitudinal component of the fm spins : @xmath288 where the sum runs over the @xmath289 lattice sites lying in the plane of the surface code .
the main part @xmath267 is the hamiltonian of the fm , _
i.e. _ , @xmath290 , which contains the symmetry - braking term @xmath291 . as above
, we identify @xmath250 as the operator projecting onto the subspace with a fixed number of magnons @xmath273 . in order to distinguish between the diagonal and off - diagonal parts of the perturbation , it is useful to apply the holstein - primakoff transformation in the harmonic approximation ( see eq .
( 6 ) in the main text ) . doing so we obtain @xmath292 in fourier space eq .
( [ eq : perturbation_z ] ) reads @xmath293 it is now straightforward to distinguish between the diagonal and the off - diagonal part of the perturbation , namely @xmath294 absorbing @xmath295 into the main part of the hamiltonian , we rewrite @xmath296 with ( in the harmonic approximation ) @xmath297 where , as in the main text @xmath298 , we assumed that the surface code is free of anyons , _
i.e. _ , @xmath299 , and we used @xmath117 .
we see from eq .
( [ eq : h0prime ] ) that the backaction effect of the surface code increases the gap of the magnons from @xmath155 to @xmath300 .
however this additional term has no weight in the thermodynamic limit since it scales with @xmath301 . using the specific choice of scaling from the main text
, we have @xmath302 while @xmath303 . in the thermodynamic limit
the magnetic length is thus just given by the external magnetic field @xmath155 @xmath304 this allows us to safely conclude that the backaction of the surface code is negligible in this case . using eq . , we find @xmath305\nonumber\\ & = \frac{a^2}{2n_{s}^2}\sum_{i , j}w_iw_j\sum_{{\bf q}\neq { \bf q}'}\frac{n_{\bf q}-n_{{\bf q}'}}{\epsilon_{\bf q}-\epsilon_{{\bf q}'}}e^{i({\bf q}-{\bf q}')\cdot({\bf r}_{i}-{\bf r}_{j})}\nonumber\\ & = \frac{a^2}{2n_{s}^2}\sum_{i , j}w_iw_j\sum_{{\bf q}',{\bf k}}\frac{n_{{\bf k}+{\bf q}'}-n_{{\bf q}'}}{\epsilon_{{\bf k}+{\bf q}'}-\epsilon_{{\bf q}'}}e^{i{\bf k}\cdot({\bf r}_{i}-{\bf r}_{j})}\nonumber\\ & = -\frac{a^2}{2n_{s}^2}\sum_{i , j}w_{i}w_{j}\sum_{{\bf q},{\bf k}}\frac{e^{\beta(\epsilon_{{\bf k}+{\bf q}}-\epsilon_{{\bf k } } ) } } { \epsilon_{{\bf k}+{\bf q}}-\epsilon_{{\bf k}}}n_{{\bf k}+{\bf q}}(n_{{\bf k}}+1)e^{i{\bf q}\cdot({\bf r}_{i}-{\bf r}_{j})}\nonumber\\ & = -\frac{a^2}{2n_{s}}\sum_{i , j}w_{i}w_{j}\sum_{\bf k}\chi_{zz}({\bf q},\omega=0)e^{i{\bf q}({\bf r}_{i}-{\bf r}_{j})}\label{eq : long}\end{aligned}\ ] ] where the last equality comes from the definition of the susceptibility in eq
. evaluated in the one - magnon approximation . following the approach of ref .
assuming that @xmath306 , we have that @xmath307 where @xmath308 . from eqs .
( [ eq : long ] ) and ( [ eq : zz ] ) , we finally find a chemical potential for the anyons @xmath309 as shown in the main text .
we note that the term @xmath310 in @xmath311 leads to an increase of the chemical potential by @xmath312 .
however , this term does not scale with @xmath6 and can be neglected for large @xmath6 .
for simplicity , we write in this appendix @xmath173 instead of @xmath209 , where @xmath209 is as given in eq . . furthermore , we are interested in the stable regime of the quantum memory , where topological defects are created on time - scales larger than the time on which fm - spins close to the toric code adjust .
we thus assume @xmath313 for all stabilizers @xmath314 . in the one - magnon approximation
, we then have @xmath315 with @xmath316 and @xmath317\approx2js{\bf k}^2 $ ] .
we define the polaron transformation @xcite @xmath322 which exactly diagonalizes @xmath173 .
we have @xmath323 = a_i - \frac{\sqrt{2s}a}{n_{s}}\sum_{p}\sum{_{\bf{k}}}\frac{1}{{\epsilon}{_{\bf{k}}}}e^{i{\bf k}({\bf r}_i-{\bf r}_{p})}\end{aligned}\ ] ] and @xmath324 = a{_{\bf{k}}}- \frac{\sqrt{2s}a}{\sqrt{n_{s}}}\sum_p\frac{1}{{\epsilon}{_{\bf{k}}}}e^{-i{\bf k}{\bf r}_p}\end{aligned}\ ] ] using these two relations , one easily shows that @xmath325 in order to further evaluate the sum @xmath329 , we go to the continuum limit and replace it by the integral @xmath330 .
we also use the small-@xmath11/small-@xmath155 expansion of the magnon dispersion , @xmath331 .
we obtain @xmath332 - 2js{\bf k}^2 t ) - \cos[{\bf k}({\bf r}_i-{\bf r}_{p})]\right ) { \nonumber}\\ & \approx\frac{a}{\pi j}\sum_{p}\frac{1}{|{\bf r}_i-{\bf r}_p|}\left(c(\frac{|{\bf r}_i-{\bf r}_p|}{\sqrt{4\pi jst } } ) + s(\frac{|{\bf r}_i-{\bf r}_p|}{\sqrt{4\pi jst } } ) - 1\right)\,,\end{aligned}\ ] ] let us first study a fm spin adjacent to the code plane . in the long - time limit @xmath335 , we have , approximating the code by a disk of radius @xmath336 around our spin of interested at @xmath212 , @xmath337 as @xmath221 is bounded by @xmath222 , this can of course only be valid for code sizes @xmath338 .
let us thus consider the opposite limit of a code which is large enough such that the integral in the integration over all code plaquettes can formally be extended to infinity .
then , the fm spins next to the code align with the local field in a diffusive way , with diffusion constant @xmath220 .
for a large enough code , the evolution of a local fm spin is independent of the code size , as expected . for a spin with distance @xmath226 to the code ,
the integration is more involved and one finds the deviation decays quadratically with the distance from the code . the results in eqs . and both diverge as @xmath335 .
this is an artefact of the harmonic ( one - magnon ) expansion .
we thus trust these results only for times @xmath341 such that @xmath223 . | in [ phys . rev . a 88 , 062313 ( 2013 ) ] we proposed and studied a model for a self - correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size .
this positive behavior is due to attractive long - range interactions mediated by a bosonic field to which the memory is coupled .
the crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five - body interactions between the stabilizer operators of the memory and the bosonic field . here
, we show that both of these ingredients appear in a low - energy effective theory of a hamiltonian that involves only two - body interactions between neighboring spins . in particular , we consider the low - energy , long - wavelength excitations of an ordered heisenberg ferromagnet ( magnons ) as a realization of the bosonic field . furthermore , we present perturbative gadgets for generating the required five - spin operators .
our hamiltonian involving only local two - body interactions is thus expected to exhibit self - correcting properties as long as the noise affecting it is in the regime where the effective low - energy description remains valid . |
because the dynamics of financial markets are of great importance in economics and econophysics @xcite , the dynamics of both stock price and trading volume have been studied for decades as a prerequisite to developing effective investment strategies .
econophysics research has found that the distribution of stock price returns exhibits power - law tails and that the price volatility time series has long - term power - law correlations @xcite . to better understand these scaling features and correlations , yamasaki _ et al .
_ @xcite and wang _ et al . _
@xcite studied the behavior of price return intervals @xmath0 between volatilities occurring above a given threshold @xmath1 . for both daily and intraday financial records
, they found that ( i ) the distribution of the scaled price interval @xmath8 can be approximated by a stretched exponential function , and ( ii ) the sequence of the price return intervals has a long term memory related to the original volatility sequence .
the scaling and memory properties of financial records are similar to those found in climate and earthquake data @xcite .
a feature of the recent history of the stock market has been large price movements associated with high volume . in the black monday stock market crash of 1987 ,
the dow jones industrials average ( djia ) plummeted 508 points , losing 22.6 percent of its value in one day , which led to the pathological situation in which the bid price for a stock actually exceeded the ask price . in this financial crash
approximately @xmath9 shares traded , a one - day trading volume three times that of the entire week previous .
understanding the precise relationship between price and volume fluctuations has thus been a topic of great interest in recent research @xcite .
trading volume data in itself contains much information about market dynamics , e.g. , the distribution of the daily traded volume displays power - law tails with an exponent within the lvy stable domain @xcite .
recently , ren and zhou @xcite studied the intraday database of two composite indices and 20 individual indices in the chinese stock markets .
they found that the intraday volume recurrence intervals show a power - law scaling , short - term correlations and long - term correlations in each stock index . in this study
we analyze u.s .
stock market data over a range broad enough to allow us to identify how several financial factors significantly affect scaling properties .
we study the daily trading volume volatility return intervals @xmath0 between two successive volume volatilities above a certain threshold @xmath1 , and find a range of power - law distributions broader than that found earlier in price volatility return intervals @xcite .
we find a unique scaling of the probability density function ( pdf ) @xmath2 for different thresholds @xmath1 .
we also perform a detailed analysis of the relation between volume volatility return intervals and four financial stock factors : ( i ) stock lifetime , ( ii ) market capitalization , ( iii ) average trading volume , and ( iv ) average trading value .
we find systematically different power - law exponents for @xmath2 when binning stocks according to these four financial factors .
similar to that found for the chinese market @xcite , we find that in the u.s .
stock market the conditional probability distribution , @xmath6 for @xmath0 following a certain interval @xmath7 , demonstrates that volume return intervals are short - term correlated .
we also find that the daily volume volatility shows a stronger long - term correlation for sequences of longer lifetime but no clear changes in long - term correlations for different stock size factors such as capitalization , volume , and trading value .
in order to obtain a sufficiently long time series , we analyze the daily trading volume volatility of 17,197 stocks listed in the u.s .
stock market for at least 350 days .
we obtain our data from the center for research in security prices ( crsp ) us stock database , which lists the daily prices of all listed nyse , amex , and nasdaq common stocks , along with basic market indices .
the period we study extends from 1 january 1989 to 31 december 2008 , a total of 5042 trading days .
for a stock trading volume time series , in a manner similar to stock price analysis @xcite , we define two basic measures : volume return @xmath10 and volume volatility @xmath11 .
the volume return @xmath10 is defined as the logarithmic change in the successive daily trading volume for each stock , @xmath12 where @xmath13 is the daily trading volume at time @xmath14 .
we define volume volatility to be the absolute value of the volume return . in order to compare different stocks , we determine the volume volatility @xmath15 by dividing the absolute returns @xmath16 by their standard deviation , @xmath17 where @xmath18 is the time average for each stock .
the threshold @xmath1 is thus measured in units of standard deviation of absolute volume return @xmath16 . for a volume volatility time series
, we collect the time intervals @xmath0 between consecutive volatilities
@xmath15 above a chosen threshold @xmath1 and construct a new time series of volume return intervals @xmath19 . fig . [ fig1](a ) shows the dependence of @xmath2 on @xmath1 , where @xmath2 is the pdf of the volume volatility return interval time series @xmath19 .
obviously , @xmath2 decays more slowly for large @xmath1 than for small @xmath1 . for large @xmath1
, @xmath2 has a higher probability of having large interval values because extreme events are rare in a high threshold series .
we next determine whether there is there any scaling in the distribution by plotting the pdfs of the volume return intervals @xmath2 , scaled with the mean volume return interval @xmath20 , for different thresholds in fig .
[ fig1](b ) .
we can see that all five threshold values @xmath1 curves ( full symbols ) callapse onto a single curve , suggesting the existence of a scaling relation , @xmath21 as the threshold @xmath1 increases , the curve ( rare events ) tends to be truncated due to the limited size of the dataset .
the tails of the scaling function can be approximated by a power - law function as shown by the dashed line in fig .
[ fig1](b ) , @xmath22 where the tail exponent is @xmath23 .
the exponent of the scaled pdfs for @xmath24 is @xmath25 by the least square method , which is the same as the unscaled pdf exponent @xmath25 as shown in fig .
[ fig1](a ) .
the power - law exponents for intraday volume recurrence intervals of several chinese stock indices are from @xmath26 to @xmath27 @xcite .
our exponents @xmath23 are larger than those in the chinese stock markets
. this might be due to differing definitions of volume volatility . in ref .
@xcite , the volume volatility is defined as intraday volume divided by the average volume at one specific minute of the trading day averaged over all trading days . here
we define the volume volatility to be the logarithmic change in the successive daily volumes [ eqs .
[ return.eq ] and [ volatility.eq ] ] . for comparison , and using the same approach , fig .
[ fig1](c ) and fig .
[ fig1](d ) show the analogous results for price volatilities ( see also the studies in refs .
note that it is not easy to distinguish between a stretched exponential and a power - law when studying price volatilities @xcite , i.e. , the power - law range is small and a stretched exponential could also provide a good fit .
in contrast , the pdfs of the volume volatility return intervals display a wide range of power - law tails , which differs from the stretched exponential tail apparent in the price return intervals @xcite . our results for volume volatility may suggest that @xmath2 for price volatility is also a power - law , but this could not be verified because the range of the observed power - law regime [ see figs .
[ fig1](c ) and [ fig1](d ) ] is more limited than the broad range of scales seen in the volume volatility [ figs .
[ fig1](a ) and [ fig1](b ) ] .
the difference between the power - law and stretched exponential behavior of @xmath2 may be related to the existence or non - existence respectively of non - linearity represented in the multifractality of the time series . when non - linear correlations appear in a time record , bugachev _ et al . _
@xcite showed that @xmath2 is a power - law . on the other hand , when non - linear correlations do not exist and
only linear correlation exists , bunde _
_ @xcite found stretched exponential behavior .
a comparison with the shuffled records allows us to see how the empirical records differ from randomized records .
we shuffle the volume volatility time series to make a new uncorrelated sequence of volatility , and then collect the time intervals above a given threshold @xmath1 to obtain synthetic random control records .
the curve that fits the shuffled records [ the open symbols in fig .
[ fig1](b ) ] is an exponential function , @xmath28 , and forms a possion distribution .
a poisson distribution indicates no correlation in shuffled volatility data , but the empirical records suggest strong correlations in the volatility .
we study the relation between the scaled pdfs @xmath29 as a function of @xmath8 for four financial factors : ( a ) stock lifetime , ( b ) market capitalization , ( c ) mean volume , and ( d ) mean trading value for threshold @xmath30 . for higher @xmath1 values , we do not have sufficient data for conclusive results @xcite . in fig .
[ fig2 ] , we plot the scaled pdfs for these four factors .
the volume return intervals characterize the distribution of large volume movements . a high probability of having a large volume return interval @xmath0 suggests a correlation in volume volatility ,
because small volatilities are followed by small volatilities and the time interval between the two large volatilities becomes relatively longer than those of random records . in order to charaterize how these four factors affect the distribution of volume return intervals
, we divide all stocks into four bins for each factor . in fig .
[ fig2](a ) , the probability that @xmath0 will be large is greater in the bin with 15@xmath3120 year old stocks ( triangles ) than in the bins of younger stock .
this indicates that small volatilities ( below the threshold ) tend to follow small volatilities and that the time intervals between large volatilities in the bin of 15@xmath3120 year - old stocks are larger than the time intervals in the bin of 5 years old stocks ( dots ) .
this also suggests that the volume volatility time records of older stocks are more auto - correlated than those of younger stocks .
the decaying parameters represented by the power - law exponents are quite different : @xmath32 for the shortest lifetime bin and @xmath33 for the longest lifetime bin
. this significant difference might be caused by differences in autocorrelation in these series . in figs .
[ fig2](b ) , [ fig2](c ) , and [ fig2](d ) , we show a similar tendencies for stock bins with different capitalizations , mean volumes , and mean trading values . trading value is defined as stock price multiplied by transaction volume . for each stock ,
we designate the lifetime average of capitalization , volume , and trading value as performance indices .
for example , the power - law exponents of the pdfs , @xmath29 , increase as the capitalization becomes larger [ see fig . [ fig2](b ) ] . to clarify the picture
, we divide all stocks into different subsets and study the behavior of the power - law exponent @xmath23 with regard to these four factors . in fig .
[ fig3](a ) , stocks are sorted into 10 subsets , from 508 days ( 2 years ) to 5080 days ( 10 years ) .
we fit the power - law tails of the volume return intervals for each subset and plot the exponent @xmath23 versus the lifetime of the stocks . in fig .
[ fig3](a ) , we can observe a systematic trend with stock lifetime .
it is seen that a smaller exponent @xmath23 which indicates a stronger correlation in older stock subsets .
similarly , we sort the stocks by capitalization , mean volume , and mean trading value , as shown in figs .
[ fig3](b ) , [ fig3](c ) , and [ fig3](d ) .
it is seen that @xmath23 decreases with increasing of all these three factors but seem to become constant for large values of capitalizations , mean volumes and mean trading values .
since all factors similarly affect the scaling of the pdf , @xmath29 , we now determine how much these factors are correlated .
to study the relations between different stock bins , we plot the relation between trading value versus capitalization , mean volume versus capitalization , and mean trading value versus mean volume for all the stocks shown in fig .
we see that larger capitalization stocks tend to have a larger trading volume and a larger trading value , which is consistent with figs . [ fig1](b ) , [ fig1](c ) , and [ fig1](d ) .
the correlation coefficients between trading value and capitalization , mean volume and capitalization , and trading value and volume are 0.62 , and 0.55 , and 0.78 , respectively .
the correlation coefficients are high because these capitalization , volume , and trading value factors are all affected by firm size .
our analyses do not , however , show a significant relationship between stock lifetime and its trading value , capitalization , and mean volume , and the correlation coefficients are all @xmath34 .
we characterize a sequence of volume return intervals in terms of the autocorrelations in the time series .
if the volume return intervals series are uncorrelated and independent of each other , their sequences can be determined only by the probability distribution . on the other hand ,
if the series is auto - correlated , the preceding value will have a memory effect on the values following in the sequence of volume volatility return intervals . in order to investigate whether short - term memory is present , we study the conditional pdf , @xmath6 , which is the probability of finding a volume return interval @xmath0 immediately after an interval of size @xmath7 . in records without memory ,
@xmath6 should be identical to @xmath2 and independent of @xmath7 .
otherwise , @xmath6 should depend on @xmath7 . because the statistics for @xmath7 of a single stock are of poor quality
, we study @xmath6 for a range of @xmath35 .
the entire dataset is partitioned into eight equal - sized subsets , @xmath36 , with intervals of increasing size @xmath37 .
figure [ fig5 ] shows the pdfs @xmath6 for @xmath38 , i.e. , small interval size @xmath39 and @xmath40 large interval size @xmath41 for different @xmath1 .
the probability of finding large @xmath8 is larger in @xmath40 ( open symbols ) than in @xmath38 ( full symbols ) , while the probability of finding small @xmath8 is larger in @xmath38 than that in @xmath40 .
thus large @xmath7 tends to be followed by large @xmath0 , and vice versa , which indicates short - term memory in the volume return intervals sequence .
moreover , note that @xmath6 in the same subset for different thresholds @xmath1 fall onto a single curve , which indicates the existence of a unique scaling for the conditional pdfs as well .
similar results were found for the volume volatility of the chinese markets @xcite and for price volatilities @xcite .
in previous studies , the price volatility series was shown to have long - term correlations . using a similar approach
, we test whether the volume volatility sequence also possesses long - term correlations . to answer this question
, we employ the detrended fluctuation analysis ( dfa ) method @xcite to further reveal memory effects in the volume volatility series . using the dfa method ,
we divide an integrated time series into boxes of equal length @xmath42 and fit a least squares line in each box .
next we compute the root - mean - square fluctuation @xmath43 of the detrended time series within a window of @xmath42 points and determine the correlation exponent @xmath44 from the scaling function @xmath45 , where @xmath46 $ ] .
the correlation exponent @xmath44 characterizes the autocorrelation in the sequence .
the time series has a long - term memory and a positive correlation if the exponent factor @xmath47 , indicating that large values tend to follow large values and small values tend to follow small values .
the time series is uncorrelated if @xmath48 and anti - correlated if @xmath49 . using the dfa method
, we analyze the price volatility and volume volatility time series by plotting in bins the relation between correlation exponent @xmath44 and the four financial factors , including stock lifetime , market capitalization , mean trading volume , and mean trading value . all the price volatility and volume volatility correlation exponents are significantly larger than 0.5 , suggesting the presence of long - term memory in both price volatility sequences and volume volatility sequences . in all of the plots ,
the price volatility series shows a stronger long - term correlation than the volume volatility series .
moreover , as shown in fig .
[ fig6](a ) , @xmath44 on average increases for the stocks with a lifetime ranging from 350 days to 3800 days ( about 15 years ) , and then shows a slight decrease , suggesting that long - lasting stocks tend to have a persistent price and volume movement on large scales .
the increasing exponent @xmath44 indicates that the volume volatility of older stocks is more correlated than that of younger stocks .
this is consistent with the indication in fig .
[ fig2](a ) that the volume volatility of older stocks are more auto - correlated .
figures [ fig6](b ) , [ fig6](c ) , and [ fig6](d ) show that there is no systematic tendency relation between @xmath44 and market capitalization , trading volume , and trading value .
we have shown the scaling properties and memory effect of volume volatility return intervals in large stock records of the u.s .
the scaled distribution of volume volatility return intervals displays unique power - law tails for different thresholds @xmath1 .
we also find different power - law exponents @xmath23 of @xmath2 for the four essential stock factors : stock lifetime , market capitalization , average trading volume , and average trading value .
these different exponents may be related to long - term correlations in the interval series .
significantly , the daily volume volatility exhibits long - term correlations , similar to that found for price volatility .
the conditional probability , @xmath6 for @xmath0 following a certain interval @xmath7 , indicates that volume return intervals are short - term correlated .
g. w. schwert , j. financ .
* 44 * , 1115 ( 1989 ) ; k. chan , k. c. chan , and g. a. karolyi , rev .
financ . stud . * 4 * , 657 ( 1991 ) ; t. bollerslev , r. y. chou , and k. f. kroner , j. econometr . * 52 * , 5 ( 1992 ) ; a. r. gallant , p. e. rossi , and g. tauchen , rev .
financ . stud . * 5 * , 199 ( 1992 ) ; b. le baron , j. business * 65 * , 199 ( 1992 ) . | we study the daily trading volume volatility of 17,197 stocks in the u.s .
stock markets during the period 19892008 and analyze the time return intervals @xmath0 between volume volatilities above a given threshold @xmath1 . for different thresholds @xmath1 ,
the probability density function @xmath2 scales with mean interval @xmath3 as @xmath4 and the tails of the scaling function can be well approximated by a power - law @xmath5 .
we also study the relation between the form of the distribution function @xmath2 and several financial factors : stock lifetime , market capitalization , volume , and trading value . we find a systematic tendency of @xmath2 associated with these factors , suggesting a multi - scaling feature in the volume return intervals .
we analyze the conditional probability @xmath6 for @xmath0 following a certain interval @xmath7 , and find that @xmath6 depends on @xmath7 such that immediately following a short / long return interval a second short / long return interval tends to occur .
we also find indications that there is a long - term correlation in the daily volume volatility .
we compare our results to those found earlier for price volatility . |
SECTION 1. FINDINGS AND PURPOSES.
(a) Findings.--Congress finds the following:
(1) Approximately 60 percent of Indian tribe members and
Alaska Natives live on or adjacent to Indian lands, which
suffer from an average unemployment rate of 45 percent.
(2) Indian tribe members and Alaska Natives own more than
197,000 businesses and generate more than $34,000,000,000 in
revenues. The service industry accounted for 17 percent of
these businesses (of which 40 percent were engaged in business
and personal services) and 15.1 percent of their total
receipts. The next largest was the construction industry (13.9
percent and 15.7 percent, respectively). The third largest was
the retail trade industry (7.5 percent and 13.4 percent,
respectively).
(3) The number of businesses owned by Indian tribe members
and Alaska Natives grew by 84 percent from 1992 to 1997, and
their gross receipts grew by 179 percent in that period. This
is compared to all businesses which grew by 7 percent, and
their total gross receipts grew by 40 percent, in that period.
(4) The Small Business Development Center program is cost
effective. Clients receiving long-term counseling under the
program in 1998 generated additional tax revenues of
$468,000,000, roughly 6 times the cost of the program to the
Federal Government.
(5) Using the existing infrastructure of the Small Business
Development Center program, small businesses owned by Indian
tribe members, Alaska Natives, and Native Hawaiians receiving
services under the program will have a higher survival rate
than the average small business not receiving such services.
(6) Business counseling and technical assistance is
critical on Indian lands where similar services are scarce and
expensive.
(7) Increased assistance through counseling under the Small
Business Development Center program has been shown to reduce
the default rate associated with lending programs of the Small
Business Administration.
(b) Purposes.--The purposes of this Act are as follows:
(1) To stimulate economies on Indian lands.
(2) To foster economic development on Indian lands.
(3) To assist in the creation of new small businesses owned
by Indian tribe members, Alaska Natives, and Native Hawaiians
and expand existing ones.
(4) To provide management, technical, and research
assistance to small businesses owned by Indian tribe members,
Alaska Natives, and Native Hawaiians.
(5) To seek the advice of local Tribal Councils on where
small business development assistance is most needed.
(6) To ensure that Indian tribe members, Alaska Natives,
and Native Hawaiians have full access to existing business
counseling and technical assistance available through the Small
Business Development Center program.
SEC. 2. SMALL BUSINESS DEVELOPMENT CENTER ASSISTANCE TO INDIAN TRIBE
MEMBERS, ALASKA NATIVES, AND NATIVE HAWAIIANS.
(a) In General.--Section 21(a) of the Small Business Act (15 U.S.C.
648(a)) is amended by adding at the end the following:
``(8) Additional grant to assist indian tribe members,
alaska natives, and native hawaiians.--
``(A) In general.--Any applicant in an eligible
State that is funded by the Administration as a Small
Business Development Center may apply for an additional
grant to be used solely to provide services described
in subsection (c)(3) to assist with outreach,
development, and enhancement on Indian lands of small
business startups and expansions owned by Indian tribe
members, Alaska Natives, and Native Hawaiians.
``(B) Eligible states.--For purposes of
subparagraph (A), an eligible State is a State that has
a combined population of Indian tribe members, Alaska
Natives, and Native Hawaiians that comprises at least 1
percent of the State's total population, as shown by
the latest available census.
``(C) Grant applications.--An applicant for a grant
under subparagraph (A) shall submit to the
Administration an application that is in such form as
the Administration may require. The application shall
include information regarding the applicant's goals and
objectives for the services to be provided using the
grant, including--
``(i) the capability of the applicant to
provide training and services to a
representative number of Indian tribe members,
Alaska Natives, and Native Hawaiians;
``(ii) the location of the Small Business
Development Center site proposed by the
applicant;
``(iii) the required amount of grant
funding needed by the applicant to implement
the program; and
``(iv) the extent to which the applicant
has consulted with local Tribal Councils.
``(D) Applicability of grant requirements.--An
applicant for a grant under subparagraph (A) shall
comply with all of the requirements of this section,
except that the matching funds requirements under
paragraph (4)(A) shall not apply.
``(E) Maximum amount of grants.--No applicant may
receive more than $300,000 in grants under this
paragraph for one fiscal year.
``(F) Regulations.--After providing notice and an
opportunity for comment and after consulting with the
Association recognized by the Administration pursuant
to paragraph (3)(A) (but not later than 180 days after
the date of enactment of this paragraph), the
Administration shall issue final regulations to carry
out this paragraph, including regulations that
establish--
``(i) standards relating to educational,
technical, and support services to be provided
by Small Business Development Centers receiving
assistance under this paragraph; and
``(ii) standards relating to any work plan
that the Administration may require a Small
Business Development Center receiving
assistance under this paragraph to develop.
``(G) Definitions.--In this section, the following
definitions apply:
``(i) Indian lands.--The term `Indian
lands' has the meaning given the term `Indian
country' in section 1151 of title 18, United
States Code, the meaning given the term `Indian
reservation' in section 151.2 of title 25, Code
of Federal Regulations (as in effect on the
date of enactment of this paragraph), and the
meaning given the term `reservation' in section
4 of the Indian Child Welfare Act of 1978 (25
U.S.C. 1903).
``(ii) Indian tribe.--The term `Indian
tribe' means any band, nation, or organized
group or community of Indians located in the
contiguous United States, and the Metlakatla
Indian Community, whose members are recognized
as eligible for the services provided to
Indians by the Secretary of the Interior
because of their status as Indians.
``(iii) Indian tribe member.--The term
`Indian tribe member' means a member of an
Indian tribe (other than a Alaska Native).
``(iv) Alaska native.--The term `Alaska
Native' has the meaning given the term `Native'
in section 3(b) of the Alaska Native Claims
Settlement Act (43 U.S.C. 1602(b)).
``(v) Native hawaiian.--The term `Native
Hawaiian' means any individual who is--
``(I) a citizen of the United
States; and
``(II) a descendant of the
aboriginal people, who prior to 1778,
occupied and exercised sovereignty in
the area that now constitutes the State
of Hawaii.
``(vi) Tribal organization.--The term
`tribal organization' has the meaning given
that term in section 4(l) of the Indian Self-
Determination and Education Assistance Act (25
U.S.C. 450b(l)).
``(H) Authorization of appropriations.--There is
authorized to be appropriated to carry out this
paragraph $7,000,000 for each of fiscal years 2006
through 2008.
``(I) Funding limitations.--
``(i) Nonapplicability of certain
limitations.--Funding under this paragraph
shall be in addition to the dollar program
limitations specified in paragraph (4).
``(ii) Limitation on use of funds.--The
Administration may carry out this paragraph
only with amounts appropriated in advance
specifically to carry out this paragraph.''.
SEC. 3. STATE CONSULTATION WITH TRIBAL ORGANIZATIONS.
Section 21(c) of the Small Business Act (15 U.S.C. 648(c)) is
amended by adding at the end the following:
``(9) Advice of local tribal organizations.--A Small
Business Development Center receiving a grant under this
section shall request the advice of tribal organization on how
best to provide assistance to Indian tribe members, Alaska
Natives, and Native Hawaiians and where to locate satellite
centers to provide such assistance.''. | Amends the Small Business Act to authorize a Small Business Development Center in an eligible state to apply for an additional Small Business Administration grant to be used solely to provide services to assist with outreach, development, and enhancement on Indian lands of small business startups and expansions owned by Indian tribe members, Alaskan Natives, and Native Hawaiians. Defines an eligible state as one in which at least one percent of its population is comprised of such tribe members and Natives. Limits each grant to $300,000 in a fiscal year.
Requires a Small Business Development Center receiving such a grant to request the advice of tribal organizations on how best to provide assistance and where to locate satellite centers to provide it. |
born of the prophet muhammad s favorite daughter , fatimah , al - hasan was declared as the legitimate successor of his father , ali ibn - abi - talib ( the last of the caliphs known to arab historians as orthodox ) , in 661 . faced by his rival , muawiyah ibn - abi - sufyan , who had been proclaimed caliph in 660 in jerusalem
, al - hasan abdicated in the same year and reasoned as follows : i have deemed it right to make peace with him and have pledged allegiance to him , since i considered whatever spares blood as better than whatever causes it to be shed . after living in retirement in al - madinah ( in present - day saudi arabia ) for eight years , al - hasan died in 669 , when he was just 45 years of age .
the belief that al - hasan died peacefully has not been ruled out by all the experts on muslim history .
however , in general , muslim theologians commonly believe that his death was caused by a fatal act of poisoning . with autopsy information
unavailable , historical documents are the only available evidence in order to investigate cases such as al - hasan s death scientifically . a few traditions , such as the one containing the following quote , mention that when al - hasan was about to die , he was asked by his younger brother al - husayn to identify his poisoner but refused to do so ( as he wanted no innocent person to be falsely accused and killed):if he / she [ the poisoner ] is not [ i.e. , not the one whom i suspect ] , i would like no innocent person to be killed because of me.still , the following tradition addresses two concurrent acts of poisoning , which resulted in two victims : al - hasan and a survivor .
jadah daughter of al - ashath ibn - qays al - kindi poisoned al - hasan ibn-ali , peace be upon both of them , and poisoned a freedwoman of his ; however , the freedwoman of his vomited the poison while al - hasan kept it in his stomach .
this tradition says that a freedwoman of al - hasan who had also been poisoned vomited the poison and survived , which means that she could have served as forensic evidence for the murder of al - hasan . but are there any historical reports in which the poison is qualitatively described and can lead to a forensic hypothesis for the murder of al - hasan ? if he / she [ the poisoner ] is not [ i.e. , not the one whom i suspect ] , i would like no innocent person to be killed because of me .
jadah daughter of al - ashath ibn - qays al - kindi poisoned al - hasan ibn-ali , peace be upon both of them , and poisoned a freedwoman of his ; however , the freedwoman of his vomited the poison while al - hasan kept it in his stomach .
that al - hasan was offered a poisoned drink by his wife jadah is reported in both shiite and sunni sources . since intoxicating drinks , such as wine , are not allowed in islamic law , the drink itself must have been a nonalcoholic drink . according to one tradition
one tradition describes the poison that was given to al - hasan as follows : it has been said that he was given gold filings to drink .
elemental gold is relatively inert , and an important use for it is in dentistry .
it dissolves in concentrated hydrochloric acid if a strong oxidizing agent is present ( e.g. , in a 3:1 mixture of concentrated hydrochloric acid and concentrated nitric acid ) .
the hydrochloric acid in the human stomach is neither concentrated nor in the presence of a strong oxidizing agent .
what could the true identity of the toxic substance that al - hasan had ingested in the drink have been if the powdered solid phase of the substance only looked like gold filings ? in order to answer this question accurately , it is useful to know the geographic source of the poison .
the tradition referred to in the introduction , which says that a freedwoman of al - hasan had also been poisoned , suggests that the plot to poison al - hasan was because of some harem jealousy .
however , madelung says that al - hasan s pursuit of women was not more covetous than that of most of his class .
it is logically appropriate to ask if the murder of al - hasan could have had a political motive force behind it .
although al - hasan abdicated , in the process of surrendering the reign , he stipulated that his rival should not be entitled to appoint his successor but that there should be an electoral council . still
, when the caliph died in 680 , he had already nominated his own son yazid as his successor and caused homage to be paid to him .
there are reports , accepted by both shiite sources and several major sunni historians , stating that the poisoning of al - hasan by jadah was at the instigation of the caliph .
a very specific report says that in order to eliminate al - hasan , the caliph , whose empire s capital was damascus , wrote to the byzantine emperor and asked him for a poisoned drink , which the emperor , despite refusing at the beginning , sent conditionally .
the mention of the conditionality of the emperor s agreement in this report is consistent with the hostility of arab byzantine relations in 669 ( the year al - hasan died ) , when byzantium had an energetic emperor , constantine iv .
the mainland of the byzantine empire in 668 ( about one year before al - hasan s death ) was approximately present - day turkey ( figure 1 ) .
in present - day western turkey , there are more than 50 mines that contain minerals with deposits of mercury .
mercury is isolated from its main ore , cinnabar ( mercury(ii ) sulfide , hgs ) , and was used in the mediterranean world for extracting metals by amalgamation as early as 500 bc .
the element does not have any known biological functions and has a long history of toxic effects .
mercury(ii ) chloride ( hgcl2 ) , for instance , which was probably first made by arabic alchemists in the 10th century , was widely used as a violent poison in the middle ages .
do the mercury mines in western turkey contain any mercury species that look like gold ?
( chris ambrose , explore byzantium , http://byzantium.seashell.net.nz/ , is credited for the image . )
( chris ambrose , explore byzantium , http://byzantium.seashell.net.nz/ , is credited for the image . ) although abandoned since the 1990s , trkn and haliky are two important mercury mine locations in turkey .
the haliky mine exists in an area made up of metamorphic rocks , including gneiss and schist .
mine locations also contain deposits of pyrite , marcasite , chalcopyrite , arsenopyrite , quartz , and calcite .
the mineral calomel ( mercury(i ) chloride , hg2cl2 ) is found as a secondary mineral in oxidized zones along with cinnabar , calcite , and limonite .
calomel can present as a yellow gold crust ( figure 2 ) and forms as tetragonal crystals presenting in a variety of formations , including tabular , prismatic , and pyramidal .
figure 2.calomel from mariposa mine , texas , usa . ( rob lavinsky , the arkenstone , www.irocks.com , is credited for the image . )
calomel from mariposa mine , texas , usa . ( rob lavinsky , the arkenstone , www.irocks.com , is credited for the image . )
the environmental assessments performed at the mine locations in turkey have utilized computer programs to aid in analysis of the soil and water samples .
the software programs aquachem and phreeqci determined that water samples taken near the haliky mine presented with oversaturation with calomel , as well as quartz and cinnabar .
without an autopsy or any diagnostic testing , it is impossible to diagnose with certainty what poisoned al - hasan .
however , we can hypothesize the type of poison used by the symptoms described in the traditions .
some clinical symptoms described by traditions of al - hasan s death are a green coloring of the skin and vomiting of blood .
these are also symptoms that can be caused by the ingestion of calomel and the resulting mercury intoxication .
calomel acts on the kidneys and causes renal tube necrosis and can lead to acute kidney failure .
the green coloring is due to a type of anemia called hypochromic anemia , also called chlorosis or green sickness .
this type of anemia is caused by a lack of hemoglobin , the oxygen binding protein responsible for nourishing our body tissues with oxygen .
hemoglobin is found within the erythrocytes or red blood cells , and a low erythrocyte count is the most common cause of hypochromic anemia .
if acute renal failure occurred , erythropoietin , the hormone that signals hemiopoetic stem cells in the bone marrow to have a cell fate of becoming erythrocytes , would not be present due to damage of the proximal renal tubule .
the promixal renal tubule is the area in which the red blood cell mass or hematocrit is determined by the kidneys .
it stands to reason that if the hematocrit level could not be correctly sensed due to renal tube necrosis , then the signal that is normally sent to the cortical labyrinth to make erythropoietin would be unlikely to occur .
the lack of this hormone would prevent new erythrocytes from being made , which in turn would result in a lower hemoglobin level , and a person affected by this would present with an ashen appearance , sometimes said to appear green .
the corrosive effects of calomel on the alimentary or gastrointestinal tract are known to cause damage and irritation of the esophagus .
kabid , an arabic word that means liver and also means interior .
if ulceration were to occur in the esophagus , a certain extent of bleeding should be expected .
when human blood reaches the stomach , it is broken down and can coagulate , very often resulting in vomiting a substance that has the appearance of coffee grounds .
this occurrence of vomiting blood is referred to as hematemesis and generally occurs due to esophagitis , bleeding ulcers , and certain cancers .
considering that the understanding of the human body in the 7th century was less extensive , the
commoner s arabic expression to refer to vomited blood clots would have been kabid .
in fact , in some rural areas in the arab world , it is still said , my liver is torn and thrust away ( kabidi mutaqatti ' mat'un ) . in several traditions , al - hasan says that he is vomiting pieces of his kabid , which could have been coagulated blood in the emesis , resembling pieces of his liver and/or internal organs due to the coffee - ground color and texture .
liver damage is another noted effect of mercury intoxication by calomel , which is due to the accumulation of deposits of mercury via the hepatic portal vein system .
this capillary type has the largest pores and is the only type that allows exchange of red blood cells through their pores .
red blood cells have susceptibility of the attachment of corrosive sublimate ( mercury(ii ) chloride , hgcl2 ) by way of a sulfhydryl attachment .
the liver is one of the areas where red blood cells are destroyed when they are damaged , which would allow for more mercury accumulation than the filtering of blood alone .
aqueous calomel ingested by the human body is converted into corrosive sublimate , which is known to have much more harmful effects than calomel alone .
( hgcl2 ) , by oxidation in the hydrochloric acid ( hcl ) within the stomach .
this reaction , which is shown by equation ( 1 ) , goes to completion , as the calculated equilibrium constant for it , at the normal human body temperature ( 37 ) , is keq = 2.4 10 .
( 1)2hg2cl2(aq)+4hcl(aq)+o2(g ) 4hgcl2(aq)+2h2o(l )
calomel absorption into the body tissues is not seen in large quantities . however , it is enough to cause the anemia mentioned previously .
effects of corrosive sublimate , such as intestinal ulceration , are thought to increase the amount absorbed due to the breakdown of protective barriers such as mucous membranes , which prevent absorption before damage .
noting that in the traditions al - hasan refers to being poisoned at least three times , if the initial poisoning had started this damage , the subsequent poisonings would have allowed a much greater amount of absorption of calomel or corrosive sublimate .
in later centuries , for example , when there was an outbreak of syphilis in europe at the end of the 15th century , calomel was routinely ingested as a medicine
. why could the calomel in al - hasan s drink have been lethal ?
after the final poisoning , according to a couple of traditions , he says that he has been poisoned three times , and according to a few other traditions , he conveys the information that he has been poisoned at least four times . if the latter is the case , the number of times he was given calomel could have been too many to survive.according to one tradition , the final poisoning was when al - hasan was breaking his fast ( islamic fast , which includes refraining from eating and drinking from dawn to dusk ) on a hot day .
if that is the case , it will naturally lead to the conclusion that he ingested a large quantity of the drink containing aqueous calomel , which is completely converted to corrosive sublimate in the human stomach according to equation ( 1).the same net ionic equation as that of equation ( 1 ) ( equation ( 2 ) ) may be written for the reaction between any acids in the to - be - ingested nonalcoholic drink and the aqueous calomel in the drink , leading to the formation of mercury(ii ) , which is the mercury in corrosive sublimate .
a couple of examples of common arabic nonalcoholic drinks in the 7th century are honey water and yogurt drink , which both contain acids .
( 2)2hg22+(aq)+4h+(aq)+o2(g ) 4hg2+(aq)+2h2o(l )
with the reaction shown by equation ( 2 ) in the to - be - ingested nonalcoholic drink , al - hasan has ingested some aqueous mercury(ii ) cation , in addition to the ingested aqueous calomel , which is converted to corrosive sublimate later ( in the human stomach , according to equation ( 1)).it is possible that the mineral calomel that was mixed with the drink was naturally accompanied by some other toxic substance(s ) .
after the final poisoning , according to a couple of traditions , he says that he has been poisoned three times , and according to a few other traditions , he conveys the information that he has been poisoned at least four times .
if the latter is the case , the number of times he was given calomel could have been too many to survive . according to one tradition ,
the final poisoning was when al - hasan was breaking his fast ( islamic fast , which includes refraining from eating and drinking from dawn to dusk ) on a hot day .
if that is the case , it will naturally lead to the conclusion that he ingested a large quantity of the drink containing aqueous calomel , which is completely converted to corrosive sublimate in the human stomach according to equation ( 1 ) .
the same net ionic equation as that of equation ( 1 ) ( equation ( 2 ) ) may be written for the reaction between any acids in the to - be - ingested nonalcoholic drink and the aqueous calomel in the drink , leading to the formation of mercury(ii ) , which is the mercury in corrosive sublimate .
a couple of examples of common arabic nonalcoholic drinks in the 7th century are honey water and yogurt drink , which both contain acids .
( 2)2hg22+(aq)+4h+(aq)+o2(g ) 4hg2+(aq)+2h2o(l )
with the reaction shown by equation ( 2 ) in the to - be - ingested nonalcoholic drink , al - hasan has ingested some aqueous mercury(ii ) cation , in addition to the ingested aqueous calomel , which is converted to corrosive sublimate later ( in the human stomach , according to equation ( 1 ) ) .
it is possible that the mineral calomel that was mixed with the drink was naturally accompanied by some other toxic substance(s ) .
records of a green hue to al - hasan s skin , which could occur due to acute renal failure , concurrent with his vomiting of blood and , apparently , coagulated blood in the emesis are decisively consistent with those of calomel intoxication .
mineral calomel can present as a yellow gold crust ( figure 2 ) , which can , in the powdered solid phase , be mistaken for gold filings ( the identity of the poison according to a certain tradition ) .
the effect of al - hasan s poisoned freedwoman s recorded experience seems to indicate that contemporaneously to al - hasan s death , both people suffered the same affliction while residing under a common household .
this , in light of several historical sources , points at al - hasan s wife jadah as the prime suspect .
a considerable number of calomel - containing mercury mines exist in present - day western turkey , which was in the heart of the byzantine empire around the time of al - hasan s death .
the caliph sought to nominate his own son as his successor ( when the caliph died , he had done so and had caused homage to be paid to the son , who actually succeeded him ) .
al - hasan was obtrusively an obstruction to that goal , because that was despite the caliph s official guarantee of al - hasan s stipulation that he ( the caliph ) should not be entitled to appoint his successor .
the report of the caliph s solicitation of the byzantine emperor by writing a letter asking the emperor for a poisoned drink is a clear example of his intent to act in furtherance of the plot , and , according to the report , the emperor s final response was a positive and deliberate agreement to that end .
the fact that neither an autopsy nor a judicial investigation was performed by the authorities at the time should not deter the use in evidence of eyewitness accounts .
mineralogical , medical , and chemical facts support the hypothesis that al - hasan s death was caused by calomel ( mercury(i ) chloride ) intoxication .
this forensic hypothesis is consistent with the historical position , reflected in ancient ( medieval ) documents , that al - hasan was poisoned by jadah , at the instigation of the caliph , and with the byzantine emperor s involvement .
the author(s ) declared no potential conflicts of interest with respect to the research , authorship , and/or publication of this article .
this research received no specific grant from any funding agency in the public , commercial , or not - for - profit sectors . | the puzzle of a mysterious death in the middle ages has been hypothesized in terms of contemporary forensic legal and scientific methods . that al - hasan ibn-ali died in 669 aged
just 45 has been forensically analyzed based on written sources that dictate eyewitness accounts of historical events .
the report of the contemporaneous poisoning of another individual who resided under the same household as al - hasan s and experienced similar , yet non - lethal , symptoms has served as the beginning of the analysis . in light of ancient ( medieval ) documents and through using mineralogical , medical , and chemical facts ,
it has been hypothesized that mineral calomel ( mercury(i ) chloride , hg2cl2 ) from a certain region in the byzantine empire ( present - day western turkey ) was the substance primarily responsible for the murder of al - hasan . |
systemic lupus erythematosus ( sle ) commonly affects females of reproductive age and rarely occurs de novo in pregnancy [ 1 , 2 ] .
roughly 60% of sle patients develop lupus nephritis ( ln ) with increased risk of neonatal and maternal morbidity .
it is also estimated that one third of patients with ln develop nephrotic - range proteinuria , which has only been rarely reported in class i and ii ln as classified by the international society of nephrology / renal pathology society ( isn / rps ) .
herein we report a unique case of sle diagnosed de novo in pregnancy complicated by concomitant minimal change disease ( mcd ) and class ii ln on renal biopsy .
a 22-year - old african american female was transferred to our hospital after delivery of her first live birth .
she initially presented to another facility for a routine antenatal visit in her 34th week of gestation and at that time complained of pedal edema .
her 24-hour urine protein was 10.9 g and she was admitted with suspicion of preeclampsia .
however , she remained normotensive and lacked features of hellp syndrome ( hemolytic anemia , elevated liver enzymes and low platelets ) or neurological disturbances .
laboratory investigations revealed a normal uric acid level , but elevated serum creatinine ( 1.4 mg / dl ) , hypoalbuminemia ( 1.6 g / dl ) , elevated triglycerides ( 1,225 mg / dl ) and total cholesterol ( 404 mg / dl ) .
fetal growth was monitored and delivery was induced at 37 weeks of gestation . upon arrival at our hospital ,
her physical examination was unremarkable except for an erythematous malar rash that she had not previously noticed and bilateral pedal edema .
repeat laboratory investigations were consistent with those done antepartum except for worsened creatinine at 2 mg / dl .
further evaluation of the nephrotic syndrome revealed speckled ana ( 1 : 160 titer ) as well as positive anti - dsdna , anti - sm and anti - rnp antibodies .
tests for anca , ssa / ssb , rf , anti - ccp , hep c ab , hep bsag , and hiv were all negative .
on postpartum day 8 , renal biopsy of 30 glomeruli showed a mild increase in mesangial cellularity and matrix consistent with class ii ln .
there was no segmental or global sclerosis , endocapillary proliferation , or cellular or fibrous crescents .
immunofluorescence studies were positive for focal mesangial granular deposits of igg , iga and c1q , but no definitive igm or c3 deposits were seen .
surprisingly , on electron microscopy the glomerular basement membrane was mildly thickened up to 521 nm with patchy effacement of foot processes .
scant mesangial electron - dense deposits with focal increase in mesangial matrix as well as tubuloreticular inclusions in the glomerular capillary endothelium were also identified .
figure 1 and figure 2 demonstrate these findings . based on the clinical features , laboratory data and biopsy findings
, a diagnosis of sle with class ii ln in addition to mcd was established .
a detailed review of the patient 's history and previous laboratory data did not raise any suspicion of indolent sle prior to this presentation .
treatment with methylprednisolone 1 g daily for 3 days followed by 1 mg / kg daily resulted in a dramatic improvement typical of mcd . within 1 month
, her creatinine returned to baseline and urinalysis showed only trace protein . of note ,
repeat testing for anti - phospholipid antibodies at a 6-month follow - up visit was not consistent with anti - phospholipid syndrome .
our patient fulfilled four of these , including malar rash , positive ana , presence of other autoantibodies and persistent proteinuria .
moreover , kidney biopsy revealed organized subcellular tubuloreticular inclusions in the endothelium , which are strongly associated with ln , albeit of higher classes than in our patient .
it is important to note that there have been only three previous reported cases of sle occurring de novo in pregnancy [ 1 , 2 ] .
our patient differed in that she presented in her third trimester , which posed a diagnostic challenge for two main reasons .
firstly , the more likely cause of proteinuria at that stage of pregnancy was preeclampsia .
however , the absence of hypertension , hyperuricemia and features of hellp syndrome made preeclampsia an unlikely etiology . secondly , a renal biopsy could have revealed the underlying pathology , but it was not advised in late pregnancy due to the risk of complications . as a result ,
her obstetrician opted for close monitoring and timely induction , thus allowing for a postpartum biopsy .
the risk of preterm delivery and fetal loss is higher in pregnant patients with sle and further increased in those with ln .
the immune system in pregnancy is ever evolving to preserve tolerance of the foreign paternal antigens carried by the fetus . as with sle
, there is a shift away from th1 cell - mediated to th2 antibody - mediated responses , which may be the unifying pathway between these otherwise seemingly distinct processes .
another interesting aspect of this case was the concomitant finding of mcd with class ii ln on renal biopsy .
nephrotic syndrome is mainly associated with class iii , iv and v ln , whilst patients with class i and ii ln have < 1 g/24 h proteinuria . in 1984 , abuelo et al .
since then there have been approximately 38 more cases described in the literature [ 9 , 10 ] , but only 7 have involved class ii ln [ 7 , 11 , 12 ] .
the pathogenesis of mcd is not yet fully understood , but factors derived from t cells that increase glomerular permeability have been reported culprits .
as mentioned before , altered t cell activity seems to be also critical to the pathogenesis of sle and may be the link between the simultaneous occurrences of mcd in sle .
additionally , there have been two previous case reports of biopsy - proven de novo mcd in pregnancy in the absence of sle . for similar reasons ,
the th2 polarization driven by fetal tolerance may have been the impetus for the development of mcd in these patients .
the interplay between these three processes sle , pregnancy and mcd is fascinating , and further work is needed to elucidate the underlying pathophysiology .
wong noted that almost all cases of mcd in sle were treated with steroids and were steroid - sensitive , as expected for mcd .
had our patient presented earlier in pregnancy or with a higher class of ln , we would have been challenged to avoid the use of potentially teratogenic immunosuppressants to achieve disease remission . instead , her response was rapid , with an outcome of a healthy newborn and control of her disease .
the altered immune state of pregnancy may have precipitated not only mcd , but also sle in our patient . as a consequence ,
the cause of her proteinuria was not initially obvious , and the renal biopsy was crucial in unmasking the underlying pathology .
this case highlights the importance of thorough investigation of proteinuria in pregnancy and raises awareness of the occurrence of mcd in lower classes of ln .
| we report the case of a 22-year - old african american female who presented to another facility for routine follow - up in the 34th week of pregnancy with lower extremity swelling and nephrotic - range proteinuria .
although she was normotensive , it was initially thought that she had preeclampsia .
she was monitored carefully and delivery was induced at 37 weeks of gestation .
she was transferred to our hospital , where she was diagnosed with systemic lupus erythematosus ( sle ) based on clinical and laboratory criteria .
renal biopsy revealed a surprising finding of minimal change disease ( mcd ) concomitant with class ii lupus nephritis ( ln ) .
she was managed with pulses and then tapering doses of steroid therapy with dramatic resolution of the nephrotic syndrome .
this case demonstrates not only the rare de novo occurrence of sle in pregnancy , but the unique finding of mcd coexisting with class ii ln .
we propose that altered t cell activity may be the link between these seemingly distinct entities . |
does the formation of a massive star differ significantly from that of a low mass star ?
this is the question at the core of all studies of high mass star formation to date .
the fact that massive stars can have kelvin - helmholtz time - scales shorter than their accretion time - scales @xcite , leads to the consequence that their main - sequence radiation can affect their own formation . hence ,
several processes such as radiation pressure ( e.g. * ? ? ?
* ) and ionization ( e.g. * ? ? ?
* ) may halt , decrease or alter accretion on to the star . with the hypothesis that these differences do not radically change the formation of massive stars ,
our main aim is to find observational evidence to suggest the contrary . in this paper
, we aim to determine whether the standard envelope plus disc model used to reproduce the spectral energy distributions ( seds ) of low mass stars ( e.g. * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ; * ? ? ?
* ) is able to reproduce the sed and observed infrared images of the nearby forming early b - type star iras20126 + 4104 .
* henceforth kz10 ) have recently modelled the line profiles of several millimetre - wavelength transitions of nh@xmath1 , c@xmath2s and ch@xmath1cn toward iras20126 + 4104 , fitting these data with two models , the first consisting of an azimuthally symmetric rotationally flattened envelope , and the second also including a flared keplerian disc .
they found that the addition of a disc was required to reproduce the velocity structure of the accreting gas within 0.128pc of the star , providing a better fit than the without - disc model .
additionally , as the model with a disc was able to adequately reproduce the data , their results showed no evidence that ionization or radiation pressure are profoundly altering the dynamics of the surrounding accretion flow . in this work ,
we carry out the same experiment , but instead model the sed and observed infrared images of iras20126 + 4104 . in comparison to the molecular line data , the sed and infrared images of iras20126 + 4104 probe different aspects of the circumstellar material .
the molecular line observations are able to measure the velocity of the gas at different temperatures , however their density determinations depend on abundances that are highly uncertain .
in contrast , the sed and infrared images probe the dust out to the edge of the envelope , which can be used to infer the structure of the gas .
hence , comparing the results from both these datasets will allow us to obtain a more complete picture of the star formation processes occurring in iras20126 + 4104 .
iras20126 + 4104 is a well studied example of a nearby forming massive star ( @xmath310@xmath4l@xmath5 , b0.5 star , * ? ? ?
. found within the cygnus - x star forming region , it is assumed to be at the same distance as the cygnus ob associations ( 1.7kpc , * ? ? ?
* ; * ? ? ?
several observations of molecular tracers at millimetre wavelengths have uncovered a @xmath00.25pc nw - se inner jet feeding a large - scale north - south bipolar outflow @xcite .
in addition , high resolution centimetre continuum images of the ionized gas toward iras20126 + 4104 have been presented by @xcite .
observations of transitions of c@xmath2s , ch@xmath1cn , ch@xmath1oh and hco@xmath6 @xcite , and nh@xmath1 ( * ? ? ?
* kz10 ) have uncovered a rotating flattened disc - like structure , perpendicular to the inner flow , with a radius between 800 and 12,000au , and a gas mass estimated from both dust continuum or molecular line observations of 0.65 - 10m@xmath5 .
further evidence of a disc is also provided by near and mid - infrared images of iras20126 + 4104 @xcite , which show a dark lane with a similar size and orientation to the disc seen in radio observations . a large ( radius@xmath01000au ) rotating structure traced by
oh masers was also found by @xcite , which is coincident with the dark lane observed in the infrared .
however , recently @xcite have presented a high - resolution ( 0.6 " ) 24.5@xmath7 m image of iras20126 + 4104 , at a slightly longer wavelength than those presented in @xcite ( @xcite , 12.5 and 18.3@xmath7 m ) , which does not contain a dark lane .
the infrared to sub - millimetre sed of iras20126 + 4104 has been previously modelled on several occasions .
both @xcite and @xcite modelled the far - ir to millimetre sed using a simple greybody to determine the dust temperature and the dust emissivity index .
@xcite , @xcite and @xcite have also modelled the sed of iras20126 + 4104 using spherically symmetric models , to determine the properties of the envelope .
more recently , @xcite modelled iras20126 + 4104 using the radiation transfer code previously employed in @xcite . their model consisted of a spherical halo with a power - law density between radii of 850au and 0.54pc , plus a constant density cylindrical edge - on disc with radii between 34 - 850au and a height of 640au .
the model provided a good fit to the data down to @xmath08@xmath7 m , however , they suggested that adding further components to the model , such as bipolar cavities and a more complex disc geometry , would improve the fit , especially in the near- to mid - ir section of the sed . in this paper , we improve upon previous infrared modelling and derive complimentary information about the properties of iras20126 + 4104 not previously obtainable from molecular line observations .
we present the observed sed , infrared images and measured brightness profiles of iras20126 + 4104 in section [ data ] ; section [ dustcode ] describes the radiation transfer dust code used to model them ; section [ modelling ] details the modelling , including model input assumptions , fitting and the genetic search algorithm used to search for the best - fitting set of model parameters ; and section [ results ] presents our results , including a comparison to the results of kz10 .
we give our conclusions in section [ conclusions ] .
the observed near - ir to sub - millimetre sed of iras20126 + 4104 is shown in figure [ seddata ] . the overplotted solid and dashed lines ( respectively the best - fitting models for an envelope plus disc and without a disc )
are discussed further in section [ results ] .
the sed data points were collected from the literature ; table [ obstable ] lists the wavelength , flux and reference for the data displayed in figure [ seddata ] .
if the fluxes were derived from apparent magnitudes , these are also given in table [ obstable ] .
we attempted to make sure all fluxes contained all of the flux from the source .
for instance , we used the 2 micron all sky survey ( 2mass ) extended source catalog fluxes for the near - ir . [ cols= "
< , < , < , < , < , < " , ] [ tablecompare ] here we discuss the properties of the disc around iras20126 + 4104 suggested by our results .
the disc radius @xmath8 for the envelope plus disc model was found by the genetic code to be 9200@xmath9au . for a keplerian velocity of 1.11kms@xmath10 at @xmath8 ,
the outer radius of the disc would therefore take @xmath03@xmath11yr to complete one orbit . as this is on the order of the time massive stars
spend in their accretion phase , it appears unlikely that the outer regions of the disc will have had the time to reach centrifugal or hydrostatic equilibrium , which occur on approximately the same time - scales .
however , our results show that , in addition to the rotationally flattened envelope , extra mass arranged in some form of flattened structure is required , for radii up to 9200au , to reproduce the observed sed and profiles .
as the dust code calculates the temperature of the envelope and disc geometry , we were able to calculate the toomre q parameter @xcite - a measure of stability towards fragmentation - in the midplane of the disc as a function of radius , @xmath12 where @xmath13 is the speed of sound in the gas , @xmath14 is the angular velocity of the disc , @xmath15 is the gravitational constant and @xmath16 is the surface density of the disc .
we found the surface density as a function of radius by integrating equation [ discdensity ] over the disc height @xmath17 . to find the sound speed
, we assumed an ideal gas composed of molecular hydrogen , @xmath18 where @xmath19 is the boltzmann constant , @xmath20 is the temperature calculated by the dust code and @xmath21 is the average molecular mass of the gas .
the toomre parameter in the disc midplane as a function of disc radius for the best - fitting envelope with disc model is shown as a black line in figure [ toomre ] . from this
, we see that the disc is stable ( @xmath22 ) , and only reaches a value less than unity at radii greater than the disc radius . thus the high temperatures and low densities within the disc stabilise it against local fragmentation .
we also show as grey lines the toomre parameter for the models with reduced @xmath23 , which , apart from one model , lie close to or above 1 at the disc radius .
therefore we conclude that across the range of uncertainty in the disc properties , the disc around iras20126 + 4104 is still stable to fragmentation . ) for the best - fitting envelope with disc model , shown as a black line , and for the models with reduced @xmath2420 , shown as grey lines.,width=336 ]
in order to determine whether the standard model of low - mass star formation can also apply to massive stars , we have modelled the near - ir to sub - millimetre sed and several mid - ir images of the accreting embedded massive star iras20126 + 4104 , using model geometries which are commonly used to describe forming low - mass stars .
we have used a monte carlo radiative transfer dust code to model the continuum absorption , emission and scattering through two scaled - up azimuthally symmetric dust geometries , the first consisting of a rotationally flattened envelope with outflow cavities , and the second which also includes a flared disc . to find the best - fitting set of model parameters , we used a genetic algorithm to search parameter space , within parameter ranges which bracketed previous results or were physically plausible .
this also allowed us to produce minimum @xmath25 surfaces for each parameter , from which we could infer how well the sed and image profiles constrained them .
we found that the two parameters most constrained by the data were the stellar mass and envelope accretion rate , which were determined to be @xmath013@xmath26 and @xmath27yr@xmath10 respectively for the envelope plus disc model , and @xmath012@xmath26 and @xmath28yr@xmath10 for the envelope without disc model .
these two parameters are actually proxies for other more directly determined properties of the source - the stellar mass in the models is a proxy for the stellar luminosity , and the envelope accretion rate is a proxy for the total mass in the envelope , which is constrained by the millimetre fluxes . the stellar luminosities for both the envelope plus and without disc models respectively are @xmath29 and @xmath30l@xmath31 , and the total masses within @xmath32 are 649 and 375m@xmath31 . the best - fitting values of the remaining parameters are given in table [ bestfit ] .
our results show that the envelope plus disc model reproduces the observed sed and images better than the envelope without disc model , although the model without a disc appears to better - reproduce the morphology of the mid - ir emission within a radius of @xmath01800au .
we have outlined several possible causes of this discontinuity , such as inner disc truncation or outflow precession .
it may be that the observed mid - ir images , which can not be fully explained by the envelope plus disc model , are showing the effect of the radiation of a massive star on its accreting material .
however , future observations and modelling are needed to determine whether precession and/or a young protostellar companion are more likely explanations .
comparing our results to those of kz10 , we note that both studies find that a model with a disc reproduces the observations more successfully than one without .
although both studies modelled completely different observations using different techniques , we find that our best - fitting model parameters are similar to those found by kz10 . while we find a higher envelope accretion rate than kz10 , and therefore a higher envelope density and total envelope mass , this difference may be due to the fact that the masses determined from the molecular line modelling depend on the assumed molecular abundances .
for example , increasing the assumed molecular abundances by a factor of 3 - 5 would bring these values into agreement .
in addition , as the observed sed is more sensitive to emission from the entire envelope , not only the material within a radius of 26,400au modelled by kz10 , we were able to probe the mass in the envelope more accurately .
our best fitting envelope plus disc model has a disc radius of 9200au . as at this radius
the disc requires @xmath03@xmath11yr to complete one orbit , we find it is unlikely that the outer regions of the disc have had time to reach centrifugal or hydrostatic equilibrium . however , by using the temperature along the disc midplane found by the dust code , we calculate that this disc would be stable to local fragmentation .
the authors would like to thank t.k .
sridharan , j. de buizer , and w. de wit for providing electronic versions of their infrared images to include in this work , and also the anonymous referee , who provided many insightful comments which significantly improved the paper . | in order to investigate whether massive stars form similarly to their low - mass counterparts , we have used the standard envelope plus disc geometry successfully applied to low - mass protostars to model the near - ir to sub - millimetre sed and several mid - ir images of the embedded massive star iras20126 + 4104 .
we have used a monte carlo radiative transfer dust code to model the continuum absorption , emission and scattering through two azimuthally symmetric dust geometries , the first consisting of a rotationally flattened envelope with outflow cavities , and the second which also includes a flared accretion disc .
our results show that the envelope plus disc model reproduces the observed sed and images more accurately than the model without a disc , although the latter model more closely reproduces the morphology of the mid - ir emission within a radius of 1.1 " or @xmath01800au .
we have put forward several possible causes of this discontinuity , including inner truncation of the disc due to stellar irradiation , or precession of the outflow cavity .
our best fitting envelope plus disc model has a disc radius of 9200au .
we find that it is unlikely that the outer regions of such a disc would be in hydrostatic or centrifugal equilibrium , however we calculate that the temperatures within the disc would keep it stable to fragmentation .
accretion , accretion discs radiative transfer stars : formation infrared : stars ism : jets and outflows reflection nebulae |
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