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Frontiers in Computational Neuroscience
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Nonlinear Response of Biological Systems Exposed to Electromagnetic Radiation: From Model Setting to Synchronization Behaviors View all 7 Articles
Jun Ma
Lanzhou University of Technology, China
Xia Shi
Beijing University of Posts and Telecommunications (BUPT), China
Veli BAYSAL
Bülent Ecevit University, Turkey
2. Model and Methods
3. Multiple Discharge Behaviors Under Electromagnetic Radiation
4. Sensitivity of Coupled Neurons
Front. Comput. Neurosci., 21 November 2017 | https://doi.org/10.3389/fncom.2017.00107
Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise
Feibiao Zhan and Shenquan Liu*
School of Mathematics, South China University of Technology, Guangzhou, China
Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons.
Neural network is composed of a large number of neurons and the connection between neural networks is through signal propagation between neurons such as chemical or electrical signal. Neurodynamics researchers really pay much attention to dynamical properties of electrical activity in neurons or neural networks starting from the establishment of a reliable Hodgkin-Huxley (Hodgkin and Huxley, 1952) model that is established by describing ion channels in neurons. Based on the Hodgkin-Huxley model, it is extensively explored that many neurons have own model of ion channels and even a neuron may have multiple models. For example, the dimensionless Hindmarsh-Rose (Hindmarsh and Rose, 1984) model is a mathematical model and it has many firing behaviors of neurons by adjusting system parameters or external forcing stimuli such as bursting, spiking, quiescent and chaotic states. It can examine transition mode of electrical activity by using bifurcation analysis (Storace et al., 2008) and its mathematical properties are analyzed in Liu and Liu (2012) in detail. Although minimized Morris-Lecar model (Morris and Lecar, 1981) is consists of two coupled first-order differential equations, it still has a variety of discharge activities and describes the nature of the barnacle giant muscle fiber. It is further investigated by improving the neuron model (Duan et al., 2010; Wang et al., 2011; Upadhyay et al., 2017) or using theoretical analysis (Tsumoto et al., 2006). In addition to these, a variety of simplified neuron model (Izhikevich, 2004; Ibarz et al., 2011) have been developed and used for theoretical and numerical exploration.
With the development of neural dynamics, investigators propose some ways to deeply research mathematical mechanism of neuron model. For example, Izhikevich (2000) make a classification of electrical activity of low-dimensional neurons using slow-fast dynamics analysis (Rinzel, 1987; Rinzel and Ermentrout, 1998). And Szmolyan and Wechselberger (2001) argue that canard theory is used to illustrate mixed-mode oscillations mechanism in neurons. Based on these ways, some explorations are more detailed via combining them with other valid research methods and there is a widely extension in specific neuron model (Gu et al., 2003, 2012; Wang et al., 2015, 2017; Lu et al., 2016; Li and Gu, 2017; Zhao and Gu, 2017). Gu and Pan (2015) determine improved neuron model and use different ion currents to discuss its bifurcation behaviors. Furthermore, some experimental works is presented in Gu et al. (2013a, 2014) and they further investigate transition mode of electrical activity using bifurcation analysis. Some authors also examine the effects of noise on the coherence resonance, stochastic resonance and firing behavior of the neuron model (Gu et al., 2013b; Jia and Gu, 2015a,b; Wang et al., 2016; Wang and Ma, 2017) in addition to adding external forcing stimulus to the neuronal system. In fact, time-varying noise increases the system's dimensions, which is also a way to explore dynamical behaviors of neuron model and it can restore authenticity of neuronal system. Recently, energy-coded neurons are proposed to understand firing behavior of neurons as a new perspective and it is discussed in Wang et al. (2009), which define a Hamilton energy and Song et al. (2015) suggest that the Hamilton energy may be higher when neuron is in the spiking states rather than bursting or chaos states. Some researchers Li et al. (2016) investigate the discharge behaviors by adding equivalent current to electromagnetic radiation in neuronal loop. Yi et al. (2012, 2015) show that spiking pattern and spiking-frequency of neurons are changed when neurons are exposed to an electric field. Therefore, the effect of electromagnetic induction on neurons or neural networks may need to be considered to set more authentic neuron model.
As reported in Lv and Ma (2016) and Lv et al. (2016), we will also use magnetic flux to describe the effect of electromagnetic induction and we further explore electrical activity of neuronal system when it is exposed to electromagnetic radiation. However, they present these results without considering noise system such as Levy noise or phase noise. In this paper, the effect of electromagnetic radiation is explored on the Morris-Lecar neuron model and phase noise is also implemented to investigate resonance mode. Specifically, we change one of them to examine dynamical behavior of electrical activity when electromagnetic radiation and noise are added to the original system at the same time. In addition, we examine bursting transition mode via presenting one-parameter bifurcation diagram and bi-parameter bifurcation diagram when only adding electromagnetic induction to the original neuronal system. Finally, we compare the electrical behavior of isolated neurons with that of coupled neurons when only adding Gaussian white noise to respective system.
We use an improved M-L neuron model, which is reported in the previous investigation and it is a real biological neuron model which describes the giant barnacle muscle fiber. As we known, its dynamical behavior is greatly abundant although the model contains only calcium ion channel and potassium ion channel. Two variables are membrane voltage V and activated gating channel n in the original model. The improved neuron model contains five first-order differential equations, which is described as follows:
{CdVdt=−ICa−IK−IL−kρ(φ)V+ID+I,dndt=ϕn∞−nτn,dIdt=ε(V0−V),dφdt=k1ν−k2φ,dQdt=ω1+2Dξ(t). (1)
{ICa=gCam∞(V)(V−VCa),m∞=12(1+tanh(V−V1V2)),IK=gKn(V)(V−VK),n∞=12(1+tanh(V−V3V4)),IL=gL(V−VL),ID=A1sin(Q(t)),ρ(φ)=α+3βφ2,τn=1/cosh(V−V32V4). (2)
Where ICa, IK, IL, ID, and I are inward calcium current, potassium current, leakage current, phase noise, and voltage-dependent feedback current, respectively. The variables V, n, φ represent membrane potential, gate variable for potassium channel and magnetic flux across membrane during the process of ion transfer, respectively. I is a feedback current, which is very sensitive to membrane potential. The function ρ(φ) is associated with magnetic flux, readers can refer to Bao et al. (2010), Wu et al. (2016), Wu F. et al. (2017); Wu J. et al. (2017), and Xu et al. (2017) to obtain more detailed information. ξ(t) is Gaussian white noise, ω1, A1 are angular frequency and amplitude for forcing currents, Q(t) is phase noise. Detailed system parameters are explained as: membrane capacitance C, maximal conductance gCa, gK, gL, reversal potential VCa, VK, VL, the other kinetics parameter ϕ, ε, V1, V2, V3, V4. Some parameters of electromagnetic radiation are α, β, k, k1, k2. Readers can refer to Morris and Lecar (1981) and Ma et al. (2017) to understand the meaning of these symbols and there are detailed data in Lv et al. (2016). Specific parameters throughout the paper are given in Table A1. Furthermore, coefficient variability (abbreviated as CV and labeled as η) of interspike intervals (ISIs) sequence (Pikovsky and Kurths, 1997) is presented as the radio of standard deviation(std) of ISIs sequence to its mean, i.e., η = std(ISIs)/mean(ISIs), and it indicates the coherence degree. In section 4, we are using electrical coupling between neurons, i.e., the coupling term is as follows: Icouple = gc(V1 − V2), where gc represents the coupling coefficient and V1(2) denote the membrane potential of one(another) of neuron.
In fact, we are familiar with the M-L model, but we still have a novel understanding and discovery for the improved M-L model via adjusting electromagnetic induction and phase noise. In this paper, we adopt fourth-order Runge-Kutta algorithm to exhibit numerical solution of the neuronal system with time step d = 0.01 ms in all of simulation and calculation, and we use MATPLOTLIB software package in PYTHON for all numerical calculation and graphic rendering.
In this section, we discuss that amplitude A1 is how to adjust electricity activity via changing the range of forcing amplitude, and we also examine firing pattern of improved M-L neuron model by adjusting magnetic flux parameter k. Moreover, we also calculate coefficient variability of interspike intervals sequence to explore the coherence degree by altering noise intensity D and it represents that the smaller the CV value is associated with a better coherence. Furthermore, we only consider the system with electromagnetic induction and without Gaussian white noise. In this process, we find that the effect of electromagnetic field on the neuronal system is two-sided. The detailed analysis is as follows.
As shown in Figure 1, electrical activity of improved neuron model can be controlled and adjusted as a random but relatively stable pattern. Specifically, the system is in a relative resting state when A1 = 1 and the firing occurs when we increase A1 to 3. We find that the number of spiking is gradually increased when we continue to increase amplitude from 3 to 5. It is described that the amplitude of phase noise makes a positive response to the system although the range of amplitude is small. Certainly, this process is reversible. That is to say, we can better adjust the spiking of neurons by regulating the amplitude so that neuronal model is more reasonable in the simulation of realistic neural network.
Figure 1. Time series of membrane potential under different amplitudes. (A) A1 = 1, (B) A1 = 3, (C) A1 = 5, (D) A1 = 10, the noise intensity is selected as D = 10, ϕ = 0.22, k = 0.0025, ω1 = 0.5.
Indeed, multiple patterns of electrical activity are detected in the improved neuron model by modifying the feedback coefficient k, which indicates the coupling strength between magnetic flux and membrane potential. It is found that magnetic flux has a great effect on the membrane potential so that multiple modes can be selected with the changing of feedback coefficient, and time sequence of membrane potential is shown in Figure 2. We also explain the discharge process in detail. First, suprathreshold spiking of system is gradually reduced. when feedback coefficient k = 0.002, the number of suprathreshold spiking is more than k = 0.0025. It is in a relatively resting state (subthreshold spiking) when k increase to 0.003. From above analysis, we can see that firing activity of membrane potential is more dependent on the feedback coefficient, which is greatly sensitive in regulating membrane potential. Next, we will consider their combined effect on neuronal suprathreshold spiking by calculating bi-parameter bifurcation diagram, which is shown in Figure 3. It is exhibited on the (k, A1) plane and presents a detailed suprathreshold change.
Figure 2. Time series of membrane potential under different feedback coefficient. (A) k = 0.002, (B) k = 0.0025, (C) k = 0.003, (D) k = 0.0035, the noise intensity is controlled as D = 10, ϕ = 0.22, A1 = 6, ω1 = 0.5.
Figure 3. Bi-parameter bifurcation diagram of suprathreshold spiking. The number of suprathreshold spiking is presented at the right sides by the colorful belt and 0 indicates the relatively resting state.
The phase noise is induced by differential equations with Gaussian white noise and it can be grasped by noise intensity D. Gaussian white noise has a good simulation of noise system in the real neural network so that discharge activity is more authentic. Therefore, it is necessary that we will incorporate noise into neuron model to simulate computation. Figure 4 exhibit time sequence of membrane potential of dynamical system, which is an improved neuron model with different noise intensity D. Especially, it is interesting that multiple oscillation modes are strengthened with the increasing of noise intensity. From the diagram, we can see that noise promote the spiking of neuronal system to some extent but it is two-sided. Its effect may be more regular on the spiking than changing amplitude or adjusting feedback coefficient. For the neuronal system, coefficient variability of ISIs sequence is often used to examine its coherence degree. Readers can refer to Jia and Gu (2015a) and Pikovsky and Kurths (1997) to get a more detailed understanding about the concept of CV. It indicates that the better coherence depends on the smaller the CV. As shown in Figure 5, it will has a good coherence in a suitable noise intensity D, and that is to say, the distance is uniform between spiking and spiking at this moment. The CV value starts to increase when noise is greater than that fixed value D = 2. In other words, appropriate noise may produce a positive response to the neuronal system.
Figure 4. Time series of membrane potential under different noise intensity D. (A) D = 1, (B) D = 3, (C) D = 5, (D) D = 10, the feedback coefficient is controlled as k = 0.0025, A1 = 6, ϕ = 0.22, ω1 = 0.5.
Figure 5. Coefficient variability of ISIs series of membrane potential. The abscissa is noise intensity D and the ordinate is the CV. Other controllable parameters are given as k = 0.0025, A1 = 6, ϕ = 0.22, ω1 = 0.5.
The above discussion is based on adding noise and electromagnetic field at the same time and then changing amplitude, feedback coefficient or noise intensity to obtain some firing behaviors of dynamical system. Next, we will discern the oscillating mode only adding electromagnetic radiation or adding Gaussian white noise. The result in Figure 6 convey that the oscillating behavior can be regulated and adjusted as an isolated pattern. In other words, appropriate mode can be selected by adding suitable magnetic flux on membrane potential. From the diagram, we can see that inverse period-adding bifurcation is observed with the increasing of feedback coefficient k and this bifurcation diagram is regular, but it eventually jumps to resting state. Obviously, we get a lot of oscillation modes of discharge activity via changing one-parameter, and it makes us very interested in the adjustment of bi-parameter.
Figure 6. Interspike intervals for time series of membrane potential with the increasing of feedback coefficient k, and no Gaussian white noise is added.
We calculate bi-parameter bifurcation diagram and show it in Figure 7. In Figure 7A, where the abscissa represents the reversal potential VK whose value is taken from −96 to −80, and the ordinate denotes the feedback coefficient k whose value is selected from 0 to 0.0015. Moreover, the color scale bar indicates a gradual process, which represents the number of spiking per burst from the regular bursting to the chaotic bursting. Examining the Figure 7A, we can see that the number of spiking per burst will continue to increase with the changing of bi-parameter until it reaches chaos in a small range of lower right corner. In addition, the spiking phenomenon can occur between two resting state. As shown in Figure 7B, we exhibit bi-parameter bifurcation diagram in the (k, gCa) plane, where the abscissa indicates the maximal conductance gCa whose value is taken from 3.3 to 5.3, and the ordinate represents the feedback coefficient k whose value is selected from 0 to 0.0015. We can see that triangular area on the left side of the diagram and trapezoidal area on the right are two resting states. And it is obvious that the spiking go through the transition process from regular bursting to chaotic bursting and then to regular bursting by adjusting these two parameters. The electrical activity is very sensitive to bi-parameter because most bursting modes have only narrow strip areas.
Figure 7. Spiking-counting diagram as the change of bi-parameter. The number of spiking per bursting is exhibited at the right sides by the colorful belt. And no Gaussian white noise is considered. (A) (k, VK) plane; the number 0 indicates quiescent condition and the number 1 represents tonic spiking whilst the number 2–45 denotes regular bursting; (B) (k, gCa) plane; similarly, the number 0 indicates quiescent condition and the number 1 represents tonic spiking; the number 2–69 denotes regular bursting whilst the number 70 indicates chaotic states.
By comparing Figure 7A with Figure 7B, it is easy to see that these two parameters have a great influence on the discharge activity. For the same feedback coefficient interval, if we change the reversal potential VK at the same time, we will get a continuous spike-adding mode. But if we transform the maximal conductance gCa, we will see that electrical activity will return to period bursting via chaotic bursting. The principle is hidden behind a large number of patterns, and it can be well discerned by simulating the neuronal system.
In this section, we will discuss dynamical response of an isolated neuron and two coupled neurons. These two systems are exposed to Gaussian white noise, and they have many different responses to the noise system. In addition, we examine how the noise affects coupled neuronal system and compare the discharge activity of coupling neuronal system with that of original coupling system without noise. Furthermore, we may find some new phenomena by comparing electrical mode of isolated neurons with that of coupled neurons under noise, and we also present a new perspective to explore neurons responding to noise. They are analyzed as follows.
It is inevitable that many realistic neuron system will be exposed to noisy environment and we find that the effect has two-sided. Therefore, we will explore neuronal system by adding the noise to neuron model without adding electromagnetic radiation. Figure 8 indicates time series of membrane potential without adding noise, and it is tonic spiking or regular bursting. Figure 9 represents time series of membrane potential after adding noise system and corresponding to Figure 8, respectively. Observing the diagram, we can discern that noise is very sensitive to the tonic spiking and its response is more intense than the regular bursting. In detail, electrical activity of tonic spiking is greatly disturbed and period-2 bursting is also disrupted. In addition, regular period-4 bursting and square wave busting have also slight perturbation and become irregular discharge mode. In general, the more the number of spiking per burst means that the mode is relatively more stable when adding noise to system. Moreover, bursting may be increased during the same time period when Gaussian white noise is introduced into the neuron system whilst the number of spiking per burst will also be fluctuant and most of them is increased. Furthermore, we can see that noise has a little control over the firing state of neuron but it may has a great effect on bistable state (down resting state and upper steady state). As we known, bursting may mean more neural information than spiking. To sum up, we may be able to infer that the more complex discharge activity is better anti-interference than tonic spiking, and this may be associated with the robustness of neural networks.
Figure 8. Time series of membrane potential under different reversal potential VK. (A) VK = −96, (B) VK = −92, (C) VK = −88, (D) VK = −84, and no noise is introduced.
Figure 9. Time sequences of membrane potential under different reversal potential VK. (A) VK = −96, (B) VK = −92, (C) VK = −88, (D) VK = −84, and Gaussian white noise is considered.
In fact, we have explored multiple modes of discharge activity in coupled neuron system by changing reversal potential and adding Gaussian white noise to system and it has more patterns than in an isolated neuron. Therefore, we are interested in the coupling system with noise. Figure 10 represents time series of membrane potential without adding noise, which are tonic spiking, regular bursting and irregular bursting. Figure 11 exhibits time series of membrane potential under noise and corresponding to Figure 10, respectively. Comparing two diagram, we find that the effect of noise on the spiking is greater than bursting and this is consistent with our analysis of single neurons. In noise system, there is a bursting that appears in the tonic spiking and period-2 bursting become many irregular bursting (the number of spiking per burst is not less than two). Moreover, it is also disrupted that bursting alternately appears in Figure 10C and it becomes unstable bursting mode. Furthermore, the change once again confirms that the effect of noise on bistable state is stronger than firing state as shown in Figure 10D. In addition, the effect of noise on down resting state of coupled system is obviously greater than that of upper steady state, but this feature is not obvious in an isolated neuron model. These are new phenomena and not present in a single neuron. It is not the same as in an isolated neuron that the noise does not increase the number of bursting during the same time (Contrast Figure 10C and Figure 11C), but the main effect of noise on the bistable state is retained. Therefore, we may be able to suggest that the exploration of neural network under noise requires a long-term process to achieve an in-depth level and this process is valuable.
Figure 10. Time series of membrane potential of coupled neurons under different reversal potential VK. (A) VK = −92, (B) VK = −88, (C) VK = −84, (D) VK = −76, and adding Gaussian white noise.
Figure 11. Time series of membrane potential of coupled neurons under different reversal potential VK. (A) VK = −92, (B) VK = −88, (C) VK = −84, (D) VK = −76, and Gaussian white noise is considered.
Tonic spiking and bursting are effective coding of signals between neurons and abundant discharge activity patterns are accompanied by complex signal propagation. The effects of electromagnetic radiation and noise on discharge activity of system are two-sided and it has been investigated by some researchers and their co-workers (Lv et al., 2016; Ma et al., 2017). Therefore, we are more interested in electrical activity of system with electromagnetic induction or noise and hope that it is controllable. In this paper, we have explored transition of electrical activity in an improved Morris-Lecar neuron model, which contains electromagnetic radiation and noise. Additionally, electromagnetic radiation is expressed through the magnetic flux and noise obeys normal distribution. By comparing the simulation of the system, we have found that there is a great change in discharge activity until external forcing stimulus is removed from system and dynamical response will be more sensitive by adjusting more bifurcation parameters. One of these, we have calculated transition of discharge activity with the changing of the feedback coefficient k. In addition, we have examined the effect of noise intensity D on coherence of electrical activity via describing the changes of coefficient variability. Furthermore, we have drew interspike intervals sequence diagram and bi-parameters bifurcation diagram to argue the effect of electromagnetic induction on the fluctuation of membrane potential. Finally, we have compared the response of noise on the electrical activity of isolated neurons with that of coupled neurons. From the above, we know that electromagnetic induction and noise can arouse different dynamical behaviors of neuronal systems. Logically, we will try to illustrate their impact on the biological meaning of real neurons. In fact, move of charged ions involves a small and easily overlooked magnetic field during the process of ion transmembrane movement. But it may be that accumulation of these small induced currents produces qualitative change in a single neuron or even in a neural network. Certainly, the effect of noise on the neuronal system is also often explored, since many realistic neural network are in a noisy environment. Therefore, we may be able to consider incorporating the magnetic flux into real neuron system because of its impact on discharge activity and noise can not be ignored. According to the simulation of the improved neurons, external bifurcation parameters can change firing mode, which may mean that neurons can select appropriate electrical behaviors due to its self-adaption that frequently appears in neural networks.
The idea of this article is proposed by SL and the specific writting is done by FZ.
This work was supported by the National Natural Science Foundation of China under Grant Nos. 11172103 and 11572127.
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Wu, J., Xu, Y., and Ma, J. (2017). Lévy noise improves the electrical activity in a neuron under electromagnetic radiation. PLoS ONE 12:e0174330. doi: 10.1371/journal.pone.0174330
Xu, Y., Ying, H., Jia, Y., Ma, J., and Hayat, T. (2017). Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7:43452. doi: 10.1038/srep43452
Yi, G., Wang, J., Tsang, K. M., Wei, X., Deng, B., and Han, C. (2015). Spike-frequency adaptation of a two-compartment neuron modulated by extracellular electric fields. Biol. Cybern. 109, 287–306. doi: 10.1007/s00422-014-0642-2
Yi, G. S., Wang, J., Han, C. X., Deng, B., and Wei, X. L. (2012). Spiking patterns of a minimal neuron to elf sinusoidal electric field. Appl. Math. Model. 36, 3673–3684. doi: 10.1016/j.apm.2011.11.012
Zhao, Z. G., and Gu, H. G. (2017). Transitions between classes of neuronal excitability and bifurcations induced by autapse. Sci. Rep. 7:6760. doi: 10.1038/s41598-017-07051-9
TABLE A1
Table A1. Fixed parameter values are used in the calculation.
Keywords: Morris-Lecar model, electromagnetic induction, Gaussian white noise, electrical activity, bursting, bifurcation
Citation: Zhan F and Liu S (2017) Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise. Front. Comput. Neurosci. 11:107. doi: 10.3389/fncom.2017.00107
Received: 26 September 2017; Accepted: 09 November 2017;
Published: 21 November 2017.
Jun Ma, Lanzhou University of Technology, China
Xia Shi, Beijing University of Posts and Telecommunications, China
Veli Baysal, Bülent Ecevit University, Turkey
Copyright © 2017 Zhan and Liu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Shenquan Liu, mashqliu@scut.edu.cn


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In the Lawton neighborhood, there was once a pedestrian bridge from Morehead to Delaware over Malletts Creek. The City removed the bridge due to safety concerns and has repeated delayed replacing the bridge.
May 3, 2016 MLive - City Council leaves $288K for debated bridge over Malletts Creek.
May 2, 2016 MLive - Ann Arbor council to reconsider 6-5 vote against replacing foot bridge.
April 19, 2016 MLive - City Council backtracks on promise to replace missing neighborhood bridge.
September 20, 2015 MLive - Ann Arbor residents still waiting after 6 years for replacement of neighborhood bridge.
"At council's last budget meeting in May, Eaton moved to allocate the $450,000 from the general fund for a new bridge. Six other councilmembers agreed--only the mayor and three councilmembers opposed it."
May 19, 2015 MLive - Ann Arbor City Council approves revised city budget in early morning hours.
"In a 7-4 vote, the council also supported a $450,000 proposal by Eaton to fund a new pedestrian bridge in the Lansdowne neighborhood."
September 6, 2011 Ann Arbor Chronicle - Lansdowne Pedestrian Bridge to Be Rebuilt.
"The bridge has been a topic of neighborhood concern dating back at least to the 2010 Ward 4 Democratic primary race between Margie Teall and Jack Eaton, a race won by the incumbent Teall."
August 13, 2010 Ann Arbor News - Residents on Ann Arbor's west side launch campaign to save Lansdowne foot bridge.


Minutes ago, I dreamed about a former priest. Yes, former. He's a friend of mine but he now left the Priesthood to join a lady who happen to be my third year high school English Teacher. They were both friends of mine and my heart breaks of the thought that they are sinning together (if leaving the priesthood to join a woman is a sin).
In my dream, I have just entered the church to attend the Eucharist. To my surprise, it was my friend priest who celebrates and presides the Mass. I cannot contain my joy! My friend who was once lost — an anointed Priest of God; a priest who is so special, so blessed; and by whose hands alone the transformation of a simple bread and wine into the Body and Blood of Christ is made possible — was found. A priest whom I consider as a shepherd has returned to tend his flock.
But when I have awaken, I was saddened by the realization that everything was a dream. It is bitter to accept the reality — the reality that in mankind, there is always and infinite strife between our soul's appetite and spirit.
For Plato, man's soul has three parts, also known as the tripartite nature of the soul, namely appetitive, spirited, and rational. Plato believed, and I adhere too, that reason should strike the balance between the two other parts of the soul. Reason, is given to humanity as a unique gift; a distinguishing factor from the animals. Therefore we should be wise to convince our spirits to control our appetites.
As illustrated by Plato, the soul is like a chariot comprised of two horses and a charioteer. The Black horse in the left is the Appetitive part, while on the right side is the Spirited part. The two horses doesn't control the chariot but the Charioteer. It was the charioteer who governs the whole system, deciding which horse to give a reign or to hold back.
Plato believed, and so do I, that through the wise and rational decision and dispositions of the charioteer (whom I consider also as man himself), the harmony of the soul will create a just and good person leading to happiness.
I await with great enthusiasm, that my friend, together with the others who have gone astray, would be able to decide wise and control their appetites with reason, and one day reunite with us and walk their old good path.
Posted on December 14, 2011, in CULTURE, Lifestyle, Philosophy, Religion and tagged appetite, decisions, dream, philosophy, plato, priest, reason, soul, spirit. Bookmark the permalink.	Leave a comment.


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The solution must come from the grassroots -- it can't be imposed from above by reform-minded members of Congress.
At a talk at UCLA last month, I said that America's growing anti-corruption movement needs to think big, not puny. That we need a fundamental change in the way America funds its campaigns, and that it will take a cross-partisan grassroots movement of outsiders to get the insiders in D.C. to embrace that change.
To kickstart that grassroots movement, I said, Congress needs a chance to innovate. This should be a time when different ideas are encouraged and tested. Which ideas will spark the energy of citizens across the country? Which can speak to citizens from across the political spectrum?
We've already seen a wide range of important new proposals. The Brennan Center and Democracy 21, led by the dean of campaign finance reform, Fred Wertheimer, has proposed a 5-to-1 match for contributions up to $250, now introduced as a bill by Reps. David Price (D-N.C.) and Chris Van Hollen (D-Maryland). In 2010, the Democratic House came close to passing the Fair Elections Now Act, which was in effect a 9 to 1 match. Rep. John Sarbanes (D-Maryland) has proposed a much more ambitious 10-to-1 match for grassroots-funded candidates, plus a tax credit to inspire even more small-dollar contributors. And just last month, Represent.US launched the American Anti-Corruption Act, crafted by Stephen Colbert's super PAC lawyer, Trevor Potter. If passed, the act would be the most ambitious political-reform proposal in a century.
Any of these proposals would be better than the system we have now. Obviously. But it should be equally obvious that the only way any of these proposals can ever hope to pass this Congress is if one of them inspires Americans from outside the beltway to stand up and demand change.
We Americans are not easily inspired. Forty years of reform have left us more cynical, not less -- and not just about Congress but also about the very idea of "reform." Eighty percent of Americans surveyed by Clarus believe that the reforms Congress has passed "have been designed more to help current members of Congress get re-elected [than] to improve the system." The biggest challenge for the next reform is not just substance but also believability: It must convince America that it, finally, offers real change.
While no one doubts that corruption is symmetrical -- Democrats are just as dependent as Republicans on the 1 percent -- the reform movement is not.
This is why it is a mistake, as some have recommended, for reformers in Congress to fix on any single plan just now. It would be an even graver mistake if they did so and and that plan struck most Americans as very weak tea. Instead, the reformers should encourage innovation among members of both parties, and watch for the ideas that actually catch. Congress must aim high -- both to get America's attention and to inspire the country that this reform might work.
For there is a nation here that could be inspired. Across the political spectrum, America is outraged at the corruption of this government. Eighty-seven percent of us named ending government corruption a top issue for the next administration -- number two on that list, chosen by just as many Republicans as Democrats. And thousands have followed the leadership of groups such as Common Cause, People for the American Way, Public Citizen, the Coffee Party, and MovetoAmend.org to get millions to demand that Congress address the outrage that is Citizens United. Democrats, independents, and Republicans alike hate this system -- at least the ones who don't count on a future on K Street. Any reform movement that hopes to win must give that incredible movement the respect it deserves.
Respect begins with listening. It is fed by open debate. And it is encouraged by the belief that the hard work of organizing -- the work that produced almost 2 million signatures demanding real change -- will be at least as important in this process as the favors of insiders.
Democrats have a real chance here. While no one doubts that the corruption of this current system is symmetrical -- Democrats are just as dependent as Republicans on funding from the tiniest slice of the 1 percent -- the reform movement is not symmetrical. The GOP has become the anti-reform party (unless by "reform" you mean increasing the corruption of a system in which the tiniest slice of the 1 percent fund America's campaigns). Only Democrats are talking about ideas that might actually end that corruption.
It is time for Democrats finally to steal a move from the Republican's playbook: Boldness inspires. If there's going to be a Tea Party for Reform, Democrats must start talking about ideas that give people a real reason to get excited.
The change we need is unlike anything America has attempted in more than a century. None of us have done this before. Or better, what has been done before is not this. There are no experts here. There is no one with a track record. All there is is the most important reform challenge that any of us will ever know -- a very slim chance that we can meet it.


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text:
Q: basename_r/dirname_r in Linux Some POSIX functions are not threadsafe. Examples are dirname and pathname.

The dirname() function need not be reentrant. A function that is not required to be reentrant is not required to be thread-safe.

On some platforms there are reentrant versions of dirname and pathname: dirname_r and pathname_r.
As far as I found out there are not reentrant version of dirname and pathname on Linux.

*

*Is that correct?

*What is the alternative?

A:
Is that correct?

According to the man page, yes.

What is the alternative?

Make it thread safe yourself, i.e. wrap the calls in a function that guards basename/dirname and copies the result into a supplied buffer while holding a mutex

A: I'm not aware of reentrant versions of dirname and basename in Linux.
However, there's various reentrant implementations of both functions in different non-standard libraries.
g_path_get_dirname and g_path_get_basename from glib are probably commonly used, and their implementation doesn't depend too much on the rest of the glib library either, so it'd be easy enough to just borrow from their implementation if you don't particularly feel like linking against glib.

redpajama_set_name: RedPajamaStackExchange


3. The cost of additional living expenses if your home is damaged and you have to live elsewhere during repairs.
Flood insurance is available from the National Flood Insurance Program - NFIP and from some private insurers. Earthquake coverage is available from private insurance companies or, in California, also through theCalifornia Earthquake Authority.
here may be limits on how much coverage you get for expensive items such as jewelry, silverware and furs. Generally, there is a limit on jewelry for $1,000 to $2,000. You should ask your agent or look it up in your policy. This information is in Section I, Personal Property, Special Limits of Liability. Insurance companies may also place a limit on what they will pay for computers.


Terry Richardson leaving UCONN (RB coach) for Miss St.
I bet Terry, a Syracuse alum, would love to have a chance to coach with an X and O wizard like Dino. It would be his best chance to become an OC some day. Terry actually took a demotion to get out of Storrs. He was an assistant head coach for UConn.
Lower level position at a higher level program.
Good idea to get off the sinking ship that is Yukon.
Terry had been at UConn a long time in two different stints but hard to deny that's not the place you want to be right now.
Terry had been at UConn a long time in two different stints but hard to deny that's not the play you want to be right now.
I am not criticizing Terry for leaving. Just pointing out it was an unusual move. Randy is at a point now where assembling and/or retaining a good staff is a great challenge.
Absolutely, totally get your point and agree. It's a mess there. I'd get out also.
Justin Outten leaves the Falcons to take the TE job at Green Bay.
I will be rooting on USC for the 2nd year in a row.
Wow, went to high school with Mark. Thrilled for him!
Worked specifically with the Cardinal wide receivers in 2017 and 2018.
Played wide receiver for Portland State in 2015 and 2016 … helped the Vikings reach the 2015 NCAA FCS playoffs … began collegiate career at Oregon State (2012-14) … 2012 OSU Offensive Scout Team Player of the Year … member of Oregon State's 2012 Alamo Bowl team and 2013 Hawaii Bowl team.
Blair Cavanaugh, Coach Cavanaugh's son is now at SU. I don't know what position will hold at SU.
SU has added Blair Cavanaugh to the coaching staff. The son of OL coach Mike Cavanaugh, Blair will be the special teams quality control coach.
Wake got a good one in Currie. I'll bet he has a bigger impact on their hoops program in the near future as Clawson seems to have a good foundation that has produced solid results.
He was responsible for the Schiano fiasco and let go.
Ouch. Based on that, when Clawson leaves they are in trouble.
He was responsible for Schiano and run out on a rail as a result.
He did a lot of good work at KSU and hired a few good coaches. Not sure how he came up with Schiano for UT but that mistake makes me like him more for sticking it to the Vols.


text:
\section{Introduction}

Since its formulation \cite{Maldacena:1997re}-\cite{W}
there have been numerous tests of
the AdS/CFT duality, see \cite{Aharony:1999ti,D'Hoker:2002aw}
for reviews. Soon afterward
the duality was extended to non-conformal field theories obtained
by deformations or vevs of the original CFT. In such cases
the duality involves an asymptotically AdS spacetime. However,
quantitative tests of the correspondence in this more general set up
are rather scarce.

Perhaps one of the simplest cases to explore is that
of the Coulomb branch of the ${\cal N}=4$ SYM theory. The theory still
possesses 16 supercharges and supersymmetry protects the vevs
from quantum corrections. This is thus an ideal case
for testing gravity/gauge theory duality away from the
conformal point. Although it has long been
recognized that there is a one to one correspondence between
(the near-horizon limit of) multicenter D3 brane
solutions and the CB of ${\cal N}=4$ SYM \cite{Kraus:1998hv}
a precise gravitational computation of the vevs was never
done (apart from in the specific cases reviewed below). These solutions
are determined by a harmonic function and Klebanov and Witten
proposed in \cite{Klebanov:1999tb} that the vevs can be
extracted from the harmonic function. The results of this
paper confirm that expectation.

More quantitative progress has been achieved for the specific
case of a distribution of D3 branes on a disc. In this
case there is an associated solution of the five dimensional
gauged supergravity \cite{Freedman:1999gk} and using the
technology of holographic renormalization \cite{dHSS}  the
expectation values (and 2-point functions) of the stress energy
tensor and of a dimension two gauge invariant operator were
computed and shown to agree with field theory expectations in
\cite{BFS1,BFS2}.

The restriction to this subsector of operators was due to starting from
the five dimensional supergravity solution. More recently in
\cite{Skenderis:2006uy} we have
developed a precise holographic map that allows one also to
treat operators dual to fields that are not part of the five
dimensional gauged
supergravity. Applying this map to the corresponding ten dimensional
supergravity solution we additionally computed the vev of
a dimension 4 operator and again found exact agreement with field
theory. This was the first quantitative computation of a vev
of an operator dual to field that is not part of the $5d$ gauged
supergravity.

In this letter we essentially solve the problem in its
most general form. We consider a point in the
CB of ${\cal N}=4$ SYM characterized in the large $N$ limit
by a general distribution of eigenvalues and we show that the
gravitationally computed vevs of {\it all} gauge invariant
operators are in {\it exact} agreement with the field
theory answer. We should note, however, there is
still an open technical issue regarding the
cancellation of certain terms that was checked only
for a specific case (see the discussion in section \ref{vevs}).

Finally we point out that one can include
non-normalizable terms in the
harmonic function appearing in the supergravity solution for separated
D3-branes and these can also be interpreted in AdS/CFT.
Such terms correspond to deformations of the SYM
theory by half supersymmetric irrelevant operators of the form
${\rm Tr}  (F^4 X^k)$.

The paper is organized as follows. In the next section we
discuss the field theory side of the story. In section
3 we review the Coulomb branch solutions; in section 4
we summarize the results from \cite{Skenderis:2006uy} whilst
section 5 contains the holographic computation of the
vevs for the general case. In section 6 we propose
a gravity dual for certain deformations of ${\cal N}=4$ SYM preserving
16 supercharges. Appendix A contains a proof of the
addition theorem that is used in the extraction
of vevs in section 5.

\section{${\cal N}=4$ SYM on the Coulomb branch}

${\cal N}=4$
SYM contains 6 scalar fields $X^{i_1}$ in the adjoint representation
of the gauge group that we take to be
$SU(N)$. The Coulomb branch (CB) of ${\cal N}=4$ SYM corresponds to giving
a vacuum expectation value (vev) to the scalars subject to the condition
$[X^{i_1}, X^{i_2}]=0.$ A useful parametrization of the CB
branch is in terms of vevs of composite operators.
The relevant operators here are the chiral primaries (CPOs),
\begin{equation} \label{CPO}
{\cal O}^{I_1} = {\cal N}_{I_1} C^{I_1}_{i_1 \cdots i_k} {\rm{Tr}}(X^{i_1}
\cdots X^{i_k}),
\end{equation}
where $C^{I_1}$ is
a totally symmetric traceless rank $k$ tensor of $SO(6)$ which is
normalized such that $\left < C^{I_1} C^{I_2} \right > = C^{I_1}_{i_1
\cdots i_k} C^{I_2}_{i_1 \cdots i_k} = \d^{I_1 I_2}$ and
${\cal N}_{I_1}$ is a normalization factor. We choose this factor
such that the normalization of the 2-point functions computed in field theory
and in supergravity is the same
\begin{equation} \label{norm}
{\cal N}_{I_1} = \frac{N}{\pi^2} 2^{k/2} (k-2) \sqrt{\frac{k-1}{k}}
\left(\frac{2 \pi^2}{\l}\right)^{k/2}
; \qquad k \neq 2,
\end{equation}
where $\l$ is the 't Hooft coupling. Note the field theory computation of the
2-point functions is done in the large $N$ limit and with
canonically normalized scalars. The $k=2$ case is obtained by replacing
the factor of $(k-2)$ by 2.

We now consider an arbitrary smooth unit
normalized distribution of eigenvalues, $\r(x)$, where $x$
parametrizes $R^6$. In the large $N$ limit the trace may be evaluated
via such a continuous eigenvalue distribution
\begin{equation}
\left < C ^{I}_{i_1 \cdots i_k} \rm{Tr} (X^{i_1} \cdots X^{i_k})
\right > = N \int d^6x \rho(x) (C^I_{i_1 \cdots i_k}
x^{i_1} \cdots x^{i_k} )
\end{equation}
giving the following formula for the vevs
\begin{equation} \label{vev}
\<{\cal O}^{I_1}\> = \frac{N^2}{\pi^2} 2^{k/2} (k-2) \sqrt{\frac{k-1}{k}}
\left(\frac{2 \pi^2}{\l}\right)^{k/2}
\int d^6x \rho(x) (C^I_{i_1 \cdots i_k}
x^{i_1} \cdots x^{i_k} ), \qquad k \neq 2,
\end{equation}
where again for $k=2$ one replaces the factor of $(k-2)$ by 2.
The aim of this paper is to reproduce this formula from supergravity
for all $k$ and general eigenvalue distributions.

Before proceeding let us briefly review the properties
of a uniform distribution of eigenvalues of $X^1$ and $X^2$
on a disc of radius $a$ and vanishing vev for the
remaining scalars, $\<X^3\> = \<X^4\>=\<X^5\>=\<X^6\>=0$.
In this case the vevs break the R symmetry from
$SO(6)$ to $SO(2) \times SO(4)$.
This example was recently discussed in some detail in \cite{Skenderis:2006uy}
and the corresponding vevs were shown to be equal to
\begin{equation} \la{vev1}
\left < {\cal O}^{2n} \right > =
\frac{ {\cal N}_{2n} a^{2n}}{ 2^n  \sqrt{2n+1}} N
\end{equation}
where the operators here are the singlets under the decomposition
of $SO(6)$ into $SO(2) \times SO(4)$.

\section{Coulomb branch solutions} \label{CBsection}

A generic Coulomb branch solution describing a
distribution of D3-branes is given by:
\begin{eqnarray} \la{cbs}
ds^2 &=& H(x_\perp) ^{-1/2} d x_{||}^2
+ H(x_\perp)^{1/2} d x_\perp^2 \\
F&=&\frac{1}{4} (d H^{-1} \wedge \omega_{||}
- *_\perp d_\perp H) \nonumber
\end{eqnarray}
where $\omega_{||}$ is the volume form in the (flat) worldvolume directions
and
$*_\perp$ and $d_\perp$ refer to the Hodge star and exterior derivative
in the flat transverse directions and $H$ is a harmonic
function,
\begin{equation} \label{harm}
\Box H =0.
\end{equation}
For the solution to be asymptotically AdS, $H$ should behave to
leading order as $r^{-4}$ when $r \to \infty$,  where $r$ is the radial
coordinate of the flat overall transverse direction. The most
general solution of (\ref{harm}) with these boundary conditions is
\begin{equation} \label{H_harm}
H = \sum_{k, I} h_{kI} \frac{Y_{k}^{I} (\vec{\theta}) }{r^{k+4}},
\end{equation}
where the coordinates on the flat $R^6$ are $(r,\vec{\theta})$ with
$\vec{\theta}$ labeling the coordinates on the $S^5$.
$Y_k^I$ is a normalized spherical
harmonic of degree $k$ with $I$ labeling its remaining quantum
numbers; normalized as
\begin{equation}
\int_{S^5} Y^{I_1}_{k_1} Y^{I_2}_{k_2} = \pi^3 \frac{\d^{I_1 I_2} \d_{k_1
    k_2}}{2^{k_1-1} (k_1+1) (k_1+2)} \equiv \d^{I_1 I_2} z_{k_1}.
\end{equation}
The leading order term is given by
$h_{00} = L^4 = 4 \pi g_s N (\a')^2$ if the total number of
D3-branes is to be $N$, whilst by
measuring distances from the centre of mass one can as usual choose the
$k=1$ terms to vanish. We will discuss more general boundary conditions
for $H$ in section \ref{def}.

The harmonic function corresponding to a source distribution
of D3-branes $\rho(x)$ (normalized to one) is given by
\begin{equation}
H = L^4 \int d^6y \frac{\rho(y)}{ \left | x - y \right |^4},
\end{equation}
We show in appendix \ref{addition_theorem} that the asymptotics of
this harmonic function can be written as in (\ref{H_harm}) with coefficients
\begin{equation} \la{exp}
h_{kI} = 2^{k} (k+1) L^4 \int d^6x \rho(x) \left (C^I_{i_1 \cdots i_k}
x^{i_1} \cdots x^{i_k} \right )
\end{equation}
where $C^I_{i_1 \cdots i_k}$ is totally symmetric and traceless and the
basis of $C^I$ is orthonormal. Comparing (\ref{exp}) with (\ref{vev})
we see that these coefficients are proportional to the vevs
of the CPOs.

In the case of a uniform distribution of D3 branes
on a disc of radius $l$  one can straightforwardly do the integral in
(\ref{exp}) \cite{Skenderis:2006uy} with the result being
\begin{equation} \label{h_disc}
h_{2n0} = L^4 2^n \sqrt{2 n +1} l^{2 n}
\end{equation}
where $I=0$ signifies that only harmonics that are singlets under
the decomposition  $SO(6) \to SO(2) \times SO(4)$ are involved.

Finally let us comment on the case of a spherical shell of D3 branes of radius
$R$, for which the harmonic function is \cite{Kraus:1998hv}
\begin{equation}
H = \frac{L^{4}}{r^4}, \hspace{0.5cm} r \ge R; \hspace{0.5cm}
H = \frac{L^4}{R^4}, \hspace{0.5cm} r < R,
\end{equation}
so the geometry is flat within the shell. The asymptotics of this
harmonic function are trivially of the form (\ref{H_harm}), with the
absence of any perturbation relative to AdS corresponding to the fact
that there are no vevs for CPOs, since there are no $SO(6)$ singlet
CPOs. The interpretation of constant terms in the harmonic function
will be discussed in section 6.

\section{General method for extracting vevs}

In this section we will give a brief review of the methods developed
in \cite{Skenderis:2006uy} for extracting vevs from a given
asymptotically $AdS_5 \times S^5$ geometry. The first step is
to write the solution as the $AdS_5 \times S^5$ solution plus
a deviation\footnote{We follow the conventions
of \cite{Skenderis:2006uy}. Our index conventions are:
$M,N,...$ are $10d$ indices, $\m,{\sst{(n)}},...$ are $AdS_5$ indices,
$a,b,...$ are $S^5$ indices. $x$ denotes AdS coordinates and $y$
$S^5$ coordinates.}
\begin{eqnarray}
g_{MN} &=& g^o_{MN} + h_{MN}, \\
F_{MNPQR} &=&  F^o_{MNPQR} + f_{MNPQR}.\nonumber} \def\bd{\begin{document}} \def\ed{\end{document}
\end{eqnarray}
where
$g^o_{MN}$ and $F^o_{MNPQR}$ are the metric and 5-form of
the $AdS_5 \times S^5$ solution. (The solutions under consideration
here do not involve the other supergravity fields, so we restrict our
discussion to the metric and five form.) Next we expand the perturbations
$h_{MN}, f_{MNPQR}$ in $S^5$ harmonics. The general expansion
is given in \cite{Skenderis:2006uy}; here we only quote the
following two components since these will be useful later:
\begin{eqnarray} \label{harm_exp}
h_{a}^a(x,y) &=& \sum \pi^{I_1}(x) Y^{I_1}(y) \\
f_{a b c d e}(x,y) &=& \sum b^{I_1}(x) \L^{I_1} \e_{abcde} Y^{I_1}(y)
\end{eqnarray}
where $Y^{I_1}$ are scalar spherical harmonics and $\L^{I_1}$
is the eigenvalue of the scalar harmonic under (minus) the d'Alembertian.
It is convenient to introduce the following linear combinations of
$\pi^{I_1}$ and $b^{I_1}$
\begin{equation} \la{l1}
s^{I_1} = \frac{1}{20 (k+2)} (\pi^{I_1} - 10 (k+4) b^{I_1}), \qquad
t^{I_1} = \frac{1}{20 (k+2)} (\pi^{I_1} + 10 k b^{I_1}),
\end{equation}
since these combinations are mass eigenstates of the linearized field equations
around $AdS_5 \times S^5$ \cite{Kim:1985ez}. The $s^{I_1}$ fields
correspond to the chiral primary operators in (\ref{CPO}) and the
$t^{I_1}$ fields to half supersymmetric operators of the
schematic form ${\rm Tr}  F^4 X^k$.

There are three ingredients that enter into the map from
coefficients of the harmonic expansion in (\ref{harm_exp}) to
vevs in the dual QFT. The first is the construction
of gauge invariant variables, if the solution is not
in de Donder gauge (which indeed is often not a convenient gauge choice for
the asymptotic expansion).
De Donder gauge, $D^a h_{(ab)}=D^a h_{a\m}=0$, means that
the harmonic expansion of the metric deviations does not involve
terms with derivatives of the harmonics. It is easy to see that
the CB metrics (\ref{cbs}) in the coordinate system
where (\ref{H_harm}) holds satisfy this requirement
(but notice that the CB solutions expressed in the coordinates of
\cite{Freedman:1999gk} are not in de Donder gauge,
as discussed in \cite{Skenderis:2006uy}).
So since we can conveniently work in de Donder gauge here,
we do not need to review the construction of gauge invariant
variables (and we simplify our notation relative to \cite{Skenderis:2006uy}
by dropping the tildes and hats from our notation).

The second ingredient is the non-linear KK map from ten dimensional fields
to five
dimensional ones. For simplicity let us restrict to the subsector
involving $s^2$ and $s^4$ fields that are singlets
under $SO(6) \to SO(2) \times SO(4)$. The non-linear reduction map to
second order in the fields reads \cite{LMRS}
\begin{eqnarray} \label{KKmap}
S^2 &=& \frac{\sqrt{8}}{3}\left(s^2 - \frac{2 \sqrt{3}}{15}  (s^2)^2
-\frac{1}{12 \sqrt{12}} D_\m s^2 D^\mu s^2 \right) \\
S^4 &=& \frac{2 \sqrt{3}}{5}\left(s^4 - \frac{83}{18 \sqrt{5}} (s^2)^2
-\frac{7}{18 \sqrt{5}} D_\m s^2 D^\mu s^2\right) \nonumber
\end{eqnarray}
where capital letters denote five dimensional fields
and small letters ten dimensional fields. The fields
$S^2$ and $S^4$ defined by (\ref{KKmap}) solve the five dimensional
equations up to second order
\begin{equation} \label{5deqn}
\Box S^2 = -\frac{4}{\sqrt{6}} (S^2)^2, \qquad \Box S^4 = 0.
\end{equation}
In (\ref{KKmap})-(\ref{5deqn}) we have included only terms that can potentially
contribute to the asymptotic expansion of $S^2$ and $S^4$ up to
the order required for extraction of vevs. More generally to extract
the vev of the operator dual to $S^{\Delta}$ one would need to retain
terms involving up to $\Delta/2$ fields. The overall field
normalization is chosen such that in the
$5d$ action, all fields are canonically normalized,
apart from an overall factor of $N^2/2 \pi^2$.

The final step is to use the method of holographic renormalization
to extract the vevs from the asymptotics of the $5d$ fields.
This is by now a standard procedure (see \cite{Skenderis:2002wp} for a
review), except that here one needs to include additional terms to
accommodate extremal couplings (see section 5.4 of \cite{Skenderis:2006uy}).
The relation between field asymptotics and vevs is most transparent
in Hamiltonian variables where the radius plays the
role of time. The 1-point functions are then related to
the radial canonical momenta of the bulk fields \cite{PS}.
For the operators ${\cal O}^2$ and ${\cal O}^4$ (which are
singlets under $SO(6) \to SO(2) \times SO(4)$) the relations are
\cite{Skenderis:2006uy}:
\begin{eqnarray}
\< {\cal O}^{4} \> &=& \pi_{(2)}^2 \nonumber} \def\bd{\begin{document}} \def\ed{\end{document} \\
\< {\cal O}^{4} \> &=& \pi_{(4)}^4
+ \frac{3 {\cal N}_{4}}{\sqrt{5} {\cal N}_{2}^2 N} (\pi^2_{(2)})^2
\label{o4_p}
\end{eqnarray}
where $\pi_{(k)}^{m}$ indicates the part of the canonical momentum
of the field $S^m$ that scales with weight $k$
and ${\cal N}_{k}$ are the normalization factors given in (\ref{norm}).
The relevant part of the canonical momenta can be expressed in terms
of the asymptotic expansion of the $5d$ fields as follows
\begin{equation} \label{mom}
\pi^k_{(2 k-4)} = \frac{N^2}{2 \pi^2} (2 k- 4) [S^k]_{k}
\end{equation}
where the notation $[A]_k$ indicates the coefficient of the $z^k$
term in $A$ and $z$ is the Fefferman-Graham radial coordinate.
The relation (\ref{mom}) holds for $k \neq 2$;
when $k=2$ one should replaces the factor $(2 k-4)$ by 2.

For reasons which will become clear later
it is useful to express the vevs directly in terms of the
coefficients that appear in the $10d$ solution. Using the results
reviewed above one obtains
\begin{eqnarray}
\< {\cal O}^2 \> &=& \frac{N^2}{2 \pi^2} \frac{2 \sqrt{8}}{3}
[s^2]_2 \\
\< {\cal O}^4 \> &=& \frac{N^2}{2 \pi^2} \frac{4 \sqrt{3}}{5}
[2 s^4
+ \frac{37}{9 \sqrt{5}} (s^2)^2 -\frac{7}{9 \sqrt{5}} (D s^2)^2]_4
\end{eqnarray}
The expression for $\< {\cal O}^4 \>$ can be further simplified
for solutions with $s^2$ only depending on the radial coordinate,
such as those under consideration in this paper. In such cases,
$[(D s^2)^2]_4 = 4 [(s^2)^2]_4$ and we obtain
\begin{equation} \label{o4}
\< {\cal O}^4 \> = \frac{N^2}{2 \pi^2} \frac{4 \sqrt{3}}{5}
[2 s^4 + \frac{1}{\sqrt{5}} (s^2)^2]_4.
\end{equation}
The general method outlined here
can be applied to extract the vevs of all other
higher dimension operators. However, the procedure becomes
complex as the operator dimension increases, since one has to retain
terms to higher and higher order in the reduction map, the field
equations and the relations which give the vevs. The purpose
of the current paper is to point out that simplifications occur for
the Coulomb branch solutions: for these
we will be able to carry out the vev computation for arbitrarily
high dimension operators.

\section{Obtaining the vevs} \label{vevs}

We now return to the Coulomb branch solutions and
express the harmonic function as
\begin{equation}
H = \frac{L^4}{r^4} + \delta H,
\end{equation}
i.e. we separate the $k=0,I=0$ term in (\ref{H_harm}) that
yields the $AdS_5 \times S^5$ part of the solution
from the remaining terms. The metric and five form field become
\begin{eqnarray}
ds^2 &=& L^2 r^2 (1 + \frac{r^4 \d H}{L^4})^{-{\textstyle{1\over2}}}
dx_{||}^2 + L^2 (1 + \frac{r^4 \delta H}{L^4})^{{\textstyle{1\over2}}}
(\frac{dr^2}{r^2} + d \Omega_{5}^2); \\
F_{5} &=& (L^4 - \frac{1}{4} r^5 \pa_{r} \delta H) d\W_5 + {\textstyle{1\over 4}} r^3 dr
\wedge \ast_{S^5} D_{a} \Delta H
+ {\textstyle{1\over 4}} d ( L^4 r^4 (1 + \frac{\delta H r^4}{L^4})^{-1})
\wedge \omega_{||}. \nonumber} \def\bd{\begin{document}} \def\ed{\end{document}
\end{eqnarray}
Note that the coordinates on $R^{3,1}$ have been rescaled as
\begin{equation} \label{resc}
x_{||} \to L^2 x_{||}
\end{equation}
so that the metric scales as $L^2$.

This coordinate system is manifestly compatible with the de Donder
gauge for fluctuations; we can immediately read off the following
expression for the field $b^I_k$ in (\ref{harm_exp}) as
\begin{equation}
b^{I}_k =  - \frac{h_{kI}}{4 L^4 k r^k}
\end{equation}
whilst the trace of the fluctuation on the sphere is
\begin{equation}
\pi = 5 \left ( (1 + \frac{r^4 \delta H}{L^4})^{1/2} - 1 \right).
\end{equation}
Retaining only linear terms in the expansion of the square root gives
\begin{equation} \label{pi_lin}
\pi^{I}_k = \frac{5 h_{kI}}{2 L^4 r^k}.
\end{equation}
Note however that there is no justification generically for retaining
only the linear term. Indeed the quadratic correction gives
\begin{equation} \label{corr}
- \frac{5}{8 z(k)} \sum_{k_1, I_1, I_2} \frac{1}{L^8 r^k} h_{k_1 I_1}
h_{(k-k_1) I_2} \left < Y^{I_1}_{k_1} Y^{I_2}_{(k-k_1)} Y^{I}_{k}
\right >,
\end{equation}
where the term in parenthesis indicates the triple overlap of the
scalar harmonics. This term is not suppressed compared to the linear term
(recall the $h_{kI}$ contain a factor of $L^4$ so the factors of
$L$ cancel in (\ref{corr})); there is no small parameter in general.
The issue of non-liner terms first appears for dimension 4 operators. In this case
we constructed the holographic map from first principles
in \cite{Skenderis:2006uy}, as reviewed in the previous section,
so we should be able to understand whether the quadratic
corrections contribute. Notice that since $h_{kI}$ is proportional
to the vev of a chiral primary operator, the quadratic correction
looks like a double trace contribution.

To understand this issue let us restrict to the special case of a disc
distribution which was the case understood in detail in
\cite{Skenderis:2006uy}. In this case $s^2$ and $s^4$ are given by
\begin{equation}
s^2 = \frac{1}{8} h_{20}, \qquad
s^4 = \frac{1}{16} h_{40} -\frac{1}{128 \sqrt{5}} (h_{20})^2,
\end{equation}
where $h_{20}$ and $h_{40}$ are given in (\ref{h_disc}). The term
in $s^4$ quadratic in  $h_{20}$ comes from (\ref{corr}). Inserting these
values in the expression for the vevs (\ref{o4}) we find that
the  $(h_{20})^2$ part of $s^4$ is
precisely cancelled by the $(s_2)^2$ term! The remaining terms
are exactly right to reproduce (\ref{vev1}). Notice that the
$(s_2)^2$ terms in (\ref{o4}) originate from two sources.
One is the non-linear terms in the KK map and the second are the
non-linear terms in the 1-point function (\ref{o4_p}). Based on this result
we conjecture that the same type of cancellation will occur
for all operators in the general case.

So now let us return to the general case and assume that such a cancellation takes
place. We thus retain only the linear term (\ref{pi_lin})
and ignore non-linear terms in the KK map and non-linear
terms in the 1-point function. The 10d fluctuations under these
assumptions are
\begin{equation}
s^{I}_{k} = \frac{h_{kI}}{4 k L^4 r^k}, \qquad t^I_k=0,
\end{equation}
so the canonically normalized five dimensional fields are equal to
\begin{equation}
S^{I}_{k} = \frac{\sqrt{(k-1)}}{2^{k/2} \sqrt{k} (k+1)} \frac{h_{kI}}{L^4 r^k},
\qquad T^I_k=0,
\end{equation}
where for completeness we also quote the values of the $t$ field.
This implies the following expression for the vev
\begin{equation}
\left < {{\cal O}}_{k}^I \right > =
\frac{N^2}{2 \pi^2} (2k - 4) [S^{I}]_{k}
= \frac{N^2}{\pi^2}
\frac{(k-2) \sqrt{(k-1)}}{2^{k/2} \sqrt{k} (k+1)} \frac{h_{kI}}{L^4},
\end{equation}
for $k \neq 2 $ whilst the formula for $k=2$ follows using the
replacement $(k-2) \rightarrow 2$. Using the identity (\ref{exp})
then gives a final expression for the vev as
\begin{equation} \label{sugra}
\left < {{\cal O}}_{k}^I \right > = \frac{N^2}{\pi^2} 2^{k/2} (k-2)
  \sqrt{\frac{k-1}{k}} \int d^6x' \rho(x') (C^I_{i_1 \cdots i_k}
(x')^{i_1} \cdots (x')^{i_k} ),
\end{equation}
for $k \neq 2$ with the analogous expression for $k=2$ being obtained
by the replacement $(k-2) \rightarrow 2$. To match supergravity
and field theory normalizations, field theory lengths
must be scaled by a factor of $\sqrt{\l/2 \pi^2}$.
This is due to the rescaling in (\ref{resc}) and is explained in
section 6.3 of \cite{Skenderis:2006uy}. Taking this factor into
account we find exact agreement between the supergravity
and field theory computations in
(\ref{sugra}) and (\ref{vev})!

This result is highly non-trivial: whilst all the vevs must necessarily
be encoded in the harmonic function, it is surprising that one can
extract them so simply by the above linearization of the ten-dimensional
fields. Note that this procedure for extracting the Coulomb branch
vevs was suggested in \cite{Klebanov:1999tb}, although the
interpretation of the neglected terms was and remains unclear.
Presumably the linearization can be rigorously justified in this case by
proving that the non-linear terms cancel when one carries out the
holographic renormalization procedure directly in ten dimensions. This
issue is currently under investigation.

One would also not anticipate that there is an analogous route for
extracting vevs from general asymptotically $AdS_5 \times S^5$
solutions. In the CB example, the simplifications arose when we
expanded the solution in a particular radial coordinate, which turned
out to be exactly the Fefferman-Graham coordinate, and then
linearized in a natural way. Had we expanded the same solutions in the coordinate
systems of \cite{Freedman:1999gk}, we would have had no motivation for
retaining the required ``linearized'' subset of terms in the
perturbations. Indeed, in the discussion of the disk distribution in
\cite{Skenderis:2006uy}, only the complete gauge invariant fields $\pi^{I}_k$
played a role. For more general supergravity solutions, even those such as the
bubbling geometries of \cite{Lin:2004nb} which are built from harmonic
functions, it is not obvious how one would even define the above procedure
or why it should be justified. By contrast, the method for extracting
vevs presented in
\cite{Skenderis:2006uy} applies to {\it all} asymptotically $AdS_5 \times S^5$ solutions.

\section{Duals of 1/2-susy deformations of ${\cal N}=4$ SYM} \label{def}

In section \ref{CBsection} we discussed the supergravity
solution (\ref{cbs}) describing a distribution of D3-branes. The
harmonic function $H$ entering the solution was
constrained to vanish as $r^{-4}$ in order for the
solution to be asymptotically AdS. We discuss here
solutions obtained by relaxing this condition, and their
interpretation using the AdS/CFT dictionary, in particular using the map
between ten dimensional fields and the gauge theory discussed in the
previous section.

The most general solution of (\ref{harm}) is
\begin{equation} \label{genh}
H = \sum_{k, I} \left(l_{k I} r^{k} + \frac{h_{k I}}{r^{k+4}}\right) Y^I_k
\end{equation}
The case with only the $k=I=0$ terms is D3 brane solution with the asymptotically
flat region included. The more general solution (\ref{genh})
still preserves 16 supercharges, and as we will shortly see, surprisingly
admits an AdS/CFT interpretation despite the fact that the solution
is not asymptotically AdS (in any usual usage of the word).

We proceed as in the previous section by writing
\begin{equation}
H = \frac{L^4}{r^4} + \delta H
\end{equation}
and keeping only the linear term in $\delta H$. The terms proportional
to $h_{k I}$ have been discussed already, so we only
consider here the new terms proportional to $l_{k I}$. From the
metric and five-form we read off
\begin{equation}
\pi_k^I = \frac{5l_{kI}}{2 L^4} r^{k+4}, \qquad
b_k^I= \frac{l_{kI}}{4 (k+4) L^4} r^{k+4}.
\end{equation}
Forming the $s$ and $t$ combinations we obtain
\begin{equation}
s^I_k=0, \qquad t_k^I = \frac{l_{kI}}{4 (k+4)} r^{k+4}.
\end{equation}
The radial behavior of the $t$ field is exactly right for the
solution to correspond to a deformation of the $N=4$ SYM theory by
the operators dual to the $t^k$ fields, with the deformation
parameter being (proportional to) $l_{kI}$. The restriction of
keeping only linear terms in $\d H$ may be justified by
considering the deformation parameters $l_{kI}$ to be
small (although the results may hold more generally
due to cancellations as in the case of $h_{kI}$).

Such a deformation was discussed in \cite{Intriligator:1999ai}
where it was argued that the gauge beta function continues to vanish.
This corresponds to the fact that the dilaton and axion are constant in
the solutions we discuss. In the same paper, it was argued
(extending earlier work \cite{Gubser:1998kv,Gubser:1998iu}) that the
full D3-brane solution (with the asymptotic flat region included)
is dual to $N=4$ SYM deformed by a dimension 8 operator. This
is precisely the operator dual to $t^0$. In this paper we
generalize this proposal to the general case of a deformation
by all operators dual to $t^k$. It is easy to check that all symmetries
(susy, R-symmetry) match between the supergravity and
field theory descriptions. Notice that the operators $t^k$
are irrelevant so one expects a strong backreaction on the
asymptotics of the dual geometry. It would be interesting
to explore this case further, especially since the geometry
is far from being asymptotically AdS so one may learn
about how holography works in more general contexts.

\section*{Acknowledgments}

The authors are supported by NWO, KS via the Vernieuwingsimplus grant
``Quantum gravity and particle physics'' and
MMT via the Vidi grant ``Holography,
duality and time dependence in string theory''.

redpajama_set_name: RedPajamaArXiv


text:
Judge for Perry Lowe
Bastrop, TX
Perry Lowe is an R&B singer, writer and producer. During his career he has recorded and performed in other genres of music as well. At age 13 he played drums and recorded with the Doak Snead band a local rockabilly group in Central Texas. Perry also produced, performed and arranged songs for Tyrone Vaughan and Jeff Haney, both are Adult Alternative artists. Perry is currently producing tracks for Hip Hop artist MADD Tha Gangsta, and R&B artists Rory Smith, Christine Fanuel. Perry is also drumming and supplying backing vocals for The Tres Womack Band. In the midst of this he is getting set to promote his new single "Settle Down" from the forthcoming CD titled My Life In A Groove.

redpajama_set_name: RedPajamaCommonCrawl


Two Special Olympic football teams took to the field at halftime in St Pat's bank holiday Monday EA Sports Cup match against Shamrock Rovers and received a very warm welcome from the crowd.
Menni Movers from Walkinstown took on Mobhi Magic from Glasnevin in a game which ended in a tight one all draw.
Lining out for both teams on the day were, Menni Movers - Ronan Cahill, Jonathan Roche, Maurice Tyrrell, Paul Waters, Conor Henshaw & Eddie Dunne and for Mobhi Magic - John Bennrt, Nathan Doherty, Peter & Michael Moylan, Leon Keogh, Barry Mc Caffery, Davic Mc Ginn, Eoin Mc Hugh, Gerard O'Riordan & Michael Windrim.


Author Solutions Inc., the Bloomington parent of self-publisher AuthorHouse, has been sold to Bertram Capital of Palo Alto, Calif., for an undisclosed price.
Author Solutions, which published one of every 30 U.S. book titles last year, was owned by Carmel-based Gazelle Tech Ventures. AuthorHouse CEO Bryan Smith said he expects Bertram to expand deeper into self-publishing and offer new products and services.


text:
Q: Force excel formula to update when non related cell value changes I need to track how many issues I close per hour.
I take a start time and compare that to the current time to see how long ive been at work, then subtract an amount of time for lunch, and subtract amount of time away from my desk to get how long Ive actually been working.
Now I take how long Ive actually been working and divide that by how many issues I have closed to see how many issues I have closed per hour.
I have the below metrics:

*

*A20:  2:00 PM  (start time)

*C20:  0:30     (Length of Lunch)

*E20:  0:00     (Length of time away from desk, different project etc..)

Formula to return decimal representation of hours worked:

*

*B20:  =HOUR(NOW()-A20-C20-E20)+MINUTE(NOW()-A20-C20-E20)/60

*F20:  25       (issues worked, this number changes throughout the day)
Now I need to do G20: =(F20/B20)
When B20 changes, G20 is updated as you'd expect.
The problem is that since none of the cells related to the formula in B20 have changed, that value is not updated before G20 is calculated
How can I force the formula in B20 to update when the value of F20 changes?
VBA would be acceptable also (and probably easier) Im just not very familiar with VBA

A: To your b20 formula add a dummy operation including f20 for example
=....+F20-F20


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text:
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 Google Chrome Frame – plug-in sviluppato da Google

Letteratura
 La notte che bruciammo Chrome (Burning Chrome) – racconto di William Gibson
 La notte che bruciammo Chrome (Burning Chrome) – raccolta di racconti di William Gibson contenente anche il racconto omonimo

Musica
 Chrome – gruppo musicale statunitense
 Chrome – singolo di Debbie Harry del 1981, dall'album KooKoo
 Chrome – album dei Catherine Wheel del 1993
 Chrome – album di Trace Adkins del 2001

Personaggi
 Chrome – personaggio dei fumetti Marvel Comics, membro degli Accoliti
 Chrome (Jenny Swensen) – personaggio del New Universe dei fumetti Marvel Comics
 Chrome Dokuro – personaggio del manga e anime Tutor Hitman Reborn!

Videogiochi
 Chrome – sparatutto in prima persona

redpajama_set_name: RedPajamaWikipedia


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Chip Yates is used to going fast, having obtained a private pilots certificate in a mere two months, and test flying an electric Long-Eze conversion (Long-ESA) within two weeks of that, but he didn't count on making the world's fastest electric aircraft emergency landing during a record-breaking speed run at Inyokern, California's desert airport on July 19. With only 58 hours in his log book, Chip managed to make the runway for a bumpy but great touchdown – a great landing being one following which you can reuse the airplane. We've reported that event already, but Chip just released a great video of the white-knuckle event.
To help document his record 202.6 mph flight, Chip's airplane was well instrumented, carried several cameras, and had a chase plane to provide eye-witness oversight.
In the two months he and fabrication partner Chris Parker of CPR Fabrication converted a Long-Eze into the world's most powerful electric airplane (258 horsepower – 58 more than Green Flight Challenge winner, Pipistrel's G4).
Chip will speak Friday, July 27th at 10:30am at AirVenture 2012 in the Innovation Hangar South, and then deliver a full-length technical presentation in the afternoon at 1:00pm in the Innovation Hangar South to review on-board telemetry and data from the record-setting flight. He'll be able to enlighten anticipated crowds on the dead cell that shortened his base leg and forced an early turn to final.
After that, he'll be back to Inyokern and more than likely go after speed and altitude records for electric aircraft while preparing for his planned tran-Atlantic flight in 2014.
Folks.. let us stay focused not on who is to be first, but who is to finally get it right (Boeing vs Lindbergh)… What we learned at this EAA event, the future of aviation is "electric" and the future of electric flight is VTOL aircraft, and the future of Electric VTOLs must be hydrogen as the energy source. And the future of that must be the generation of the hydrogen within the aircraft itself during those many hours that most planes sit in the hangar… There are a dozen ways of doing that, and I hope Dr. Mark Moore at NASA Langley will be permitted to show us his approach to a hydrogen fueled VTOLs… He is my Sensei…"Do.. not try".