a remark on a standard and linear vector network equilibrium problem with capacity constraints in this paper weak vector equilibrium principle with capacity constraints is introduced a necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained when the number of paths connecting with each pair of source and sink is less than or equal to 2 a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained a generalized weak vector equilibrium principle is also introduced without any additional assumption a necessary and sufficient condition for a weak vector minimum cost flow to be a generalized weak vector equilibrium flow is obtained

time scales of spike train correlation for neural oscillators with common drive we examine the effect of the phase resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation we use linear response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type i vs type ii models and across the different time scales over which spike correlations can be assessed we find that on long time scales type i oscillators transfer correlations much more efficiently than type ii oscillators on short time scales this trend reverses with the relative efficiency switching at a time scale that depends on the mean and standard deviation of input currents this switch occurs over time scales that could be exploited by downstream circuits

representational accuracy of stochastic neural populations fisher information is used to analyze the accuracy with which a neural population encodes d stimulus features it turns out that the form of response variability has a major impact on the encoding capacity and therefore plays an important role in the selection of an appropriate neural model in particular in the presence of baseline firing the reconstruction error rapidly increases with d in the case of poissonian noise but not for additive noise the existence of limited range correlations of the type found in cortical tissue yields a saturation of the fisher information content as a function of the population size only for an additive noise model we also show that random variability in the correlation coefficient within a neural population as found empirically considerably improves the average encoding quality finally the representational accuracy of populations with inhomogeneous tuning properties either with variability in the tuning widths or fragmented into specialized subpopulations is superior to the case of identical and radially symmetric tuning curves usually considered in the literature

the effect of a refractory period on the power spectrum of neuronal discharge the interspike intervals in steady state neuron firing are assumed to be independently and identically distributed random variables in the simplest model discussed each interval is assumed to be the sum of a random neuron refractory period and a statistically independent interval due to a stationary external process whose statistics are assumed known the power spectral density hence the autocorrelation of the composite neuron firing renewal process is derived from the known spectrum of the external process and from the unknown spectrum of the neuron refraction process the results are applied to spike trains recorded in a previous study 2 of single neurons in the visual cortex of an awake monkey two models are demonstrated that may produce peaks in the power spectrum near 40 hz

on some models for multivariate binary variables parallel in complexity with the multivariate gaussian distribution it is shown that both the simple form of the rasch model for binary data and a generalisation are essentially equivalent to special dichotomised gaussian models in these the underlying gaussian structure is of single factor form that is the correlations between the binary variables arise via a single underlying variable called in psychometrics a latent trait the implications for scoring of the binary variables are discussed in particular regarding the scoring system as in effect estimating the latent trait in particular the role of the simple sum score in effect the total number of successes is examined relations with the principal component analysis of binary data are outlined and some connections with the quadratic exponential binary model are sketched

spike output jitter mean firing time and coefficient of variation to understand how a single neurone processes information it is critical to examine the relationship between input and output marsalek koch and maunsell s study focused on output jitter standard deviation of output interpike interval found that for the integrate and fire if whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation the i f model with leakage is also briefly considered

information geometric measures as robust estimators of connection strengths and external inputs information geometry has been suggested to provide a powerful tool for analyzing multineuronal spike trains among several advantages of this approach a significant property is the close link between information geometric measures and neural network architectures previous modeling studies established that the first and second order information geometric measures corresponded to the number of external inputs and the connection strengths of the network respectively this relationship was however limited to a symmetrically connected network and the number of neurons used in the parameter estimation of the log linear model needed to be known recently simulation studies of biophysical model neurons have suggested that information geometry can estimate the relative change of connection strengths and external inputs even with asymmetric connections inspired by these studies we analytically investigated the link between the information geometric measures and the neural network structure with asymmetrically connected networks of n neurons we focused on the information geometric measures of orders one and two which can be derived from the two neuron log linear model because unlike higher order measures they can be easily estimated experimentally considering the equilibrium state of a network of binary model neurons that obey stochastic dynamics we analytically showed that the corrected first and second order information geometric measures provided robust and consistent approximation of the external inputs and connection strengths respectively these results suggest that information geometric measures provide useful insights into the neural network architecture and that they will contribute to the study of system level neuroscience

synchronization of networks of heterogeneous agents with common nominal behavior this paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior the agents are modeled as possibly nonlinear perturbed versions of a common siso nominal lti operator and they are interconnected via a sparse memoryless interconnection operator coherent with the communication graph underlying the network the network is said to synchronize if the outputs of the agents tend to align along given directions the most important case being consensus or agreement the paper provides a general result based on iqcs that ensures synchronization of the network with robustness w r t uncertainties in the interconnection and in each agent s dynamics scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix yielding the generalization of the very popular linear consensus algorithm the wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples whenever possible graphical criteria are proposed for checking the required conditions

sensitivity analysis for abstract equilibrium problems we develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well known results on variational inequalities in the literature even though we have worked under arbitrary constraints k with holder property that have been decisive in our treatment we have obtained in a similar spirit of domokos j math anal appl 230 1999 382 389 the best lower bound for the continuity modulus despite of the properties of the boundary of k

assessing neuronal coherence with single unit multi unit and local field potentials the purpose of this study was to obtain a better understanding of neuronal responses to correlated input in particular focusing on the aspect of synchronization of neuronal activity the first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input for poisson neurons we could derive that the peak of the coherence between the correlated input and multi unit activity increases proportionally with the square root of the number of neurons in the multi unit recording the coherence between two typical multi unit recordings 2 to 10 single units with partially correlated input increases proportionally with the number of units in the multi unit recordings the second aim of this study was to investigate to what extent the amplitude and signal to noise ratio of the coherence between input and output varied for single unit versus multi unit activity and how they are affected by the duration of the recording the same problem was addressed for the coherence between two single unit spike series and between two multi unit spike series the analytical results for the poisson neuron and numerical simulations for the conductance based leaky integrate and fire neuron and for the conductance based hodgkin huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording the only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function the results of analytical derivations and computer simulations for model neurons show that the coherence for multi unit activity is larger than that for single unit activity this is in agreement with the results of experimental data obtained from monkey visual cortex v4 finally we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate

synchronous firing and higher order interactions in neuron pool the stochastic mechanism of synchronous firing in a population of neurons is studied from the point of view of information geometry higher order interactions of neurons which cannot be reduced to pairwise correlations are proved to exist in synchronous firing in a neuron pool where each neuron fires stochastically the probability distribution q r of the activity r which is the fraction of firing neurons in the pool is studied when q r has a widespread distribution in particular when q r has two peaks the neurons fire synchronously at one time and are quiescent at other times the mechanism of generating such a probability distribution is interesting because the activity r is concentrated on its mean value when each neuron fires independently because of the law of large numbers even when pairwise interactions or third order interactions exist the concentration is not resolved this shows that higher order interactions are necessary to generate widespread activity distributions we analyze a simple model in which neurons receive common overlapping inputs and prove that such a model can have a widespread distribution of activity generating higher order stochastic interactions

synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance the subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population it was recently found that conductancebased synaptic drive can lead to distributions with a significant skew here it is demonstrated that the underlying shot noise caused by poissonian spike arrival also skews the membrane distribution but in the opposite sense using a perturbative method we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution to first order in the perturbation theory the voltage distribution is a gaussian modulated by a prefactor that captures the skew the gaussian component is identical to distributions derived using current based models with an effective membrane time constant the well known effective time constant approximation can therefore be identified as the leading order solution to the full conductance based model the higher order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations the diffusion approximation misses these shot noise effects implying that analytical approaches such as the fokker planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation it is further demonstrated that quantities used for fitting theory to experiment such as the voltage mean and variance are robust against these non gaussian effects the effective time constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added

stimulus dependent correlations in threshold crossing spiking neurons we consider a threshold crossing spiking process as a simple model for the activity within a population of neurons assuming that these neurons are driven by a common fluctuating input with gaussian statistics we evaluate the cross correlation of spike trains in pairs of model neurons with different thresholds this correlation function tends to be asymmetric in time indicating a preference for the neuron with the lower threshold to fire before the one with the higher threshold even if their inputs are identical the relationship between these results and spike statistics in other models of neural activity is explored in particular we compare our model with an integrate and fire model in which the membrane voltage resets following each spike the qualitative properties of spike cross correlations emerging from the threshold crossing model are similar to those of bursting events in the integrate and fire model this is particularly true for generalized integrate and fire models in which spikes tend to occur in bursts as observed for example in retinal ganglion cells driven by a rapidly fluctuating visual stimulus the threshold crossing model thus provides a simple analytically tractable description of event onsets in these neurons

dynamics of moment neuronal networks a theoretical framework is developed for moment neuronal networks mnns within this framework the behavior of the system of spiking neurons is specified in terms of the first and second order statistics of their interspike intervals i e the mean the variance and the cross correlations of spike activity since neurons emit and receive spike trains which can be described by renewal but generally non poisson processes we first derive a suitable diffusion type approximation of such processes two approximation schemes are introduced the usual approximation scheme uas and the ornstein uhlenbeck scheme it is found that both schemes approximate well the input output characteristics of spiking models such as the if and the hodgkin huxley models the mnn framework is then developed according to the uas scheme and its predictions are tested on a few examples

population coding in neuronal systems with correlated noise neuronal representations of external events are often distributed across large populations of cells we study the effect of correlated noise on the accuracy of these neuronal population codes our main question is whether the inherent error in the population code can be suppressed by increasing the size of the population n in the presence of correlated noise we address this issue using a model of a population of neurons that are broadly tuned to an angular variable in two dimensions the fluctuations in the neuronal activities are modeled as gaussian noises with pairwise correlations that decay exponentially with the difference between the preferred angles of the correlated cells we assume that the system is broadly tuned which means that both the correlation length and the width of the tuning curves of the mean responses span a substantial fraction of the entire system length the performance of the system is measured by the fisher information fi which bounds its estimation error by calculating the fi in the limit of a large n we show that positive correlations decrease the estimation capability of the network relative to the uncorrelated population the information capacity saturates to a finite value as the number of cells in the population grows in contrast negative correlations substantially increase the information capacity of the neuronal population these results are supplemented by the effect of correlations on the mutual information of the system our analysis provides an estimate of the effective number of statistically independent degrees of freedom denoted n mathrm eff that a large correlated system can have according to our theory n mathrm eff remains finite in the limit of a large n estimating the parameters of the correlations and tuning curves from experimental data in some cortical areas that code for angles we predict that the number of effective degrees of freedom embedded in localized populations in these areas is less than or of the order of ensuremath approx 10 2

correlation transfer in stochastically driven neural oscillators over long and short time scales in the absence of synaptic coupling two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics but also on the length of the observation window over which the correlation is calculated in this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales a quantity that provides a convenient proxy for the spike count correlation over short time scales we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales we also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales these analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type i oscillators transfer correlations more faithfully than do type ii over long time scales while the reverse holds true for the better understood case of short time scales

increasing inhibitory input increases neuronal firing rate why and when diffusion process cases increasing inhibitory input to single neuronal models such as the fitzhugh nagumo model and the hodgkin huxley model can sometimes increase their firing rates a phenomenon which we term inhibition boosted firing ibf here we consider neuronal models with diffusion approximation inputs i e they share the identical first and second order statistics of the corresponding poisson process inputs using the integrate and fire model and the if fhn model we explore theoretically how and when ibf can happen for both models it is shown that there is a critical input frequency at which the efferent firing rate is identical when the neuron receives purely excitatory inputs or exactly balanced inhibitory and excitatory inputs when the input frequency is lower than the critical frequency ibf occurs

the high conductance state of cortical networks we studied the dynamics of large networks of spiking neurons with conductance based nonlinear synapses and compared them to networks with current based linear synapses for systems with sparse and inhibition dominated recurrent connectivity weak external inputs induced asynchronous irregular firing at low rates membrane potentials fluctuated a few millivolts below threshold and membrane conductances were increased by a factor 2 to 5 with respect to the resting state this combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo many aspects of the asynchronous irregular state in conductance based networks could be sufficiently well characterized with a simple numerical mean field approach in particular it correctly predicted an intriguing property of conductance based networks that does not appear to be shared by current based models they exhibit states of low rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers simulations of larger networks up to 350 000 neurons demonstrated that the survival time of self sustained activity increases exponentially with network size

on lewis simulation method for point processes a simple and efficient method of simulation is discussed for point processes that are specified by their conditional intensities the method is based on the thinning algorithm which was introduced recently by lewis and shedler for the simulation of nonhomogeneous poisson processes algorithms are given for past dependent point processes containing multivariate processes the simulations are performed for some parametric conditional intensity functions and the accuracy of the simulated data is demonstrated by the likelihood ratio test and the minimum akaike information criterion aic procedure

correlated inhibitory and excitatory inputs to the coincidence detector analytical solution we present a solution for the steady state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory input spike trains all excitatory spike trains have identical binomial count distributions which includes poisson statistics as a special case and arbitrary pairwise cross correlations between them the same applies to the inhibitory inputs and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other thus for each population independently the correlation may range from complete independence to perfect correlation identical processes we find that inhibition if made sufficiently strong will result in an inverted u shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates this leads to the prediction that higher presynaptic input rates may lead to lower postsynaptic output rates where the output rate may fall faster than the inverse of the input rate and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression in general we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

neural coding higher order temporal patterns in the neurostatistics of cell assemblies recent advances in the technology of multiunit recordings make it possible to test hebb s hypothesis that neurons do not function in isolation but are organized in assemblies this has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron spike train data we mention three possible measures for the presence of higher order patterns of neural activation coef ficients of log linear models connected cumulants and redundancies and present arguments in favor of the coefficients of loglinear models we present test statistics for detecting the presence of higher order interactions in spike train data by parameterizing these interactions in terms of coefficients of log linear models we also present a bayesian approach for inferring the existence or absence of interactions and estimating their strength the two methods the frequentist and the bayesian one are shown to be consistent in the sense that interactions that are detected by either method also tend to be detected by the other a heuristic for the analysis of temporal patterns is also proposed finally a bayesian test is presented that establishes stochastic differences between recorded segments of data the methods are applied to experimental data and synthetic data drawn from our statistical models our experimental data are drawn from multiunit recordings in the prefrontal cortex of behaving monkeys the somatosensory cortex of anesthetized rats and multiunit recordings in the visual cortex of behaving monkeys

a comparison of descriptive models of a single spike train by information geometric measure in examining spike trains different models are used to describe their structure the different models often seem quite similar but because they are cast in different formalisms it is often difficult to compare their predictions here we use the information geometric measure an orthogonal coordinate representation of point processes to express different models of stochastic point processes in a common coordinate system within such a framework it becomes straightforward to visualize higher order correlations of different models and thereby assess the differences between models we apply the information geometric measure to compare two similar but not identical models of neuronal spike trains the inhomogeneous markov and the mixture of poisson models it is shown that they differ in the second and higher order interaction terms in the mixture of poisson model the second and higher order interactions are of comparable magnitude within each order whereas in the inhomogeneous markov model they have alternating signs over different orders this provides guidance about what measurements would effectively separate the two models as newer models are proposed they also can be compared to these models using information geometry

ising distribution as a latent variable model during the past decades the ising distribution has attracted interest in many applied disciplines as the maximum entropy distribution associated to any set of correlated binary spin variables with observed means and covariances however numerically speaking the ising distribution is un practical so alternative models are often preferred to handle correlated binary data one popular alternative especially in life sciences is the cox distribution or the closely related dichotomized gaussian distribution and log normal cox point process where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution this article explores the conditions for a principled replacement of the ising distribution by a cox distribution it shows that the ising distribution itself can be treated as a latent variable model and it explores when this latent variable has a quasi normal distribution a variational approach to this question reveals a formal link with classic mean field methods especially opper and winther s adaptive tap approximation this link is confirmed by weak coupling plefka expansions of the different approximations and then by numerical tests overall this study suggests that an ising distribution can be replaced by a cox distribution in practical applications precisely when its parameters lie in the mean field domain

impact of correlated neural activity on decision making performance stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations neurons in the populations however do not spike independently spike events are correlated from cell to cell to what degree does this apparent redundancy have an impact on the accuracy with which decisions can be made and the computations required to optimally decide we explore these questions for two illustrative models of correlation among cells each model is statistically identical at the level of pairwise correlations but differs in higher order statistics that describe the simultaneous activity of larger cell groups we find that the presence of correlations can diminish the performance attained by an ideal decision maker to either a small or large extent depending on the nature of the higher order correlations moreover although this optimal performance can in some cases be obtained using the standard integration to bound operation in others it requires a nonlinear computation on incoming spikes overall we conclude that a given level of pairwise correlations even when restricted to identical neural populations may not always indicate redundancies that diminish decision making performance

on the holder continuity of solutions to parametric multivalued vector equilibrium problems we consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces sufficient conditions for the local uniqueness and holder continuity of the solutions are established as consequences some new results for variational inequalities are derived and compared with recent papers on the subject

a unifying framework for robust synchronization of heterogeneous networks via integral quadratic constraints a general framework for analysing robust synchronization in large scale heterogenous networks is proposed based on the theory of integral quadratic constraints iqcs dynamic agents are represented as linear time invariant single input single output systems the agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization where their outputs are steered to the same possibly time varying signal the main technical hindrance to applying iqcs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents outputs synchronize it is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems iqc methods can be applied directly to synchronization analysis without recourse to loop transformations which may obscure the inherent structural properties of the multi agent networked systems decentralized and scalable conditions for synchronization are proposed within this setting the iqc framework is demonstrated to unify and generalize some of the existing results in the literature including certain nyquist type consensus certificates for time delay systems moreover it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization

including long range dependence in integrate and fire models of the high interspike interval variability of cortical neurons many different types of integrate and fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains within this context the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals however another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long range dependence we investigate the conditions if any under which such models produce output spike trains with both interspike interval variability and long range dependence similar to those that have previously been measured from actual cortical neurons we first show analytically that a large class of high variability integrate and fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes this class of models subsumes a majority of previously published models including those that use excitation inhibition balance correlated inputs partial reset or nonlinear leakage to produce outputs with high variability next we study integrate and fire models that have nonpoissonian renewal point process inputs instead of the poisson point process inputs used in the preceding class of models the confluence of our analytical and simulation results implies that the renewal input model is capable of producing high variability and long range dependence comparable to that seen in spike trains recorded from cortical neurons but only if the interspike intervals of the inputs have infinite variance a physiologically unrealistic condition finally we suggest a new integrate and fire model that does not suffer any of the previously mentioned shortcomings by analyzing simulation results for this model we show that it is capable of producing output spike trains with interspike interval variability and long range dependence that match empirical data from cortical spike trains this model is similar to the other models in this study except that its inputs are fractional gaussian noise driven poisson processes rather than renewal point processes in addition to this model s success in producing realistic output spike trains its inputs have long range dependence similar to that found in most subcortical neurons in sensory pathways including the inputs to cortex analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike interval variability at their outputs furthermore in our analysis of this model we show that the superposition of many fractional gaussian noise driven poisson processes does not approximate a poisson process which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a poisson process

well posedness by perturbations of mixed variational inequalities in banach spaces in this paper we consider an extension of the notion of well posedness by perturbations introduced by zolezzi for a minimization problem to a mixed variational inequality problem in a banach space we establish some metric characterizations of the well posedness by perturbations we also show that under suitable conditions the well posedness by perturbations of a mixed variational inequality problem is equivalent to the well posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem also we derive some conditions under which the well posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution

impact of correlated inputs on the output of the integrate and fire model for the integrate and fire model with or without reversal potentials we consider how correlated inputs affect the variability of cellular output for both models the variability of efferent spike trains measured by coefficient of variation cv of the interspike interval is a nondecreasing function of input correlation when the correlation coefficient is greater than 0 09 the cv of the integrate and fire model without reversal potentials is always above 0 5 no matter how strong the inhibitory inputs when the correlation coefficient is greater than 0 05 cv for the integrateand fire model with reversal potentials is always above 0 5 independent of the strength of the inhibitory inputs under a given condition on correlation coefficients we find that correlated poisson processes can be decomposed into independent poisson processes we also develop a novel method to estimate the distribution density of the first passage time of the integrate and fire model

how to expand around mean field theory using high temperature expansions high temperature expansions performed at a fixed order parameter provide a simple and systematic way to derive and correct mean field theories for statistical mechanical models for models like spin glasses which have general couplings between spins the authors show that these expansions generate the thouless anderson palmer equations at low order they explicitly calculate the corrections to tap theory for these models for ferromagnetic models they show that their expansions can easily be converted into 1 d expansions around mean field theory where d is the number of spatial dimensions only a small finite number of graphs need to be calculated to generate each order in 1 d for thermodynamic quantities like free energy or magnetization unlike previous 1 d expansions the expansions are valid in the low temperature phases of the models considered they consider alternative ways to expand around mean field theory besides 1 d expansions in contrast to the 1 d expansion for the critical temperature which is presumably asymptotic these schemes can be used to devise convergent expansions for the critical temperature they also appear to give convergent series for thermodynamic quantities and critical exponents they test the schemes using the spherical model where their properties can be studied using exact expressions

population coding and decoding in a neural field a computational study this study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable a general prototype model for the encoding process is proposed in which neural responses are correlated with strength specified by a gaussian function of their difference in preferred stimuli based on the model we study the effect of correlation on the fisher information compare the performances of three decoding methods that differ in the amount of encoding information being used and investigate the implementation of the three methods by using a recurrent network this study not only rediscovers main results in existing literatures in a unified way but also reveals important new features especially when the neural correlation is strong as the neural correlation of firing becomes larger the fisher information decreases drastically we confirm that as the width of correlation increases the fisher information saturates and no longer increases in proportion to the number of neurons however we prove that as the width increases further wider than 2 times the effective width of the turning function the fisher information increases again and it increases without limit in proportion to the number of neurons furthermore we clarify the asymptotic efficiency of the maximum likelihood inference mli type of decoding methods for correlated neural signals it shows that when the correlation covers a nonlocal range of population excepting the uniform correlation and when the noise is extremely small the mli type of method whose decoding error satisfies the cauchy type distribution is not asymptotically efficient this implies that the variance is no longer adequate to measure decoding accuracy

dynamics of learning in multilayer perceptrons near singularities the dynamical behavior of learning is known to be very slow for the multilayer perceptron being often trapped in the plateau it has been recently understood that this is due to the singularity in the parameter space of perceptrons in which trajectories of learning are drawn the space is riemannian from the point of view of information geometry and contains singular regions where the riemannian metric or the fisher information matrix degenerates this paper analyzes the dynamics of learning in a neighborhood of the singular regions when the true teacher machine lies at the singularity we give explicit asymptotic analytical solutions trajectories both for the standard gradient sgd and natural gradient ngd methods it is clearly shown in the case of the sgd method that the plateau phenomenon appears in a neighborhood of the critical regions where the dynamical behavior is extremely slow the analysis of the ngd method is much more difficult because the inverse of the fisher information matrix diverges we conquer the difficulty by introducing the blow down technique used in algebraic geometry the ngd method works efficiently and the state converges directly to the true parameters very quickly while it staggers in the case of the sgd method the analytical results are compared with computer simulations showing good agreement the effects of singularities on learning are thus qualitatively clarified for both standard and ngd methods

semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems abstract in this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous all kinds of semicontinuity are considered lower semicontinuity upper semicontinuity hausdorff upper semicontinuity and closedness moreover we investigate both the weak and strong solutions of quasiequilibrium problems

physiological gain leads to high isi variability in a simple model of a cortical regular spiking cell to understand the interspike interval isi variability displayed by visual cortical neurons softky koch 1993 it is critical to examine the dynamics of their neuronal integration as well as

behaviors of spike output jitter in the integrate and fire model we consider behaviors of output jitter in the simplest spiking model the integrate and fire model the full spectrum of behaviors is found the output jitter is sensitive to the input distribution and can be a constant diverge to infinity or converge to zero exact formulas for the convergence or the divergence of output jitter are given our results suggest that the exponential distribution is the critical case a faster rate of decrease in the distribution tail as compared to the exponential distribution tail ensures the convergence of output jitter whereas slower decay in the distribution tail causes the divergence of output jitter

holder continuity of perturbed solution set for convex optimization problems abstract in this paper we first establish sufficient conditions for the local uniqueness and holder continuity of perturbed solution set for a scalar optimization problem then by using a linear scalarization method we obtain the holder continuity of two classes of perturbed solution sets for a multiobjective programming problem respectively we also give some examples to illustrate that our main results are applicable these examples are also given to illustrate that our main results are new and different from the ones in literature

maximum likelihood decoding of neuronal inputs from an interspike interval distribution an expression for the probability distribution of the interspike interval of a leaky integrate and fire lif model neuron is rigorously derived based on recent theoretical developments in the theory of stochastic processes this enables us to find for the first time a way of developing maximum likelihood estimates mle of the input information e g afferent rate and variance for an lif neuron from a set of recorded spike trains dynamic inputs to pools of lif neurons both with and without interactions are efficiently and reliably decoded by applying the mle even within time windows as short as 25 msec

dependence of neuronal correlations on filter characteristics and marginal spike train statistics correlated neural activity has been observed at various signal levels e g spike count membrane potential local field potential eeg fmri bold most of these signals can be considered as superpositions of spike trains filtered by components of the neural system synapses membranes and the measurement process it is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are in this study we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations we demonstrate that correlation functions and statistical second order measures like the variance the covariance and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains we point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations in many applications the coherence allows a filter independent quantification of correlated activity in different network models we discuss the estimation of network connectivity from the high frequency coherence of simultaneous intracellular recordings of pairs of neurons

behavior of integrate and fire and hodgkin huxley models with correlated inputs we assess both numerically and theoretically how positively correlated poisson inputs affect the output of the integrate and fire and hodgkin huxley models for the integrate and fire model the variability of efferent spike trains is an increasing function of input correlation and of the ratio between inhibitory and excitatory inputs interestingly for the hodgkin huxley model the variability of efferent spike trains is a decreasing function of input correlation and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs in terms of the signal to noise ratio of efferent spike trains the integrate and fire model works better in an environment of asynchronous inputs but the hodgkin huxley model has an advantage for more synchronous correlated inputs in conclusion the integrate and fire and hodgkin huxley models respond to correlated inputs in totally opposite ways

applying the multivariate time rescaling theorem to neural population models statistical models of neural activity are integral to modern neuroscience recently interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing however any statistical model must be validated by an appropriate goodness of fit test kolmogorov smirnov tests based on the time rescaling theorem have proven to be useful for evaluating point process based statistical models of single neuron spike trains here we discuss the extension of the time rescaling theorem to the multivariate neural population case we show that even in the presence of strong correlations between spike trains models that neglect couplings between neurons can be erroneously passed by the univariate time rescaling test we present the multivariate version of the time rescaling theorem and provide a practical step by step procedure for applying it to testing the sufficiency of neural population models using several simple analytically tractable models and more complex simulated and real data sets we demonstrate that important features of the population activity can be detected only using the multivariate extension of the test

synaptic depression leads to nonmonotonic frequency dependence in the coincidence detector in this letter we extend our previous analytical results mikula niebur 2003 for the coincidence detector by taking into account probabilistic frequency dependent synaptic depression we present a solution for the steady state output rate of an ideal coincidence detector receiving an arbitrary number of input spike trains with identical binomial count distributions which includes poisson statistics as a special case and identical arbitrary pairwise cross correlations from zero correlation independent processes to perfect correlation identical processes synapses vary their efficacy probabilistically according to the observed depression mechanisms our results show that synaptic depression if made sufficiently strong will result in an inverted u shaped curve for the output rate of a coincidence detector as a function of input rate this leads to the counterintuitive prediction that higher presynaptic input rates may lead to lower postsynaptic output rates where the output rate may fall faster than the inverse of the input rate

integrate and fire and hodgkin huxley models with current inputs for the integrate and fire model and the hodgkin huxley model we consider how current inputs including wave and square wave affect their outputs firstly the usual approximation is employed to approximate the models with current inputs which quantitatively reveals the difference between instantaneous and noninstantaneous current inputs when the rising time of wave inputs is long or the ratio between the inhibitory and excitatory inputs is close to one the usual approximation fails to approximate the wave inputs in the integrate and fire model for the hodgkin huxley model the usual approximation in general gives an unsatisfying approximation a novel approach based upon a superposition of coloured and white noise is then proposed to replace the usual approximation numerical results show that the novel approach substantially improves the approximation within widely physiologically reasonable regions of the rising time of wave inputs

large scale heterogeneous networks the davis wielandt shell and graph separation we consider a large scale network of interconnected heterogeneous dynamical components scalable stability conditions are derived that involve the input output properties of individual subsystems and the interconnection matrix the analysis is based on the davis wielandt shell a higher dimensional version of the numerical range with important convexity properties this can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix the results include small gain and passivity approaches as special cases with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

generation of spike trains with controlled auto and cross correlation functions emerging evidence indicates that information processing as well as learning and memory processes in both the network and single neuron levels are highly dependent on the correlation structure of multiple spike trains contemporary experimental as well as theoretical studies that involve quasi realistic neuronal stimulation thus require a method for controlling spike train correlations this letter introduces a general new strategy for generating multiple spike trains with exactly controlled mean firing rates and correlation structure defined in terms of auto and cross correlation functions our approach nonlinearly transforms random gaussian distributed processes with a predistorted correlation structure into nonnegative rate processes which are then used to generate doubly stochastic poisson point processes with the required correlation structure we show how this approach can be used to generate stationary or nonstationary spike trains from small or large groups of neurons with diverse auto and cross correlation structures we analyze and derive analytical formulas for the high order correlation structure of generated spike trains and discuss the limitations of this approach

on holder continuity of approximate solutions to parametric equilibrium problems abstract we establish verifiable sufficient conditions for holder continuity of approximate solutions to parametric equilibrium problems when solutions may be not unique many examples are provided to illustrate the need of considering approximate solutions instead of exact solutions and the essentialness of the imposed assumptions as applications we derive this holder continuity for constrained minimization variational inequalities and fixed point problems

the effects of input rate and synchrony on a coincidence detector analytical solution we derive analytically the solution for the output rate of the ideal coincidence detector the solution is for an arbitrary number of input spike trains with identical binomial count distributions which includes poisson statistics as a special case and identical arbitrary pairwise crosscorrelations from zero correlation independent processes to complete correlation identical processes

solving the inverse ising problem by mean field methods in a clustered phase space with many states in this work we explain how to properly use mean field methods to solve the inverse ising problem when the phase space is clustered that is many states are present the clustering of the phase space can occur for many reasons e g when a system undergoes a phase transition but also when data are collected in different regimes e g quiescent and spiking regimes in neural networks mean field methods for the inverse ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference e g in the low temperature phase of the curie weiss model in this work we explain how to modify mean field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures low temperature phases of curie weiss and hopfield models

singularities affect dynamics of learning in neuromanifolds the parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units a parameter space forms a geometrical manifold called the neuromanifold in the case of neural networks such a model is identified with a statistical model and a riemannian metric is given by the fisher information matrix however the matrix degenerates at singularities such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities arma time series model and many other cases the standard statistical paradigm of the cramer rao theorem does not hold and the singularity gives rise to strange behaviors in parameter estimation hypothesis testing bayesian inference model selection and in particular the dynamics of learning from examples prevailing theories so far have not paid much attention to the problem caused by singularity relying only on ordinary statistical theories developed for regular nonsingular models only recently have researchers remarked on the effects of singularity and theories are now being developed this article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures we demonstrate our recent results on these problems simple toy models are also used to show explicit solutions we explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically because the fisher information matrix degenerates that the model selection criteria such as aic bic and mdl fail to hold in these models that a smooth bayesian prior becomes singular in such models and that the trajectories of dynamics of learning are strongly affected by the singularity causing plateaus or slow manifolds in the parameter space the natural gradient method is shown to perform well because it takes the singular geometrical structure into account the generalization error and the training error are studied in some examples

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

decorrelation of spiking variability and improved information transfer through feedforward divisive normalization response variability is often positively correlated in pairs of similarly tuned neurons in the visual cortex many authors have considered correlated variability to prevent postsynaptic neurons from averaging across large groups of inputs to obtain reliable stimulus estimates however a simple average of variability ignores nonlinearities in cortical signal integration this study shows that feedforward divisive normalization of a neuron s inputs effectively decorrelates their variability furthermore we show that optimal linear estimates of a stimulus parameter that are based on normalized inputs are more accurate than those based on nonnormalized inputs due partly to reduced correlations and that these estimates improve with increasing population size up to several thousand neurons this suggests that neurons may possess a simple mechanism for substantially decorrelating noise in their inputs further work is needed to reconcile this conclusion with past evidence that correlated noise impairs visual perception

self organizing dual coding based on spike time dependent plasticity it has been a matter of debate how firing rates or spatiotemporal spike patterns carry information in the brain recent experimental and theoretical work in part showed that these codes especially a population rate code and a synchronous code can be dually used in a single architecture however we are not yet able to relate the role of firing rates and synchrony to the spatiotemporal structure of inputs and the architecture of neural networks in this article we examine how feedforward neural networks encode multiple input sources in the firing patterns we apply spiketime dependent plasticity as a fundamental mechanism to yield synaptic competition and the associated input filtering we use the fokker planck formalism to analyze the mechanism for synaptic competition in the case of multiple inputs which underlies the formation of functional clusters in downstream layers in a self organizing manner depending on the types of feedback coupling and shared connectivity clusters are independently engaged in population rate coding or synchronous coding or they interact to serve as input filters classes of dual codings and functional roles of spike time dependent plasticity are also discussed

stimulus dependent correlations and population codes the magnitude of correlations between stimulus driven responses of pairs of neurons can itself be stimulus dependent we examine how this dependence affects the information carried by neural populations about the stimuli that drive them stimulus dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances we use fisher information to quantify these effects and show that although stimulus dependent correlations often carry little information directly their modulatory effects on the overall information can be large in particular if the stimulus dependence is such that correlations increase with stimulus induced firing rates this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus however in the presence of additional strong spatial decay of correlations such stimulus dependence may have a negative impact opposite relationships hold when correlations decrease with firing rates

ising model for neural data model quality and approximate methods for extracting functional connectivity we study pairwise ising models for describing the statistics of multineuron spike trains using data from a simulated cortical network we explore efficient ways of finding the optimal couplings in

optimally decoding the input rate from an observation of the interspike intervals a neuron extensively receives both inhibitory and excitatory inputs what is the ratio r between these two types of input so that the neuron can most accurately read out input information rate we explore the issue in this paper provided that the neuron is an ideal observer decoding the input information with the attainment of the cramer rao inequality bound it is found that in general adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information by calculating the fisher information of an integrate and fire neuron we determine the optimal ratio r for decoding the input information from an observation of the efferent interspike intervals surprisingly the fisher information can be zero for certain values of the ratio seemingly implying that it is impossible to read out the encoded information at these values by analysing the maximum likelihood estimate of the input information it is concluded that the input information is in fact most easily estimated at the points where the fisher information vanishes

the effects of pair wise and higher order correlations on the firing rate of a postsynaptic neuron coincident firing of neurons projecting to a common target cell is likely to raise the probability of firing of this postsynaptic cell therefore synchronized firing constitutes a significant event for postsynaptic neurons and is likely to play a role in neuronal information processing physiological data on synchronized firing in cortical networks are based primarily on paired recordings and cross correlation analysis however pair wise correlations among all inputs onto a postsynaptic neuron do not uniquely determine the distribution of simultaneous postsynaptic events we develop a framework in order to calculate the amount of synchronous firing that based on maximum entropy should exist in a homogeneous neural network in which the neurons have known pair wise correlations and higher order structure is absent according to the distribution of maximal entropy synchronous events in which a large proportion of the neurons participates should exist even in the case of weak pair wise correlations network simulations also exhibit these highly synchronous events in the case of weak pair wise correlations if such a group of neurons provides input to a common postsynaptic target these network bursts may enhance the impact of this input especially in the case of a high postsynaptic threshold the proportion of neurons participating in synchronous bursts can be approximated by our method under restricted conditions when these conditions are not fulfilled the spike trains have less than maximal entropy which is indicative of the presence of higher order structure in this situation the degree of synchronicity cannot be derived from the pair wise correlations

perturbation analysis of error bounds for systems of conic linear inequalities in banach spaces for a general constrained or unconstrained system of conic inequalities we provide sufficient conditions to ensure the existence of a common error bound for each of the systems obtained from the original one when the given data undergoes a small perturbation moreover we also give some dual characterizations on the existence of error bounds for systems of conic inequalities

higher order statistics of input ensembles and the response of simple model neurons pairwise correlations among spike trains recorded in vivo have been frequently reported it has been argued that correlated activity could play an important role in the brain because it efficiently modulates the response of a postsynaptic neuron we show here that a neuron s output firing rate critically depends on the higher order statistics of the input ensemble we constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations but differed with regard to the higher order interactions within the population the first ensemble was characterized by clusters of spikes synchronized over the whole population in the second ensemble the size of spike clusters was on average proportional to the pairwise correlation for both input models we assessed the role of the size of the population the firing rate and the pairwise correlation on the output rate of two simple model neurons a continuous firing rate model and a conductance based leaky integrate and fire neuron an approximation to the mean output rate of the firing rate neuron could be derived analytically with the help of shot noise theory interestingly the essential features of the mean response of the two neuron models were similar for both neuron models the three input parameters played radically different roles with respect to the postsynaptic firing rate depending on the interaction structure of the input for instance in the case of an ensemble with small and distributed spike clusters the output firing rate was efficiently controlled by the size of the input population in addition to the interaction structure the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate

integrate and fire neurons driven by correlated stochastic input neurons are sensitive to correlations among synaptic inputs however analytical models that explicitly include correlations are hard to solve analytically so their influence on a neuron s response has been difficult to ascertain to gain some intuition on this problem we studied the firing times of two simple integrate and fire model neurons driven by a correlated binary variable that represents the total input current analytic expressions were obtained for the average firing rate and coefficient of variation a measure of spike train variability as functions of the mean variance and correlation time of the stochastic input the results of computer simulations were in excellent agreement with these expressions in these models an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains however the magnitude of the changes depends differentially on the relative values of the input mean and variance the increase in firing rate is higher when the variance is large relative to the mean whereas the increase in variability is higher when the variance is relatively small in addition the firing rate always tends to a finite limit value as the correlation time increases toward infinity whereas the coefficient of variation typically diverges these results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains

exact solutions for rate and synchrony in recurrent networks of coincidence detectors we provide analytical solutions for mean firing rates and cross correlations of coincidence detector neurons in recurrent networks with excitatory or inhibitory connectivity with rate modulated steady state spiking inputs we use discrete time finite state markov chains to represent network state transition probabilities which are subsequently used to derive exact analytical solutions for mean firing rates and cross correlations as illustrated in several examples the method can be used for modeling cortical microcircuits and clarifying single neuron and population coding mechanisms we also demonstrate that increasing firing rates do not necessarily translate into increasing cross correlations though our results do support the contention that firing rates and cross correlations are likely to be coupled our analytical solutions underscore the complexity of the relationship between firing rates and cross correlations

quantifying higher order correlations in a neuronal pool abstract recent experiments involving a relatively large population of neurons have shown a very significant amount of higher order correlations however little is known of how these affect the integration and firing behavior of a population of neurons beyond the second order statistics to investigate how higher order inputs statistics can shape beyond pairwise spike correlations and affect information coding in the brain we consider a neuronal pool where each neuron fires stochastically we develop a simple mathematically tractable model that makes it feasible to account for higher order spike correlations in a neuronal pool with highly interconnected common inputs beyond second order statistics in our model correlations between neurons appear from q gaussian inputs into threshold neurons the approach constitutes the natural extension of the dichotomized gaussian model where the inputs to the model are just gaussian distributed and therefore have no input interactions beyond second order we obtain an exact analytical expression for the joint distribution of firing quantifying the degree of higher order spike correlations truly emphasizing the functional aspects of higher order statistics as we account for beyond second order inputs correlations seen by each neuron within the pool we determine how higher order correlations depend on the interaction structure of the input showing that the joint distribution of firing is skewed as the parameter q increases inducing larger excursions of synchronized spikes we show how input nonlinearities can shape higher order correlations and enhance coding performance by neural populations

nonlinear population codes theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information however recent theoretical studies have investigated the effect of crosscorrelations in the trial to trial fluctuations of the neuronal responses on the accuracy of the representation assuming that only the first order statistics of the neuronal responses are tuned to the stimulus these studies have shown that in the presence of correlations similar to those observed experimentally in cortical ensembles of neurons the amount of information in the population is limited yielding nonzero error levels even in the limit of infinitely large populations of neurons in this letter we study correlated neuronal populations whose higher order statistics and in particular response variances are also modulated by the stimulus we ask two questions does the correlated noise limit the accuracy of the neuronal representation of the stimulus and how can a biological mechanism extract most of the information embedded in the higher order statistics of the neuronal responses specifically we address these questions in the context of a population of neurons coding an angular variable we show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise this information cannot be extracted by linear readout schemes including the linear population vector instead we propose a bilinear readout scheme that involves spatial decorrelation quadratic non linearity and population vector summation we show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters with an efficiency that grows linearly with the population size this code can be implemented using biologically plausible neurons

information geometric measure for neural spikes this study introduces information geometric measures to analyze neural firing patterns by taking not only the second order but also higher order interactions among neurons into account information geometry provides useful tools and concepts for this purpose including the orthogonality of coordinate parameters and the pythagoras relation in the kullback leibler divergence based on this orthogonality we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders as a result purely pairwise triple wise and higher order interactions are singled out we also demonstrate the benefits of our proposal by using several examples

the holder continuity of solutions to generalized vector equilibrium problems in this paper by using a weaker assumption we discuss the holder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set valued one but not a single valued one these results extend the recent ones in the literature several examples are given for the illustration of our results

synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled langevin model the synchrony and variability of the coupled langevin model subjected to spatially correlated additive and multiplicative noise are discussed we have employed numerical simulations and the analytical augmented moment method which is the second order moment method for local and global variables h hasegawa phys rev e 67 041903 2003 it has been shown that the synchrony of an ensemble is increased decreased by a positive negative spatial correlation in both additive and multiplicative noise although the variability for local fluctuations is almost insensitive to spatial correlations that for global fluctuations is increased decreased by positive negative correlations when a pulse input is applied the synchrony is increased for the correlated multiplicative noise whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise an application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals which accounts for some neuronal experiments

common input explains higher order correlations and entropy in a simple model of neural population activity simultaneously recorded neurons exhibit correlations whose underlying causes are not known here we use a population of threshold neurons receiving correlated inputs to model neural population recordings we show analytically that small changes in second order correlations can lead to large changes in higher order redundancies and that the resulting interactions have a strong impact on the entropy sparsity and statistical heat capacity of the population our findings for this simple model may explain some surprising effects recently observed in neural population recordings

holder continuity and upper estimates of solutions to vector quasiequilibrium problems abstract in this paper we establish the holder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set valued our main assumptions are weaker than those in the literature and the results extend and improve the recent ones furthermore as an application of holder continuity we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters

cumulants of hawkes point processes we derive explicit closed form expressions for the cumulant densities of a multivariate self exciting hawkes point process generalizing a result of hawkes in his earlier work on the covariance density and bartlett spectrum of such processes to do this we represent the hawkes process in terms of a poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible family trees representing complex interactions between point events we also consider the problem of computing the integrated cumulants characterizing the average measure of correlated activity between events of different types and derive the relevant equations

generation of correlated spike trains neuronal spike trains display correlations at diverse timescales throughout the nervous system the functional significance of these correlations is largely unknown and computational investigations can help us understand their role in order to generate correlated spike trains with given statistics several case specific methods have been described in the litterature this letter presents two general methods to generate sets of spike trains with given firing rates and pairwise correlation functions along with efficient simulation algorithms

generation of synthetic spike trains with defined pairwise correlations recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross correlation this report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation pairs of spike trains with any pairwise correlation can be generated and higher order correlations are compatible with common synaptic input relations between allowable mean rates and correlations within a population are discussed the algorithm is highly efficient its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross correlated pairs

conditional mixture model for correlated neuronal spikes analysis of correlated spike trains is a hot topic of research in computational neuroscience a general model of probability distributions for spikes includes too many parameters to be of use in analyzing real data instead we need a simple but powerful generative model for correlated spikes we developed a class of conditional mixture models that includes a number of existing models and analyzed its capabilities and limitations we apply the model to dynamical aspects of neuron pools when hebbian cell assemblies coexist in a pool of neurons the condition is specified by these assemblies such that the probability distribution of spikes is a mixture of those of the component assemblies the probabilities of activation of the hebbian assemblies change dynamically we used this model as a basis for a competitive model governing the states of assemblies

can spike coordination be differentiated from rate covariation there has been a long and lively debate on whether rate covariance and temporal coordination of spikes regarded as potential origins for correlations in cortical spike signals fulfill different roles in the cortical code in this context studies that report spike coordination have often been criticized for ignoring fast nonstationarities which would result in wrongly assigned spike coordination the underlying hypothesis of this critique is that spike coordination is essentially identical to rate covariation only on a shorter timescale this study investigates the validity of this critique we provide a decomposition for the cross correlation function of doubly stochastic point processes where each of the components corresponds precisely to the concepts of dependence under investigation this allows us to correct the correlation function for rate effects which implies that spike coordination and rate covariation are statistically separable concepts of dependence furthermore we present direct and intuitive model implementations of the discussed concepts and illustrate that their difference is not a matter of timescale analysis of data generated by our models and analytical description of the relevant estimators reveals however that spike coordination dramatically influences the accuracy of rate covariance estimation as a consequence extreme parameter combinations can lead to situations where the concept of dependence cannot be identified empirically however for a wide range of parameters the concept of dependence underlying a given data set can be identified regardless of its timescale

convergence condition of the tap equation for the infinite ranged ising spin glass model it is shown that the power expansion of the gibbs potential of the sk model up to second order in the exchange couplings leads to the tap equation this result remains valid for the general including a ferromagnetic exchange sk model theorems of power expansions and resolvent techniques are employed to solve the convergence problem the convergence condition is presented for the whole temperature range and for general distributions of the local magnetisations

theory of input spike auto and cross correlations and their effect on the response of spiking neurons spike correlations between neurons are ubiquitous in the cortex but their role is not understood here we describe the firing response of a leaky integrate and fire neuron lif when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations input correlations are characterized in terms of the firing rates fano factors correlation coefficients and correlation timescale of the neurons driving the target neuron we show that the sum of the presynaptic spike trains cannot be well described by a poisson process in fact the total input current has a nontrivial two point correlation function described by two main parameters the correlation timescale how precise the input correlations are in time and the correlation magnitude how strong they are therefore the total current generated by the input spike trains is not well described by a white noise gaussian process instead we model the total current as a colored gaussian process with the same mean and two point correlation function leading to the formulation of the problem in terms of a fokker planck equation solutions of the output firing rate are found in the limit of short and long correlation timescales the solutions described here expand and improve on our previous results moreno de la rocha renart parga 2002 by presenting new analytical expressions for the output firing rate for general if neurons extending the validity of the results for arbitrarily large correlation magnitude and by describing the differential effect of correlations on the mean driven or noise dominated firing regimes also the details of this novel formalism are given here for the first time we employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations we expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission

a canonical neural circuit for cortical nonlinear operations a few distinct cortical operations have been postulated over the past few years suggested by experimental data on nonlinear neural response across different areas in the cortex among these the energy model proposes the summation of quadrature pairs following a squaring nonlinearity in order to explain phase invariance of complex v1 cells the divisive normalization model assumes a gain controlling divisive inhibition to explain sigmoid like response profiles within a pool of neurons a gaussian like operation hypothesizes a bell shaped response tuned to a specific optimal pattern of activation of the presynaptic inputs a max like operation assumes the selection and transmission of the most active response among a set of neural inputs we propose that these distinct neural operations can be computed by the same canonical circuitry involving divisive normalization and polynomial nonlinearities for different parameter values within the circuit hence this canonical circuit may provide a unifying framework for several circuit models such as the divisive normalization and the energy models as a case in point we consider a feedforward hierarchical model of the ventral pathway of the primate visual cortex which is built on a combination of the gaussian like and max like operations we show that when the two operations are approximated by the circuit proposed here the model is capable of generating selective and invariant neural responses and performing object recognition in good agreement with neurophysiological data

measure of correlation orthogonal to change in firing rate there are a number of measures of correlation for spikes of two neurons and for spikes at two successive time bins in one neuron covariance correlation coefficient mutual information and information geometric measure in the log linear model it is desirable to have a measure that is not affected by change in the firing rates of neurons we explain the superiority of the information geometric measure from the point of view of geometry by which the correlation and firing rates are separated orthogonally that is without correlation we then analyze characteristics of other measures and show analytically how they are related to firing rates

stability of weak vector variational inequality abstract in this paper a key assumption is introduced by virtue of a parametric gap function then by using the key assumption sufficient conditions of the continuity and hausdorff continuity of a solution set map for a parametric weak vector variational inequality are obtained in banach spaces with the objective space being finite dimensional