information theoretical analysis of the statistical dependencies among three variables applications to written language we develop the information theoretical concepts required to study the statistical dependencies among three variables some of such dependencies are pure triple interactions in the sense that they cannot be explained in terms of a combination of pairwise correlations we derive bounds for triple dependencies and characterize the shape of the joint probability distribution of three binary variables with high triple interaction the analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables and to assess whether the information between two variables is or is not mediated by a third variable these concepts are applied to the analysis of written texts we find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words but also on the presence or absence of nearby pairs of words we identify the words enclosing the key semantic concepts of the text the triplets of words with high pairwise and triple interactions and the words that mediate the pairwise interactions between other words

a boundary value problem for second order fuzzy differential equations abstract in this paper we interpret a two point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept we present a new concept of solutions and utilizing the generalized differentiability we investigate the problem of finding new solutions some examples are provided for which the new solutions are found

a generalization of sylow s third theorem keywords number of chains p perfect normal closure p group quotient weak cone points third sylow theorem reference ctg article 1988 001doi 10 1016 0021 8693 88 90268 2 record created on 2008 12 16 modified on 2017 05 12

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

mean field approximations for coupled populations of generalized linear model spiking neurons with markov refractoriness there has recently been a great deal of interest in inferring network connectivity from the spike trains in populations of neurons one class of useful models that can be fit easily to spiking data is based on generalized linear point process models from statistics once the parameters for these models are fit the analyst is left with a nonlinear spiking network model with delays which in general may be very difficult to understand analytically here we develop mean field methods for approximating the stimulus driven firing rates in both the time varying and steady state cases auto and cross correlations and stimulus dependent filtering properties of these networks these approximations are valid when the contributions of individual network coupling terms are small and hence the total input to a neuron is approximately gaussian these approximations lead to deterministic ordinary differential equations that are much easier to solve and analyze than direct monte carlo simulation of the network activity these approximations also provide an analytical way to evaluate the linear input output filter of neurons and how the filters are modulated by network interactions and some stimulus feature finally in the case of strong refractory effects the mean field approximations in the generalized linear model become inaccurate therefore we introduce a model that captures strong refractoriness retains all of the easy fitting properties of the standard generalized linear model and leads to much more accurate approximations of mean firing rates and cross correlations that retain fine temporal behaviors

on the non contractibility of the order complex of the coset poset of a classical group let g be a classical group and suppose that g does not contains non trivial graph automorphisms in this paper we prove that the order complex of the coset poset of g is non contractible in order to prove it we show that pg 1 does not vanish where pg s is the dirichlet polynomial associated to the group g

on the existence of solutions to periodic boundary value problems for fuzzy linear differential equations in this work we provide sufficient conditions which guarantee the existence of solutions to periodic boundary value problems for first order linear fuzzy differential equations by using generalized differentiability and switching points in comparison with some previous works we consider equations whose coefficient may change its sign a finite number of times in the interval of interest we also study the existence of solutions which are crisp or real at the switching points where the diameter of the level sets changes from nonincreasing to nondecreasing character

two point boundary value problems of undamped uncertain dynamical systems in this paper we study two point boundary value problems of a class of uncertain dynamical systems i e undamped uncertain dynamical systems we introduce the concept of large solutions and small solutions for two point boundary value problems of undamped uncertain dynamical systems and under some conditions establish the existence and uniqueness of large solutions and small solutions and settle the relationship between large solutions and small solutions

characterization of compact subsets of fuzzy sets a characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space rn the metric for which is the supremum over the hausdorff distances between corresponding level sets it is shown that a closed subset is compact if and only if it is uniformly support bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable

existence of global solutions to nonlinear fuzzy volterra integro differential equations abstract in this paper we introduce new solutions for fuzzy differential equations as mixed solutions and prove the existence and uniqueness of global solutions for fuzzy initial value problems involving integro differential operators of volterra type one example is also given by applying mixed solution concept to fuzzy linear differential equations for obtaining their global solutions

error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations using a fixed point technique the sequence of successive approximations and a recent quadrature formula for fuzzy number valued functions it is constructed a numerical method for the solution of nonlinear fuzzy fredholm integral equations moreover the error estimate of the method and a criterion to stop the corresponding algorithm are given

cortical activity flips among quasi stationary states parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden markov process the parallel spike trains were considered as a multivariate poisson process whose vector firing rates change with time as a consequence of this approach the complete recording can be segmented into a sequence of a few statistically discriminated hidden states whose dynamics are modeled as a first order markov chain the biological validity and benefits of this approach were examined in several independent ways i the statistical consistency of the segmentation and its correspondence to the behavior of the animals ii direct measurement of the collective flips of activity obtained by the model and iii the relation between the segmentation and the pair wise short term cross correlations between the recorded spike trains comparison with surrogate data was also carried out for each of the above examinations to assure their significance our results indicated the existence of well separated states of activity within which the firing rates were approximately stationary with our present data we could reliably discriminate six to eight such states the transitions between states were fast and were associated with concomitant changes of firing rates of several neurons different behavioral modes and stimuli were consistently reflected by different states of neural activity moreover the pair wise correlations between neurons varied considerably between the different states supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons

an equivalence lemma for a class of fuzzy implicit integro differential equations abstract in the current paper an equivalence lemma is proposed which converts a second order implicit form of nonlinear fuzzy volterra integro differential equation to four different kinds of nonlinear integral equations based on kind of gh differentiability of the first and second derivatives finally some examples are given to illustrate the theoretical results

improved predictor corrector method for solving fuzzy initial value problems in this paper an improved predictor corrector ipc method is proposed to solve the fuzzy initial value problem the ipc method is generated by combining an explicit three step method and an implicit two step method the methods are compared with the methods discussed in t allahviranloo n ahmady e ahmady numerical solution of fuzzy differential equations by predictor corrector method information sciences 177 7 2007 1633 1647 and are shown to be more accurate the convergence and stability of the proposed methods are also presented in detail these methods are illustrated by solving some examples

a flexible method to measure synchrony in neuronal firing neurons can transmit information about the characteristics of a stimulus through the spike rate of neurons and synchronization of the neurons various association measure can be used to describe how synchronous two spike trains are we propose a new measure of synchrony the conditional synchrony measure which is the probability of firing together given that at least one of the two neurons is active focus is on the specification of a flexible marginal model for multivariate correlated binary data together with a pseudolikelihood estimation approach to adequately and directly describe the measures of interest a joint model must allow different time and covariate dependent firing rates for each neuron and also must account for the association between them the association between neurons might depend on covariates as well

numerical solution of fuzzy differential equations by predictor corrector method in this paper three numerical methods to solve the fuzzy ordinary differential equations are discussed these methods are adams bashforth adams moulton and predictor corrector predictor corrector is obtained by combining adams bashforth and adams moulton methods convergence and stability of the proposed methods are also proved in detail in addition these methods are illustrated by solving two fuzzy cauchy problems

some topological properties of solutions to fuzzy differential systems in this paper the initial value problems of fuzzy differential systems are investigated by using a kind of new methods at first the concept of relatively open sets is introduced then some basic topological properties of solutions for the initial value problems of fuzzy differential systems are obtained

the cauchy problem for continuous fuzzy differential equations abstract we prove a version of the classical peano s theorem for the initial value problem for a fuzzy differential equation in the metric space of normal fuzzy convex sets with distance given by the maximum of the hausdorff distances between level sets

monotone method for fuzzy differential equations we develop the monotone iterative technique to approximate the extremal solutions for the initial value problem relative to a fuzzy differential equation in a fuzzy functional interval to our procedure it is crucial to have at our disposal fuzzy comparison results and several properties of sets of fuzzy functions and fuzzy numbers including a compactness result in spaces of fuzzy functions which are useful from the point of view of applications

initial and boundary value problems for fuzzy differential equations we prove a wintner type result for fuzzy ivps and a superlinear type result for fuzzy bvps both results rely on a generalized schauder theorem in metric spaces

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

a class of linear differential dynamical systems with fuzzy initial condition this paper investigates linear first order fuzzy differential dynamical systems where the initial condition is described by a fuzzy number we use a complex number representation of the a level sets of the fuzzy system and prove theorems that provide the solutions under such representation which is applicable to practical computations and also has some implications for theory then the paper shows some properties of the two dimensional dynamical systems and their phase portraits are described by means of examples there may be a significant difference between the solutions according to whether the matrix is nonnegative or not finally the paper points out future research on the fuzzy dynamical systems

bayesian estimation of stimulus responses in poisson spike trains a bayesian method is developed for estimating neural responses to stimuli using likelihood functions incorporating the assumption that spike trains follow either pure poisson statistics or poisson statistics with a refractory period the bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases however the bayesian estimate of the variance of the variance is much lower this allows the bayesian method to provide more precise interval estimates of responses sensitivity of the bayesian method to the poisson assumption was tested by conducting simulations perturbing the poisson spike trains with noise this did not affect bayesian estimates of mean and variance to a significant degree indicating that the bayesian method is robust the bayesian estimates were less affected by the presence of noise than estimates provided by the standard method

on fuzzy boundary value problems the statement that a two point boundary value problem of fuzzy differential equation is equivalent to a fuzzy integral equation was pointed out by lakshmikantham et al and o regan et al recently bede gave a counterexample to show that this statement does not hold and he also argued that in many cases two point boundary value problems have no solutions under a new structure and certain conditions we show that a two point boundary value problem is equivalent to a fuzzy integral equation we also prove the existence of solutions to the two point boundary value problem in some sense this is an amendment to results of lakshmikantham et al and o regan et al and it is an answer to one of bede s problems

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

polynomial ideals and classes of finite groups the object of this note is to discuss the properties of some polynomials on a countable set of indeterminates attached to any finite group which generalize the eulerian functions of a group defined by p hall 1936 quart j math 7 134 151 in particular i will define some classes of finite groups associated to prime ideals of the polynomial ring and i will show that each finite group has a unique largest quotient in such a class of groups this work is a generalization of the notion of the b group introduced in an earlier paper bouc 1996 j algebra183 664 736 through a systematic use of the polynomial formalism of section 7 2 5 there for the reader s convenience however this paper is self contained and the proofs of the results already stated are included

two point boundary value problems of uncertain dynamical systems abstract recent research shows that in many cases there are no solutions periodic solutions etc to fuzzy two point boundary value problems in the sense of h derivatives to overcome the disadvantage of h derivatives in studying fuzzy two point boundary value problems in this paper we study fuzzy two point boundary value problems in the sense of differential inclusions i e two point boundary value problems of uncertain dynamical systems we obtain the existence and uniqueness of solutions and the existence of periodic solutions to two point boundary value problems of uncertain dynamical systems after introducing the concept of big solutions to two point boundary value problems of undamped uncertain dynamical systems we establish the existence and uniqueness of big solutions discuss the relationship between solutions and big solutions and further get a conclusion concerning the solutions of two point boundary value problems of uncertain dynamical systems

numerical methods forfuzzy differential inclusions in this paper a numerical method for solving fuzzy differential inclusions is considered fuzzy reachable set can be approximated by proposed method with complete error analysis which is discussed in detail the method is illustrated by solving some linear and nonlinear fuzzy initial value problems

on interactive fuzzy boundary value problems abstract in this paper we use the concept of interactivity between fuzzy numbers for the solution to a linear fuzzy boundary value problem fbvp we show that a solution of a fbvp with non interactive fuzzy numbers as boundary values can be obtained by the zadeh s extension principle in addition we show it is possible to obtain a fuzzy solution by means of the extension principle based on joint possibility distributions for the case where the boundary values are given by interactive fuzzy numbers examples of fbvps with both cases interactive and non interactive are presented also from arithmetic operations for linearly correlated fuzzy numbers we compare our solutions to the one proposed by gasilov et al we conclude that the fuzzy solution in the interactive case when the boundary values are linearly correlated fuzzy numbers is contained in the fuzzy solution for the non interactive case finally we present the fuzzy solution for a nonlinear fbvp with gaussian fuzzy numbers as boundary values

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

neutral stability rate propagation and critical branching in feedforward networks recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks critical branching neutral stability and production of a wide range of firing patterns we seek the simplest setting in which these properties emerge clarifying their origin and relationship in random feedforward networks of mccullochs pitts neurons two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity when neurons have low thresholds we show that there is always a connectivity for which the properties in question all occur that is these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer this fails to occur however when neurons have high thresholds a key tool in explaining this difference is the eigenstructure of the resulting mean field markov chain as this reveals which activity modes will be preserved from layer to layer we extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise and find that both of these features extend the parameter ranges over which networks produce the properties of interest

periodic problems of first order uncertain dynamical systems it is well known that there are no periodic solutions to fuzzy differential equations in the sense of hukuhara derivatives i e h derivatives so fuzzy differential equations in the sense of h derivatives cannot be used to describe periodic phenomena in the real world to overcome this disadvantage this paper studies periodic problems of first order fuzzy differential equations in the sense of differential inclusions i e periodic problems of first order uncertain dynamical systems and obtains the existence of periodic solutions for first order uncertain dynamical systems

the coset poset and probabilistic zeta function of a finite group abstract we investigate the topological properties of the poset of proper cosets xh in a finite group g of particular interest is the reduced euler characteristic which is closely related to the value at 1 of the probabilistic zeta function of g our main result gives divisibility properties of this reduced euler characteristic

hybrid metric dynamical systems with impulses abstract combining the concepts of hybrid dynamical system and metric dynamical system we introduce the concept of hybrid metric dynamical system hmds having as base space a metric space we give a comparison result for hmds we also establish the concept of hmds with impulses present a comparison result and study the stability of a solution

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

comparison results for fuzzy differential equations in this paper we present several comparison results for the solutions of fuzzy differential equations by using the hukuhara derivative these results constitute the extension to the fuzzy context of some comparison results for the solutions of linear differential equations besides some side results about the hukuhara difference and the partial orderings are given we illustrate the applicability of the new results by showing several examples

oscillation property for fuzzy delay differential equations in this paper we obtain an oscillation criterion of solutions and the existence of nonoscillatory solutions to a class of fuzzy delay differential equation fdde of second order some examples are given to illustrate the main theorems

exploiting history dependent effects to infer network connectivity we present an approach to distinguish between causal connections and common input connections among nodes in a network by modeling how the activity of a node depends on its own recent history we demonstrate how this history dependence predicts different patterns of activity depending on the nature of the network connectivity in particular a causal connection between a pair of observed nodes can be distinguished from common input connections that originate from nodes whose activity remains unobserved this work builds on previous results where this same distinction was made based on modeling how the activity of a node depends on measured external variables such as stimuli the results have a potentially broad range of application as the analysis can be based on a fairly generic class of models

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

network information and connected correlations entropy and information provide natural measures of correlation among elements in a network we construct here the information theoretic analog of connected correlation functions irreducible n point correlation is measured by a decrease in entropy for the joint distribution of n variables relative to the maximum entropy allowed by all the observed n 1 variable distributions we calculate the connected information terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source

a class of linear differential dynamical systems with fuzzy matrices abstract this paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices we use a complex number representation of the level sets of the fuzzy system and obtain the solution by employing such representation it is applicable to practical computations and has also some implications for the theory of fuzzy differential equations we then present some properties of the 2 dimensional dynamical systems and their phase portraits some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear we finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems

order complexes of coset posets of finite groups are not contractible abstract we show that the order complex of the poset of all cosets of all proper subgroups of a finite group g is never f 2 acyclic and therefore never contractible this settles a question of k s brown

subgroup graph methods for presentations of finitely generated groups and the connectivity of associated simplicial complexes abstract in this article we generalize the theory of subgroup graphs of subgroups of free groups developed by i kapovich and a myasnikov based on a work by j stallings to finite index subgroups of finitely generated groups given a presentation of a finitely generated group g x r and a finite connected x regular graph which fulfills the relators r we associate to a finite index subgroup h of g conversely the schreier coset graph of h with respect to x and g is such a graph firstly we study and prove various properties of h in relation to the graph secondly we prove that for many finitely generated infinite groups the order and nerve complexes that we associate to g are contractible in particular this is the case for free and free abelian groups fuchsian groups of genus g 2 infinite right angled coxeter groups artin and pure braid groups infinite virtually cyclic groups baumslag solitar groups as well as the free product of at least two of these and all finite index subgroups of these groups

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

a note on two point boundary value problems associated with non linear fuzzy differential equations in recent papers lakshmikantham et al and o regan et al assert that two point boundary value problem for a fuzzy differential equation is equivalent to an integral equation and the proofs of the main results in the above cited papers use this equivalence we prove by a counterexample that by using h differentiability or hukuhara differentiability this assertion does not hold moreover it is proved that a large class of two point boundary value problems have no solutions at all under h differentiability or hukuhara differentiability

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

solution method for a boundary value problem with fuzzy forcing function in this paper we present a new approach to a non homogeneous fuzzy boundary value problem we consider a linear differential equation with real coefficients but with a fuzzy forcing function and fuzzy boundary values we assume that the forcing function is a triangular fuzzy function unlike previous studies we look for a solution that is a fuzzy set of real functions not a fuzzy valued function each of these real functions satisfies the boundary value problem with some membership degree we have developed a method that finds this solution and demonstrated its effectiveness using a test example to show that the approach can be extended to other types of fuzzy numbers we extended it to the trapezoidal case for a particular example we used the product t norm to demonstrate how a new solution type can be obtained

crowns and factorization of the probabilistic zeta function of a finite group abstract we employ the concept of crown to study the generalized euler factors of the probabilistic zeta function of finite groups

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

the probabilistic zeta function of finite simple groups abstract let g be a finite group there exists a uniquely determined dirichlet polynomial p g s such that if t n then p g t gives the probability of generating g with t randomly chosen elements we show that it may be recognized from the knowledge of p g s whether g frat g is a simple group

ensemble inhibition and excitation in the human cortex an ising model analysis with uncertainties the pairwise maximum entropy model also known as the ising model has been widely used to analyze the collective activity of neurons however controversy persists in the literature about seemingly inconsistent findings whose significance is unclear due to lack of reliable error estimates we therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive markov chain monte carlo after the convergence of the main optimization algorithm we apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake sleep cycle our analysis shows that the ising model captures neuronal collective behavior much better than the independent model during wakefulness light sleep and deep sleep when both excitatory e and inhibitory i neurons are modeled ignoring the inhibitory effects of i neurons dramatically overestimates synchrony among e neurons furthermore information theoretic measures reveal that the ising model explains about 80 95 of the correlations depending on sleep state and neuron type thermodynamic measures show signatures of criticality although we take this with a grain of salt as it may be merely a reflection of long range neural correlations

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

unitary events in multiple single neuron spiking activity i detection and significance it has been proposed that cortical neurons organize dynamically into functional groups cell assemblies by the temporal structure of their joint spiking activity here we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons the statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint surprise the method is tested and calibrated on the basis of simulated stationary spike trains of independently firing neurons into which coincident joint spike events were inserted under controlled conditions the sensitivity and specificity of the method are investigated for their dependence on physiological parameters firing rate coincidence precision coincidence pattern complexity and temporal resolution of the analysis in the companion article in this issue we describe an extension of the method designed to deal with nonstationary firing rates

effect of interacting second and third order stimulus dependent correlations on population coding asymmetries spike correlations among neurons are widely encountered in the brain although models accounting for pairwise interactions have proved able to capture some of the most important features of population activity at the level of the retina the evidence shows that pairwise neuronal correlation analysis does not resolve cooperative population dynamics by itself by means of a series expansion for short time scales of the mutual information conveyed by a population of neurons the information transmission can be broken down into firing rate and correlational components in a proposed extension of this framework we investigate the information components considering both second and higher order correlations we show that the existence of a mixed stimulus dependent correlation term defines a new scenario for the interplay between pairwise and higher than pairwise interactions in noise and signal correlations that would lead either to redundancy or synergy in the information theoretic sense

finite state automata resulting from temporal information maximization and a temporal learning rule we extend linkser s infomax principle for feedforward neural networks to a measure for stochastic interdependence that captures spatial and temporal signal properties in recurrent systems this measure stochastic interaction quantifies the kullback leibler divergence of a markov chain from a product of split chains for the single unit processes for unconstrained markov chains the maximization of stochastic interaction also called temporal infomax has been previously shown to result in almost deterministic dynamics this letter considers temporal infomax on constrained markov chains where some of the units are clamped to prescribed stochastic processes providing input to the system temporal infomax in that case leads to finite state automata either completely deterministic or weakly nondeterministic transitions between internal states of these systems are almost perfectly predictable given the complete current state and the input but the activity of each single unit alone is virtually random the results are demonstrated by means of computer simulations and confirmed analytically it is furthermore shown numerically that temporal infomax leads to a high information flow from the input to internal units and that a simple temporal learning rule can approximately achieve the optimization of temporal interaction we relate these results to experimental data concerning the correlation dynamics and functional connectivities observed in multiple electrode recordings

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

maximal subgroups of direct products we determine all maximal subgroups of the direct product g n of n copies of a group g if g is finite we show that the number of maximal subgroups of g n is a quadratic function of n if g is perfect but grows exponentially otherwise we deduce a theorem of wiegold about the growth behaviour of the number of generators of g n

on the shellability of the order complex of the subgroup lattice of a finite group we show that the order complex of the subgroup lattice of a finite group g is nonpure shellable if and only if g is solvable a by product of the proof that nonsolvable groups do not have shellable subgroup lattices is the determination of the homotopy types of the order complexes of the subgroup lattices of many minimal simple groups

a peano theorem for fuzzy differential equations with evolving membership grade abstract the peano theorem on the existence without possible uniqueness of solutions has been a perplexing problem in the theory of fuzzy differential equations the difficulty appears to be due to the standard use of the supremum metric defined by the supremum over the hausdorff metric between the level sets of the fuzzy sets another may have been the classical formulation of fuzzy differential equations in terms of the hukuhara derivative of the level sets here a peano theorem is established for fuzzy differential equations formulated in a recent paper by the authors by combining hullermeier s suggestion of defining fuzzy differential equations at each level set via differential inclusions with aubin s morphological equations which allow non local set evolution a major difference from previous publications is the use of the endograph metric end essentially the hausdorff metric between the endographs in r n 0 1 of fuzzy sets instead of the supremum metric another is that the membership grades of the fuzzy sets are also allowed to evolve under the fuzzy differential equations the result applies for a very general class of fuzzy sets without additional assumptions of fuzzy convexity compact supports or even normality

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

ulam type stability of first order linear impulsive fuzzy differential equations abstract in this paper we consider ulam stability concepts for first order linear impulsive fuzzy differential equations which generalize standard definitions for impulsive differential equations sufficient conditions are established to guarantee that our equations are ulam stable numerically examples are also provided to illustrate our results

solution of linear differential equations with fuzzy boundary values we investigate linear differential equations with boundary values expressed by fuzzy numbers in contrast to most approaches which search for a fuzzy valued function as the solution we search for a fuzzy set of real functions as the solution we define a real function as an element of the solution set if it satisfies the differential equation and its boundary values are in intervals determined by the corresponding fuzzy numbers the membership degree of the real function is defined as the lowest value among membership degrees of its boundary values in the corresponding fuzzy sets to find the fuzzy solution we use a method based on the properties of linear transformations we show that the fuzzy problem has a unique solution if the corresponding crisp problem has a unique solution we prove that if the boundary values are triangular fuzzy numbers then the value of the solution at a given time is also a triangular fuzzy number the defined solution is the same as one of the solutions obtained by zadeh s extension principle for a second order differential equation with constant coefficients the solution is expressed in analytical form examples are given to describe the proposed approach and to compare it to a method that uses the generalized hukuhara derivative which demonstrates the advantages of our method

encoding through patterns regression tree based neuronal population models although the existence of correlated spiking between neurons in a population is well known the role such correlations play in encoding stimuli is not we address this question by constructing pattern based encoding models that describe how time varying stimulus drive modulates the expression probabilities of population wide spike patterns the challenge is that large populations may express an astronomical number of unique patterns and so fitting a unique encoding model for each individual pattern is not feasible we avoid this combinatorial problem using a dimensionality reduction approach based on regression trees using the insight that some patterns may from the perspective of encoding be statistically indistinguishable the tree divisively clusters the observed patterns into groups whose member patterns possess similar encoding properties these groups corresponding to the leaves of the tree are much smaller in number than the original patterns and the tree itself constitutes a tractable encoding model for each pattern our formalism can detect an extremely weak stimulus driven pattern structure and is based on maximizing the data likelihood not making a priori assumptions as to how patterns should be grouped most important by comparing pattern encodings with independent neuron encodings one can determine if neurons in the population are driven independently or collectively we demonstrate this method using multiple unit recordings from area 17 of anesthetized cat in response to a sinusoidal grating and show that pattern based encodings are superior to those of independent neuron models the agnostic nature of our clustering approach allows us to investigate encoding by the collective statistics that are actually present rather than those such as pairwise that might be presumed

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem