the renewal equation for persistent diffusion persistent diffusion in one dimension in which the velocity of the diffusing particle is a dichotomic markov process is considered the flow is non markovian but the position and the velocity together constitute a markovian diffusion process we solve the coupled forward kolmogorov equations and the coupled backward kolmogorov equations with appropriate initial conditions to establish a generalized matrix form of the renewal equation connecting the probability densities and first passage time distributions for persistent diffusion

cone valued lyapunov functions and stability for impulsive functional differential equations abstract the stability criteria in terms of two measures for impulsive functional differential equations are established via cone valued lyapunov functions and razumikhin technique the stability can be deduced from the q 0 q stability of comparison impulsive differential equations an example is given to illustrate the advantages of the results obtained

serial correlation in neural spike trains experimental evidence stochastic modeling and single neuron variability the activity of spiking neurons is frequently described by renewal point process models that assume the statistical independence and identical distribution of the intervals between action potentials however the assumption of independent intervals must be questioned for many different types of neurons we review experimental studies that reported the feature of a negative serial correlation of neighboring intervals commonly observed in neurons in the sensory periphery as well as in central neurons notably in the mammalian cortex in our experiments we observed the same short lived negative serial dependence of intervals in the spontaneous activity of mushroom body extrinsic neurons in the honeybee to model serial interval correlations of arbitrary lags we suggest a family of autoregressive point processes its marginal interval distribution is described by the generalized gamma model which includes as special cases the log normal and gamma distributions which have been widely used to characterize regular spiking neurons in numeric simulations we investigated how serial correlation affects the variance of the neural spike count we show that the experimentally confirmed negative correlation reduces single neuron variability as quantified by the fano factor by up to 50 which favors the transmission of a rate code we argue that the feature of a negative serial correlation is likely to be common to the class of spike frequency adapting neurons and that it might have been largely overlooked in extracellular single unit recordings due to spike sorting errors

on the φ0 stability of comparison differential systems for many years now the variety of problems of the qualitative properties of differential equations in the context of lyaponov second method has been successfully investigated in a unified way using the comparison principle s in this method the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comparison equations in order to successfully employ this method it is generally required that the comparison systems possess some special properties the conditions under which the scalar comparison equations possess positivity and stability behaviour have been investigated using scalar lyapunov function method by brauer l siljak and grujic 9 and others ladde 3 gave suficient conditions for nonnegativity and stability of solutions of systems of comparison equations in his investigation of stability of comparison differential systems ladde 3 considered the asymptotic stability and exponential asymptotic stability of the comparison differential system using the method of vector lyapunov functions however imbedded in the method of vector lyapunov function is the requirement of quasimonotone nondecreasing property of the comparison system but quasimonotonicity of the comparison system is not a necessary condition for the system to be stable thus the limitation of the application potential of this general and effective method is due to the fact that

application of the θ method to a telegraphic model of fluid flow in a dual porosity medium abstract this work focuses mainly on the study of numerical solutions which are obtained using the method of a generalized warren and root model that includes a second order wave like equation in its formulation the solutions approximately describe the single phase hydraulic head in fractures by considering the finite velocity of propagation by means of a cattaneo like equation the corresponding discretized model is obtained by utilizing a non uniform grid and a non uniform time step a simple relationship is proposed to give the time step distribution convergence is analyzed by comparing results from explicit fully implicit and crank nicolson schemes with exact solutions a telegraphic model of fluid flow in a single porosity reservoir with relaxation dynamics the warren and root model and our studied model which is solved with the inverse laplace transform we find that the flux and the hydraulic head have spurious oscillations that most often appear in small time solutions but are attenuated as the solution time progresses furthermore we show that the finite difference method is unable to reproduce the exact flux at time zero obtaining results for oilfield production times which are in the order of months in real units is only feasible using parallel implicit schemes in addition we propose simple parallel algorithms for the memory flux and for the explicit scheme

bimodality of the interspike interval distributions for subordinated diffusion models of integrate and fire neurons abstract a subordinated langevin process with a random operational time in the form of an inverse strictly increasing levy type subordinator is considered as a generalization of the conventional perfect and leaky integrate and fire neuron models the parent process is given by standard brownian motion the effect of the random activity of synaptic inputs which arises from other neurons forming local and distant networks is modeled via a levy exponent of the subordinator using a first passage time formulation in an external force field we find exact expressions for the laplace transform of the output interspike interval isi density more detailed analysis is presented on the properties of the isi distribution in the case of the levy exponent which corresponds to the truncated double order time fractional diffusion equation for the probability density of the membrane potential particularly it is shown that at some parameter regimes the isi density exhibits a bimodal structure moreover it is demonstrated that the isis regularity is maximized at an intermediate value of the mean input current

ϕ0 stability of hybrid impulsive dynamic systems on time scales abstract in this paper we shall employ the method of cone valued lyapunov functions and comparison principle to investigate the 0 stability of impulsive hybrid systems on time scales

practical stability of impulsive hybrid differential systems in terms of two measures on time scales abstract in this paper we establish a new comparison theorem on time scales and give some new stability criteria for impulsive hybrid differential systems

on 0 stability for nonlinear volterra integrodifferential systems 0 stability and lipschitz 0 stability notions of ordinary differential equations odes are introduced in this paper we extend these notions to systems of integro differential equations ides and give some criteria of these notions our technique depends on liapunov s direct method

higher order statistics of a bistable system driven by dichotomous colored noise exact expressions for first and higher order residence time statistics count statistics and spectral properties of a bistable system driven by dichotomous colored noise are put forward and discussed the employed method is based on a discrete kinetic scheme and is valid for a wide range of parameter values of the colored noise this permits a detailed analysis of the effects of noise correlations for arbitrary correlation times it is found that at a characteristic correlation time of the dichotomous noise the residence time sequence becomes poissonian in particular all correlations between residence times disappear we also find that correlations become strongest for a finite strength of the driving force the analytical results can also be used to infer the underlying driving parameters in the case of noise with long range temporal correlations

firing statistics of a neuron model driven by long range correlated noise we study the statistics of the firing patterns of a perfect integrate and fire neuron model driven by additive long range correlated ornstein uhlenbeck noise using a quasistatic weak noise approximation we obtain expressions for the interspike interval isi probability density the power spectral density and the spike count fano factor we find unimodal long tailed isi densities lorenzian power spectra at low frequencies and a minimum in the fano factor as a function of counting time the implications of these results for signal detection are discussed

persistent diffusion on a line we consider solutions to the telegraph equation describing persistent diffusion on a line under various initial conditions the first passage time distribution is evaluated in closed form biased persistent diffusion is also considered a direct derivation of the telegraph equation from the stochastic equation for the displacement is presented in an appendix

stability and boundedness criteria of nonlinear impulsive systems employing perturbing lyapunov functions this paper develops a new comparison principle for nonlinear impulsive differential systems then the stability practical stability and boundedness of impulsive differential systems are proved by using the method of perturbing lyapunov functions the notion of perturbing lyapunov functions enables us to discuss stability properties of impulsive systems under much weaker assumptions the reported novel results complement the existing results it may provide a greater prospect for solving problems which exhibit impulsive effects

onset of negative interspike interval correlations in adapting neurons negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts one of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents in this work based on a hidden markov model and a proper statistical description of conditional responses we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation we derive the serial correlation coefficients for arbitrary lags under a small adaptation scenario in this case the behavior of correlations is universal and depends on the first order statistical description of an exponentially driven time inhomogeneous stochastic process

statistical properties of a class of nonlinear systems driven by colored multiplicative gaussian noise we derive the time dependent univariate and bivariate probability distribution function for an overdamped system with a quadratic potential driven by colored gaussian noise whose amplitude depends on the system state x as x alpha particular attention is paid to the effect of the correlation function of the noise on the statistical properties of the system we obtain exact expressions for the fractional moments as well as the correlation function of the system and calculate the fractal dimension we also consider the special case of a constant potential and determine the criteria for anomalous diffusion and stochastic localization of free particles

integrated approach to the assessment of long range correlation in time series data to assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods the spectral method and the random walk analysis the first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results we thus advocate an integrated approach which requires the use of both methods in a consistent fashion we provide the theoretical foundation of this approach and illustrate the main ideas using examples the second objective relates to the observation of long range anticorrelation hurst exponent hl1 2 in real world time series data the very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur using examples we discuss the possible factors that could contribute to the false claim of long range anticorrelations and demonstrate the particular importance of the integrated approach in this case

coding stimulus amplitude by correlated neural activity while correlated activity is observed ubiquitously in the brain its role in neural coding has remained controversial recent experimental results have demonstrated that correlated but not single neuron activity can encode the detailed time course of the instantaneous amplitude i e envelope of a stimulus these have furthermore demonstrated that such coding required and was optimal for a nonzero level of neural variability however a theoretical understanding of these results is still lacking here we provide a comprehensive theoretical framework explaining these experimental findings specifically we use linear response theory to derive an expression relating the correlation coefficient to the instantaneous stimulus amplitude which takes into account key single neuron properties such as firing rate and variability as quantified by the coefficient of variation the theoretical prediction was in excellent agreement with numerical simulations of various integrate and fire type neuron models for various parameter values further we demonstrate a form of stochastic resonance as optimal coding of stimulus variance by correlated activity occurs for a nonzero value of noise intensity thus our results provide a theoretical explanation of the phenomenon by which correlated but not single neuron activity can code for stimulus amplitude and how key single neuron properties such as firing rate and variability influence such coding correlation coding by correlated but not single neuron activity is thus predicted to be a ubiquitous feature of sensory processing for neurons responding to weak input

phase transition and hysteresis in an ensemble of stochastic spiking neurons an ensemble of stochastic nonleaky integrate and fire neurons with global delayed and excitatory coupling and a small refractory period is analyzed simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics whereas for coupling greater than the critical value the stochastic dynamics loses its influence and the units organize into several clusters with self sustained activity all units within one cluster spike in unison and the clusters themselves are phase locked theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths the bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically these results may be extensible to pulse coupled oscillators

the ornstein uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex cortical neurons of behaving animals generate irregular spike sequences recently there has been a heated discussion about the origin of this irregularity softky and koch 1993 pointed out the inability of standard single neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible shadlen and newsome 1994 on the other hand demonstrated that a standard leaky integrate and fire model can reproduce the irregularity if the inhibition is balanced with the excitation motivated by this discussion we attempted to determine whether the ornstein uhlenbeck process which is naturally derived from the leaky integration assumption can in fact reproduce higher order statistics of biological data for this purpose we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher order statistics of the interspike intervals consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient which are respectively a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution it is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values this fact suggests that the leaky integrate and fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons

ϕ0 stability of an impulsive system obtained from perturbing lyapunov functions abstract this paper focuses on the stability of the zero solution for the impulsive differential system at fixed times using the method of perturbing lyapunov functions on the basis of the method some sufficient conditions for the above stability to hold are given

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

models of stochastic biperiodic oscillations and extended serial correlations in electroreceptors of paddlefish two types of minimal models were used to study stochastic oscillations in sensory receptors composed of two coupled oscillators as in the electroreceptors of paddlefish they have populations of cells in sensory epithelia undergoing approximately 26 hz oscillations these are coupled unidirectionally via synaptic excitation to a few afferent neurons each of whose terminal contains a 30 70 hz oscillator expressed as a dominant peak in the power spectra of spontaneous afferent firing corresponding to the mean firing rate the two distinct types of internal noisy oscillators result in stochastic biperiodic firing patterns of the primary afferent sensory neurons however the functions of the oscillations have remained elusive motivating this study the models we used here are based on the circle map or on the ermentraut koppell canonical phase theta neuron model parameters were chosen according to experimental data we used the models to demonstrate that the presence of epithelial oscillations leads to extended negative correlations of afferent interspike intervals and to show that the correlation structure depends crucially on the ratio of the afferent to epithelial oscillation frequencies being most pronounced when this ratio is close to 2 as observed in experiments our studies of stochastic versions of these models are of general interest for a wide range of coupled excitable systems especially for understanding the functional roles of noisy oscillations in auditory and other types of hair cell primary afferent sensory receptors

analysis of spike statistics in neuronal systems with continuous attractors or multiple discrete attractor states attractor networks are likely to underlie working memory and integrator circuits in the brain it is unknown whether continuous quantities are stored in an analog manner or discretized and stored in a set of discrete attractors in order to investigate the important issue of how to differentiate the two systems here we compare the neuronal spiking activity that arises from a continuous line attractor with that from a series of discrete attractors stochastic fluctuations cause the position of the system along its continuous attractor to vary as a random walk whereas in a discrete attractor noise causes spontaneous transitions to occur between discrete states at random intervals we calculate the statistics of spike trains of neurons firing as a poisson process with rates that vary according to the underlying attractor network since individual neurons fire spikes probabilistically and since the state of the network as a whole drifts randomly the spike trains of individual neurons follow a doubly stochastic poisson point process we compare the series of spike trains from the two systems using the autocorrelation function fano factor and interspike interval isi distribution although the variation in rate can be dramatically different especially for short time intervals surprisingly both the autocorrelation functions and fano factors are identical given appropriate scaling of the noise terms since the range of firing rates is limited in neurons we also investigate systems for which the variation in rate is bounded by either rigid limits or because of leak to a single attractor state such as the ornstein uhlenbeck process in these cases the time dependence of the variance in rate can be different between discrete and continuous systems so that in principle these processes can be distinguished using second order spike statistics

quasi static small strain plasticity in the limit of vanishing hardening and its numerical approximation the quasi static rate independent evolution of the prager ziegler type model of plasticity with hardening is shown to converge to the rate independent evolution of the prandtl reuss elastic perfectly plastic model based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of gamma convergence for rate independent systems an unconditionally convergent numerical scheme is devised and two and three dimensional numerical experiments are presented a two sided energy inequality is a posteriori verified to document experimental convergence rates

the periodogram and allan variance reveal fractal exponents greater than unity in auditory nerve spike trains auditory nerve spike trains exhibit fractal behavior and therefore traditional renewal point process models fail to describe them adequately previous measures of the fractal exponent of these spike trains are based on the fano factor and consequently cannot exceed unity two estimates of the fractal exponent are considered which do not suffer from this limit one derived from the allan variance which was developed by the authors and one based on the periodogram these measures indicate that fractal exponents do indeed exceed unity for some nerve spike recordings from stimulated primary afferent cat auditory nerve fibers

on perturbing liapunov functional perturbing liapunov function method was introduced for systems of ordinary differential equations in this paper we will extend this method to systems of functional differential equations and discuss stability and boundedness properties via the concept of perturbing liapunov function

response to a periodic stimulus in a perfect integrate and fire neuron model driven by colored noise the output interspike interval statistics of a stochastic perfect integrate and fire neuron model driven by an additive exogenous periodic stimulus is considered the effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise using a first passage time formulation exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime and their dependence on input parameters e g the noise correlation time and amplitude as well as the frequency of an input current is analyzed it is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects such as sign reversals of the interspike interval correlations versus noise switching rate as well as versus the frequency of periodic forcing a power law like decay of oscillations of the serial correlation coefficients in the long lag limit amplification of the output signal modulation in the instantaneous firing rate of the neural response etc the features of spike statistics in the limits of slow and fast noises are also discussed

accuracy of rate coding when shorter time window and higher spontaneous activity help it is widely accepted that neuronal firing rates contain a significant amount of information about the stimulus intensity nevertheless theoretical studies on the coding accuracy inferred from the exact spike counting distributions are rare we present an analysis based on the number of observed spikes assuming the stochastic perfect integrate and fire model with a change point representing the stimulus onset for which we calculate the corresponding fisher information to investigate the accuracy of rate coding we analyze the effect of changing the duration of the time window and the influence of several parameters of the model in particular the level of the presynaptic spontaneous activity and the level of random fluctuation of the membrane potential which can be interpreted as noise of the system the results show that the fisher information is nonmonotonic with respect to the length of the observation period this counterintuitive result is caused by the discrete nature of the count of spikes we observe also that the signal can be enhanced by noise since the fisher information is nonmonotonic with respect to the level of spontaneous activity and in some cases also with respect to the level of fluctuation of the membrane potential

φ 0 boundedness and practical φ 0 stability of difference equations in this paper we develop the notions of f 0 boundedness and practical f 0 stability for difference equations via perturbing cone valued lyapunov functions and obtain sufficient conditions of f 0 boundedness and practical f 0 stability

diffusion laws for random walks on various heterogeneous lattices diffusion laws and diffusion coefficients are given for random walks on lattices whose scattering probabilities differ from site to site models are considered in which the direction of the particle after scattering depends on its direction before scattering

fractional gaussian noise enhanced information capacity of a nonlinear neuron model with binary signal input this paper reveals the effect of fractional gaussian noise with hurst exponent h 1 2 1 on the information capacity of a general nonlinear neuron model with binary signal input the fgn and its corresponding fractional brownian motion exhibit long range strong dependent increments it extends standard brownian motion to many types of fractional processes found in nature such as the synaptic noise in the paper for the subthreshold binary signal sufficient conditions are given based on the forbidden interval theorem to guarantee the occurrence of stochastic resonance while for the suprathreshold binary signal the simulated results show that additive fgn with hurst exponent h 1 2 1 could increase the mutual information or bits count the investigation indicated that the synaptic noise with the characters of long range dependence and self similarity might be the driving factor for the efficient encoding and decoding of the nervous system

emergence of spike correlations in periodically forced excitable systems in sensory neurons the presence of noise can facilitate the detection of weak information carrying signals which are encoded and transmitted via correlated sequences of spikes here we investigate the relative temporal order in spike sequences induced by a subthreshold periodic input in the presence of white gaussian noise to simulate the spikes we use the fitzhugh nagumo model and to investigate the output sequence of interspike intervals isis we use the symbolic method of ordinal analysis we find different types of relative temporal order in the form of preferred ordinal patterns that depend on both the strength of the noise and the period of the input signal we also demonstrate a resonancelike behavior as certain periods and noise levels enhance temporal ordering in the isi sequence maximizing the probability of the preferred patterns our findings could be relevant for understanding the mechanisms underlying temporal coding by which single sensory neurons represent in spike sequences the information about weak periodic stimuli

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

integrate and fire neurons with threshold noise a tractable model of how interspike interval correlations affect neuronal signal transmission many neurons exhibit interval correlations in the absence of input signals we study the influence of these intrinsic interval correlations of model neurons on their signal transmission properties for this purpose we employ two simple firing models one of which generates a renewal process while the other leads to a nonrenewal process with negative interval correlations different methods to solve for spectral statistics in the presence of a weak stimulus spike train power spectra cross spectra and coherence functions are presented and their range of validity is discussed using these analytical results we explore a lower bound on the mutual information rate between output spike train and input stimulus as a function of the system s parameters we demonstrate that negative correlations in the baseline activity can lead to enhanced information transfer of a weak signal by means of noise shaping of the background noise spectrum we also show that an enhancement is not compulsory char22 for a stimulus with power exclusively at high frequencies the renewal model can transfer more information than the nonrenewal model does we discuss the application of our analytical results to other problems in neuroscience our results are also relevant to the general problem of how a signal affects the power spectrum of a nonlinear stochastic system

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

exact results for power spectrum and susceptibility of a leaky integrate and fire neuron with two state noise this paper provides exact expressions for the power spectrum and the susceptibility of a leaky integrate and fire neuron driven by asymmetric two state noise the authors give an intuitive discussion of the undamped periodic oscillations resulting from their equations and also consider effects of additional broadband noise

stability and boundedness of nonlinear impulsive systems in terms of two measures via perturbing lyapunov functions this paper develops the concepts of stability practical stability and boundedness in terms of two measures for nonlinear impulsive differential systems using the method of perturbing lyapunov functions the notion of perturbing lyapunov functions enables us to discuss stability properties of solutions of nonlinear impulsive differential systems in terms of two measures under much weaker assumptions the novel results offer a way to unify a variety of stability results found in the relative literature

on practical stability of perturbed differential systems the notions of practical stability of systems of ordinary differential equations ode was introduced in this paper we will extend practical stability notion to a new type of stability called practical f 0 stability of perturbed systems of ordinary differential equations and given some criteria and results our technique depends on cone vector liapunov function method

on lipschitz stability for comparison systems of differential equations via limiting equation lipschitz f 0 stability notion was introduced in this paper we will discuss the notion of lipschitz f 0 stability of comparison systems of differential equations our technique depends on limiting equation method

uniform eventual lipschitz stability of impulsive systems on time scales in this paper we discuss the uniform eventual lipschitz stability of impulsive system on time scales by using comparison method lyapunov function and analysis technology some criteria of such stability for system with impulses on time scales are obtained an example is presented to illustrate the efficiency of proposed results

on total φ 0 stability of nonlinear systems of differential equations the notions of f 0 stability of systems of ordinary differential equations odes were introduced in this paper we will extend the f 0 stability notion to a new type of stability called total f 0 stability and give some criteria and results our technique depends on liapunov s direct method

first passage probabilities and mean number of sites visited by a persistent random walker in one and two dimensional lattices we study the first passage probability and mean number of sites visited by a discrete persistent random walker on a lattice in one and two dimensions this is performed by using the multistate formulation of the process we obtain explicit expressions for the generating functions of these quantities to evaluate these expressions we study the system in the strongly persistent limit in the one dimensional case we recover the behavior of the continuous one dimensional persistent random walk telegrapher process in two dimensions we obtain an explicit expression for the probability distribution in the strongly persistent limit however the laplace transforms required to evaluate the first passage processes could only be evaluated in the asymptotic limit corresponding to long times in which regime we recover the behavior of normal two dimensional diffusion

convergence of solutions of kinetic variational inequalities in the rate independent quasi static limit this paper discusses the convergence of kinetic variational inequalities to rate independent quasi static variational inequalities mathematical formulations as well as existence and uniqueness results for kinetic and rate independent quasi static problems are provided sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate independent ones when the size of initial perturbations and the rate of application of the forces tend to 0 an application to three dimensional elastic plastic systems with hardening is given

stability in terms of two measures of dynamic system on time scales by using a notion of upper quasi monotone nondecreasing this paper presents a new comparison principle which connects the solutions of two higher dimensional dynamic systems on time scales then the stability criteria of a solution of a dynamic system in terms of two measures are obtained finally two examples are provided to illustrate our results

discrimination with spike times and isi distributions we study the discrimination capability of spike time sequences using the chernoff distance as a metric we assume that spike sequences are generated by renewal processes and study how the chernoff distance depends on the shape of interspike interval isi distribution first we consider a lower bound to the chernoff distance because it has a simple closed form then we consider specific models of isi distributions such as the gamma inverse gaussian ig exponential with refractory period er and that of the leaky integrate and fire lif neuron we found that the discrimination capability of spike times strongly depends on high order moments of isi and that it is higher when the spike time sequence has a larger skewness and a smaller kurtosis high variability in terms of coefficient of variation cv does not necessarily mean that the spike times have less discrimination capability spike sequences generated by the gamma distribution have the minimum discrimination capability for a given mean and variance of isi we used series expansions to calculate the mean and variance of isis for lif neurons as a function of the mean input level and the input noise variance spike sequences from an lif neuron are more capable of discrimination than those of ig and gamma distributions when the stationary voltage level is close to the neuron s threshold value of the neuron

hybrid systems on time scales in this paper we study hybrid dynamic systems on time scales using lyapunov like functions we obtain sufficient conditions for the practical stability of hybrid dynamic systems on time scales

effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise the behavior of a stochastic perfect integrate and fire pif model of neurons is considered the effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing levy type subordinator using a first passage time formulation we find exact expressions for the output interspike interval isi statistics particularly it is shown that at some parameter regimes the isi density exhibits a multimodal structure moreover it is demonstrated that the coefficient of variation the serial correlation coefficient and the fano factor display a nonmonotonic dependence on the mean input current i e the isi s regularity is maximized at an intermediate value of the features of spike statistics analytically revealed in our study are compared with previously obtained results for a perfect integrate and fire neuron model driven by dichotomous noise without subordination

a convergence analysis of an h version finite element method with high order elements for two dimensional elasto plasticity problems in this paper we will give an h version finite element method for a two dimensional nonlinear elasto plasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a high order h version semidiscretization scheme is presented the existence and uniqueness of the solution for the semidiscrete problem are guaranteed by using some special properties of the constitutive law and finally we will show that as the maximum element size h longrightarrow 0 the solution of the semidiscrete problem will converge to the solution of the continuous problem the high order h version discretization scheme introduced here is unusual if the partition of the spatial space only has rectangles or parallelograms involved then there would not be any limit on the element degree however if the partition of the spatial space has some triangular elements then only certain combinations of finite element spaces for displacement and stress functions can be used the discretization scheme also provides a useful idea for applications of hp version or high order h version finite element methods for two dimensional problems where the elasto plastic body is not a polygon such as a disk or an annulus

interspike interval attractors from chaotically driven neuron models abstract sequences of intervals between firing times interspike intervals isis from single neuron models with chaotic forcing are investigated we analyze how the dynamical properties of the chaotic input determine those of the output isi sequence and assess how various biophysical parameters affect this input output relationship the attractors constructed from delay embeddings of isis and of the chaotic input are compared from the points of view of geometry and nonlinear forecastability for the three integrate and fire if models investigated the similarity between these attractors is high only when the mean firing rate is high and when firings occur over a large range of the input signal when these conditions are satisfied isis are related to input values at which firings occur by a simple map and their distribution can be derived from that of input signal values attractor reconstruction is found to be more sensitive to mean firing rate than to isi distribution at low firing rates for which the input is under sampled and isis become larger than the short term prediction horizon or when the dynamics do not allow a smooth invertible mapping between signal and isis information is lost our results relevant to all dynamical systems generating events show that information about continuous time dynamics is difficult to retrieve at low event rates and that information about inputs can be isolated only under restricted conditions

on stability for impulsive perturbed systems via cone valued lyapunov function method the notion of f 0 stability recently was introduced in this paper we will extend this notion to the so called eventual f 0 stability for impulsive systems of differential equations under more relax conditions our technique depends on lyapunov s direct method

exact numerical simulation of power law noises many simulations of stochastic processes require colored noises i describe here an exact numerical method to simulate power law noises the method can be extended to more general colored noises and is exact for all time steps even when they are unevenly spaced as may often happen for astronomical data see e g n r lomb astrophys space sci 39 447 1976 the algorithm has a well behaved computational complexity it produces a nearly perfect gaussian noise and its computational efficiency depends on the required degree of noise gaussianity

on stability of nonlinear systems of ordinary differential equations the notions of f 0 stability h 0 h stability integral and eventual stability of nonlinear systems of ordinary differential equations ode s are introduced our aim in this paper is to improve and extend these notions to new types of stability namely f 0 l p stability h 0 h integral stability and h 0 h eventual stability of systems of ode s respectively and given some criteria our technique depends on liapunov direct method

recurrent biological neural networks the weak and noisy limit a perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network a series expansion is constructed that converges for networks with noisy membrane potential and weak synaptic connectivity the terms of the series can be interpreted as loops of interactions between neurons so the technique is called a loop expansion a diagrammatic method is introduced that allows for construction of analytic expressions for the parameter dependencies of the spike probability function and correlation functions an analytic expression is obtained to predict the effect of the surrounding network on a neuron during an intracellular current injection the analytic results are compared with simulations to test the range of their validity and significant effects of the the recurrent connections in network are accurately predicted by the loop expansion

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

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

on cone perturbing liapunov function for impulsive differential systems the concept of f 0 stability and f 0 boundedness recently were introduced for systems of ordinary differential equations odes perturbing liapunov function method was discussed for systems of odes and extend to systems of functional differential equations fdes in this paper we extend these notions to impulsive systems of differential equations via cone perturbing liapunov function method

neuron dynamics in the presence of 1 f noise interest in understanding the interplay between noise and the response of a nonlinear device cuts across disciplinary boundaries it is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors most studies of noise in nonlinear devices are limited to either time correlated noise with a lorentzian spectrum of which the white noise is a limiting case or just white noise we use analytical theory and numerical simulations to study the impact of the more ubiquitous natural noise with a 1 f frequency spectrum specifically we study the impact of the 1 f noise on a leaky integrate and fire model of a neuron the impact of noise is considered on two quantities of interest to neuron function the spike count fano factor and the speed of neuron response to a small steplike stimulus for the perfect nonleaky integrate and fire model we show that the fano factor can be expressed as an integral over noise spectrum weighted by a low pass filter function given by f t f sinc 2 ft this result elucidates the connection between low frequency noise and disorder in neuron dynamics under 1 f noise spike dynamics lacks a characteristic correlation time inducing the leaky and nonleaky models to exhibit nonergodic behavior and the fano factor increasing logarithmically as a function of time we compare our results to experimental data of single neurons in vivo teich heneghan lowen ozaki and kaplan j opt soc am a 14 529 1997 and show how the 1 f noise model provides much better agreement than the usual approximations based on lorentzian noise the low frequency noise however complicates the case for an information coding scheme based on interspike intervals by introducing variability in the neuron response time on a positive note the neuron response time to a step stimulus is remarkably nearly optimal in the presence of 1 f noise an explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli

interspike interval statistics of neurons driven by colored noise a perfect integrate and fire model driven by colored noise is studied by means of the interspike interval isi density and the serial correlation coefficient exact and approximate expressions for these functions are derived for weak dichotomous or gaussian noise respectively it is shown that correlations in the input result in positive correlations in the isi sequence and in a reduction of isi variability the results also indicate that for weak noise the noise distribution only shapes the isi density but not the isi correlations which are determined by the noise s correlation function

dynamic plasticity models the evolution of an elastic plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities this system is posed as an evolution equation in hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity

a study on correlated exponential random walks based on the linear boltzmann transport formulation we investigate the statistics of correlated exponential random walks that are continuous in space and discrete in time we show that asymptotically the correlated random walk process is diffusive and derive an effective diffusion constant we investigate the power spectral characteristics of the associated random forces we also present some results on the first passage time distribution and establish that asymptotically it reduces to that associated with simple gaussian walks

statistics of a neuron model driven by asymmetric colored noise irregular firing of neurons can be modeled as a stochastic process here we study the perfect integrate and fire neuron driven by dichotomous noise a markovian process that jumps between two states i e possesses a non gaussian statistics and exhibits nonvanishing temporal correlations i e represents a colored noise specifically we consider asymmetric dichotomous noise with two different transition rates using a first passage time formulation we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval time interval between two subsequent neural action potentials and the power spectrum of the spike train furthermore we extend the model by including additional gaussian white noise and we give approximations for the interspike interval isi statistics in this case numerical simulations are used to validate the exact analytical results for pure dichotomous noise and to test the approximations of the isi statistics when gaussian white noise is included the results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics

a new approach to practical stability of impulsive functional differential equations in terms of two measures in this work we consider a new approach to the practical stability theory of impulsive functional differential equations with lyapunov functionals and razumikhin technique we use a new technique in the division of lyapunov functions given by shunian zhang and obtain conditions sufficient for the uniform practical asymptotical stability of impulsive delay differential equations an example is also discussed to illustrate the advantage of the proposed results

statistics of a leaky integrate and fire model of neurons driven by dichotomous noise the behavior of a stochastic leaky integrate and fire model of neurons is considered the effect of temporally correlated random neuronal input is modeled as a colored two level dichotomous markovian noise relying on the riemann method exact expressions for the output interspike interval density and for the serial correlation coefficient are derived and their dependence on noise parameters such as correlation time and amplitude is analyzed particularly noise induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established the features of spike statistics analytically revealed in our study are compared with recently obtained results for a perfect integrate and fire neuron model

on the asymptotic stability of systems with impulses by the direct method of lyapunov abstract in the present paper the asymptotic and globally asymptotic stability of the zero solution of systems with impulses is investigated for this purpose piecewise continuous auxiliary functions are used which are an analogue of lyapunov s functions the theorem of marachkov on the asymptotic stability of systems without impulses is generalized the results obtained are formulated in six theorems

on stability of nonlinear systems of functional differential equations the aim of this paper is to extend some results of f 0 stability for systems of functional differential equations f d e and to give results via razumikhin s method

distortion of neural signals by spike coding analog neural signals must be converted into spike trains for transmission over electrically leaky axons this spike encoding and subsequent decoding leads to distortion we quantify this distortion by deriving approximate expressions for the mean square error between the inputs and outputs of a spiking link we use integrate and fire and poisson encoders to convert naturalistic stimuli into spike trains and spike count and inter spike interval decoders to generate reconstructions of the stimulus the distortion expressions enable us to compare these spike coding schemes over a large parameter space we verify that the integrate and fire encoder is more effective than the poisson encoder the disparity between the two encoders diminishes as the stimulus coefficient of variation cv increases at which point the variability attributed to the stimulus overwhelms the variability attributed to poisson statistics when the stimulus cv is small the interspike interval decoder is superior as the distortion resulting from spike count decoding is dominated by a term that is attributed to the discrete nature of the spike count in this regime additive noise has a greater impact on the interspike interval decoder than the spike count decoder when the stimulus cv is large the average signal excursion is much larger than the quantization step size and spike count decoding is superior

on the stability of elastic plastic systems with hardening abstract this paper discusses the stability of quasi static paths for a continuous elastic plastic system with hardening in a one dimensional bar domain mathematical formulations as well as existence and uniqueness results for dynamic and quasi static problems involving elastic plastic systems with linear kinematic hardening are recalled in the paper the concept of stability of quasi static paths used here is essentially a continuity property of the system dynamic solutions relatively to the quasi static ones when as in lyapunov stability the size of initial perturbations is decreased and the rate of application of the forces which plays the role of the small parameter in singular perturbation problems is also decreased to 0 the stability of the quasi static paths of these elastic plastic systems is the main result proved in the paper

plasticity models and nonlinear semigroups abstract the evolution of an elastic plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities this system is posed as an evolution equation in hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity weak solutions are obtained in a very general situation strong solutions arise in the presence of kinematic work hardening or viscosity and the solution is even more regular under a stability assumption connecting the constraint set with the divergence operator

on relative ϕ0 stability of impulsive hybrid systems via perturbing lyapunov functions abstract this paper obtains some sufficient conditions for the relative 0 stability of the two impulsive hybrid systems by using the method of perturbing lyapunov functions

on stability of nonlinear differential systems via cone valued liapunov function method the notions of partial relative and f 0 stability of ordinary differential equations odes are introduced in e p akpan o akinyele j math anal appl 164 1992 307 324 v lakshmikantham s leela differential and integral inequalities vol 1 academic press new york 1969 in this paper we extend these notions to new types of stability namely f 0 relative and f 0 partial stability of odes using cone valued liapunov function method and comparison technique

large deviations of ergodic counting processes a statistical mechanics approach the large deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations here we study this formalism through a statistical mechanics approach that is with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential we show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones providing is this way an alternative measurement interpretation of the thermodynamic approach general results are obtained for renewal counting processes that is those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution the underlying statistical mechanics is controlled by the same waiting time distribution rescaled by an exponential decay measured by the free energy function a scale invariance shift closure and intermittence phenomena are obtained and interpreted in this context similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution