noise in integrate and fire neurons from stochastic input to escape rates we analyze the effect of noise in integrate and fire neurons driven by time dependent input and compare the diffusion approximation for the membrane potential to escape noise it is shown that for time dependent subthreshold input diffusive noise can be replaced by escape noise with a hazard function that has a gaussian dependence on the distance between the noise free membrane voltage and threshold the approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics

computation in a single neuron hodgkin and huxley revisited a spiking neuron computes by transforming a complex dynamical input into a train of action potentials or spikes the computation performed by the neuron can be formulated as dimensional reduction or feature detection followed by a nonlinear decision function over the low dimensional space generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low dimensional features from experimental data and information theory can be used to evaluate the quality of the low dimensional approximation we apply these methods to analyze the simplest biophysically realistic model neuron the hodgkin huxley hh model using this system to illustrate the general methodological issues we focus on the features in the stimulus that trigger a spike explicitly eliminating the effects of interactions between spikes one can approximate this triggering feature space as a two dimensional linear subspace in the high dimensional space of input histories capturing in this way a substantial fraction of the mutual information between inputs and spike time we find that an even better approximation however is to describe the relevant subspace as two dimensional but curved in this way we can capture 90 of the mutual information even at high time resolution our analysis provides a new understanding of the computational properties of the hh model while it is common to approximate neural behavior as integrate and fire the hh model is not an integrator nor is it well described by a single threshold

dynamic response of planar cracks in an infinitely long piezoelectric strip the problem of determining the electro elastic fields around an array of parallel planar cracks in an infinitely long piezoelectric strip is considered the cracks acted upon by dynamic loads are either electrically impermeable or permeable a semi analytic method based on the theory of exponential fourier transformation is presented for solving the problem in the laplace transform domain the laplace transforms of the jumps in the displacements and electric potential across opposite crack faces are determined by solving a system of hypersingular integral equations once these displacement and electric potential jumps are obtained the displacements and electric potential and other physical quantities of interest such as the crack tip stress and electric displacement intensity factors can be recovered with the help of a suitable algorithm for inverting laplace transforms the stress and electric displacement intensity factors are computed for some specific cases of the problem

statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks dynamical stochastic models of single neurons and neural networks often take the form of a system of n 2 coupled stochastic differential equations we consider such systems under the assumption that third and higher order central moments are relatively small in the general case a system of 1 n n13 generally nonlinear coupled ordinary differential equations holds for the approximate means variances and covariances for the general linear system the solutions of these equations give exact results this is illustrated in a simple case generally the moment equations can be solved numerically results are given for a spiking fitzhugh nagumo model neuron driven by a current with additive white noise differential equations are obtained for the means variances and covariances of the dynamical variables in a network of n connected spiking neurons in the presence of noise s1063 651x 96 03511 8 pacs number s 87 10 1e 05 40 1j 02 50 2r

from spiking neurons to rate models a cascade model as an approximation to spiking neuron models with refractoriness a neuron that is stimulated repeatedly by the same time dependent stimulus exhibits slightly different spike timing at each trial we compared the exact solution of the time dependent firing rate for a stochastically spiking neuron model with refractoriness spike response model with that of an inhomogeneous poisson process subject to the same stimulus to arrive at a mapping between the two models we used alternatively i a systematic parameter free volterra expansion of the exact solution or ii a linear filter combined with nonlinear poisson rate model linear nonlinear poisson cascade model with a single free parameter both the cascade model and the second order volterra model showed excellent agreement with the exact rate dynamics of the spiking neuron model with refractoriness even for strong and rapidly changing input cascade rate models are widely used in systems neuroscience our method could help to connect experimental rate measurements to the theory of spiking neurons

effects of correlated variability on information entropies in nonextensive systems we have calculated the tsallis entropy and fisher information matrix entropy of spatially correlated nonextensive systems by using an analytic non gaussian distribution obtained by the maximum entropy method the effects of the correlated variability on the fisher information matrix are shown to be different from those on the tsallis entropy the fisher information is increased decreased by a positive negative correlation whereas the tsallis entropy is decreased with increasing absolute magnitude of the correlation independently of its sign this fact arises from the difference in their characteristics it implies from the cramer rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation a critical comparison is made between the present study and previous ones employing the gaussian approximation for the correlated variability due to multiplicative noise

collective behavior of networks with linear vlsi integrate and fire neurons we analyze in detail the statistical properties of the spike emission process of a canonical integrate and fire neuron with a linear integrator and a lower bound for the depolarization as often used in vlsi implementations mead 1989 the spike statistics of such neurons appear to be qualitatively similar to conventional exponential integrate and fire neurons which exhibit a wide variety of characteristics observed in cortical recordings we also show that contrary to current opinion the dynamics of a network composed of such neurons has two stable fixed points even in the purely excitatory network corresponding to two different states of reverberating activity the analytical results are compared with numerical simulations and are found to be in good agreement

second order randic index of fluoranthene type benzenoid systems fluoranthene type benzenoid system are polycyclic conjugated molecules consisting of two benzenoid fragments connected by two carbon carbon bonds so as to form a five membered ring fluoranthene type benzenoid system and its congeners are compounds which in view of their chemical and physical properties belong among benzenoid hydrocarbons let f denotes a fluoranthene type benzenoid system whose second order randic index is denoted by r2 f in this paper we give the expression of r2 f in terms of their inlet features and we find the minimal and maximal value of the second order randic index over the set of cata catacondensed fluoranthene type benzenoid systems and characterize their corresponding graphs

fast global oscillations in networks of integrate and fire neurons with low firing rates we study analytically the dynamics of a network of sparsely connected inhibitory integrate and fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate in the limit when the number of neurons n 1 the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized the activity becomes oscillatory when the inhibitory feedback is strong enough the period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input in large but finite networks the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold their characteristics are determined as functions of systems parameters in these two different regimes the results are found to be in good agreement with numerical simulations

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

extremality of degree based graph entropies abstract many graph invariants have been used for the construction of entropy based measures to characterize the structure of complex networks based on shannon s entropy we study graph entropies which are based on vertex degrees by using so called information functionals when considering shannon entropy based graph measures there has been very little work to find their extremal values the main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers further conjectures to determine extremal values of graph entropies are given

the general connectivity indices of fluoranthene type benzenoid systems the general connectivity index r g of a graph g v e is defined as r g u v e g d u d v where u v is an edge of g du and dv denote the degrees of the vertices u and v respectively and 0 is an arbitrary real number in this paper we give the expressions for computing the general connectivity indices of fluoranthene type benzenoid systems and we determine the extremal values of r g in f benzenoid systems with h hexagons for some real number especially the extremal values of r g in cata catacondensed fluoranthene type benzenoid systems with h hexagons were studied

unifying framework for neuronal assembly dynamics starting from single spiking neurons we derive a system of coupled differential equations for a description of the dynamics of pools of extensively many equivalent neurons contrary to previous work the derivation is exact and takes into account microscopic properties of single neurons such as axonal delays and refractory behavior simulations show a good quantitative agreement with microscopically modeled pools of spiking neurons the agreement holds both in the quasistationary and nonstationary dynamical regimes including fast transients and oscillations the model is compared with other pool models based on differential equations it turns out that models of the graded response category can be understood as a first order approximation of our pool dynamics furthermore the present formalism gives rise to a system of equations that can be reduced straightforwardly so as to gain a description of the pool dynamics to any desired order of approximation finally we present a stability criterion that is suitable for handling pools of neurons due to its exact derivation from single neuron dynamics the present model opens simulation possibilities for studies that rely upon biologically realistic large scale networks composed of assemblies of spiking neurons

dynamic green s functions in anisotropic piezoelectric thermoelastic and poroelastic solids a procedure is described to generate fundamental solutions or green s functions for time harmonic point forces and sources the linearity of the field equations permits the green s function to be represented as an integral over the surface of a unit sphere where the integrand is the solution of a one dimensional impulse response problem the method is demonstrated for the theories of piezoelectricity thermoelasticity and poroelasticity time domain analogues are discussed and compared with known expressions for anisotropic elasticity

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

responses of a hodgkin huxley neuron to various types of spike train inputs numerical investigations have been made of responses of a hodgkin huxley hh neuron to spike train inputs whose interspike interval isi is modulated by deterministic semi deterministic chaotic and stochastic signals as deterministic one we adopt inputs with the time independent isi and with time dependent isi modulated by sinusoidal signal the rossler and lorentz models are adopted for chaotic modulations of isi stochastic isi inputs with the gamma distribution are employed it is shown that distribution of output isi data depends not only on the mean of isis of spike train inputs but also on their fluctuations the distinction of responses to the three kinds of inputs can be made by return maps of input and output isis but not by their histograms the relation between the variations of input and output isis is shown to be different from that of the integrate and fire if model because of the refractory period in the hh neuron

maximum likelihood estimation of a stochastic integrate and fire neural encoding model we examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy leaky integrate and fire spike generation mechanism this model provides a biophysically more realistic alternative to models based on poisson memoryless spike generation and can effectively reproduce a variety of spiking behaviors seen in vivo we describe the maximum likelihood estimator for the model parameters given only extracellular spike train responses not intracellular voltage data specifically we prove that the log likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques we develop an efficient algorithm for computing the maximum likelihood solution demonstrate the effectiveness of the resulting estimator with numerical simulations and discuss a method of testing the model s validity using time rescaling and density evolution techniques

dynamics of encoding in neuron populations some general mathematical features the use of a population dynamics approach promises efficient simulation of large assemblages of neurons depending on the issues addressed and the degree of realism incorporated in the simulated neurons a wide range of different population dynamics formulations can be appropriate here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common this underlying structure serves as a guide toward efficient means of simulation as an example we derive the general population firing rate frequency response and show how it may be used effectively to address a broad range of interacting population response and stability problems a few specific cases will be worked out a summary of this work appears at the end before the appendix

characterization of subthreshold voltage fluctuations in neuronal membranes synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons this is the case for the cerebral cortex where ongoing activity leads to strong barrages of synaptic inputs which act as the main source of synaptic noise affecting on neuronal dynamics here we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise described by ornstein uhlenbeck processes we derive and solve the fokker planck equation for this system which describes the time evolution of the probability density function for the membrane potential we obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in hodgkin huxley type models with stochastic synaptic inputs the differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high conductance states similar to in vivo conditions because the steady state membrane potential distribution is easily obtained experimentally this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons

moment analysis of the hodgkin huxley system with additive noise abstract we consider a classical space clamped hodgkin huxley hh model neuron stimulated by a current which has a mean together with additive gaussian white noise of amplitude a system of 14 deterministic first order nonlinear differential equations is derived for the first and second order moments means variances and covariances of the voltage v and the subsidiary variables n m and h the system of equations is integrated numerically with a fourth order runge kutta method as long as the variances as determined by these deterministic equations remain small the latter accurately approximate the first and second order moments of the stochastic hodgkin huxley system describing spiking neurons on the other hand for certain values of when rhythmic spiking is inhibited by larger amplitude noise the solutions of the moment equation strongly overestimate the moments of the voltage a more refined analysis of the nature of such irregularities leads to precise insights about the effects of noise on the hodgkin huxley system for suitable values of which enable rhythmic spiking we analyze by numerical examples from both simulation and solutions of the moment equations the three factors which tend to promote its cessation namely the increasing variance the nature and shape of the basins of attraction of the limit cycle and stable equilibrium point and the speed of the process

dynamical mean field theory of noisy spiking neuron ensembles application to the hodgkin huxley model a dynamical mean field approximation dma previously proposed by the present author h hasegawa phys rev e 67 041903 2003 has been extended to ensembles described by a general noisy spiking neuron model ensembles of n unit neurons each of which is expressed by coupled k dimensional differential equations des are assumed to be subject to spatially correlated white noises the original mathrm kn dimensional stochastic des have been replaced by k k 2 dimensional deterministic des expressed in terms of means and the second order moments of local and global variables the fourth order contributions are taken into account by the gaussian decoupling approximation our dma has been applied to an ensemble of hodgkin huxley hh neurons k 4 for which effects of the noise the coupling strength and the ensemble size on the response to a single spike input have been investigated numerical results calculated by the dma theory are in good agreement with those obtained by direct simulations although the former computation is about a thousand times faster than the latter for a typical hh neuron ensemble with n 100

generalized fisher information matrix in nonextensive systems with spatial correlation by using the q gaussian distribution derived by the maximum entropy method for spatially correlated n unit nonextensive systems we have calculated the generalized fisher information matrix of g ensuremath theta n ensuremath theta m for ensuremath theta 1 ensuremath theta 2 ensuremath theta 3 ensuremath mu q ensuremath sigma q 2 s where ensuremath mu q ensuremath sigma q 2 and s denote the mean variance and degree of spatial correlation respectively for a given entropic index q it has been shown from the cram er rao theorem that 1 an accuracy of an unbiased estimate of ensuremath mu q is improved degraded by a negative positive correlation s 2 that of ensuremath sigma q 2 is worsen with increasing s and 3 that of s is much improved for s ensuremath simeq ensuremath 1 n ensuremath 1 or s ensuremath simeq 1 0 though it is worst at s n ensuremath 2 2 n ensuremath 1 our calculation provides a clear insight to the long standing controversy whether the spatial correlation is beneficial or detrimental to decoding in neuronal ensembles we discuss also a calculation of the q gaussian distribution applying the superstatistics to the langevin model subjected to spatially correlated inputs

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

dynamical mean field theory of spiking neuron ensembles response to a single spike with independent noises a semianalytical dynamical mean field theory has been developed for a study of dynamics of an ensemble of n unit fitzhugh nagumo neurons subject to white noises assuming weak noises and the gaussian distribution of state variables we have driven equations of motions for moments of local and global variables dynamical mean field approximation dma has replaced original 2n dimensional stochastic differential equations des by eight dimensional deterministic des whereas the conventional moment method yields n 2n 3 dimensional deterministic des for local variables we have discussed the dependence of the spike firing precision and the synchronization on the noise intensity synaptic coupling and the size of the neuron ensemble the spike timing precision is shown to be improved by increasing the size of the neuron ensemble even when there are no couplings among neurons when the coupling is introduced neurons in ensembles respond to an input spike with a partial synchronization results calculated by our dma theory are in good agreement with those obtained by direct simulations dma theory is extended to a large cluster which can be divided into multiple subclusters according to their functions a model calculation has demonstrated that when the noise intensity is moderate the spike propagation with a fairly precise timing is possible among noisy subclusters with feed forward couplings as in the synfire chain we have compared dma theory with the conventional moment method showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean field approximation

the space clamped hodgkin huxley system with random synaptic input inhibition of spiking by weak noise and analysis with moment equations we consider a classical space clamped hodgkin huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by ornstein uhlenbeck processes using numerical solutions of the stochastic model system obtained by an euler method it is found that with excitation only there is a critical value of the steady state excitatory conductance for repetitive spiking without noise and for values of the conductance near the critical value small noise has a powerfully inhibitory effect for a given level of inhibition there is also a critical value of the steady state excitatory conductance for repetitive firing and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking furthermore near the critical value inverse stochastic resonance was observed when noise was present only in the inhibitory input process the system of deterministic differential equations for the approximate first and second order moments of the model is derived they are solved using runge kutta methods and the solutions are compared with the results obtained by simulation for various sets of parameters including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex the mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels in the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells the assumptions underlying the moment equation approach are not satisfied the simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks although suppression of firing is corroborated for the system of moment equations there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations

effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons a neuron in an active cortical circuit is subject to a fluctuating synaptic drive mediated by conductance changes it was recently demonstrated that synaptic conductance effects in vivo significantly alter the integrative properties of neurons these effects are missed in models that approximate the synaptic drive as a fluctuating current here the membrane potential distribution and firing rate are derived for the integrate andfire neuron withd correlated conductance based synaptic input using the fokker planck formalism a number of different input scenarios are examined including balanced drive and fluctuation changes at constant conductance the latter of which corresponds to shifts in synchrony in the presynaptic population this minimal model captures many experimentally observed conductance related effects such as reduced membranepotential fluctuations in response to increasing synaptic noise the solvability of the model allows for a direct comparison with current based approaches providing a basis for assessing the validity of existing approximation schemes that have dealt with conductance change in particular a commonly used heuristic approach whereby the passive membrane time constant is replaced by a drive dependent effective time constant is examined it is demonstrated that this approximation is valid in the same limit that the underlying diffusion approximation holds both for d correlated as well as filtered synaptic drive

noise induced phase separation mean field results we present a study of a phase separation process induced by the presence of spatially correlated multiplicative noise we develop a mean field approach suitable for conserved order parameter systems and use it to obtain the phase diagram of the model mean field results are compared with numerical simulations of the complete model in two dimensions additionally a comparison between the noise driven dynamics of conserved and nonconserved systems is made at the level of the mean field approximation

reduction of the hodgkin huxley equations to a single variable threshold model it is generally believed that a neuron is a threshold element that fires when some variable u reaches a threshold here we pursue the question of whether this picture can be justified and study the four dimensional neuron model of hodgkin and huxley as a concrete example the model is approximated by a response kernel expansion in terms of a single variable the membrane voltage the first order term is linear in the input and its kernel has the typical form of an elementary postsynaptic potential higher order kernels take care of nonlinear interactions between input spikes in contrast to the standard volterra expansion the kernels depend on the firing time of the most recent output spike in particular a zero order kernel that describes the shape of the spike and the typical after potential is included our model neuron fires if the membrane voltage given by the truncated response kernel expansion crosses a threshold the threshold model is tested on a spike train generated by the hodgkin huxley model with a stochastic input current we find that the threshold model predicts 90 percent of the spikes correctly our results show that to good approximation the description of a neuron as a threshold element can indeed be justified

the connectivity index of a weighted graph abstract let g be a simple graph and consider the m connectivity index m x g i 1 i n hellip i m 1 1 d i 1 d i m d i m 1 where i 1 i 2 i m 1 runs over all paths of length m in g and di denotes the degree of the vertex i we find upper bounds for m g using the eigenvalues of the laplacian matrix of an associated weighted graph the method provides also lower bounds for 1 g

a closed crack tip model for interface cracks inthermopiezoelectric materials abstract the interface crack problem of a bimaterial thermopiezoelectric solid was treated byapplying the extended version of strohs formalism and singular integral equation approach theinterface crack considered is subjected to combined thermal mechanical and electric loads under the applied loading the interface crack is assumed to be partially opened formulation ofthe problem results in a set of singular integral equations which are solved numerically thestudy shows that the contact zone is extremely small in comparison with the crack length basedon the formulation some physically meaningful quantities of interest such as stress intensityfactors and size of contact zone for a particular material group are analyzed

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

analytic expressions for rate and cv of a type i neuron driven by white gaussian noise we study the one dimensional normal form of a saddle node system under the influence of additive gaussian white noise and a static bias current input parameter a model that can be looked upon as the simplest version of a type i neuron with stochastic input this is in contrast with the numerous studies devoted to the noise driven leaky integrate and fire neuron we focus on the firing rate and coefficient of variation cv of the interspike interval density for which scaling relations with respect to the input parameter and noise intensity are derived quadrature formulas for rate and cv are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model we also show that caution must be used to extend these results to the neuron model with multiplicative gaussian white noise the correspondence between the first passage time statistics for the saddle node model and the neuron model is obtained only in the stratonovich interpretation of the stochastic neuron model while previous results have focused only on the ito interpretation the correct stratonovich interpretation yields cvs that are still relatively high although smaller than in the ito interpretation it also produces certain qualitative differences especially at larger noise intensities our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type i neurons from their firing statistics we also briefly discuss the effect of finite boundaries finite values of threshold and reset on the firing statistics

dynamic representation formulas and fundamental solutions for piezoelectricity abstract representation formulas and fundamental solutions of the governing equations of transient piezoelectricity are obtained through a generalization of the reciprocal theorem and the plane wave transform method it is shown that dynamic fundamental and singular solutions can be reduced to one dimensional integral expressions by means of a slowness surface the article provides the necessary mathematical foundations towards the development of the boundary element method for nonstationary three dimensional electroelastic problems

comment on characterization of subthreshold voltage fluctuations in neuronal membranes by m rudolph and a destexhe in two recent articles rudolph and destexhe 2003 2005 studied a leaky integrator model an rc circuit driven by correlated colored gaussian conductance noise and gaussian current noise in the first article they derived an expression for the stationary probability density of the membrane voltage in the second they modified this expression to cover a larger parameter regime here we show by standard analysis of solvable limit cases white noise limit of additive and multiplicative noise sources only slow multiplicative noise only additive noise and by numerical simulations that their first result does not hold for the general colored noise case and uncover the errors made in the derivation of a fokker planck equation for the probability density furthermore we demonstrate analytically including an exact integral expression for the time dependent mean value of the voltage and by comparison to simulation results that the extended expression for the probability density works much better but still does not exactly solve the full colored noise problem we also show that at stronger synaptic input the stationary mean value of the linear voltage model may diverge and give an exact condition relating the system parameters for which this takes place

dynamical mean field approximation to small world networks of spiking neurons from local to global and or from regular to random couplings by extending a dynamical mean field approximation previously proposed by the author h hasegawa phys rev e 67 041903 2003 we have developed a semianalytical theory which takes into account a wide range of couplings in a small world network our network consists of noisy n unit fitzhugh nagumo neurons with couplings whose average coordination number z may change from local z n to global couplings z n ensuremath 1 and or whose concentration of random couplings p is allowed to vary from regular p 0 to completely random p 1 we have taken into account three kinds of spatial correlations the on site correlation the correlation for a coupled pair and that for a pair without direct couplings the original 2n dimensional stochastic differential equations are transformed to 13 dimensional deterministic differential equations expressed in terms of means variances and covariances of state variables the synchronization ratio and the firing time precision for an applied single spike have been discussed as functions of z and p our calculations have shown that with increasing p the synchronization is worse because of increased heterogeneous couplings although the average network distance becomes shorter results calculated by our theory are in good agreement with those by direct simulations

generalized rate code model for neuron ensembles with finite populations we have proposed a generalized langevin type rate code model subjected to multiplicative noise in order to study stationary and dynamical properties of an ensemble containing a finite number n of neurons calculations using the fokker planck equation have shown that owing to the multiplicative noise our rate model yields various kinds of stationary non gaussian distributions such as ensuremath gamma inverse gaussian like and log normal like distributions which have been experimentally observed the dynamical properties of the rate model have been studied with the use of the augmented moment method amm which was previously proposed by the author from a macroscopic point of view for finite unit stochastic systems in the amm the original n dimensional stochastic differential equations des are transformed into three dimensional deterministic des for the means and fluctuations of local and global variables the dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the amm are in good agreement with those obtained by direct simulation the synchronization in the neuronal ensemble is discussed the variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise which may be a conceivable origin of the observed large variability in cortical neurons

exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack based on the complex potential approach the two dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied the explicit closed form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole when the elliptic hole degenerates into a crack the field intensity factors are obtained it is shown that the stress intensity factors are the same as that of isotropic material while the electric displacement intensity factor depends on both the material properties and the mechanical loads but not on the electric loads in other words the uniform electric loads have no influence on the field singularities it is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials

the transient response of a piezoelectric strip with a vertical crack under electromechanical impact load in this paper the dynamic electromechanical response of a piezoelectric strip with a central crack vertical to the boundary was investigated based on the superposition principle and integral transform techniques the present problem was reduced to the solution of two pairs of dual integral equations to accommodate the finite size of the strip two diaerent fourier transforms about the x and y coordinates were assumed the solution was obtained in the laplace transformed domain in terms of fredholm integral equations of the second kind by a modified copson s method the laplace inversion was then carried out to obtain the resulting dynamic stress and electric displacement intensities unlike the findings observed in the static fracture behavior of piezoelectric materials the present study indicates that the dynamic electric field will retard or promote the crack propagation at the diaerent loading stages furthermore the dynamic electric response is proportional to the electric impact and is independent of the applied mechanical impact it is also shown that both the mechanical and electric response around the crack tip are greatly influenced by the free boundaries of the piezoelectric strip 7 2000 elsevier science ltd all rights reserved

stationary and dynamical properties of information entropies in nonextensive systems the tsallis entropy and fisher information entropy matrix are very important quantities expressing information measures in nonextensive systems stationary and dynamical properties of the information entropies have been investigated in the n unit coupled langevin model subjected to additive and multiplicative white noise which is one of typical nonextensive systems we have made detailed analytical and numerical study on the dependence of the stationary state entropies on additive and multiplicative noise external inputs couplings and number of constitutive elements n by solving the fokker planck equation fpe by both the proposed analytical scheme and the partial difference equation method transient responses of the information entropies to an input signal and an external force have been investigated we have calculated the information entropies also with the use of the probability distribution derived by the maximum entropy method whose result is compared to that obtained by the fpe the cramer rao inequality is shown to be expressed by the extended fisher entropy which is different from the generalized fisher entropy obtained from the generalized kullback leibler divergence in conformity with the tsallis entropy the effect of additive and multiplicative colored noise on information entropies is discussed also

population dynamics of spiking neurons fast transients asynchronous states and locking an integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate and fire type is discussed it is analytically shown that transients from a state of incoherent firing can be immediate the stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived the response of a population of noisy integrate and fire neurons to an input current of small amplitude is calculated and characterized by a linear filter l the stability of perfectly synchronized locked solutions is analyzed

what causes a neuron to spike the computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output white noise stimulus and reverse correlation the spike triggered average and spike triggered covariance are often used in experimental neuroscience to ask neurons which dimensions in stimulus space they are sensitive to and to characterize the nonlinearity of the response in this article we apply reverse correlation to the simplest model neuron with temporal dynamics the leaky integrate and fire model and find that for even this simple case standard techniques do not recover the known neural computation to overcome this we develop novel reverse correlation techniques by selectively analyzing only isolated spikes and taking explicit account of the extended silences that precede these isolated spikes we discuss the implications of our methods to the characterization of neural adaptation although these methods are developed in the context of the leaky integrate and fire model our findings are relevant for the analysis of spike trains from real neurons

analysis of a central crack normal to a piezoelectric orthotropic interface this study is concerned with the general solution of the field intensity factors and energy release rate for a griffith crack normal to the interface between a rectangular piezoelectric ceramic and two same rectangular orthotropic materials of finite length under combined in plane electrical and anti plane mechanical loading both electrically continuous and impermeable crack surface conditions are considered employing fourier transforms and fourier series the problem is reduced to dual integral forms the solution to the resulting expressions is expressed in terms of fredholm integral equation of the second kind analytical solutions are provided for a number of cases to study the influence of material combinations geometry crack surface boundary and loading conditions the work also examines the influence of the crack boundary conditions on the results of the stress intensity factors and the energy release rate