restricted ornstein uhlenbeck process and applications in neuronal models with periodic input signals restricted gauss markov processes are used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals the first passage time problem through a time dependent threshold is explicitly developed numerical simulation and asymptotic results for firing densities are provided

stepsize control for mean square numerical methods for stochastic differential equations with small noise a strategy for controlling the stepsize in the numerical integration of stochastic differential equations sdes is presented it is based on estimating the pth mean of local errors the strategy leads to stepsize sequences that are identical for all computed paths for the family of euler schemes for sdes with small noise we derive computable estimates for the dominating term of the pth mean of local errors and show that the strategy becomes efficient for reasonable stepsizes numerical experience is reported for test examples including scalar sdes and a stochastic circuit model

on a stochastic leaky integrate and fire neuronal model the leaky integrate and fire neuronal model proposed in stevens and zador 1998 in which time constant and resting potential are postulated to be time dependent is revisited within a stochastic framework in which the membrane potential is mathematically described as a gauss diffusion process the first passage time probability density miming in such a context the firing probability density is evaluated by either the volterra integral equation of buonocore nobile and ricciardi 1987 or when possible by the asymptotics of giorno nobile and ricciardi 1990 the model examined here represents an extension of the classic leaky integrate and fire one based on the ornstein uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness it also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time mean median coefficient of variation and skewness finally implementations of this model are provided in connection with certain experimental evidence discussed in the literature

first passage time statistics of brownian motion with purely time dependent drift and diffusion abstract systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a brownian motion bm driven by time dependent drift and diffusion coefficients modeling such systems requires solving the associated fokker planck equation subject to an absorbing barrier transitional probabilities are derived via the method of images whose applicability to time dependent problems is shown to be limited to state independent drift and diffusion coefficients that only depend on time and are proportional to each other first passage time statistics such as the survival probabilities and first passage time densities are obtained analytically the analysis includes the study of different functional forms of the time dependent drift and diffusion including power law time dependence and different periodic drivers as a case study of these theoretical results a stochastic model of water resources availability in snowmelt dominated regions is presented where both temperature effects and snow precipitation input are incorporated

on the construction of a special class of time inhomogeneous diffusion processes a special class of time inhomogeneous diffusion processes generated starting from gauss markov processes conditioned on the same initial state is considered this class includes many interesting diffusion processes with time dependent infinitesimal drift and variance for which the transition probability density function is explicitly determined moreover closed form results for the first passage time density through suitable time varying boundaries are obtained special cases generated starting from wiener and ornstein uhlenbeck processes are considered and widely discussed

decay of unstable states examination of the scaling theory abstract the behavior of the solution for an exactly solvable bistable model is analyzed the decay processes of unstable states are discussed the results of the scaling theory are tested it is concluded that the scaling theory is not valid for the model even when the potential barrier is very high

a transition to sharp timing in stochastic leaky integrate and fire neurons driven by frozen noisy input the firing activity of intracellularly stimulated neurons in cortical slices has been demonstrated to be profoundly affected by the temporal structure of the injected current mainen sejnowski 1995 this suggests that the timing features of the neural response may be controlled as much by its own biophysical characteristics as by how a neuron is wired within a circuit modeling studies have shown that the interplay between internal noise and the fluctuations of the driving input controls the reliability and the precision of neuronal spiking cecchi et al 2000 tiesinga 2002 fellous rudolph destexhe sejnowski 2003 in order to investigate this interplay we focus on the stochastic leaky integrate and fire neuron and identify the holder exponent h of the integrated input as the key mathematical property dictating the regime of firing of a single unit neuron we have recently provided numerical evidence taillefumier magnasco 2013 for the existence of a phase transition when becomes less than the statistical holder exponent associated with internal gaussian white noise h 1 2 here we describe the theoretical and numerical framework devised for the study of a neuron that is periodically driven by frozen noisy inputs with exponent h 0 in doing so we account for the existence of a transition between two regimes of firing when h 1 2 and we show that spiking times have a continuous density when the holder exponent satisfies h 1 2 the transition at h 1 2 formally separates rate codes for which the neural firing probability varies smoothly from temporal codes for which the neuron fires at sharply defined times regardless of the intensity of internal noise

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

variable step size control in the numerical solution of stochastic differential equations we introduce a variable step size method for the numerical approximation of pathwise solutions to stochastic differential equations sdes the method which is dependent on a representation of bro

diffusion in a class of exactly solvable non harmonic potentials intrinsic effects induced by non linearities abstract this paper deals with the problem of a particle that diffuses in a potential with a reflecting barrier and has a point of stable equilibrium and a point of unstable equilibrium based on the exact solutions obtained earlier for the fokker planck equation of a class of these models we analyze the behavior of the probability density the mean path and the onset time which determines the transition from unimodal to bimodal probability densities the study is made over different initial positions two of them very close to the unstable point which permits a clear comparison among the subsequent evolutions and the observation of some intrinsic effects induced by non linearities

exact propagator and eigenfunctions for multistable models with arbitrarily prescribed n lowest eigenvalues the author presents a method to construct potentials for schrodinger equations with some prescribed features for which all eigenfunctions and the time dependent propagator can be explicitly calculated the prescribed features can be formulated by choosing arbitrarily the n lowest eigenvalues alternatively one can prescribe some qualitative behaviour for the potential like the number and relative depths of wells and barriers the results can also be applied to the construction of fokker planck models with prescribed properties and explicitly calculable transition probability density the method is based on ideas of supersymmetric quantum mechanics and the theory of solitons that can be traced back to the work of darboux 1894 and crum 1955

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

a phase transition in the first passage of a brownian process through a fluctuating boundary with implications for neural coding finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple looking problem of vast practical importance in physics biology chemistry neuroscience economics and industrial engineering problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding such as neuronal integrators with irregular inputs and internal noise we show that the probability p t that a gauss markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary as measured by its holder exponent h the critical value occurs when the roughness of the boundary equals the roughness of the process so for diffusive processes the critical value is hc 1 2 for smoother boundaries h 1 2 the probability density is a continuous function of time for rougher boundaries h 1 2 the probability is concentrated on a cantor like set of zero measure the probability density becomes divergent almost everywhere either zero or infinity the critical point hc 1 2 corresponds to a widely studied case in the theory of neural coding in which the external input integrated by a model neuron is a white noise process as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs we argue that this transition corresponds to a sharp boundary between rate codes in which the neural firing probability varies smoothly and temporal codes in which the neuron fires at sharply defined times regardless of the intensity of internal noise

a first passage problem for a bivariate diffusion process numerical solution with an application to neuroscience when the process is gauss markov we consider a bivariate gauss markov process and we study the first passage time of one component through a constant boundary we prove that its probability density function is the unique solution of a new integral equation and we propose a numerical algorithm for its solution convergence properties of this algorithm are discussed and the method is applied to the study of the integrated brownian motion and to the integrated ornstein uhlenbeck process finally a model of neuroscience interest is discussed

the darboux transformation and solvable double well potential models for schrodinger equations the darboux transformation a method used to transform a schrodinger type equation to a schrodinger equation with a new potential is discussed an exactly solvable double well potential model for the one dimensional schrodinger equation is obtained

gauss markov processes in the presence of a reflecting boundary and applications in neuronal models abstract gauss markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined furthermore the first passage time density through a time dependent threshold is studied by using analytical numerical and asymptotic methods the restricted gauss markov processes are then used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time varying input signals

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

non linear dynamics of systems coupled with external noise some exact results abstract we solve exactly a class of non linear stochastic differential equations describing a variety of physical and chemical relevant systems coupled to external sources of noise the static and dynamic solutions are valid in the whole space of parameters including the critical points of non equilibrium instabilities critical slowing down is found and an unexpected long time tail evolution is predicted near and at the critical point this last effect is completely due to the coupling with the external noise

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

associated harmonic oscillator potential models for schrodinger equations by means of the darboux transformation the associated harmonic oscillator potential problem is solved analytically for properly chosen parameters the potentials appear as asymmetric double wells the penetration problem is discussed for inverted potentials

exact results for the diffusion in a class of asymmetric bistable potentials we solve the fokker planck equations with drifts deriving from a class of asymmetric nonharmonic potentials which include bistable cases an analytical expression for the probability current over the potential barrier is obtained finally we compare our exact results with those obtained by kramers approximation

exact propagator for generalized ornstein uhlenbeck processes a closed form expression for the propagator is derived in terms of modified bessel functions for the fokker planck equation for a physically important generalization of the ornstein uhlenbeck process where the diffusion constant d p is a function of the momentum the closed form is found for the general case d p approximately p alpha where alpha or 0 and leads to the standard gaussian form for alpha 0 the propagator for the specific case d p approximately p 1 is used to derive analytic expressions for probability distributions and correlation coefficients an exact expression is found for the constant of proportionality for the anomalous diffusion of the mean square displacement of a particle at short times

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

an integral algorithm for numerical integration of one dimensional additive colored noise problems we present an integral closed algorithm for solving a langevin equation driven by an additive colored noise both the mean first passage time in a bistable system and the diffusion current in a titled periodic potential are calculated and the comparison with existing algorithms is carried out the dependence of the numerical results on the time steps is studied our algorithm is shown to have high accuracy and stability

a haar like construction for the ornstein uhlenbeck process the classical haar construction of brownian motion uses a binary tree of triangular wedge shaped functions this basis has compactness properties which make it especially suited for certain classes of numerical algorithms we present a similar basis for the ornstein uhlenbeck process in which the basis elements approach asymptotically the haar functions as the index increases and preserve the following properties of the haar basis all basis elements have compact support on an open interval with dyadic rational endpoints these intervals are nested and become smaller for larger indices of the basis element and for any dyadic rational only a finite number of basis elements is nonzero at that number thus the expansion in our basis when evaluated at a dyadic rational terminates in a finite number of steps we prove the covariance formulae for our expansion and discuss its statistical interpretation

exact numerical simulation of the ornstein uhlenbeck process and its integral a numerical simulation algorithm that is exact for any time step ensuremath delta tg0 is derived for the ornstein uhlenbeck process x t and its time integral y t the algorithm allows one to make efficient unapproximated simulations of for instance the velocity and position components of a particle undergoing brownian motion and the electric current and transported charge in a simple r l circuit provided appropriate values are assigned to the ornstein uhlenbeck relaxation time ensuremath tau and diffusion constant c a simple taylor expansion in ensuremath delta t of the exact simulation formulas shows how the first order simulation formulas which are implicit in the langevin equation for x t and the defining equation for y t are modified in second order the exact simulation algorithm is used here to illustrate the zero ensuremath tau limit theorem textcopyright 1996 the american physical society

solvable models of the fokker planck equation an approach based on the gel fand levitan method from a given solvable fokker planck equation one can construct a number of other solvable models for diffusion in a stable or bistable potential fields using the gel fand levitan method of the inverse scattering theory the simplest way of achieving this is to change the lowest eigenvalue and or the normalization of the lowest eigenfunction of the ordinary differential equation obtained by separating the time dependent part for these cases it is shown that the new probability distribution is expressible in terms of integrals involving the original probability distribution and the gel fand levitan kernel the possibility of changing the lowest eigenvalue enables one to find bistable potential fields which would correspond to a well defined long time relaxation rate for the probability current

weak convergence of marked point processes generated by crossings of multivariate jump processes applications to neural network modeling abstract we consider the multivariate point process determined by the crossing times of the components of a multivariate jump process through a multivariate boundary assuming to reset each component to an initial value after its boundary crossing we prove that this point process converges weakly to the point process determined by the crossing times of the limit process this holds for both diffusion and deterministic limit processes the almost sure convergence of the first passage times under the almost sure convergence of the processes is also proved the particular case of a multivariate stein process converging to a multivariate ornstein uhlenbeck process is discussed as a guideline for applying diffusion limits for jump processes we apply our theoretical findings to neural network modeling the proposed model gives a mathematical foundation to the generalization of the class of leaky integrate and fire models for single neural dynamics to the case of a firing network of neurons this will help future study of dependent spike trains

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary

time optimal control of t s fuzzy models via lie algebra this paper investigates a geometric property of time optimal problem in the takagi sugeno t s fuzzy model via lie algebra we will focus on the existence of a time optimal solution singularity of switching function and number of switching these inherent problems are considered because of their rich geometric properties the sufficient condition for the existence of a time optimal solution reveals the controllability of t s fuzzy model that can be found by the generalized rank condition the time optimal controller can be found as the bang bang type with a finite number of switching by applying the maximum principle in the study of the singularity problem we will focus on the switching function whenever it vanishes over a finite time interval finally we show that the bounded number of switching can be found if the t s model also a nonlinear system is solvable

on a class of birth death processes with time varying intensity functions abstract in this paper we investigate on a class of time inhomogeneous birth death chains obtained by applying the composition method to two time inhomogeneous double ended chains then we consider the corresponding restricted birth death process with zero reflecting boundary finally starting from the restricted process we construct a time inhomogeneous bd chain symmetric with respect to zero state we obtain closed form expressions for the transition probabilities and for the conditional moments furthermore the first passage time problem is also taken in consideration finally various numerical computations are performed for periodic intensity functions

the fokker planck equation for a bistable potential univ estadual paulista unesp inst biociencia letras ciencias exatas dept fis br 15054000 sao jose do rio preto sp brazil

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

estimation of the input parameters in the ornstein uhlenbeck neuronal model the stochastic ornstein uhlenbeck neuronal model is studied and estimators of the model input parameters depending on the firing regime of the process are derived closed expressions for the laplace transforms of the first two moments of the normalized first passage time through a constant boundary in the suprathreshold regime are derived which is used to define moment estimators in the subthreshold regime the exponentiality of the first passage time is utilized to characterize the input parameters in the threshold regime and for the wiener process approximation analytic expressions for the first passage time density are used to derive the maximum likelihood estimators of the parameters the methods are illustrated on simulated data under different conditions including misspecification of the intrinsic parameters of the model finally known approximations of the first passage time moments are improved

exact solution for the diffusion in bistable potentials we solve analytically the fokker planck equation for a one parameter family of symmetric attractive nonharmonic potentials which include double well situations the exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density in particular for the bistable potentials we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni to bimodal probability densities

analysis of reflected diffusions via an exponential time based transformation let x t be a time homogeneous diffusion process with state space 0 infty where 0 is a reflecting or entrance endpoint and let z denote a random variable that describes the process x t evaluated at an exponentially distributed random time we propose a method to obtain closed form expressions for the conditional density and the mean of a new diffusion process y t with the same state space and with the same infinitesimal variance whose drift depends on the infinitesimal moments of x t and on the hazard rate function of z this method also allows us to obtain the laplace transform of the first passage time density of y t through a lower constant boundary we then discuss the relation between y t and the process x t subject to catastrophes as well as the interpretation of y t as a diffusion in a decreasing potential we study in detail some special cases concerning diffusion processes obtained when x t is the wiener ornstein uhlenbeck bessel and rayleigh process

integrated stationary ornstein uhlenbeck process and double integral processes abstract we find a representation of the integral of the stationary ornstein uhlenbeck isou process in terms of brownian motion b t moreover we show that under certain conditions on the functions f and g the double integral process dip d t t g s s f u d b u d s can be thought as the integral of a suitable gauss markov process some theoretical and application details are given among them we provide a simulation formula based on that representation by which sample paths probability densities and first passage times of the isou process are obtained the first passage times of the dip are also studied

estimating nonstationary input signals from a single neuronal spike train neurons temporally integrate input signals translating them into timed output spikes because neurons nonperiodically emit spikes examining spike timing can reveal information about input signals which are determined by activities in the populations of excitatory and inhibitory presynaptic neurons although a number of mathematical methods have been developed to estimate such input parameters as the mean and fluctuation of the input current these techniques are based on the unrealistic assumption that presynaptic activity is constant over time here we propose tracking temporal variations in input parameters with a two step analysis method first nonstationary firing characteristics comprising the firing rate and non poisson irregularity are estimated from a spike train using a computationally feasible state space algorithm then information about the firing characteristics is converted into likely input parameters over time using a transformation formula which was constructed by inverting the neuronal forward transformation of the input current to output spikes by analyzing spike trains recorded in vivo we found that neuronal input parameters are similar in the primary visual cortex v1 and middle temporal area whereas parameters in the lateral geniculate nucleus of the thalamus were markedly different

estimation of time dependent input from neuronal membrane potential the set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron estimation of the time varying input rates from intracellularly recorded membrane potential is investigated here for that purpose the membrane potential dynamics must be specified we consider the ornstein uhlenbeck stochastic process one of the most common single neuron models with time dependent mean and variance assuming the slow variation of these two moments it is possible to formulate the estimation problem by using a state space model we develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical bayes approach then the input firing rates are directly available from the moments the proposed method is applied to three simulated data examples constant signal sinusoidally modulated signal and constant signal with a jump for the constant signal the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method further the proposed method accurately estimates both continuous and discontinuous time variable signals in the case of the signal with a jump which does not satisfy the assumption of slow variability the robustness of the method is verified it can be concluded that the method provides reliable estimates of the total input firing rates which are not experimentally measurable

abstract data type systems abstract this paper is concerned with the foundations of an extension of pure type systems by abstract data types hence the name of abstract data type systems adts generalize inductive types as they are defined in the calculus of constructions by providing definitions of functions by pattern matching on the one hand and relations among constructors of the inductive type on the other it also generalizes the first order framework of abstract data types by providing function types and higher order equations the first half of the paper describes the framework of adts while the second half investigates cases where adts are strongly normalizing this is shown to be the case for the polymorphic lambda calculus with possibly subtypes enriched by higher order algebraic rules obeying a strong generalization of primitive recursion of higher type that we call the general schema this covers in particular the case of inductive types whose constructors do not have functional arguments we conjecture that this result holds true for all calculi of the so called barendregt s cube on the other hand the definition of a schema for the higher order rules allowing for more general inductive types is left open

pseudospectral solution of the fokker planck equation with equilibrium bistable states the eigenvalue spectrum and the approach to equilibrium the fokker planck equation with a constant diffusion coefficient and a particular polynomial drift coefficient can exhibit a bistable equilibrium distribution such model systems have been used to study chemical reactions nucleation climate optical bistability and other phenomena in this paper we consider a particular choice for the drift coefficient of the form a x x 5 x 3 to exemplify the statistical behaviour of such systems the transformation of the fokker planck equation to a schrodinger equation leads to a potential that belongs to the class of potentials in supersymmetric susy quantum mechanics a pseudospectral method based on nonclassical polynomials is used to determine the spectrum of the fokker planck operator and of the schrodinger equation the converged numerical eigenvalues are compared with wkb and swkb approximations of the eigenvalues

first exit times of harmonically trapped particles a didactic review we revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by a one or multidimensional ornstein uhlenbeck process we start by recalling the main derivation steps of a propagator using langevin and fokker planck equations the mean exit time the moment generating function and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed we also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing fokker planck operator we discuss several applications of first exit times such as the detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single particle tracking experiments adhesion bond dissociation under mechanical stress characterization of active periods of trend following and mean reverting strategies in algorithmic trading on stock markets relation to the distribution of first crossing times of a moving boundary by brownian motion some extensions are described including diffusion under quadratic double well potential and anomalous diffusion

markov analysis of stochastic resonance in a periodically driven integrate and fire neuron we model the dynamics of the leaky integrate and fire neuron under periodic stimulation as a markov process with respect to the stimulus phase this avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long standing reset problem the neuron exhibits stochastic resonance both with respect to input noise intensity and stimulus frequency the latter resonance arises by matching the stimulus frequency to the refractory time of the neuron the markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism