temporal complexity of the order parameter at the phase transition we study a decision making model in a condition where it is equivalent to the two dimensional ising model and we show that at the onset of phase transition it generates temporal complexity namely nonstationary and nonergodic fluctuations we argue that this is a general property of criticality thereby opening the door to the application of the recently discovered phenomenon of complexity matching for an efficient transfer of information to occur a perturbing complex network must share the same temporal complexity as the perturbed complex network

design of fixed lag smoother using covariance information based on innovations approach in linear discrete time stochastic systems this paper newly designs the recursive least squares rls wiener fixed lag smoother and filter using the covariance information in linear discrete time stochastic systems the estimators require the information of the observation matrix the system matrix for the state variable related with the signal the variance of the state variable the cross variance function of the state variable with the observed value and the variance of the white observation noise it is assumed that the signal is observed with additive white noise the current fixed lag smoothing algorithm has a characteristic as shown in theorem 1 that the fixed lag smoothing estimate of the state vector is calculated in the reverse direction of time

new design of estimators using covariance information with uncertain observations in linear discrete time systems this paper proposes recursive least squares rls filtering and fixed point smoothing algorithms with uncertain observations in linear discrete time stochastic systems the estimators require the information of the auto covariance function in the semi degenerate kernel form the variance of white observation noise the observed value and the probability that the signal exists in the observed value the auto covariance function of the signal is factorized in terms of the observation vector the system matrix and the cross variance function of the state variable that generates the signal with the signal these quantities are obtained from the auto covariance data of the signal it is shown that the semi degenerate kernel is expressed in terms of these quantities

new design of fixed lag smoother using covariance information in linear discrete time stochastic systems this paper proposes recursive least squares fixed lag smoothing and filtering algorithms in linear discrete time stochastic systems the estimators require the information of the factorized autocovariance function of the signal namely the estimation algorithms use the observation matrix the system matrix for the state variable and the crossvariance function between the state variable and the signal also it is assumed that the variance of the white observation noise is known

peclet dependent memory kernels for transport in heterogeneous media transport in heterogeneous media can be described by partial differential equations which exhibit convolutions with time and or space memory kernels in this work we characterize the full time spectrum of time memory kernels by applying a nonparametric inversion algorithm to macroscopic synthetic data for heterogeneous porous media our findings put into evidence the inherent nonuniqueness of the transport parameters for nonlocal transport models notably we find that the peclet number can be interpreted as an ancillary parameter of a family of probability distribution functions that characterizes the memory kernels of transport

h fixed lag smoothing for linear discrete time varying systems with uncertain observations this paper deals with the problem of h fixed lag smoothing for linear discrete time varying systems with uncertain observations and l 2 norm bounded noise first the design of h smoother is equivalent to the problem that a certain indefinite quadratic form with respect to a new state space constraints has a minimum and the smoother is such that the minimum is positive then by introducing a krein space stochastic system and applying re organized innovation analysis approach the minimum of indefinite quadratic form and its existence condition are derived finally through analyzing the existence condition of the minimum and guaranteeing the positivity of the minimum a sufficient and necessary condition for the existence of an h smoother is proposed and the smoother is obtained in terms of two standard riccati difference equations a numerical example is given to show the effectiveness of the proposed method

second order polynomial estimators from uncertain observations using covariance information this paper presents recursive least mean squared error second order polynomial filtering and fixed point smoothing algorithms to estimate a signal from uncertain observations when only the information on the moments up to fourth order of the signal and observation noise is available the estimators require the autocovariance and crosscovariance functions of the signal and their second order powers in a semidegenerate kernel form and the probability that the signal exists in the observed values

derivation of fixed interval smoothing algorithm using covariance information in distributed parameter systems this paper proposes a recursive least mean squared error fixed interval smoothing algorithm in distributed parameter systems it is assumed that the state space model of the signal to be estimated is unknown and the algorithm only requires the second order moments of the signal and the white noise perturbing its observations practical application of the proposed algorithm is illustrated with a restoration image problem

nonlinear estimation using correlation information the approximate karhunen loegraveve kl expansions are used as a tool for systems identification providing an approximate state model for the signal of interest the identified model can then be used to derive sequential algorithms for the nonlinear estimation problem by using standard estimation techniques the proposed solution is specially indicated in those situations where a state equation is not at hand and the only information available is the correlation matrix of the signal

identification of non linear stochastic systems by state dependent parameter estimation the paper outlines how improved estimates of time variable parameters in models of stochastic dynamic systems can be obtained using recursive filtering and fixed interval smoothing techniques with the associated hyper parameters optimized by maximum likelihood based on prediction error decomposition it then shows how by exploiting special data re ordering and back fitting procedures similar recursive parameter estimation techniques can be utilized to estimate much more rapid state dependent parameter sdp variations in this manner it is possible to identify and estimate a widely applicable class of nonlinear stochastic systems as illustrated by several examples that include simulated and real data from chaotic processes finally the paper points out that such sdp models can form the basis for new methods of signal processing automatic control and state estimation for nonlinear stochastic systems

fixed interval smoothing problem from uncertain observations with correlated signal and noise this paper presents recursive filtering and fixed interval smoothing algorithms from observations corrupted by additive and multiplicative noises additive noise is a white process correlated with the signal and multiplicative noise is modelled by a sequence of independent bernoulli random variables it is assumed that both autocovariance function of signal and crosscovariance function about signal and observation noise are expressed in a semi degenerate kernel form the algorithms are obtained by an innovation approach without using the state space model but only covariance information of signal and observation noise and probability that signal exists in the observed values

fixed interval smoothing for markovian switching systems a suboptimal approach to the fixed interval smoothing problem for markovian switching systems is examined a smoothing algorithm is developed that uses two multiple model filters where one of the filters propagates in the forward time direction and the other one propagates in the backward time direction a backward time filtering algorithm based on the interacting multiple model concept is also developed results from a simulation example are given to illustrate the performance of the smoothing algorithm with respect to that of filtering the example involves radar tracking of a mach 1 aircraft

linear smoothing for discrete time systems in the presence of correlated disturbances and uncertain observations this paper considers the smoother with the least mean squared error lmse within the class of linear smoothers for discrete linear systems whose observations may contain noise alone and the probability of this occurring is known systems with uncertain observations also we assume that state and measurement noises are correlated the present results together with hermoso linares s results on prediction and filtering give a complete treatment of the lmse linear estimation problem for such systems

linear estimation for discrete time systems in the presence of time correlated disturbances and uncertain observations this note considers optimum linear recursive estimation for linear discrete time systems with uncertain observations in cases where state and measurement noises are correlated the different kinds of estimation problems treated include one stage prediction and filtering

linear least square estimation algorithms involving correlated signal and noise recursive algorithms are designed for the computation of the optimal linear filter and all types of predictors and smoothers of a signal vector corrupted by a white noise correlated with the signal these algorithms are derived under both continuous and discrete time formulation of the problem the only hypothesis imposed is that the correlation functions involved are factorizable kernels the main contribution of this work with respect to previous studies lies in allowing correlation between the signal and the observation noise which is useful in applications to feedback control and feedback communications moreover recursive computational formulas are obtained for the error covariances associated with the above estimates

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

technical communique new design of linear least squares fixed interval smoother using covariance information this paper derives recursive linear least squares fixed interval smoothing algorithm using covariance information by applying an invariant imbedding method to a wiener hopf integral equation the algorithm is obtained for the white plus coloured observation noise the signal process is nonstationary stochastic autocovariance functions of the signal and the coloured noise are expressed using a degenerate kernel the degenerate kernel can represent general covariance functions of nonstationary stochastic processes by a finite sum of nonrandom functions

generalized continuous time random walks master equations and fractional fokker planck equations continuous time random walks which generalize random walks by adding a stochastic time between jumps provide a useful description of stochastic transport at mesoscopic scales the continuous time random walk model can accommodate certain features such as trapping which are not manifest in the standard macroscopic diffusion equation the trapping is incorporated through a waiting time density and a fractional diffusion equation results from a power law waiting time a generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force here we have derived the master equations for continuous time random walks with space and time dependent forcing for two cases when the force is evaluated at the start of the waiting time and at the end of the waiting time the differences persist in low order spatial continuum approximations however the two processes are shown to be governed by the same fokker planck equations in the diffusi

analysis parameter estimation and optimal control of time delay systems via chebyshev series the chebyshev delay operational matrix is introduced first and then applied to approximate the solutions of linear time invariant and time varying delay systems with arbitrary time delay the parameter identification problem of the delay control system is also studied furthermore an approximate solution of the optimal control problem with quadratic performance measure is then discussed four examples are given and the results are shown to be very accurate and satisfactory

numerical solutions of optimal control for time delay systems by hybrid of block pulse functions and legendre polynomials using the operational properties of general block pulse functions and legendre polynomials the linear inverse time systems are transformed into a system of algebraic equations the numerical solutions of the systems are derived moreover applying the results to the linear quadratic optimal control problems the approximate solutions of optimal control of time delay systems are derived

hybrid legendre block pulse functions for the numerical solutions of system of nonlinear fredholm hammerstein integral equations in this paper the numerical technique based on hybrid legendre block pulse function has been developed to approximate the solution of system of nonlinear fredholm hammerstein integral equations these functions are formed by the hybridization of legendre polynomials and block pulse functions these functions are orthonormal and have compact support on 0 1 the proposed method reduces the system of integral equations to a system of nonlinear algebraic equations that can be solved easily by any usual numerical method the numerical results obtained by the presented method have been compared with those obtained by legendre wavelet method lwm numerical examples are presented to illustrate the accuracy of the method

brief papers relation between filter using covariance information and kalman filter this paper presents sequential algorithms for the optimal impulse function kalman gain and the error variance in linear least squares filtering problems when the autocovariance function of the signal is given in the form of a semi degenerate kernel and the additive observation noise in white gaussian a digital simulation result indicates that the algorithms presented in this paper are feasible and that the values of kalman gain and the error variance calculated by these algorithms approach to those obtained by the kalman filter theory for time sufficiently large

distribution of first return times in correlated stationary signals we present an analytical expression for the first return time frt probability density function of a stationary correlated signal precisely we start by considering a stationary discrete time ornstein uhlenbeck ou process with exponential decaying correlation function the first return time distribution for this process is derived by adopting a well known formalism typically used in the study of the frt statistics for nonstationary diffusive processes then by a subordination approach we treat the case of a stationary process with power law tail correlation function and diverging correlation time we numerically test our findings obtaining in both cases a good agreement with the analytical results we notice that neither in the standard ou nor in the subordinated case a simple form of waiting time statistics like stretched exponential or similar can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior

solving system of volterra fredholm integral equations with bernstein polynomials and hybrid bernstein block pulse functions this work approximates the unknown functions based on the bernstein polynomials and hybrid bernstein block pulse functions in conjunction with the collocation method for the numerical solution of system of fredholm volterra integral equations in both methods the system of integral equations is approximated by the gauss quadrature formula with respect to the legendre weight function the proposed methods reduce the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical methods moreover the convergence analysis of these algorithms will be shown by preparing some theorems numerical experiments are presented to show the superiority and efficiency of proposed methods in comparison with some other well known methods

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

the design of on line linear least squares estimators given covariance specifications via an imbedding method the method of invariant imbedding is employed to develop on line algorithms for all types of linear least squares estimators filter fixed point fixed lag and fixed interval smoothers fixed point fixed lead and fixed interval predictors using covariance specifications for nonstationary stochastic signals in the presence of white gaussian plus colored noise two design procedures are given one is based on the initial value solution of the function i y t which is the solution to a fredholm integral equation of the second kind and the other on that of the function h t s which is the impulse response function obeyed by a generalized wiener hopf integral equation

non markovian stochastic liouville equation and its markovian representation extensions of the continuous time random walk approach some specific features and extensions of the continuous time random walk ctrw approach are analyzed in detail within the markovian representation mr and ctrw based non markovian stochastic liouville equation sle in the mr ctrw processes are represented by multidimensional markovian ones in this representation the probability density function pdf w t of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some markovian controlling process within the mr the non markovian sle which describes the effect of ctrw like noise on the relaxation of dynamic and stochastic systems is generalized to take into account the influence of relaxing systems on the statistical properties of noise some applications of the generalized non markovian sle are discussed in particular it is applied to study two modifications of the ctrw approach one of them considers cascaded ctrws in which the controlling process is actually a ctrw like one controlled by another ctrw process controlled in turn by a third one etc within the mr a simple expression for the pdf w t of the total controlling process is obtained in terms of markovian variants of controlling pdfs in the cascade the expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long time tailed w t the cascaded ctrws can model the effect of the complexity of a system on the relaxation kinetics in glasses fractals branching media ultrametric structures etc another ctrw modification describes the kinetics of processes governed by fluctuating w t within the mr the problem is analyzed in a general form without restrictive assumptions on the correlations of pdfs of consecutive renewals the analysis shows that fluctuations of w t can strongly affect the kinetics of the process possible manifestations of this effect are discussed

linear response to perturbation of nonexponential renewal processes we study the linear response of a two state stochastic process obeying the renewal condition by means of a stochastic rate equation equivalent to a master equation with infinite memory we show that the condition of perennial aging makes the response to coherent perturbation vanish in the long time limit

prediction of the intensity process of doubly stochastic multichannel poisson processes this paper is concerned with the problem of predicting the intensity process of an observed doubly stochastic multichannel poisson process under the only hypothesis that the covariance function of the intensity process is separable recursive algorithms for the computation of the optimal linear filter and predictor are designed approximate solutions to the nonlinear filtering and prediction problems are also given the main advantage of the proposed solutions is that they can be applied to those situations where the intensity process does not satisfy a stochastic differential equation

numerical solution of distributed order fractional differential equations by hybrid functions in this paper a new numerical method for solving the distributed fractional differential equations is presented the method is based upon hybrid functions approximation the properties of hybrid functions consisting of block pulse functions and bernoulli polynomials are presented the riemann liouville fractional integral operator for hybrid functions is introduced this operator is then utilized to reduce the solution of the distributed fractional differential equations to a system of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique

correlation function and generalized master equation of arbitrary age we study a two state statistical process with a non poisson distribution of sojourn times in accordance with earlier work we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation these three methods yield exact expressions thus coinciding with the recent result by godreche and luck fj stat phys 104 489 s2001dg actually non poisson statistics yields infinite memory at the probability level thereby breaking any form of markovian approximation including the one adopted herein to find an approximated analytical formula for this reason we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions we find that although not exact a simple analytical expression for the correlation function of arbitrary age is very accurate we establish a connection between the correlation function and a generalized master equation of the same age thus this formalism related to models used in glassy materials allows us to illustrate an approach to the statistical treatment of blinking quantum dots bypassing the limitations of the conventional liouville treatment

robust continuous time smoothers without two sided stochastic integrals we consider the problem of fixed interval smoothing of a continuous time partially observed nonlinear stochastic dynamical system existing results for such smoothers require the use of two sided stochastic calculus the main contribution of the paper is to present a robust formulation of the smoothing equations under this robust formulation the smoothing equations are nonstochastic parabolic partial differential equations with random coefficients and hence the technical machinery associated with two sided stochastic calculus is not required furthermore the robust smoothed state estimates are locally lipschitz in the observations which is useful for numerical simulation as examples finite dimensional robust versions of the benes and hidden markov model smoothers and smoothers for piecewise linear dynamics are derived these finite dimensional smoothers do not involve stochastic integrals

arma prediction of widely linear systems by using the innovations algorithm a new autoregressive moving average arma predictor for widely linear systems is presented by using the innovations algorithm and under an improper treatment the main characteristics of this predictor are its facility of implementation from a practical standpoint and a better performance with respect to the conventional predictor obtained from a proper processing

numerical solutions of integrodifferential systems by hybrid of general block pulse functions and the second chebyshev polynomials in this paper integrodifferential systems are converted into a system of algebraic equations by hybrid of general block pulse functions and the second chebyshev polynomials the approximate solutions of integrodifferential systems are derived the numerical examples illustrate that the algorithm is valid

numerical solution of linear fredholm integral equation by using hybrid taylor and block pulse functions in this paper we use a combination of taylor and block pulse functions on the interval 0 1 that is called hybrid functions to estimate the solution of a linear fredholm integral equation of the second kind we convert the integral equation to a system of linear equations and by using numerical examples we show our estimation have a good degree of accuracy

technical communique new design of linear discrete time predictor using covariance information a discrete one stage predictor algorithm using covariance information in linear systems is derived the algorithm is obtained for white gaussian observation noise the signal is a nonstationary or stationary stochastic process the auto covariance function of the signal is expressed using a semi degenerate kernel of discrete time systems the semi degenerate kernel can represent general covariance functions of random processes by a finite sum of nonrandom functions

second order complex random vectors and normal distributions complex random vectors are usually described by their covariance matrix this is insufficient for a complete description of second order statistics and another matrix called the relation matrix is necessary some of its properties are analyzed and used to express the probability density function of normal complex vectors various consequences are presented

numerical solution of time varying systems with a stretch by general legendre wavelets using the general legendre wavelets a function with a stretch is expanded the property of the general operational matrix of integration is given and the general legendre wavelets stretch matrix is introduced the direct algorithm for a product of a matrix function and a vector function is proposed furthermore the time varying systems with a stretch are solved by the general legendre wavelets the numerical examples illustrate that the algorithms are applicable

new design of fixed interval smoother using covariance information in linear stochastic continuous time systems this paper proposes recursive least squares fixed interval smoothing and filtering algorithms in linear continuous time stochastic systems the estimators require the information of the autocovariance function of the signal the variance of white observation noise and the observed value the autocovariance function of the signal is expressed in the form of the semi degenerate kernel