identifiability of general arma processes using linear cumulant based estimators abstract cumulants of order greater than two may be used to estimate the parameters of non gaussian arma processes observed in additive colored gaussian noise the arma model may be causal or non causal mixed phase and have inherent all pass factors and repeated poles recent counterexamples to existing algorithms based on third order cumulants have given rise to questions of uniqueness and consistency of the parameter estimates two new order and parameter estimation algorithms are derived and consistency of the estimators is established these algorithms involve the solution of sets of linear equations and may be based on cumulants of any order greater than three it is demonstrated that the counterexamples do not apply to the new methods

arma parameter estimation using only output cumulants several algorithms are developed to estimate the parameters of a causal nonminimum phase autoregressive moving average arma p q system which is excited by an unobservable independently identically distributed non gaussian process the output is contaminated by additive colored gaussian noise of unknown power spectral density a fundamental result is presented pertaining to the identifiability of ar parameters based on the yule walker equations drawn from a specific set of p 1 1 d slices of the kth k 2 order output cumulant several ma parameter estimation algorithms are developed one method uses q 1 d slices of the output cumulant a second method uses only two 1 d cumulant slices these methods do not involve computation of the residual i e ar compensated time series or polynomial factorization multidimensional versions of the various algorithms are presented a simulation study demonstrating the effectiveness of the algorithms is included

a generalization of joint diagonalization criteria for source separation in the field of blind source separation joint diagonalization based approaches constitute an important framework leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices jade and simultaneous third order tensor diagonalization stotd algorithms however they are often restricted to the case of cumulants of order four in this paper we extend the results leading to jade and stotd to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results this also leads us to generalize some links between contrast functions and joint diagonalization criteria on which these algorithms are based in turn one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast moreover for the two generalized jade and stotd contrasts the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression whatever the cumulant order finally some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint diagonalization of cumulant matrices

permanence and stability of a diffusive predator prey model with disease in the prey abstract we investigate a 3 dimensional system of the predator prey dynamics with disease for the prey this system is a reaction diffusion model with ratio dependent michaelis menten functional response and diffusion in a bounded domain by applying the comparison principle liapunov function and linearized method we are able to achieve the sufficient conditions of the permanence the global stability of the boundary equilibria and the positive equilibrium and the local stability of the positive equilibrium numerical simulations are also given to illustrate the applications

separation of independent sources from correlated inputs the characterization of independent stationary stochastic components sources is generally achieved by using the spectral matrix of partially correlated measurements which are linearly related to the components of interest in the general case where no assumptions are made concerning the way the sources are mixed on the measurements the spectral matrix is not able to extract the true sources while spectral analysis only uses second order properties of independent stochastic sources a procedure based on higher order analysis fourth order cross cumulants is developed this approach leads to a complete identification of the sources

pattern formation of a spatial predator prey system abstract there are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors to investigate how these migration directed movement and diffusion random movement affect predator prey systems we have studied the spatiotemporal complexity in a predator prey system with holling tanner form a theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated at the same time we present the properties of pattern solutions the results of numerical simulations show that migration has prominent effect on the pattern formation of the population i e changing turing pattern into traveling pattern this study suggests that modelling by migration and diffusion in predator prey systems can account for the dynamical complexity of ecosystems

modelling and analysis of a delayed predator prey model with disease in the predator in this paper we study a predator prey model with a transmissible disease spreading in the predator population and a time delay representing the gestation period of the predator by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcations at the disease free equilibrium and the coexistence equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle sufficient conditions are derived for the global stability of the predator extinction equilibrium and the disease free equilibrium and the global attractiveness of the coexistence equilibrium of the system respectively numerical simulations are carried out to support the theoretical analysis

fitting noncausal autoregressive signal plus noise models to noisy non gaussian linear processes the problem of estimating the parameters of a noncausal autoregressive signal model from noisy observations is considered the signal is assumed to be non gaussian the measurement noise is allowed to be non gaussian two techniques that use both autocorrelations and third order autocumulants of the data are presented for parameter estimation knowledge of the probability distribution of the driving noise is not required several simulation examples are presented to illustrate the two methods the problem of model order selection is also addressed

3d source simulation method for static fields in inhomogeneous media in this paper an integral approach based on the source simulation method ssm for the solution of three dimensional 3d static electric fields is presented this is an extension of the well known charge simulation method to the electric and current static fields the formulation allows the solution of 3d electrostatic or static current field problems where several perfectly conducting bodies electrodes are placed in inhomogeneous media only electrode surfaces and dielectric interfaces need to be discretized by triangular elements matrix coefficients are accurately evaluated by using closed integral forms of 1 r and of grad 1 r dirichlet and neumann conditions can be imposed on the different conducting bodies in particular floating potential problem can also be solved the method of images allows ground plane to be taken into account the procedure has been applied to several practical cases and it represents an efficient tool for the evaluation of lumped circuit parameters such as capacitances of 3d conducting bodies and ground resistances of grounding systems copyright 2006 john wiley sons ltd

reaction diffusion predator prey parasite system and spatiotemporal complexity abstract this paper deals with the spatial pattern formation in a diffusive predator prey parasite ppp model where predator feeds on infected prey following type ii response function and infection spreads among prey species through horizontal transmission the study is accomplished with respect to an ecological parameter that quantifies the reproductive gain of predator and two epidemiological parameters which measure the force of infection and virulence of the disease we show analytically that the interior equilibrium loses its stability through hopf bifurcation in the absence of diffusion if the reproductive gain of predator crosses some threshold value in case of diffusive system it is shown that the interior equilibrium which is otherwise stable may lose its stability due to diffusion criteria for the occurrence of various types of instability like turing hopf turing and pure hopf associated with the ppp model are presented with illustrations our simulation results reveal that this diffusion driven instability creates various spatio temporal patterns like spot stripe mixture of spots stripes and spiral patterns depending upon the values of ecological and diffusion parameters turing instability and the corresponding patterns are also observed with the variation of two epidemiological parameters interestingly the epidemiological parameters that measure the infection rate and virulence of the disease show opposite patterns with their increasing values

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

role of additional food in eco epidemiological system with disease in the prey an eco epidemiological model supplying additional food is proposed the dynamics of the system is studied both analytically and numerically optimal control problem is formulated and solved bifurcation is carried out with respect to additional food results show that disease free system can be obtained supplying additional food an eco epidemiological system with disease in the prey incorporating additional food to predator is proposed the main objective of this study is to show the role of additional food in an eco epidemiological system we analyze the proposed system by calculating two reproduction numbers the dynamical behavior of the system is investigated from the point of view of stability and persistence both analytically and numerically using pontryagin s maximum principle an optimal control problem is formulated and solved in presence of additional food to achieve the control of disease numerical results illustrate that there exists a critical infection rate above which disease free system can not be reached in absence of additional food on the other hand suitable additional food has the capability to obtain a disease free system up to certain infection level the system becomes disease free also in presence of seasonally varying infection rate providing suitable additional food to predator this study introduces a new non chemical method for controlling disease in eco epidemiological system

nonsymmetrical contrasts for sources separation in this paper the problem of the blind separation of independent sources is considered our approach relies on high order inverse criteria after generalizing the definition of classical contrast functions we exhibit a wide class of generally nonsymmetrical functions that will be called generalized contrasts and whose maximization is proved to be a sufficient condition for source separation we also establish a connection with cumulant matching showing an equivalence between the two approaches then in the case of two sources a statistical study of the estimated parameter based on one of these new contrasts is presented finally computer simulations illustrate the results and demonstrate all the interest we can find in considering a nonsymmetrical contrast

impact of the fear effect in a prey predator model incorporating a prey refuge abstract in this paper we investigate the influence of anti predator behaviour due to the fear of predators with a holling type ii prey predator model incorporating a prey refuge we first provide the existence and stability of equilibria of the model next we give the existence of hopf bifurcation and limit cycle in addition we study the impact of the fear effect on the model analytically and numerically and find that the fear effect can not only reduce the population density of predator at the positive equilibrium but also stabilize the system by excluding the existence of periodic solutions moreover we also find that prey refuge has great impact on the persistence of the predator

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

self adaptive source separation i convergence analysis of a direct linear network controlled by the herault jutten algorithm it is known that self adaptive separation of a linear mixture of non gaussian independent sources can be achieved with a feedback linear neural network that is adapted by the herault jutten 1991 algorithm yet realizability of the feedback requires implementation constraints an equivalent direct without feedback network is considered that is free of these constraints while the self adaptive rule is kept unchanged the separating states are shown to be equilibrium points their stability status is studied in the case of two sources then we show that the algorithm is convergent in the quasi quadratic mean sense toward a separating state for a small enough step size

cumulant based independence measures for linear mixtures this paper deals with independence measures for linear mixtures of mutually independent random variables such measures also known as contrasts constitute useful criteria in solving blind source separation problems by making use of the schur convexity properties we show that it is possible to define a wide ranging class of contrast functions based on the auto cumulants of the components of the random vector being considered among the most appealing characteristics of these new contrast functions is that they can be used to combine cumulants of different orders in a flexible way furthermore extensions of existing cross cumulant base contrasts are proposed finally some particularization of our approach to measures of decorrelation is considered a general characterization of these decorrelation measures using strictly schur convex functions is provided

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

hopf bifurcation for a delayed predator prey diffusion system with dirichlet boundary condition a delayed predator prey diffusion system with beddington deangelis functional response under dirichlet boundary condition is investigated the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained via the implicit function theorem moreover taking feedback time delay as the bifurcation parameter hopf bifurcation near the positive steady state solution is proved to occur at a sequence of critical values we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns the direction of hopf bifurcation is forward when parameter m in model 1 2 is sufficiently large numerical simulations and numerical solutions are presented to illustrate our theoretical results

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

travelling waves and global attractivity of an sirs disease model with spatial diffusion and temporary immunity an sirs disease model with saturation incidence rate time delay and spatial diffusion is studied by analyzing the corresponding characteristic equations the local stability of an endemic steady state and a disease free steady state is discussed by comparison arguments if the basic reproductive number is greater than unity sufficient conditions are obtained for the global attractivity of the endemic steady state the existence of a travelling wave solution is established by using the technique of upper and lower solutions and schauder s fixed point theorem

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

globally convergent blind source separation based on a multiuser kurtosis maximization criterion we consider the problem of recovering blindly i e without the use of training sequences a number of independent and identically distributed source user signals that are transmitted simultaneously through a linear instantaneous mixing channel the received signals are hence corrupted by interuser interference iui and we can model them as the outputs of a linear multiple input multiple output mimo memoryless system assuming the transmitted signals to be mutually independent i i d and to share the same non gaussian distribution a set of necessary and sufficient conditions for the perfect blind recovery up to scalar phase ambiguities of all the signals exists and involves the kurtosis as well as the covariance of the output signals we focus on a straightforward blind constrained criterion stemming from these conditions from this criterion we derive an adaptive algorithm for blind source separation which we call the multiuser kurtosis muk algorithm at each iteration the algorithm combines a stochastic gradient update and a gram schmidt orthogonalization procedure in order to satisfy the criterion s whiteness constraints a performance analysis of its stationary points reveals that the muk algorithm is free of any stable undesired local stationary points for any number of sources hence it is globally convergent to a setting that recovers them all

superefficiency in blind source separation blind source separation is the problem of extracting independent signals from their mixtures without knowing the mixing coefficients nor the probability distributions of source signals and may be applied to eeg and meg imaging of the brain it is already known that certain algorithms work well for the extraction of independent components the present paper is concerned with superefficiency of these based on the statistical and dynamical analysis in a statistical estimation using t examples the covariance of any two extracted independent signals converges to 0 of the order of 1 t on line dynamics shows that the covariance is of the order of spl eta when the learning rate spl eta is fixed to a small constant in contrast with the above general properties a surprising superefficiency holds in blind source separation under certain conditions where superefficiency implies that covariance decreases in the order of 1 t sup 2 or of spl eta sup 2 the paper uses the natural gradient learning algorithm and method of estimating functions to obtain superefficient procedures for both batch estimation and on line learning a standardized estimating function is introduced to this end superefficiency does not imply that the error variances of the extracted signals decrease in the order of 1 t sup 2 or spl eta sup 2 but implies that their covariances and independencies do