analytic derivatives for estimation of linear dynamic models abstract this paper develops two algorithms algorithm 1 computes the exact gaussian log likelihood function its exact gradient vector and an asymptotic approximation of its hessian matrix for discrete time linear dynamic models in state space form algorithm 2 derived from algorithm 1 computes the exact sample information matrix of this likelihood function the computed quantities are analytic not numerical approximations and should therefore be useful for reliably quickly and accurately i checking local identifiability of parameters by checking the rank of the information matrix ii using the gradient vector and hessian matrix to compute maximum likelihood estimates of parameters with newton methods and iii computing asymptotic covariances cramer rao bounds of the parameter estimates with the hessian or the information matrix the principal contribution of the paper is algorithm 2 which extends to multivariate models the univariate results of porat and friedlander 1 by relying on the kalman filter instead of the levinson durbin filter used by porat and friedlander algorithms 1 and 2 can automatically handle any pattern of missing or linearly aggregated data although algorithm 1 is well known it is treated in detail in order to make the paper self contained

smoothing splines for longitudinal data in a longitudinal data model with fixed and random effects polynomials are used to model the fixed effects and smoothing polynomial splines are used to model the within subject random effect curves the splines are generated by modelling the data for each subject as observations of an integrated random walk with observational error the initial conditions for each subject s deviation from the fixed effect curve are assumed to have zero mean and arbitrary covariance matrix which is estimated by maximum likelihood producing an empirical bayes estimate this is in contrast to modelling a single curve using a diffuse prior an example is presented using unbalanced longitudinal data from a pilot study in breast cancer patients

estimation prediction and interpolation for nonstationary series with the kalman filter abstract we show how our definition of the likelihood of an autoregressive integrated moving average arima model with missing observations alternative to that of kohn and ansley and based on the usual assumptions made in estimation of and forecasting with arima models permits a direct and standard state space representation of the nonstationary original data so that the ordinary kalman filter and fixed point smoother can be efficiently used for estimation forecasting and interpolation in this way the problem of estimating missing values in nonstationary series is considerably simplified the results are extended to regression models with arima errors and a computer program is available from the authors

discrete time deterministic and stochastic models for the spread of rabies discrete spatial and temporal models for the spread and control of rabies are developed analyzed and simulated first a deterministic model is formulated then an analogous stochastic model the models are structured with respect to space m patches age juveniles and adults and disease state for each patch there are six state variables corresponding to either juveniles or adults and their disease state susceptible infected or vaccinated the models have seven stages which repeat every year the impact of different vaccination strategies on the dynamics of the deterministic and stochastic models are compared in particular the relationships among the vaccination proportion the width of the vaccination barrier the initial number infected and the transmissibility of the disease are examined an estimate for the probability of disease elimination is given for the stochastic model it is shown that in some cases where the deterministic model predicts disease persistence the stochastic model predicts a high probability of disease elimination

the likelihood for a state space model summary this paper derives an expression for the likelihood for a state space model the expression can be evaluated with the kalman filter initialized at a starting state estimate of zero and associated estimation error covariance matrix of zero adjustment for initial conditions can be made after filtering accordingly initial conditions can be modelled without filtering implications in particular initial conditions can be modelled as diffuse the connection between the diffuse and concentrated likelihood is also displayed

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

the exact likelihood for a state space model with stochastic inputs abstract in this work we derive exact and approximate expressions for the conditional mean and variance of the initial state of a state space model allowing for unit roots and stochastic inputs these results provide adequate initial conditions to compute the exact likelihood using the kalman filter the exact conditional moments are the best choice when the stochastic structure of the inputs is known if this is not the case the approximate expressions are a good alternative as some simulation results illustrate

filtering and smoothing algorithms for state space models abstract the paper reviews and generalizes recent filtering and smoothing algorithms for observations generated by a state model in particular the paper discusses the modified kalman filter derived by ansley and kohn 1985 and kohn and ansley 1986 to deal with state space models having partially diffuse initial conditions and shows how to compute the limiting normalized likelihood of the observations for such models the paper also discusses and generalizes the new smoothing algorithm presented by kohn and ansley 1987c 1989 and extends it to state space models with partially diffuse initial conditions

a bayesian approach to additive semiparametric regression abstract we present a bayesian approach to estimating an additive semiparametric regression model which is robust to outliers the unknown curves are estimated by posterior means and are shown to be smoothing splines by using markov chain monte carlo an o mn algorithm is produced where n is the sample size and m is the total number of markov chain iterations previous exact approaches required o n3 operations making the estimation of large data sets impractical efficient methods for estimating the posterior means using mixture and backfitting estimates are developed the properties of the curve estimates are studied empirically using both simulated and real examples

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

a reproducing kernel hilbert space approach for q ball imaging diffusion magnetic resonance mr imaging has enabled us to reveal the white matter geometry in the living human brain the q ball technique is widely used nowadays to recover the orientational heterogeneity of the intra voxel fiber architecture this article proposes to employ the funk radon transform in a hilbert space with a reproducing kernel derived from the spherical laplace beltrami operator thus generalizing previous approaches that assume a bandlimited diffusion signal the function estimation problem is solved within a tikhonov regularization framework while a gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands shortcomings of q ball imaging are discussed

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

semiparametric bayesian inference in smooth coefficient models abstract we describe procedures for bayesian estimation and testing in cross sectional panel data and nonlinear smooth coefficient models the smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate in the approach we describe points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves the algorithms we describe are quite simple to implement for example estimation testing and smoothing parameter selection can be carried out analytically in the cross sectional smooth coefficient model we apply our methods using data from the national longitudinal survey of youth nlsy using the nlsy data we first explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability we also examine a model of female labor supply and use this example to illustrate how the described techniques can been applied in nonlinear settings

efficient generalized cross validation for state space models summary for a signal plus noise model with a state space representation an efficient procedure is given for obtaining the trace of the influence matrix where the influence matrix expresses the estimated signal vector as a linear combination of the observed data this allows an 0 n evaluation of the generalized cross validation criterion function our approach is very efficient requiring the addition of only one equation to the ordinary kalman filter and extends to models with linear regressors in the observation equation important applications are to spline smoothing in regression and to variance components models for seasonal time series

global asymptotic behavior of a chemostat model with discrete delays this paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat the model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations in the case where only two species are engaged in competition it is shown that competitive exclusion holds for any monotone growth response functions sufficient conditions are also obtained for the model to exhibit competitive exclusion in the n species case in regard to the delay effects on the qualitative outcome of competition it is demonstrated that when the delays are relatively small the predictions of the model are identical with the predictions given by corresponding models without time delays however including large delays in the model may alter the predicted outcome of competition the techniques used also work when different removal rates are permitted an

diagnosing shocks in time series abstract efficient means of modeling aberrant behavior in times series are developed our methods are based on state space forms and allow test statistics for various interventions to be computed from a single run of the kalman filter smoother the approach encompasses existing detection methodologies departures commonly observed in practice such as outlying values level shifts and switches are readily dealt with new diagnostic statistics are proposed implications for structural models autoregressive integrated moving average models and models with explanatory variables are given

heteroclinic orbits for retarded functional differential equations abstract suppose is a heteroclinic orbit of a ck functional differential equation x t x i with limit set and limit set being either hyperbolic equilibrium points or periodic orbits necessary and sufficient conditions are given for the existence of an ftf close to in ck with the property that x t tf x t has a heteroclinic orbit gg close to the orbits gg are obtained from the zeros of a finite number of bifurcation functions g f r d r d 1 transversality of is characterized by the nondegeneracy of the derivative d g it is also shown that the tf which have heteroclinic orbits near are on a ck submanifold of finite codimension max 0 ind or on the closure of it where ind is the index of

on the time to extinction in recurrent epidemics summary an approximation is derived for the expected time to extinction in a stochastic model for recurrent epidemics numerical illustrations indicate that the approximation is crude but that it has the correct order of magnitude the quasi stationary distribution plays an important role in the derivation approximations for the critical community size and for the persistence threshold are derived comments are made on the classical study by bartlett 1956 1960

trend estimation and de trending via rational square wave filters this paper gives an account of some techniques of linear filtering which can be used for extracting trends from economic time series of limited duration and for generating de trended series a family of rational square wave filters is described which enable designated frequency ranges to be selected or rejected their use is advocated in preference to other filters which are commonly used in quantitative economic analysis

a fast algorithm for signal extraction influence and cross validation in state space models summary a fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model the resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector the ideas of studentized residuals and leverage from regression analysis are generalized to state space models and the new algorithm is used to compute the various measures the results are also applied to obtain a new efficient algorithm for polynomial spline smoothing suppose observations are generated by a gaussian signal plus noise process with the signal described by a state space model such a model for the signal occurs often in practice for example when the signal is the output of a stochastic difference or differential equation this paper presents a new algorithm for signal extraction that is the computa tion of the conditional mean and variance of the signal given the observations the usual method for signal extraction is to use the kalman filter see for example anderson moore 1979 p 105 followed by a smoothing step using an algorithm such as the fixed interval smoothing algorithm anderson moore 1979 p 187 our approach also uses the kalman filter but for the smoothing step introduces a new set of recursions which are more efficient than those for the fixed interval smoothing algorithm as for the fixed interval smoothing algorithm recursions for estimating the signal and its variance are carried out separately so that considerable additional savings can be made if the signal estimate alone is required the development uses ideas introduced by ansley kohn 1987a a remarkable property of the new recursions is that they can be applied immediately

nonparametric spline regression with prior information summary by using prior information about the regression curve we propose new nonparametric regression estimates we incorporate two types of information first we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation the regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty we discuss in particular growth and decay curves and take a time transformation to obtain a tractable solution the second type of prior information is linear equality constraints we estimate unknown parameters by generalized cross validation or maximum likelihood and obtain efficient 0 n algorithms to compute the estimate of the regression curve and the cross validation and maximum likelihood criterion functions

asymptotic profile of the positive steady state for an sis epidemic reaction diffusion model effects of epidemic risk and population movement abstract identifying the epidemic risk for infectious disease is crucial in order to effectively perform control measures in a series of our work from an analytical aspect we study the effects of epidemic risk and population movement on the spatiotemporal transmission of infectious disease via an sis epidemic reaction diffusion model proposed by allen et al 2008 in 36 in allen et al 2008 36 peng 2009 37 it was assumed that the habitat of the populations consists of only the low and high risk areas the present paper concerns a more complicated heterogeneous environment where the moderate risk area occurs and deals with two cases i only the moderate and high risk areas exist ii the low moderate and high risk areas coexist in each case we rigorously determine the asymptotic profile of the positive steady state i e the endemic equilibrium as the migration rate of either the susceptible or infected population tends to zero our results show how epidemic risk and population movement affect the spatial distribution of infectious disease and thereby suggest important implications for predicting the patterns of disease occurrence and designing optimal control strategies numerical simulations are carried out to support the theoretical results

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

estimation prediction and interpolation for arima models with missing data abstract we show how to define and then compute efficiently the marginal likelihood of an arima model with missing observations the computation is carried out by using the univariate version of the modified kalman filter introduced by ansley and kohn 1985a which allows a partially diffuse initial state vector we also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate

estimating integrated higher order continuous time autoregressions with an application to money income causality an algorithm is presented for computing the gaussian maximum likelihood estimator of the parameters of a multivariate continuous time autoregressive process with multiple roots that equal zero some of the variables might be observed at a point in time stocks and some might be observed as an integral over a unit interval flows this algorithm based on the kalman bucy filter is used to investigate the possibility that previous findings that money granger causes industrial production spuriously arose because time averaged variables were analyzed using discrete time methods

signal extraction for finite nonstationary time series summary for a signal plus noise model where both signal and noise are generated by nonstation ary arima autoregressive integrated moving average models we use the transformation approach of ansley kohn 1985 to construct an estimate of the signal and obtain its mean squared error given a finite number of observations a method for efficient computa tion of the signal estimate and its mean squared error is also presented consider observations z t generated by the signal plus noise nmodel z t s t n t 1s1 where both signal s t and noise n t follow nonstationary arima processes we give a solution to the finite sample signal extraction problem by defining an estimate of the signal s t given observations z 1 z n and finding its mean squared error the major difficulty in handling the model with nonstationary components is that the distribution of the observations is not defined unless assumptions are made about the initial values of the series moreover it is usually very difficult to formulate reasonable assumptions about the initial values because they affect the correlation structure of the whole series see for example the discussion of bell 1984 p 652 kohn ansley 1986 use a transformation approach to overcome the initial value problem in defining the likelihood and obtaining predittors and interpolators for an arima model which may have missing values this approach does not require any assumptions about the initial values and generalizes the usual differencing approach of box jenkins 1976 for the case where there are no missing observations in the present paper we apply the transformation approach of kohn ansley 1986 and ansley kohn 1985 to solve the signal extraction problem we define a linear estimator a t of s t so that s t sa t is invariant to the initial values and furthermore is unbiased in the sense that e s t s t 0 moreover it has minimum mean squared error amongst all such estimators our approach allows missing observations and extends to signal extraction for several additive signals when each is an arima process we also show how to compute the signal estimate and its mean squared error efficiently by writing the model in state space form placing a diffuse prior on the initial values of the process and then using the modified kalman filter and the modified smoothing algorithm of ansley kohn 1985 and kohn ansley 1986 gersch kitagawa 1983 kitagawa gersch 1984 and harvey todd 1983 use

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

the performance of cross validation and maximum likelihood estimators of spline smoothing parameters abstract an important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter in this article we report on an extensive simulation study that investigates the finite sample performance of generalized cross validation cross validation and marginal likelihood estimators of the smoothing parameter in splines of orders 2 and 3 the performance criterion for both the estimate of the function and its first derivative is measured by the square root of integrated squared error marginal likelihood using splines of degree 5 emerges as an attractive alternative to the other estimators in that it usually outperforms them and is also faster to compute

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

regularization networks fast weight calculation via kalman filtering regularization networks are nonparametric estimators obtained from the application of tychonov regularization or bayes estimation to the hypersurface reconstruction problem their main drawback back is that the computation of the weights scales as o n sup 3 where n is the number of data in this paper we show that for a class of monodimensional problems the complexity can be reduced to o n by a suitable algorithm based on spectral factorization and kalman filtering moreover the procedure applies also to smoothing splines

monotone semiflows in scalar non quasi monotone functional differential equations abstract by introducing a stronger than pointwise ordering conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi monotone typically the maximum delay must be the smaller the more quasi monotonicity is violated the theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations

fully bayesian spline smoothing and intrinsic autoregressive priors summary there is a well known bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors the limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form which we call partially informative normal we derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance components a condition crucial for successful implementation of the gibbs sampler the results apply for fully bayesian smoothing

exact initial kalman filtering and smoothing for nonstationary time series models abstract this article presents a new exact solution for the initialization of the kalman filter for state space models with diffuse initial conditions for example the regression model with stochastic trend seasonal and other nonstationary autoregressive integrated moving average components requires a partially diffuse initial state vector the proposed analytical solution is easy to implement and computationally efficient the exact solution for smoothing is also given missing observations are handled in a straightforward manner all proofs rely on elementary results

benchmarking small area estimators this paper considers benchmarking issues in the context of small area estimation we find optimal estimators within the class of benchmarked linear estimators under linear constraints this extends existing results for external and internal benchmarking and also links the two necessary and sufficient conditions for self benchmarking are found for an augmented model most results of this paper are found using ideas of orthogonal projection copyright 2013 oxford university press

estimation filtering and smoothing in state space models with incompletely specified initial conditions on definit la vraisemblance pour un modele d espace d etats avec des conditions initiales incompletement specifiees par transformation des donnees pour eliminer la dependance sur des conditions non specifiees on etend cette approche pour obtenir des estimations sur les vecteurs d etat les predicteurs et les interpolateurs pour des observations manquantes

estimation and prediction for a class of dynamic nonlinear statistical models abstract a class of nonlinear state space models characterized by a single source of randomness is introduced a special case the model underpinning the multiplicative holt winters method of forecasting is identified maximum likelihood estimation based on exponential smoothing instead of a kalman filter and with the potential to be applied in contexts involving non gaussian disturbances is considered a method for computing prediction intervals is proposed and evaluated on both simulated and real data

nonparametric spline regression with autoregressive moving average errors summary we estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model unknown parameters are estimated by either maximum likelihood cross validation or generalized cross validation by expressing the problem in state space form we obtain 0 n algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross validation functions the finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given

exact likelihood of vector autoregressive moving average process with missing or aggregated data summary this note points out that by using the kalman filter with nonconstant coefficients we can compute the exact likelihood of an autoregressive moving average process observed with noise when some of our observations are either missing or aggregated

fast evaluation of the distribution of the durbin watson and other invariant test statistics in time series regression abstract a method is given for evaluating p values in o n operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals the best known of these is the durbin watson statistic although several others have been discussed in the literature the method is numerically exact in the sense that the user specifies the error tolerance at the outset as with existing exact methods the problem is reexpressed in terms of the distribution function of a single quadratic form in independent normals which is evaluated by numerically inverting its characteristic function existing methods however calculate the characteristic function by reducing the matrix defining the quadratic form to either eigenvalue or tridiagonal form each of which requires o n 3 operations for sample size n whereas the new method uses a modification of the kalman filter to do it in o n operations moreover the new method has minimal storage requiremen

kalman filtering methods for computing information matrices for time invariant periodic and generally time varying varma models and samples abstract under general conditions the inverse sample information matrix can be used to establish a cramer rao lower bound of the covariance matrix of parameter estimates of a model and the inverse asymptotic information matrix is the asymptotic covariance matrix of the parameter estimates the paper does two things first it derives a recursive kalman filtering method for computing exact sample and asymptotic information matrices for time invariant periodic or generally time varying gaussian vector autoregressive moving average varma models and samples second it specializes the recursive method to a nonrecursive method for computing exact asymptotic information matrices for time invariant or periodic varma models and samples

markov chain monte carlo in conditionally gaussian state space models summary a bayesian analysis is given for a state space model with errors that are finite mixtures of normals and with coefficients that can assume a finite number of different values a sequence of indicator variables determines which components the errors belong to and the values of the coefficients the computation is carried out using markov chain monte carlo with the indicator variables generated without conditioning on the states previous approaches use the gibbs sampler to generate the indicator variables conditional on the states in many problems however there is a strong dependence between the indicator variables and the states causing the gibbs sampler to converge unacceptably slowly or even not to converge at all the new sampler is implemented in o n operations where n is the sample size permitting an exact bayesian analysis of problems that previously had no computationally tractable solution we show empirically that the new sampler can be much more efficient than previous approaches and illustrate its applicability to robust nonparametric regression with discontinuities and to a time series change point problem

a bayesian approach to state space multivariate time series modeling abstract time series modeling is mainly a model specification exercise recognizing this fact a new bayesian procedure is developed that takes full advantage of the subjective probability foundations of the bayesian approach allowing logical consistency in the face of an unknown model the computational demands of this new procedure have been greatly reduced relative to earlier techniques through the application of linear systems theory linear systems theory substitutes a formal model approximation based on the rank of an autocovariance matrix of the time series for the more arbitrary model selection processes of some other procedures this formalization ensures that the most important elements of the series dynamics are included in the model model selection procedures and an approach to the construction of optimal composite forecasts are derived using bayesian methodologies two empirical applications demonstrate the tractability and the accuracy of the new procedure

new generic quasi convergence principles with applications in this paper essentially strongly order preserving and conditionally set condensing semiflows are considered obtained is a new type of generic quasi convergence principles implying the existence of an open and dense set of stable quasi convergent points when the state space is order bounded the generic quasi convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations giving some results of theoretical and practical significance

global properties of a general dynamic model for animal diseases a case study of brucellosis and tuberculosis transmission abstract animal diseases such as brucellosis and tuberculosis can be transmitted through an environmentally mediated mechanism but the topics of most modeling work are based on infectious contact and direct transmission which leads to the limited understanding of the transmission dynamics of these diseases in this paper we propose a new deterministic model which incorporates general incidences various stages of infection and a general shedding rate of the pathogen to analyze the dynamics of these diseases under the biologically motivated assumptions we derive the basic reproduction number r 0 show the uniqueness of the endemic equilibrium and prove the global asymptotically stability of the equilibria some specific examples are used to illustrate the utilization of our results in addition we elaborate the epidemiological significance of these results which are very important for the prevention and control of animal diseases

fixed interval estimation in state space models when some of the data are missing or aggregated summary ansley kohn s 1982 geometrical derivation of the kalman filter fixed interval smoothing algorithm is extended to the case where some of the observations are missing or aggregated and the state covariance matrix may be singular estimates of missing observations are also obtained the theory is then applied to the interpolation of missing data in multivariate autoregressive moving average models

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

spatial spread of rabies revisited influence of age dependent diffusion on nonlinear dynamics we consider the spatio temporal patterns of disease spread involving structured populations we start with a general model framework in population biology and spatial ecology where the individual s spatial movement behaviors depend on its maturation status and we show how delayed reaction diffusion equations with nonlocal interactions arise naturally we then consider the impact of this delayed nonlocal interaction on the disease spread by revisiting the spatial spread of rabies in continental europe during the period between 1945 and 1985 we show how the distinction of territorial patterns between juvenile and adult foxes the main carriers of the rabies under consideration yields a class of partial differential equations involving delayed and nonlocal terms that are implicitly defined by a hyperbolic parabolic equation and we show how incorporating this distinction into the model leads to a formula describing the relation of the minimal wave speed and the maturation time of foxes we show how the ho

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

qualitative analysis of a prey predator model with stage structure for the predator in this paper we propose a diffusive prey predator model with stage structure for the predator we first analyze the stability of the nonnegative steady states for the reduced ode system and then study the same question for the corresponding reaction diffusion system with homogeneous neumann boundary conditions we find that a hopf bifurcation occurs in the ode system but no turing pattern happens in the reaction diffusion system however when a natural cross diffusion term is included in the model we can prove the emergence of stationary patterns i e nonconstant positive stationary solutions for this system moreover these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion

stage structured models of intra and inter specific competition within age classes abstract in some species larvae and adults experience competition in completely different ways simple stage structured models without larval competition usually yield a single delay equation for the adults using an age structured system incorporating competition among both larvae and adults we derive a system of distributed delay equations for the numbers of larvae and adults the system is neither cooperative nor reducible to a single equation for either variable positivity boundedness and uniform strong persistence are established linear stability analysis of equilibria is difficult due to the strong coupling but results are proved for small delays using monotone systems theory and exponential ordering for small delay we prove a theorem on generic convergence to equilibria which does not directly follow from standard theory but can be proved indirectly using comparison arguments finally we consider an extension to two strain competition and prove theorems on the linear stability of the boundary equilibria

a signal extraction approach to the estimation of treatment and control curves abstract suppose that the response of a group of subjects which we call the control group is monitored over time at a given time after the start of the experiment the experimenter intervenes and applies a treatment to a subset of the group we propose a signal extraction approach to the simultaneous estimation of the treatment and control mean response curves and their rates of change imposing a smooth transition constraint between the two curves at the time of intervention by expressing the model in state space form we show how to compute the likelihood and the cross validation function efficiently in o n operations together with the response curve estimates and their standard errors we also show that the curve estimates are solutions to a penalized least squares problem a small simulation study to assess the performance of the generalized cross validation and marginal likelihood estimates of the smoothing parameter is carried out and the methodology in the article is applied to an experiment

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

fast likelihood evaluation and prediction for nonstationary state space models summary a recursive procedure for initializing the kalman filter is displayed the recursion is for nonstationary state space models the procedure imposes small computational and programming burden over and above the kalman filter the procedure is superior to other suggested approaches in both computational speed and general applicability general properties of the method are investigated details of the initialization for the arima p d q and basic structural models are considered

forecasting time series with complex seasonal patterns using exponential smoothing an innovations state space modeling framework is introduced for forecasting complex seasonal time series such as those with multiple seasonal periods high frequency seasonality non integer seasonality and dual calendar effects the new framework incorporates box cox transformations fourier representations with time varying coefficients and arma error correction likelihood evaluation and analytical expressions for point forecasts and interval predictions under the assumption of gaussian errors are derived leading to a simple comprehensive approach to forecasting complex seasonal time series a key feature of the framework is that it relies on a new method that greatly reduces the computational burden in the maximum likelihood estimation the modeling framework is useful for a broad range of applications its versatility being illustrated in three empirical studies in addition the proposed trigonometric formulation is presented as a means of decomposing complex seasonal time series and it is show

longitudinal data analysis for linear gaussian models with random disturbed highest derivative polynomial subject effects for linear regression analysis of longitudinal data with gaussian response i propose a new model to generalize the traditional class of random effects models in which the random effects are deterministic polynomials with coefficients randomly distributed over subjects with mean zero the generalization is accomplished by adding zero mean gaussian disturbances to the highest derivative of each random coefficient subject polynomial independently at each observation time the resulting random effects which have mean zero at each observation time are called disturbed highest derivative polynomials dhdps the disturbances induce serial correlation and also allow the subject specific dhdp time trends to be non linear i do not estimate the subject specific dhdp time trends analysis is based on the marginal model that is the fixed effects or population model obtained by integrating the random polynomial coefficients and all disturbances out of the joint distribution of themselves and the response vector this allows a population averaged interpretation one can select the dhdp order by an information criterion when the population time trend is not correctly modelled the optimal dhdp order will be larger than when it is correctly modelled one can make the covariance matrix of the regression coefficients robust to errors in modelling the within subject dependence i describe the relationship of a dhdp to a smoothing polynomial spline and show how to replace the dhdp model with a smoothing polynomial spline model for the within subject dependence in the marginal model

convergence in smooth strongly monotone flows defined by semilinear parabolic equations on considere des equations paraboliques semi lineaires dy dt ay f y ou a est un operateur sectoriel sur un banach x ayant une resolvante compacte et f est une c 2 application de l espace des puissances fractionnaires x 0 1 dans x soit y t une solution qui est quasi convergente mais non convergente alors il existe un voisinage u de y 0 y 0 avec la propriete suivante si z u y 0 a une trajectoire bornee et soit z y 0 soit z y 0 alors la solution partant de z converge vers un equilibre

a signal extraction approach to modeling hormone time series with pulses and a changing baseline abstract hormones serve as regulating signals for many biological processes in recent years it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern in addition to the absolute concentration level is important in regulating biological processes consequently it is necessary to characterize the latent secretion patterns from measurements of concentration levels the characterization is complicated by the presence of a biological circadian rhythm when hormone concentrations are plotted over time the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline this is a result of a mixture of pulsatile secretions and a circadian rhythm in this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series a smoothing spline is used to model the baseline and a multiprocess dynamic linear model is used to model the pulsati

on the periodic solutions of periodic multi species competitive systems with delays the paper considers general n species periodic kolmogorov competitive systems of functional differential equations with finite or infinite delays applying schauder s fixed point theorem a criterion on the existence of the positive periodic solutions is established as applications the existence and global asymptotic stability of the single species logistic periodic model and n species lotka volterra type periodic model with delays are discussed