short note a new minimum storage runge kutta scheme for computational acoustics a new fourth order six stage runge kutta numerical integrator that requires 2n storage n is the number of degrees of freedom of the system with low dissipation and dispersion and a relatively large stability interval is proposed these features make it a suitable time advancing method for solving wave propagation problems in computational acoustics some numerical experiments are presented to show the favourable behaviour of the new scheme as compared with the ldd46 and ldd25 methods proposed by stanescu and habashi j comput phys 143 1998 674 and the standard fourth order runge kutta method

mixed effects nonlinear regression for unbalanced repeated measures repeated measures data such as clinical pharmacokinetic data growth data and dose response data are often inherently nonlinear with respect to a given response function and are frequently incomplete and or unbalanced nonlinear random effects models together with a variety of estimation procedures have been proposed for the analysis of such data this paper is concerned with a straightforward procedure for estimating and comparing the parameters of a generalized mixed effects nonlinear regression model the asymptotic properties of the proposed estimators are given and large sample tests of hypothesis provided the results are applied to in vitro data on the water transport kinetics of hemodialyzers used in the treatment of patients with chronic renal failure

evaluating decision rules for nitrogen fertilization it is important both for farmer profit and for the environment to correctly dose nitrogen fertilizer for crop growth fertilizer recommendations are embodied in decision rules which give a recommended dose of nitrogen n as a function of information available at the time the decision is made in this paper we first propose a criterion for evaluating decision rules the proposed criterion is the expectation of the objective function when the decision rule is implemented the major problem here is the estimation of this criterion two estimators are considered a model based and a nonparametric estimator a simulation study shows that in essentially all cases the nonparametric estimator is better or no worse than the model based estimator the bias in the nonparametric estimator is always very small

canonical euler splitting method for nonlinear composite stiff evolution equations in this paper a new splitting method called canonical euler splitting method ces is constructed and studied which can be used for the efficient numerical solution of general nonlinear composite stiff problems in evolution equations of various type such as ordinary differential equations odes semi discrete unsteady partial differential equations pdes and ordinary or partial volterra functional differential equations vfdes and can significantly improve the computing speed on the basis of ensuring the computing quality stability consistency and convergence theories of this method are established a series of numerical experiments are given which check the efficiency of ces method and confirm our theoretical results

runge kutta methods for hyperbolic conservation laws with stiff relaxation terms underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well resolved we design a second order runge kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit which thus is able to capture the correct physical behaviors with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved

comparing linear and nonlinear mixed model approaches to cosinor analysis the cosinor model used for variables governed by circadian and other biological rhythms is a nonlinear model in the amplitude and acrophase parameters that has a linear representation upon transformation with linear cosinor analysis amplitude and acrophase for each harmonic can be computed as nonlinear functions of the estimated linear regression coefficients here a flexible mixed model approach to cosinor analysis is considered where the fixed effect parameters may enter nonlinearly as acrophase and amplitude for each harmonic or linearly after transformation to regression coefficients in addition the random effects may enter nonlinearly as subject specific deviations from the acrophases and amplitudes or linearly as subject specific deviations from the regression coefficients it is also possible for the fixed effects to enter nonlinearly while the random effects enter linearly additionally we evaluate whether including higher order linear harmonic terms as random effects that is rao khatri covariance adjustment improves precision applying the delta method to nonlinear functions of the parameters from linear mixed cosinor models to obtain approximate variances produces results that are often identical to results from nonlinear mixed models consequently traditional linear cosinor analysis can often be used to estimate and compare the nonlinear parameters of interest that is amplitudes and acrophases via the delta method this is advantageous since the nonlinear mixed model may have convergence difficulties for more complex models however for some multiple group analyses the linear cosinor transformation should not be used and we clarify when the two methods are equivalent and when they differ

dynamical behavior of an epidemic model with a nonlinear incidence rate abstract in this paper we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action by carrying out global qualitative and bifurcation analyses it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region when such a region exists it is shown that the model undergoes a bogdanov takens bifurcation i e it exhibits a saddle node bifurcation hopf bifurcations and a homoclinic bifurcation existence of none one or two limit cycles is also discussed

additive and iterative operator splitting methods and their numerical investigation as an alternative to the classical splitting methods two new splitting schemes have been developed recently the additive and the iterative splitting in this paper we discuss the most important properties the advantages and disadvantages of these schemes and investigate their performance on simple examples as well as on more complex physical models

a general approach for two stage analysis of multilevel clustered non gaussian data in this article we propose a two stage approach to modeling multilevel clustered non gaussian data with sufficiently large numbers of continuous measures per cluster such data are common in biological and medical studies utilizing monitoring or image processing equipment we consider a general class of hierarchical models that generalizes the model in the global two stage gts method for nonlinear mixed effects models by using any square root n consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model and by extending the stage 2 model to accommodate random effects from multiple levels of clustering the second stage model is a standard linear mixed effects model with normal random effects but the cluster specific distributions conditional on random effects can be non gaussian this methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest for estimation of the population parameters we propose a conditional restricted maximum likelihood creml approach and establish the asymptotic properties of the creml estimators the proposed general approach is illustrated using quartiles as cluster specific parameters estimated in the first stage and applied to the data example from a collagen fibril development study we demonstrate using simulations that in samples with small numbers of independent clusters the creml estimators may perform better than conditional maximum likelihood estimators which are a direct extension of the estimators from the gts method

anticommutator analogues of certain identities involving repeated commutators the generalization of the baker hausdorff lemma and its anticommutator analogue is formulated additionally the anticommutator analogues of several well known operator identities involving repeated commutators are derived it is pointed out that these are more convenient for application whenever the operators in question satisfy simpler repeated anticommutator relations and in particular when they anticommute than the repeated commutator relations the diagonalization of two spin 1 hamiltonians in which the anticommutator analogue of the baker hausdorff lemma is used to good advantage is presented

goodness of fit in generalized nonlinear mixed effects models in recent years generalized linear and nonlinear mixed effects models have proved to be powerful tools for the analysis of unbalanced longitudinal data to date much of the work has focused on various methods for estimating and comparing the parameters of mixed effects models very little work has been done in the area of model selection and goodness of fit particularly with respect to the assumed variance covariance structure in this paper we present a goodness of fit statistic which can be used in a manner similar to the r2 criterion in linear regression for assessing the adequacy of an assumed mean and variance covariance structure in addition we introduce an approximate pseudo likelihood ratio test for testing the adequacy of the hypothesized convariance structure these methods are illustrated and compared to the usual normal theory likelihood methods akaike s information criterion and the likelihood ratio test using three examples simulation results indicate the pseudo likelihood ratio test compares favorably with the standard normal theory likelihood ratio test but both procedures are sensitive to departures from normality

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

space time domain decomposition for parabolic problems we analyze a space time domain decomposition iteration for a model advection diffusion equation in one and two dimensions the discretization of this iteration is the block red black variant of the waveform relaxation method and our analysis provides new convergence results for this scheme the asymptotic convergence rate is super linear and it is governed by the diffusion of the error across the overlap between subdomains hence it depends on both the size of this overlap and the diffusion coefficient in the equation however it is independent of the number of subdomains provided the size of the overlap remains fixed the convergence rate for the heat equation in a large time window is initially linear and it deteriorates as the number of subdomains increases the duration of the transient linear regime is proportional to the length of the time window for advection dominated problems the convergence rate is initially linear and it improves as the the ratio of advection to diffusion increases moreover it is independent of the size of the time window and of the number of subdomains numerical calculations illustrate our analysis

design in nonlinear mixed effects models optimization using the fedorov wynn algorithm and power of the wald test for binary covariates we extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi exponential model we first show the relevance of the predicted standard errors ses given by the computation of the population fisher information matrix using the r function pfim in comparison to those computed with the stochastic approximation expectation maximization algorithm implemented in the monolix software we then highlight the usefulness of the fedorov wynn fw algorithm for designs optimization compared to the simplex algorithm from the predicted se of pfim we compute the predicted power of the wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power using the fw algorithm we investigate the influence of the design on the power and show that for optimized designs with the same total number of samples the power increases when the number of subjects increases and the number of samples per subject decreases a simulation study is also performed with the nlme function of r to confirm this result and show the relevance of the predicted powers compared to those observed by simulation

a mollification based operator splitting method for convection diffusion equations the main goal of this paper is to show that discrete mollification is a suitable ingredient in operator splitting methods for the numerical solution of nonlinear convection diffusion equations in order to achieve this goal we substitute the second step of the operator splitting method of karlsen and risebro 1997 1 for a mollification step and prove that the convergence features are fairly well preserved we end the paper with illustrative numerical experiments

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

operator spltting methods for systems of convection diffusion equations nonlinear error mechanisms and correction strategies abstract many numerical methods for systems of convection diffusion equations are based on an operator splitting formulation where convective and diffusive forces are accounted for in separate substeps we describe the nonlinear mechanism of the splitting error in such numerical methods in the one dimensional case a mechanism that is intimately linked to the local linearizations introduced implicitly in the hyperbolic convection steps by the use of an entropy condition for convection dominated flows we demonstrate that operator splitting methods typically generate a numerical widening of viscous fronts unless the splitting step is of the same magnitude as the diffusion scale to compensate for the potentially damaging splitting error we propose a corrected operator splitting cos method for general systems of convection diffusion equations with the ability of correctly resolving the nonlinear balance between the convective and diffusive forces in particular cos produces viscous shocks with a correct structure also when the splitting step is large a front tracking method for systems of conservation laws which in turn relies heavily on a riemann solver constitutes an important part of our cos strategy the proposed cos method is successfully applied to a system modeling two phase multicomponent flow in porous media and a triangular system modeling three phase flow

analysis of operator splitting for advection diffusion reaction problems from air pollution modelling abstract operator or time splitting is often used in the numerical solution of initial boundary value problems for differential equations it is for example standard practice in computational air pollution modelling where we encounter systems of three dimensional time dependent partial differential equations of the advection diffusion reaction type for such systems little attention has been devoted to the analysis of splitting and to the question why splitting can work so well from the theoretical point of view the success of splitting is primarily determined by the splitting error this paper presents an analysis of operator splitting aimed at providing insight into the splitting error using the lie operator formalism a general expression is derived for a three term strang splitting in the pure initial value case for a class of advection diffusion reaction problems the splitting error is analyzed in greater detail a special case is discussed in which the splitting error can be reduced also some attention is paid to the use of operator splitting in initial boundary value problems

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

stability of the richardson extrapolation applied together with the θ method consider a system of ordinary differential equations odes dy dt f t y where a t a b with b a b y is a vector containing s components and c y a is given the q method is applied to solve approximately the system of odes on a set of prescribed grid points if n is the number of time steps that are to be carried out then this numerical method can be defined using the following set of relationships y n y n 1 h 1 q f t n 1 y n 1 h qf t n y n q 0 5 1 0 n 1 2 n h b a n t n t n 1 h t 0 nh t 0 a t n b as a rule the accuracy of approximations y n n 1 2 n can be improved by applying the richardson extrapolation under the assumption that the stability of the computational process is preserved therefore it is natural to require that the combined numerical method richardson extrapolation the q method is in some sense stable it is proved in this paper that the combined method is strongly a stable when q 2 3 1 0 it is furthermore shown that some theorems proved in a previous paper by the same authors farago et al 2009 1 are simple corollaries of the main result obtained in the present work the usefulness of the main result in the solution of many problems arising in different scientific and engineering areas is demonstrated by performing a series of tests with an extremely badly scaled and very stiff atmospheric chemistry scheme which is actually used in several well known large scale air pollution models

optimized explicit finite difference schemes for spatial derivatives using maximum norm we propose an optimized scheme using the maximum norm and the simulated annealing the maximum norm offers the largest set of possible solutions for solvers to search the explicit finite difference operator is greatly improved by our optimized scheme we use a tight error limitation to make accuracy improvement to be high and solid our optimized scheme allows greater saving of computational cost and memory demand conventional explicit finite difference methods have difficulties in handling high frequency components due to strong numerical dispersions one can reduce the numerical dispersions by optimizing the constant coefficients of the finite difference operator different from traditional optimized schemes that use the 2 norm and the least squares we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing algorithm both theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three aspects first it provides us with much more flexibility when designing the objective functions thus we can use various possible forms and contents to make the objective functions more reasonable second it allows for tighter error limitation which is shown to be necessary to avoid rapid error accumulations for simulations on large scale models with long travel times finally it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits which means greater savings in computational efforts and memory demand

bayesian approach for a nonlinear growth model nonlinear least squares methods are currently used for fitting a well known growth model namely the jenss model to the length measurements of a child followed throughout the first six years of life an empirical bayes approach is developed for fitting the model and the prior distribution of the growth model parameters is estimated from a large sample of least squares parameters an expression which is proportional to the posterior distribution is derived so that the posterior mode can be estimated given the observations on a child this posterior mode provides bayes estimates of the jenss curve parameters for the child

a noumerov type method with minimal phase lag for the integration of second order periodic initial value abstract in a recent paper 2 we gave a noumerov type method with minimal phase lag for the integration of second order initial value problems y f t y y t0 y0 y t0 y 0 however the method given there is implicit we show here the interesting result that if the noumerov type methods of 2 are made explicit with the help of the classical second order method then there exists a selection of the free parameter for which the resulting method has a considerably small frequency distortion of size 1 40320 h 6 and also a slightly larger interval of periodicity of size 2 75 than the phase lag of size 1 12096 h 6 and interval of periodicity of size 2 71 for the implicit method 2 more interestingly it turns out that noumerov made explicit of chawla 3 also has less frequency distortion than the implicit noumerov method we shall assume a familiarity with the notation and discussion given in 2

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

convergence of operator splittings for locally lipschitz continuous operators in banach spaces operator splitting is analyzed in the general framework of banach spaces the convergence of sequential splitting and additive splitting is proven for problems with locally lipschitz continuous operators suitable time step size is calculated from the size of the set where the lipschitz property holds numerical examples are presented to confirm the theoretical results

a note on iterated splitting schemes iterated splittings seem attractive in view of consistency and local accuracy in this note it will be shown however that for stiff systems the stability properties are quite poor specific runge kutta implementations can improve stability but this leads to classes of methods that are better studied in their own right

an operator splitting method for nonlinear convection diffusion equations we present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection diffusion equation u t nabla cdot vec f u varepsilon delta u the method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation in the case m 1 dimensional splitting is used to reduce the m dimensional convection problem to a series of one dimensional problems we show that the method produces a compact sequence of approximate solutions which converges to the exact solution finally a fully discrete method is analyzed and demonstrated in the case of one and two space dimensions

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

richardson extrapolated sequential splitting and its application during numerical time integration the accuracy of the numerical solution obtained with a given step size often proves unsatisfactory in this case one usually reduces the step size and repeats the computation while the results obtained for the coarser grid are not used however we can also combine the two solutions and obtain a better result this idea is based on the richardson extrapolation a general technique for increasing the order of an approximation method this technique also allows us to estimate the absolute error of the underlying method in this paper we apply richardson extrapolation to the sequential splitting and investigate the performance of the resulting scheme on several test examples

uncertainty propagation using infinite mixture of gaussian processes and variational bayesian inference uncertainty propagation in flow through porous media problems is a challenging problem this is due to the high dimensionality of the random property fields e g permeability and porosity as well as the computational complexity of the models that are involved the usual approach is to construct a surrogate response surface and then use it instead of the expensive model to carry out the uncertainty propagation task however the construction of the surrogate surface is hampered by various aspects such as the limited number of model evaluations that one can afford the curse of dimensionality multi variate responses with non trivial correlations potential localized features of the response and or discontinuities in this work we extend upon the concept of the multi output gaussian process mgp to effectively deal with all of these difficulties simultaneously this non trivial extension involves an infinite mixture of mgp s that is trained using variational bayesian inference prior to observing any data a dirichlet process is used to generate the components of the mgp mixture the bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations i e we can derive error bars for the statistics of interest the automatic detection of the mixture components by the variational inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions finally correlations between the components of multi variate responses are captured by the underlying mgp model in a natural way

qualitative study of a stochastic sirs epidemic model with information intervention abstract in this paper we consider a stochastic sirs epidemic model with information intervention first of all the existence and uniqueness of the global positive solution are obtained then we derive sufficient conditions for the extinction and persistence of the disease moreover by establishing appropriate lyapunov function the existence of a stationary distribution is discussed some numerical simulations are given to illustrate our analytical results

runge kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics in this paper a new runge kutta method with minimal dispersion and dissipation error is developed the chebyshev pseudospectral method is utilized using spatial discretization and a new fourth order six stage runge kutta scheme is used for time advancing the proposed scheme is more efficient than the existing ones for acoustic computations

on richardson extrapolation for low dissipation low dispersion diagonally implicit runge kutta schemes abstract in the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate but also properly describe the amplitude and phase of the propagating waves it is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation dispersion and stability analysis it is illustrated that the combination of various optimized schemes with richardson extrapolation is not optimal for minimal dissipation and dispersion errors optimized third order and fourth order methods are obtained and it is shown that the proposed methods combined with richardson extrapolation result in fourth and fifth orders of accuracy correspondingly while preserving optimality and stability the numerical applications include the linear wave equation a stiff system of reaction diffusion equations and the nonlinear euler equations with oscillatory initial conditions it is demonstrated that the extrapolated third order scheme outperforms the recently developed fourth order diagonally implicit runge kutta scheme in terms of accuracy and stability

ergodic stationary distribution and extinction of a stochastic sirs epidemic model with logistic growth and nonlinear incidence abstract a stochastic sirs model with logistic growth and nonlinear incidence rate is probed in this paper we exemplify that the proposed stochastic sirs model reveals a global and positive solution by applying suitable lyapunov functions the sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic sirs model are derived furthermore we acquire the sufficient conditions for extinction of the infectious disease

operator splitting for chemical reaction systems with fast chemistry abstract splitting methods are frequently used for large scale chemical reaction systems the main reason is the reduced computational cost for solving the subproblems in comparison to the time integration of the full problem however a splitting error is introduced the most popular splitting schemes are the first order lie trotter splitting and the second order strang splitting however in case of stiff differential equations the strang splitting suffers from order reduction and both schemes have order one for stiff differential equations therefore the step size restrictions due to the low order can result in a prohibitive small step size hence splitting schemes with order larger than one are necessary for stiff differential equations the richardson extrapolation of the lie trotter splitting is a second order scheme in this paper we examine differential equations with a fast chemical source term and a slow transport term thus all stiffness of the system is related to the chemical source term we show that the richardson extrapolation does not suffer from order reduction in this case furthermore we perform a stability analysis of the extrapolated splitting scheme for a linear test problem thereby the operators of the test problem do not commute

high order low dissipation low dispersion diagonally implicit runge kutta schemes high order low dissipation low dispersion diagonally implicit runge kutta schemes are analyzed and introduced based on the optimization of amplification and phase errors for wave propagation various optimized schemes can be obtained the new scheme shows negligible dissipation it is illustrated mathematically and numerically that the new scheme preserves fourth order accuracy while the recently developed diagonally implicit runge kutta scheme does not the numerical applications contain the advection equation with and without a stiff nonlinear source term and an oscillatory test the new scheme is a stable as desired for the solution of stiff problems

random effects and variances as a synthesis of nonlinear regression analyses of mitochondrial electron transport summary this cross disciplinary paper develops random effects and variances methods especially for small samples within effects and applies them to mitochondrial enzyme kinetics a new force flux kinetic model is introduced for the alternative oxidase of plant mitochondria the results of 42 experiments are published and the force flux function is fitted by nonlinear regression for each experiment the results of the regression analyses are synthesized by a random effects model specifying random nonlinear regression coefficients and random variances within experiments distributed in an inverse gamma distribution the paper shows how random nonlinear regression coefficients analysis can summarize the results of a long series of similar biological experiments and sharpen the analysis of the results of each a large data set often consists of a family of components each of which can be fitted with the same model there is a within component variation for each compo nent and random effects variation between components the interpretation of the data requires not only regression analysis of each component but also a subsequent synthesis of the results of such analysis into an overall summary achieved by specifying random regression coefficients and random error variances in the example which follows the individual samples are so small that random variances are specified and contracted predictors of them are computed which are more accurate than the individual estimates they are required for weights in the analysis the residual maximum likelihood estimates of the random effects variance matrices are sometimes singular a lagrange multiplier method is introduced to compute them the strength of the integrated analysis comes however at the price of a complex set of decisions as to how the different components of the computation are to be fitted together the paper shows how this is done by a flow diagram for the computations as well as describing each individual component

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

optimal design in random effects regression models summary an approach is proposed to optimal design of experiments for estimating randomeffects regression models the population designs are defined by the number of subjects and the individual designs to be performed cost functions associated with individual designs are incorporated for a given maximal cost an algorithm is proposed for finding the statistical population design that maximises the determinant of the fisher information matrix of the population parameters the fisher information matrix is formulated for linear models and normal distributions the approach is applied to the design of an optimal experiment in toxicokinetics using a first order linearisation of the model several cost functions and designs of various orders are studied an example illustrates the optimal population designs and the increased efficiency of some optimal designs over more standard designs

a semi implicit mid point rule for stiff systems of ordinary differential equations the paper introduces a new semi implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations the existence of a quadratic asymptotic expansion in terms of the stepsize is shown moreover the new discretization is analyzed in the light of well known stability models the efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples

ergodic stationary distribution of a stochastic sirs epidemic model incorporating media coverage and saturated incidence rate abstract this study investigates the disease dynamics of a sirs epidemic model as affected by environment fluctuations and media coverage a unique global positive solution for the epidemic model is obtained the stochastic endemic dynamics of the system is discussed by constructing suitable lyapunov functions and the ergodic stationary distribution of the stochastic model is established based on the method of khasminskii the extinction of the epidemic disease is also analyzed

implicit solution of the unsteady euler equations for high order accurate discontinuous galerkin discretizations efficient solution techniques for high order accurate time dependent problems are investigated for solving the two dimensional non linear euler equations in this work the spatial discretization consists of a high order accurate discontinuous galerkin dg approach implicit time integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods standard backwards differencing methods bdf1 and bdf2 as well as a second order crank nicholson cn2 and a fourth order implicit runge kutta irk4 scheme are considered in an attempt to balance the spatial and temporal accuracy of the overall approach the implicit system arising at each time step is solved using a p multigrid approach which is shown to produce h independent convergence rates while remaining relatively insensitive to the time step size the crank nicholson methodology although not l stable demonstrates superior performance compared to the bdf2 scheme for the problems chosen in this work however the fourth order accurate implicit runge kutta scheme is found to be the most efficient in terms of computational cost for a given accuracy level as compared to the lower order schemes in spite of the added cost per time step and the benefits of this scheme increase for tighter error tolerances

shape invariant modeling of circadian rhythms with random effects and smoothing spline anova decompositions medical studies often collect physiological and or psychological measurements over time from multiple subjects to study dynamics such as circadian rhythms under the assumption that the expected response functions of all subjects are the same after shift and scale transformations shape invariant models have been applied to analyze this kind of data the shift and scale parameters provide efficient and interpretable data summaries while the common shape function is usually modeled nonparametrically to provide flexibility however due to the deterministic nature of the shift and scale parameters potential correlations within a subject are ignored furthermore the shape of the common function may depend on other factors such as disease in this article we propose shape invariant mixed effects models a second stage model with fixed and random effects is used to model individual shift and scale parameters a second stage smoothing spline anova model is used to study potential covariate effects on the common shape function we apply our methods to a real data set to investigate disease effects on circadian rhythms of cortisol a hormone that is affected by stress we find that patients with cushing s syndrome lost circadian rhythms and their 24 hour means were elevated to very high levels patients with major depression had the same circadian shape and phases as normal subjects however their 24 hour mean levels were elevated and amplitudes were dampened for some patients

multilevel mixed linear model analysis using iterative generalized least squares summary models for the analysis of hierarchically structured data are discussed an iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case there is a discussion of applications to complex surveys longitudinal data and estimation in multivariate models with missing responses an example is given using educational data

operator splitting methods in respect of eigenvalue problems for nonlinear equations and applications for burgers equations in this article we consider iterative operator splitting methods for nonlinear differential equations with respect to their eigenvalues the main focus of the proposed idea is the fixed point iterative scheme that linearizes our underlying equations on the basis of the approximated eigenvalues of such linearized systems we choose the order of the operators for our iterative splitting scheme the convergence properties of such a mixed method are studied and demonstrated we confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator splitting methods by providing improved results and convergence rates we apply our results to deposition processes

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

application of richardson extrapolation for multi dimensional advection equations abstract a crank nicolson type scheme which is of order two with respect to all independent variables is used in the numerical solution of multi dimensional advection equations normally the order of accuracy of any numerical scheme can be increased by one when the well known richardson extrapolation is used it is proved that in this particular case the order of accuracy of the combined numerical method the method consisting of the crank nicolson scheme and the richardson extrapolation is not three but four

corrected operator splitting for nonlinear parabolic equations we present a corrected operator splitting cos method for solving nonlinear parabolic equations of a convection diffusion type the main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps as opposed to a standard operator splitting os which fails to do so cos is based on solving a conservation law for modeling convection a heat type equation for modeling diffusion and finally a certain residual conservation law for necessary correction the residual equation represents the entropy loss generated in the hyperbolic convection step in os the entropy loss manifests itself in the form of too wide shock fronts the purpose of the correction step in cos is to counterbalance the entropy loss so that correct width of nonlinear shock fronts is ensured the polygonal method of dafermos j math anal appl 38 1972 pp 33 41 constitutes an important part of our solution strategy it is shown that cos generates a compact sequence of approximate solutions which converges to the solution of the problem finally some numerical examples are presented where we compare os and cos methods with respect to accuracy

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

accelerated degradation tests modeling and analysis high reliability systems generally require individual system components having extremely high reliability over long periods of time short product development times require reliability tests to be conducted with severe time constraints frequently few or no failures occur during such tests even with acceleration thus it is difficult to assess reliability with traditional life tests that record only failure times for some components degradation measures can be taken over time a relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure time distribution this article describes degradation reliability models that correspond to physical failure mechanisms we explain the connection between degradation reliability models and failure time reliability models acceleration is modeled by having an acceleration model that describes the effect that temperature or another accelerating variable has on

regional optimization of fertilization using a hierarchical linear model utilization of regional data for optimizing fertilizer strategy is considered it is argued that a hierarchical mixed effects model is a reasonable parsimonious way to model the data such models take into account the correlations between yield responses at the same site also they conveniently let one model the differences between years or between sites as a function of year and site characteristics we specifically develop the case of a linear in the parameters response model but hierarchical models could also be based on nonlinear response functions given the estimated parameters the calculation of an optimal fertilizer strategy which depends on the site and year characteristics is usually straightforward a number of measures of the quality of this strategy are proposed among these are the risk which measures yield loss caused by using estimated rather than true parameter values another measure of interest is the potential gain from having a model that explains all the between year or all the between site variability the effect of potassium on sown prairies in france is treated as an example

high order embedded runge kutta formulae abstract the criteria to be satisfied by embedded runge kutta pairs of formulae are reviewed two new formulae of orders 6 and 8 are presented together with tests on their efficiency relative to other high order formulae in current use

an analysis of operator splitting techniques in the stiff case operator splitting methods are commonly used in many applications we focus here on the case where the evolution equations to be simulated are stiff we will more particularly consider the case of two operators a stiff one and a nonstiff one this occurs in numerous application fields e g combustion air pollution and reactive flows the classical analysis of the splitting error may then fail since the chosen splitting timestep t is in practice much larger than the fastest time scales the asymptotic expansion t 0 is therefore no longer valid we show here that singular perturbation theory provides an interesting framework for the study of splitting error some new results concerning the order of local errors are derived the main result deals with the choice of the sequential order for the operators the stiff operator must always be last in the splitting scheme

evaluation by simulation of tests based on non linear mixed effects models in pharmacokinetic interaction and bioequivalence cross over trials we propose tests based on non linear mixed effects models nlmem in pharmacokinetic interaction and bioequivalence cross over trials comparing two treatments or two formulations to compare the logarithm of the area under the curve auc using these models two approaches are studied in the first one concentration data are analysed globally with and without the estimation of a treatment effect and in the second one they are analysed separately in each treatment group with the estimation of the individual parameters four tests for comparison of the logarithm auc between two treatment arms are studied a likelihood ratio test lrt a wald test and two tests parametric and non parametric comparing the individual empirical bayes eb estimates these tests are adapted to the case of equivalence except the lrt which does not have any simple extension we evaluate by simulation of the type i error and the power for both comparison and equivalence tests they are compared to the standard tests recommended by the fda and the emea based on non compartmental nc auc trials for a usual pk model are simulated under h0 and several h1 using s plus software and analysed with the nlme function different configurations of the number of subjects n 12 24 and 40 and of the number of samples per subject j 10 5 and 3 are studied the type i error of lrt and wald comparison test in the 5000 replications of interaction cross over trials is found to be 20 9 per cent and 21 7 per cent respectively in the original design n 12 j 10 which is far superior to 5 per cent and decreases when n increases when n is fixed is found to increase with j power is satisfactory for both tests after correction of the significance threshold results of eb and nc tests are similar with satisfactory powers and a type i error close to 5 per cent except when j 3 for eb tests similar results are obtained for equivalence tests except for eb and nc student tests which are not of a great interest nc tests keep their place when the number of samples per subject j is large but nlmem seem useful for cross over studies performed in special populations where j limited the evaluation by monte carlo simulations of empirical threshold seems however necessary because of the inflation of the type i error copyright 2005 john wiley sons ltd

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

a relative off set orthogonality convergence criterion for nonlinear least squares an orthogonality convergence criterion using relative offset is proposed this criterion is compared to currently used criteria and its advantages are discussed

models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

linear and nonlinear mixed effects models for censored hiv viral loads using normal independent distributions summary hiv rna viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays hence the responses are either left or right censored linear and nonlinear mixed effects models with modifications to accommodate censoring are routinely used to analyze this type of data and are based on normality assumptions for the random terms however those analyses might not provide robust inference when the normality assumptions are questionable in this article we develop a bayesian framework for censored linear and nonlinear models replacing the gaussian assumptions for the random terms with normal independent ni distributions the ni is an attractive class of symmetric heavy tailed densities that includes the normal student s t slash and the contaminated normal distributions as special cases the marginal likelihood is tractable using approximations for nonlinear models and can be used to develop bayesian case deletion influence diagnostics based on the kullback leibler divergence the newly developed procedures are illustrated with two hiv aids studies on viral loads that were initially analyzed using normal censored mixed effects models as well as simulations

iterative operator splitting methods with higher order time integration methods and applications for parabolic partial differential equations in this paper we design higher order time integrators for systems of stiff ordinary differential equations we combine implicit runge kutta and bdf methods with iterative operator splitting methods to obtain higher order methods the idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently we compare our new methods with the higher order fractional stepping runge kutta methods developed for stiff ordinary differential equations the benefit is the individual handling of each operator with adapted standard higher order time integrators the methods are applied to equations for convection diffusion reactions and we obtain higher order results finally we discuss the applications of the iterative operator splitting methods to multi dimensional and multi physical problems

persistence and extinction for a class of stochastic sis epidemic models with nonlinear incidence rate abstract in this paper a class of stochastic sis epidemic models with nonlinear incidence rate is investigated it is shown that the extinction and persistence of the disease in probability are determined by a threshold value r 0 that is if r 0 1 and an additional condition holds then disease dies out and if r 0 1 then disease is weak permanent with probability one to obtain the permanence in the mean of the disease a new quantity r 0 is introduced and it is proved that if r 0 1 the disease is permanent in the mean with probability one furthermore the numerical simulations are presented to illustrate some open problems given in remarks 1 3 and 5 of this paper

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

efficient implementation of stable richardson extrapolation algorithms richardson extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations odes obtained by different numerical methods including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods some stability results related to two implementations of the richardson extrapolation active richardson extrapolation and passive richardson extrapolation are formulated and proved in this paper an advanced atmospheric chemistry scheme which is commonly used in many well known operational environmental models is applied in a long sequence of experiments in order to demonstrate the fact that a it is indeed possible to improve the accuracy of the numerical results when the richardson extrapolation is used also when very difficult badly scaled and stiff non linear systems of odes are to be treated b the computations can become unstable when the combination of the trapezoidal rule and the active richardson extrapolation is used c the application of the active richardson extrapolation with the backward euler formula is leading to a stable computational process d experiments with different algorithms for solving linear systems of algebraic equations are very useful in the efforts to select the most suitable approach for the particular problems solved and e the computational cost of the richardson extrapolation is much less than that of the underlying numerical method when a prescribed accuracy has to be achieved

a stochastic sis epidemic model incorporating media coverage in a two patch setting in this paper we investigate the stochastic disease dynamics of an sis epidemic model on two patches incorporating media coverage we give the global existence and positivity of the solutions and the sufficient conditions for almost surely exponentially stability of the disease free equilibrium which means that the disease will be stochastic extinction furthermore we perform some numerical simulations to validate the analytical finding

the convergence of diagonally implicit runge kutta methods combined with richardson extrapolation runge kutta methods are widely used in the solution of systems of ordinary differential equations richardson extrapolation is an efficient tool for enhancing the accuracy of time integration schemes in this paper we investigate the convergence of the combination of any of the diagonally implicit including also the explicit runge kutta methods with active richardson extrapolation and show that the numerical solution obtained converges under rather natural conditions

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

a case study in exploratory functional data analysis geometrical features of the internal carotid artery this pilot study is a product of the aneurisk project a scientific program that aims at evaluating the role of vascular geometry and hemodynamics in the pathogenesis of cerebral aneurysms by means of functional data analyses we explore the aneurisk dataset to highlight the relations between the geometric features of the internal carotid artery expressed by its radius profile and centerline curvature and the aneurysm location after introducing a new similarity index for functional data we eliminate ancillary variability of vessel radius and curvature profiles through an iterative registration procedure we then reduce data dimension by means of functional principal components analysis last a quadratic discriminant analysis of functional principal components scores allows us to discriminate patients with aneurysms in different districts

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

a stochastic sirs epidemic model with logistic growth and general nonlinear incidence rate abstract in this paper we consider a stochastic sirs epidemic model with logistic growth and general nonlinear incidence rate we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic lyapunov function which provides us a good description of persistence we find that the hypothetical conditions on the nonlinear function are relative weak and valid for many forms of incidence rate

weighted sequential splittings and their analysis operator splitting is a widely used procedure in the numerical solution of parabolicproblems several splitting methods have been constructed and used in the fields of applied mathematics in this paper the weighted sequential splittings are introduced and their local splitting error is analyzed new results are presented for the case where the subproblems of the weighted splitting schemes are solved numerically the results are illustrated with test examples for ordinary differential systems

diagonally implicit runge kutta nystro m methods for oscillatory problems implicit runge kutta nystrom rkn methods are constructed for the integration of second order differential equations possessing an oscillatory solution based on a linear homogeneous test model we analyse the phase errors or dispersion introduced by these methods and derive so called dispersion relations diagonally implicit rkn methods of relatively low algebraic order are constructed which have a high order of dispersion up to 10 application of these methods to a number of test examples linear as well as nonlinear yields a greatly reduced phase error when compared with conventional dirkn methods

a bayesian approach to nonlinear random effects models nonlinear random effects models are considered from the bayesian point of view the method of analysis follows closely that of lindley and smith 1972 journal of the royal statistical society series b 34 1 42 the numerical method is related to the em algorithm

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures