stabilized multiscale finite element method for the stationary navier stokes equations abstract in the paper a stabilized multiscale finite element method for the stationary incompressible navier stokes equations is considered the method is a petrov galerkin approach based on the multiscale enrichment of the standard polynomial space enriched with the unusual bubble functions which no longer vanish on every element boundary for the velocity space the stability of the p 1 p 0 triangular element or the q 1 p 0 quadrilateral element is established and the optimal error estimates of the stabilized multiscale finite element method for the stationary navier stokes equations are obtained

regression analysis for a functional response functional responses are encountered when units are observed over time although the whole function itself is not observed a sufficiently large number of evaluations as is common with modern recording equipment are assumed to be available functional regression analysis relates the smooth functional response y t to known covariates x by a linear combination of parameter functions t which are to be estimated the model takes the standard form y t x t t t this approach provides an alternative to standard longitudinal data methods used in the biological sciences where less and noisier data necessitate parametric modeling the methodology is illustrated by an application in ergonomics

hopf bifurcation and turing instability in spatial homogeneous and inhomogeneous predator prey models abstract this paper is concerned with two species spatial homogeneous and inhomogeneous predator prey models with beddington deangelis functional response for the spatial homogeneous model the asymptotic behavior of the interior equilibrium and the existence of hopf bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered furthermore the direction of hopf bifurcation and the stability of bifurcated periodic solutions are investigated for the model with no flux boundary conditions turing instability of the interior equilibrium solution is studied in particular turing instability region regarding the parameters is established finally to verify our theoretical results some numerical simulations are also included

permanence of periodic holling type predator prey system with stage structure for prey abstract in this paper we study the permanence of the following periodic holling type predator prey system with stage structure for prey x 1 t a t x 2 t b t x 1 t d t x 1 2 t e t x 1 t p t x 1 t y t x 2 t c t x 1 t f t x 2 2 t y t y t g t h t x 1 t p t x 1 t q t y t sufficient and necessary condition which guarantee the predator and the prey species to be permanent is obtained some new results are obtained

multi quadric quasi interpolation method coupled with fdm for the degasperis procesi equation in this paper the degasperis procesi dp equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form u p based on the equivalent formulation of dp equation a new numerical method is presented the multi quadric mq quasi interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order tvd method is used to approximate the time derivative several examples are presented to demonstrate the effectiveness of the proposed method

k means inverse regression li suggested the method of sliced inverse regression for dimension reduction in regressions with a univariate response in this article we extend that method to multivariate regressions by introducing a new way of performing the slicing this method applies for any number of response variables and may be particularly useful at the outset of an analysis before positing a multivariate model the emphasis is on application no new asymptotic theory is presented

incorporating parametric effects into functional principal components analysis summary the ideas of functional principal component analysis are extended to deal with data that are hybrids of functional and parametric effects the parametric effects may be more general than just the addition of a multiple of a given function a detailed development is given in the case of shifts of the time axis for functions observed on a periodic interval and some remarks are made for the extension to a far more general case given data a procrustes fitting method can be used to estimate the parametric effects several possible ways of treating the estimated parameter values are discussed the methods are illustrated by reference to temperature data at 35 canadian weather stations

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

cook s distance measures for varying coefficient models with functional responses the aim of this article is to develop cook s distance measures for assessing the influence of both atypical curves and observations under varying coefficient model with functional responses our cook s distance measures include cook s distances for deleting multiple curves and for deleting multiple grid points and their scaled cook s distances we systematically investigate some theoretical properties of these diagnostic measures simulation studies are conducted to evaluate the finite sample properties of these cook s distances under different scenarios a real diffusion tensor tract dataset is analyzed to illustrate the use of our diagnostic measures

functional quadratic regression summary we extend the common linear functional regression model to the case where the dependency of a scalar response on a functional predictor is of polynomial rather than linear nature focusing on the quadratic case we demonstrate the usefulness of the polynomial functional regression model which encompasses linear functional regression as a special case our approach works under mild conditions for the case of densely spaced observations and also can be extended to the important practical situation where the functional predictors are derived from sparse and irregular measurements as is the case in many longitudinal studies a key observation is the equivalence of the functional polynomial model with a regression model that is a polynomial of the same order in the functional principal component scores of the predictor processes theoretical analysis as well as practical implementations are based on this equivalence and on basis representations of predictor processes we also obtain an explicit representation of the regression surface that defines quadratic functional regression and provide functional asymptotic results for an increasing number of model components as the number of subjects in the study increases the improvements that can be gained by adopting quadratic as compared to linear functional regression are illustrated with a case study that includes absorption spectra as functional predictors

persistence and global stability for n species ratio dependent predator prey system with time delays abstract a n species ratio dependent predator prey food chain model with time delays is investigated it is shown that the system is permanent under some appropriate conditions and sufficient conditions are obtained for the global stability of the positive equilibrium of the system

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

modeling hazard rates as functional data for the analysis of cohort lifetables and mortality forecasting as world populations age the analysis of demographic mortality data and demographic predictions of future mortality have met with increasing interest the study of mortality patterns and the forecasting of future mortality with its associated impacts on social welfare health care and societal planning has become a more pressing issue an ideal set of data to study patterns of change in long term mortality is the well known historical swedish cohort mortality data because of its high quality and long span of more than two centuries we explore the use of functional data analysis to model these data and to derive mortality forecasts specifically we address the challenge of flexibly modeling these data while including the effect of the birth year by regarding log hazard functions derived from observed cohort lifetables as random functions a functional model for the analysis of these cohort log hazard functions extending functional principal component approaches by introducing time varying eigenfunc

functional mixed effects models in this article a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced the linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects which are modeled as realizations of zero mean stochastic processes the fixed functional effects and the random functional effects are modeled in the same functional space which guarantee the population average and subject specific curves have the same smoothness property these models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures can include continuous covariates as well as dummy factors in both the fixed or random design matrices and include the nested curves models as special cases two estimation procedures are proposed the first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software the second procedure is a sequential estimation procedure using kalman filtering this algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets a generalized maximum likelihood gml ratio test is proposed for inference and model selection an application to comparison of cortisol profiles is used as an illustration

convergence results in a well known delayed predator prey system abstract in this paper we provide a detailed and explicit procedure of obtaining some regions of attraction for the positive steady state assumed to exist of a well known lotka volterra type predator prey system with a single discrete delay our procedure requires the delay length to be small a detailed example is presented the method used here is to construct a proper liapunov functional in a restricted region

functional data analysis for sparse longitudinal data we propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data the method aims at irregularly spaced longitudinal data where the number of repeated measurements available per subject is small in contrast classical functional data analysis requires a large number of regularly spaced measurements per subject we assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random subject specific trajectory plus measurement errors basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories and the estimation of the variance of the measurement errors the eigenfunction basis is estimated from the data and functional principal components score estimates are obtained by a conditioning step this conditional estimation method is conceptually simple and straightforward to implement

continuously additive models for nonlinear functional regression summary we introduce continuously additive models which can be viewed as extensions of additive regression models with vector predictors to the case of infinite dimensional predictors this approach produces a class of flexible functional nonlinear regression models where random predictor curves are coupled with scalar responses in continuously additive modelling integrals taken over a smooth surface along graphs of predictor functions relate the predictors to the responses in a nonlinear fashion we use tensor product basis expansions to fit the smooth regression surface that characterizes the model in a theoretical investigation we show that the predictions obtained from fitting continuously additive models are consistent and asymptotically normal we also consider extensions to generalized responses the proposed class of models outperforms existing functional regression models in simulations and real data examples

assessing extrema of empirical principal component functions the difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite dimensional settings local maxima and minima in principal component functions are of direct importance they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign we explore statistical properties of the relationship between extrema of empirical principal component functions and their counterparts for the true principal component functions it is shown that empirical principal component funcions have relatively little trouble capturing conventional extrema but can experience difficulty distinguishing a shoulder in a curve from a small bump for example when the true principal component function has a shoulder the probability that the empirical principal component function has instead a bump is approximately equal to 1 2 we suggest and describe the performance of bootstrap methods for assessing the strength of extrema it is shown that the subsample bootstrap is more effective than the standard bootstrap in this regard a bootstrap likelihood is proposed for measuring extremum strength exploratory numerical methods are suggested

hybrid chebyshev polynomial scheme for solving elliptic partial differential equations abstract in this paper we propose hybrid chebyshev polynomial scheme hcps which couples the chebyshev polynomial scheme and the method of fundamental solutions into a single matrix system this hybrid formulation requires solving only one system of equations and opens up the possibilities for solving a large class of partial differential equations in this paper we consider various boundary value problems and in particular the challenging cauchy navier equation the solution is approximated by the sum of the particular solution and the homogeneous solution chebyshev polynomials are used to approximate a particular solution of the given partial differential equation and the method of fundamental solutions is used to approximate the homogeneous solution numerical results show that our proposed approach is efficient accurate and stable

the effect of stage structure on the permanence of a predator prey system with time delay abstract a delayed predator prey system with stage structure for the prey and time delay due to the gestation of the predator is investigated by using an iteration technique and comparison arguments respectively sufficient conditions are derived for the global stability of the positive equilibrium and the two boundary equilibria of the proposed model numerical simulations are presented to illustrate the main results

horvitz thompson estimators for functional data asymptotic confidence bands and optimal allocation for stratified sampling when dealing with very large datasets of functional data survey sampling approaches are useful in order to obtain estimators of simple functional quantities without being obliged to store all the data we propose a horvitz thompson estimator of the mean trajectory in the context of a superpopulation framework we prove under mild regularity conditions that we obtain uniformly consistent estimators of the mean function and of its variance function with additional assumptions on the sampling design we state a functional central limit theorem and obtain asymptotic confidence bands stratified sampling is studied in detail and we also obtain a functional version of the usual optimal allocation rule considering a mean variance criterion these techniques are illustrated by a test population of n 18 902 electricity meters for which we have individual electricity consumption measures every 30 minutes over one week we show that stratification can substantially improve both the accuracy of the estimators and reduce the width of the global confidence bands compared with simple random sampling without replacement

osculatory interpolation in the method of fundamental solution for nonlinear poisson problems abstract the method of fundamental solution also known as the f trefftz method or the singularity method is an efficient numerical method for the solution of laplace equation for both two and three dimensional problems in recent years the method has also been applied for the solution of poisson equations by finding the particular solution to the nonhomogeneous terms in general approximate particular solutions are constructed using the interpolation of the nonhomogeneous terms by the radial basis functions the method has been validated in recent papers this paper presents an improvement of the solution procedure for such problems the improvement is achieved by using radial basis functions called osculatory radial basis functions such functions make use of the normal gradient at boundary to obtain improved interpolation the efficacy of the method is demonstrated for some prototypical nonlinear poisson problems and for multiple poisson equations

stability in a predator prey model with crowley martin function and stage structure for prey abstract this paper is concerned with a stage structured predator prey system with crowley martin functional response by analyzing the characteristic equation the local stability of the equilibria is investigated the persistence of system and global asymptotic stability of the positive equilibrium are carried out finally several numerical simulations to illustrate the theoretical analysis are also given

fundamental kernel based method for backward space time fractional diffusion problem based on kernel based approximation technique we devise in this paper an efficient and accurate numerical scheme for solving a backward space time fractional diffusion problem bstfdp the kernels used in the approximation are the fundamental solutions of the space time fractional diffusion equation expressed in terms of inverse fourier transform of mittag leffler functions the use of inverse fast fourier transform ifft technique enables an accurate and efficient evaluation of the fundamental solutions and gives a robust numerical algorithm for the solution of the bstfdp since the bstfdp is intrinsic ill posed we apply the standard tikhonov regularization technique to obtain a stable solution to the highly ill conditioned resultant system of linear equations for choosing optimal regularization parameter we combine the regularization technique with the generalized cross validation gcv method for an optimal placement of the source points in the use of fundamental solutions meanwhile the proposed algorithm also speeds up the previous method given in dou and hon 2014 several numerical examples are constructed to verify the accuracy and efficiency of the proposed method

functional data analysis with application to periodically stimulated foetal heart rate data ii functional logistic regression functional regression is used to model longitudinal data where the number of measurements on the functional covariate is much greater than the number of subjects in the study thus functional regression can be thought of as singular longitudinal analysis we have modified existing functional regression techniques to the case of a functional covariate with a repeated stimulus we applied this modified functional regression to periodically stimulated foetal heart rates the heart rate tracings were used as a predictor of the child s psychomotor development at approximately 18 months of age in the past this type of data has been analysed using the partially subjective concept of habituation by using the entire heart rate tracings through functional regression we have the advantage that habituation does not need to be defined and all available information is used to predict later child development

generalized functional linear models we propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function a linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function and the expected value of the response is related to this linear predictor via a link function if in addition a variance function is specified this leads to a functional estimating equation which corresponds to maximizing a functional quasi likelihood this general approach includes the special cases of the functional linear model as well as functional poisson regression and functional binomial regression the latter leads to procedures for classification and discrimination of stochastic processes and functional data we also consider the situation where the link and variance functions are unknown and are estimated nonparametrically from the data using a semiparametric quasi likelihood procedure an essential step in our proposal is dimension reduction by approximating the predictor processes with a truncated karhunen loeve expansion we develop asymptotic inference for the proposed class of generalized regression models in the proposed asymptotic approach the truncation parameter increases with sample size and a martingale central limit theorem is applied to establish the resulting increasing dimension asymptotics we establish asymptotic normality for a properly scaled distance between estimated and true functions that corresponds to a suitable l 2 metric and is defined through a generalized covariance operator as a consequence we obtain asymptotic tests and simultaneous confidence bands for the parameter function that determines the model the proposed estimation inference and classification procedures and variants with unknown link and variance functions are investigated in a simulation study we find that the practical selection of the number of components works well with the aic criterion and this finding is supported by theoretical considerations we include an application to the classification of medflies regarding their remaining longevity status based on the observed initial egg laying curve for each of 534 female medflies

a quasi f test for functional linear models with functional covariates and its application to longitudinal data functional linear models are useful in analyzing data from designed experiments and observational studies with functional responses as well as longitudinal data with a large number of repeated measures on each subject we propose a quasi f test for functional linear models with functional covariates and outcomes we develop a numerical procedure and an efficient approximation for computing p values and present a simple way to test individual predictors for illustration we apply the proposed procedure to a longitudinal depression data set with repeatedly measured methamphetamine use as a predictor we conduct a simulation study to assess the size and the power of the test

functional regression analysis using an f test for longitudinal data with large numbers of repeated measures analysis abstract longitudinal data sets from certain fields of biomedical research often consist of several variables repeatedly measured on each subject yielding large number of observations this characteristic complicates the use of standard longitudinal modeling strategies such as random effects models and marginal models where rigorous assumptions on intra subject correlation structure are required an innovative way to model the data is to apply functional regression analysis an emerging statistical approach in which observations of the same subject are viewed as a sample from a functional space no assumptions are needed for the intra subject correlation structure shen and faraway satistica sinica 2004 1239 1257 introduced an f test for linear models with functional responses this paper illustrates how to apply this f test and functional regression analysis to the setting of longitudinal data where intra subject repeated measures are viewed as discrete samples from an underlying curve with continuous function forms a smoking cessation study for methadone maintained tobacco smokers is analyzed for demonstration in estimating the treatment effects the functional regression analysis provides meaningful clinical interpretations and the functional f test provides consistent results supported by a random effects linear regression model

some tools for functional data analysis multivariate data analysis permits the study of observations which are finite sets of numbers but modern data collection situations can involve data or the processes giving rise to them which are functions functional data analysis involves infinite dimensional processes and or data the paper shows how the theory of l splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions spline smoothing rests on a partition of a function space into two orthogonal subspaces one of which contains the obvious or structural components of variation among a set of observed functions and the other of which contains residual components this partitioning is achieved through the use of a linear differential operator and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints these data analysis tools are illustrated by a study of variation in temperature precipitation patterns among some canadian weather stations

principal components analysis of sampled functions this paper describes a technique for principal components analysis of data consisting ofn functions each observed atp argument values this problem arises particularly in the analysis of longitudinal data in which some behavior of a number of subjects is measured at a number of points in time in such cases information about the behavior of one or more derivatives of the function being sampled can often be very useful as for example in the analysis of growth or learning curves it is shown that the use of derivative information is equivalent to a change of metric for the row space in classical principal components analysis the reproducing kernel for the hilbert space of functions plays a central role and defines the best interpolating functions which are generalized spline functions an example is offered of how sensitivity to derivative information can reveal interesting aspects of the data

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

implicit explicit time discretization coupled with finite element methods for delayed predator prey competition reaction diffusion system the main purpose of this paper is to develop the two step implicit explicit imex time discretization coupled with finite element methods for solving delayed predator prey competition reaction diffusion system finite element methods are used to discretize the space variables both imex two step one leg methods and imex linear two step methods are considered in time discretization where the nonlinear reaction part is discretized explicitly and the diffusion part is discretized implicitly the l 2 norm error estimates with handling the breaking points are derived these methods only require solving two independent linear systems with the same coefficient matrix at different time and avoid solving large scale systems of nonlinear algebraic equations thus the resulting schemes are efficient some numerical experiments are presented to confirm the theoretical results

frats functional regression analysis of dti tract statistics diffusion tensor imaging dti provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo this paper presents a functional regression framework called frats for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest such as age diagnostic status and gender in real applications the functional regression framework consists of four integrated components the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates a global test statistic for testing hypotheses of interest and a resampling method for approximating the p value of the global test statistic the proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy mean diffusivity and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment significant age and gestational age effects on the five diffusion properties were found in both tracts the resulting analysis pipeline can be used for understanding normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles

operator valued kernels for learning from functional response data in this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions a data is represented by a set of functions and the label is also a function we focus on the use of reproducing kernel hilbert space theory to learn from such functional data basic concepts and properties of kernel based learning are extended to include the estimation of function valued functions in this setting the representer theorem is restated a set of rigorously defined infinite dimensional operator valued kernels that can be valuably applied when the data are functions is described and a learning algorithm for nonlinear functional data analysis is introduced the methodology is illustrated through speech and audio signal processing experiments

canonical correlation analysis when the data are curves summary it is not immediately straightforward to extend canonical correlation analysis to the context of functional data analysis where the data are themselves curves or functions the obvious approach breaks down and it is necessary to use a method involving smoothing in some way such a method is introduced and discussed with reference to a data set on human gait the breakdown of the unsmoothed method is illustrated in a practical context and is demonstrated theoretically a consistency theorem for the smoothed method is proved in an increasing number of problems in a wide range of fields the data observed are not the univariate or multivariate observations of classical statistics but are func tions observed continuously ramsay and dalzell 1991 give the name functional data analysis to the analysis of data of this kind in most cases the observations will be functions of time or a closely related variable but there are clearly applications where the functions are surfaces observed over two or three dimensional space the motivating example for the present paper is a set of data on children s gait collected by the motion analysis laboratory at children s hospital san diego california see olshen et al 1989 for full details for each of a number of children several angles made by the child s joints knee hip etc are observed during the child s gait cycle one aim of the study is to gain understanding of the gait cycle of a normal child to make comparisons with children suffering from walking diffi culties these data motivated rice and silverman 1991 to discuss the extension of principal component analysis to the functional setting and to explain how smoothing can be incorporated into the analysis in a natural way in a substantial complemen tary paper ramsay and dalzell 1991 discuss different approaches to regression and principal component analysis in functional data analysis illustrating their work by a meteorological example the insights of functional data analysis may be helpful in chemometrics for instance a standard chemometric problem is the analysis of spectra observed in chromatography and these are to all intents and purposes functional observations another obvious area of potential relevance is the analysis of growth curve data the focus in the present paper will be on canonical correlation analysis cca in the gait example one might ask how variability in the knee angle cycle is related to

stable periodic orbits for a class of three dimensional competitive systems abstract it is shown that for a dissipative three dimensional competitive and irreducible system of ordinary differential equations having a unique equilibrium point at which point the jacobian matrix has negative determinant either the equilibrium point is stable or there exists an orbitally stable periodic orbit if in addition the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable the additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic in this case the morse smale conditions hold and the flow is structurally stable

multivariate varying coefficient model for functional responses motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

almost periodic dynamics of a delayed three level food chain model abstractthis paper is concerned with the dynamics of a three level food chain model with time delays by means of mawhin s continuation theorem of coincidence degree theory we investigate the existence of positive almost periodic solutions in a three level food chain model with time delays a set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained in addition the global asymptotical stability of the almost periodic solution of the above model is also studied finally two examples and simulations are also given to illustrate the main results in this paper

kernel smoothing of data with correlated errors abstract kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y f x e where f x is a smooth deterministic mean function and e is an error process with mean zero in this article the mean squared error of kernel estimators is computed for processes with correlated errors and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence the standard techniques for bandwidth selection such as cross validation and generalized cross validation are shown to perform very badly when the errors are correlated standard selection techniques are shown to favor undersmoothing when the correlations are predominantly positive and oversmoothing when negative the selection criteria can however be adjusted to correct for the effect of correlation in simulations the standard selection criteria are shown to behave as predicted the corrected criteria are shown to be very effective when the correlation functi

periodic solutions of an n species lotka volterra type food chain model with time delays an n species periodic lotka volterra type simple food chain model with time delays is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory and by constructing suitable lyapunov functionals sufficient conditions are derived for the existence uniqueness and global stability of positive periodic solutions of the model numerical simulations are presented to illustrate our main results

statistical inferences for functional data with modem technology development functional data are being observed frequently in many scientific fields a popular method for analyzing such functional data is smoothing first then estimation that is statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another however little is known about this substitution effect on functional data analysis in this paper this problem is investigated when the local polynomial kernel lpk smoothing technique is used for individual function reconstructions we find that under some mild conditions the substitution effect can be ignored asymptotically based on this we construct lpk reconstruction based estimators for the mean covariance and noise variance functions of a functional data set and derive their asymptotics we also propose a gcv rule for selecting good bandwidths for the lpk reconstructions when the mean function also depends on some time independent covariates we consider a functional linear model where the mean function is linearly related to the covariates but the covariate effects are functions of time the lpk reconstruction based estimators for the covariate effects and the covariance function are also constructed and their asymptotics are derived moreover we propose a l 2 norm based global test statistic for a general hypothesis testing problem about the covariate effects and derive its asymptotic random expression the effect of the bandwidths selected by the proposed gcv rule on the accuracy of the lpk reconstructions and the mean function estimator is investigated via a simulation study the proposed methodologies are illustrated via an application to a real functional data set collected in climatology

interpretable support vector machines for functional data support vector machines svm has been shown to be a powerful nonparametric classication technique even for high dimensional data although predictive ability is important obtaining an easy to interpret classier

numerical solutions of elliptic partial differential equations using chebyshev polynomials we present a simple and effective chebyshev polynomial scheme cps combined with the method of fundamental solutions mfs and the equilibrated collocation trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations pdes in this paper cps is applied in a two step approach first chebyshev polynomials are used to approximate a particular solution of a pde chebyshev nodes which are the roots of chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence then the resulting homogeneous equation is solved by boundary type methods including the mfs and the equilibrated collocation trefftz method numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient

diagnostics for linear models with functional responses linear models where the response is a function and the predictors are vectors are useful in analyzing data from designed experiments and other situations with functional observations residual analysis and diagnostics are considered for such models studentized residuals are defined and their properties are studied chi squared quantile quantile plots are proposed to check the assumption of gaussian error process and outliers jackknife residuals and an associated test are proposed to detect outliers cook s distance is defined to detect influential cases the methodology is illustrated by an example from a robust design study

generalized semiparametrically structured ordinal models motivated by recent work studying massive imaging data in the neuroimaging literature we propose multivariate varying coefficient models mvcm for modeling the relation between multiple functional responses and a set of covariates we develop several statistical inference procedures for mvcm and systematically study their theoretical properties we first establish the weak convergence of the local linear estimate of coefficient functions as well as its asymptotic bias and variance and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate we establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions we propose a global test for linear hypotheses of varying coefficient functions and derive its asymptotic distribution under the null hypothesis we also propose a simultaneous confidence band for each individual effect curve we conduct monte carlo simulation to examine the finite sample performance of the proposed procedures we apply mvcm to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment

case deletion measures for models with incomplete data summary this paper proposes several case deletion measures for assessing the influence of an observation for complicated models with real missing data or hypothetical missing data corresponding to latent random variables the idea is to generalise cook s 1977 approach to the conditional expectation of the complete data loglikelihood function in the em algorithm on the basis of the diagnostic measures a procedure is proposed for detecting influential observations two examples illustrate our methodology we show that the method can be applied efficiently to a wide variety of complicated problems that are difficult to handle by existing methods

gaussian process modeling of a functional output with information from boundary and initial conditions and analytical approximations a partial differential equation pde models a physical quantity as a function of space and time these models are often solved numerically with the finite element fe method and the computer outp

fadtts functional analysis of diffusion tensor tract statistics the aim of this paper is to present a functional analysis of a diffusion tensor tract statistics fadtts pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest such as age diagnostic status and gender and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies the fadtts integrates five statistical tools i a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates ii a weighted least squares estimation of the varying coefficient functions iii a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties iv a global test statistic to test hypotheses of interest and v a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions simulated data are used to evaluate the finite sample performance of fadtts we apply fadtts to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment fadtts can be used to facilitate the understanding of normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles the advantages of fadtts compared with the other existing approaches are that they are capable of modeling the structured inter subject variability testing the joint effects and constructing their simultaneous confidence bands however fadtts is not crucial for estimation and reduces to the functional analysis method for the single measure