lieb thirring type inequalities and gagliardo nirenberg inequalities for systems this paper is devoted to inequalities of lieb thirring type let v be a nonnegative potential such that the corresponding schrodinger operator has an unbounded sequence of eigenvalues i v i n we prove that there exists a positive constant c such that if d 2 then x i n i v c z rd v d 2 dx

the thermal equilibrium solution of a generic bipolar quantum hydrodynamic model the thermal equilibrium state of a bipolar isothermic quantum fluid confined to a bounded domain d 1 2 or d 3 is entirely described by the particle densities n p minimizing the energy where g 1 2 are strictly convex real valued functions it is shown that this variational problem has a unique minimizer in and some regularity results are proven the semi classical limit is carried out recovering the minimizer of the limiting functional the subsequent zero space charge limit leads to extensions of the classical boundary conditions due to the lack of regularity the asymptotics can not be settled on sobolev embedding arguments the limit is carried out by means of a compactness by convexity principle

multiscale simulation of transport in an open quantum system resonances and wkb interpolation a numerical scheme for the one dimensional stationary schrodinger poisson model is described the scheme is used to simulate a resonant tunneling diode and provides an important reduction of the simulation time the improvement is twofold first the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the wkb asymptotics then the discretization of the energy variable which is a parameter for the schrodinger equation is improved by approaching the wavefunctions in the double barrier region by its projection on the resonant states following the work of presilla sjostrand and jona lasinio on schrodinger equations with concentrated non linearities ann phys 240 1995 1 21

the range of a perturbed levy process a necessary and sufficient fourier analytic condition is given for a real valued levy process x to be such that all perturbations x f of x by measurable functions f have range with positive lebesgue measure the condition is compared to one due to kesten for the range of x alone to have positive lebesgue measure and in some cases it is found to coincide whereas in others it is stronger

joint mean covariance models with applications to longitudinal data unconstrained parameterisation summary we provide unconstrained parameterisation for and model a covariance using covariates the cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix the entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity gabriel s antedependence models dempster s covariance selection models and the class of graphical models the likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data a graphical method similar to that based on the correlogram in time series is developed and used to identify parametric models for nonstationary covariances

schrodinger poisson systems in dimension d 3 the whole space case after a study made for bounded domains and in the periodic case we investigate the variational formulation of schrodinger poisson systems set on the whole space d d 3 this variational formulation leads to a uniqueness result while the existence of a solution is proved only for small data because of the lack of coerciveness the end of this paper briefly presents the extension of this formalism to a physically relevant problem where the potential is periodic in one direction

new bounds on the lieb thirring constants improved estimates on the constants l d for 1 2 3 2 d n in the inequalities for the eigenvalue moments of schrodinger operators are established

multiplicity and concentration for the nonlinear schrodinger equation with critical frequency abstract we consider the nonlinear schrodinger equation e e 2 v v x v v p 1 v 0 in r n and the limit problem l u u p 1 u 0 in with boundary condition u 0 on where int x r n v x inf v 0 is assumed to be non empty connected and smooth we prove the existence of an infinite number of solutions for e and l sharing the topology of their level sets as seen from the ljusternik schnirelman scheme denoting their solutions as v k e k n and u k k n respectively we show that for fixed k n and up to rescaling v k e the energy of v k e converges to the energy of u k it is also shown that the solutions v k e for e concentrate exponentially around and that up to rescaling and up to a subsequence they converge to a solution of l

static solutions of the vlasov einstein system static solutions of the so 3 symmetric vlasov einstein system are studied via a variational approach for the constitutive relation of the emden fowler type e f e 1 f k we prove the existence of such solutions of sufficiently small mass energy provided 0 k 3 2 these solutions are local minimizers of the energy casimir functional subjected to a variational barrier

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

on singular limits of mean field equations mean field equations arise as steady state versions of convection diffusion systems where the convective field is determined by solution of a poisson equation whose right hand side is affine in the solutions of the convection diffusion equations in this paper we consider the repulsive coupling case for a system of two convection diffusion equations for general diffusivities we prove the existence of a unique solution of the mean field equation by a variational analysis of a saddle point problem usually without coercivity also we analyze the small debye length limit and prove convergence to either the so called charge neutral case or to a double obstacle problem for the limiting potential depending on the data

an extension of arnol d s second stability theorem for the euler equations abstract a general tool to prove nonlinear stability for stationary solutions of infinite dimensional hamiltonian systems is the energy casimir method proposed by arnol d for the two dimensional incompressible euler equations and generalized since to other flows arnol d s stability theorems are based on a uniform estimate for the second variation of the energy casimir functional leading to a strict convexity condition in this paper we develop the method of supporting functionals and show that a local convexity condition equivalent to the convexity of the quasi energy invariant of the linearized euler equations is also a sufficient condition for genuine stability of the fully nonlinear euler equations

bayesian analysis of covariance matrices and dynamic models for longitudinal data summary parsimonious modelling of the within subject covariance structure while heeding its positive definiteness is of great importance in the analysis of longitudinal data using the cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse wishart priors our priors offer many advantages with regard to elicitation positive definiteness computations using gibbs sampling shrinking covariances toward a particular structure with considerable flexibility and modelling covariances using covariates bayesian estimation methods are developed and the results are compared using two simulation studies these simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

stability analysis of a vlasov wave system describing particles interacting with their environment we study a kinetic equation of the vlasov wave type which arises in the description of the behaviour of a large number of particles interacting weakly with an environment composed of an infinite collection of local vibrational degrees of freedom modeled by wave equations we use variational techniques to establish the existence of large families of stationary states for this system and analyze their stability

quasineutral limit of a time dependent drift diffusion poisson model for p n junction semiconductor devices abstract in this paper the vanishing debye length limit of the bipolar time dependent drift diffusion poisson equations modelling insulated semiconductor devices with p n junctions i e with a fixed bipolar background charge is studied for sign changing and smooth doping profile with good boundary conditions the quasineutral limit zero debye length limit is performed rigorously by using the multiple scaling asymptotic expansions of a singular perturbation analysis and the carefully performed classical energy methods the key point in the proof is to introduce a density transform and two weighted liapunov type functionals first and then to establish the entropy production integration inequality which yields the uniform estimate with respect to the scaled debye length the basic point of the idea involved here is to control strong nonlinear oscillation by the interaction between the entropy and the entropy dissipation

gait analysis and the bootstrap this paper is about random coefficient trigonometric regression models and their use in gait analysis here gait analysis means free speed walking on a level surface our study focuses on bootstrap based prediction regions for the angular rotation curves of test children when the relevant training data are gathered from normal children of comparable ages considerations that led to our choice of model and use of the bootstrap are given prediction regions and empirical bootstrap distributions are displayed as is their application to several test cases also included is a study of the almost sure asymptotic behavior of the theoretical bootstrap probability of the prediction regions

relative entropies for kinetic equations in bounded domains irreversibility stationary solutions uniqueness the relative entropy method describes the irreversibility of the vlasov poisson and vlasov boltzmann poisson systems in bounded domains with incoming boundary conditions uniform in time estimates are deduced from the entropy in some cases these estimates are sufficient to prove the convergence of the solution to a unique stationary solution as time goes to infinity the method is also used to analyse other types of boundary conditions such as mass and energy preserving diffuse reflection boundary conditions and to prove the uniqueness of stationary solutions for some special collision terms

joint models for the association of longitudinal binary and continuous processes with application to a smoking cessation trial joint models for the association of a longitudinal binary and a longitudinal continuous process are proposed for situations in which their association is of direct interest the models are parameterized such that the dependence between the two processes is characterized by unconstrained regression coefficients bayesian variable selection techniques are used to parsimoniously model these coefficients a markov chain monte carlo mcmc sampling algorithm is developed for sampling from the posterior distribution using data augmentation steps to handle missing data several technical issues are addressed to implement the mcmc algorithm efficiently the models are motivated by and are used for the analysis of a smoking cessation clinical trial in which an important question of interest was the effect of the exercise treatment on the relationship between smoking cessation and weight gain

automatic estimation of multivariate spectra via smoothing splines summary the classical method for estimating the spectral density of a multivariate time series is first to calculate the periodogram and then to smooth it to obtain a consistent estimator typically to ensure the estimate is positive definite all the elements of the periodogram are smoothed the same way there are however many situations for which different components of the spectral matrix have different degrees of smoothness we propose a bayesian approach that uses markov chain monte carlo techniques to fit smoothing splines to each component real and imaginary of the cholesky decomposition of the periodogram matrix the spectral estimator is then obtained by reconstructing the spectral estimator from the smoothed cholesky decomposition components our technique produces an automatically smoothed spectral matrix estimator along with samples from the posterior distributions of the parameters to facilitate inference

computing the steady states for an asymptotic model of quantum transport in resonant heterostructures in this article we propose a rapid method to compute the steady states including bifurcation diagrams of resonant tunneling heterostructures in the far from equilibrium regime those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear schrodinger poisson system after a summary of the existing theoretical results the asymptotic model is explicitly adapted to physically realistic situations and numerical results are shown in various cases

asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity the nordstrom vlasov system is a relativistic lorentz invariant generalization of the vlasov poisson system in the gravitational case the asymptotic behavior of solutions and the non linear stability of steady states are investigated it is shown that solutions of the nordstrom vlasov system with energy greater or equal to the mass satisfy a dispersion estimate in terms of the conformal energy when the energy is smaller than the mass we prove the existence and non linear orbital stability of a class of static solutions isotropic polytropes against general perturbations the proof of orbital stability is based on a variational problem associated to the minimization of the energy functional under suitable constraints

relating the classical covariance adjustment techniques of multivariate growth curve models to modern univariate mixed effects models summary the relationship between the modern univariate mixed model for analyzing longitudinal data popularized by laird and ware 1982 biometrics38 963 974 and its predecessor the classical multivariate growth curve model summarized by grizzle and allen 1969 biometrics25 357 381 has never been clearly established here the link between the two methodologies is derived and balanced polynomial and cosinor examples cited in the literature are analyzed with both approaches relating the two models demonstrates that classical covariance adjustment for higher order terms is analogous to including them as random effects in the mixed model the polynomial example clearly illustrates the relationship between the methodologies and shows their equivalence when all matrices are properly defined the cosinor example demonstrates how results from each method may differ when the total variance covariance matrix is positive definite but that the between subjects component of that matrix is not so constrained by the growth curve approach additionally advocates of each approach tend to consider different covariance structures modern mixed model analysts consider only those terms in a model s expectation or linear combinations and preferably the most parsimonious subset as candidates for random effects classical growth curve analysts automatically consider all terms in a model s expectation as random effects and then investigate whether covariance adjusting for higher order terms improves the model we apply mixed model techniques to cosinor analyses of a large unbalanced data set to demonstrate the relevance of classical covariance structures that were previously conceived for use only with completely balanced data

non linear stability of gaseous stars we construct steady states of the euler poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional their minimizing property implies the non linear stability of such states against general i e not necessarily spherically symmetric perturbations the mathematical approach is based on previous stability results for the vlasov poisson system by y guo and g rein exploiting the energy casimir technique the analysis is conditional in the sense that it assumes the existence of solutions to the initial value problem for the euler poisson system which preserve mass and energy the relation between the euler poisson and the vlasov poisson system in this context is also explored

estimation of average treatment effect with incompletely observed longitudinal data application to a smoking cessation study we study the problem of estimation and inference on the average treatment effect in a smoking cessation trial where an outcome and some auxiliary information were measured longitudinally and both were subject to missing values dynamic generalized linear mixed effects models linking the outcome the auxiliary information and the covariates are proposed the maximum likelihood approach is applied to the estimation and inference on the model parameters the average treatment effect is estimated by the g computation approach and the sensitivity of the treatment effect estimate to the nonignorable missing data mechanisms is investigated through the local sensitivity analysis approach the proposed approach can handle missing data that form arbitrary missing patterns over time we applied the proposed method to the analysis of the smoking cessation trial

finite mixture varying coefficient models for analyzing longitudinal heterogenous data this paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a california civil addict program each component of the mixture is characterized by a varying coefficient mixed effect model we use the bayesian p splines approach to approximate the varying coefficient functions we develop markov chain monte carlo algorithms to estimate the smooth functions unknown parameters and latent variables in the model we use modified deviance information criterion to determine the number of components in the mixture a simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate we apply the proposed model to the heroin treatment study furthermore we identify heterogeneous longitudinal patterns copyright 2011 john wiley sons ltd

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

miscellanea random coefficient autoregressive models for longitudinal data summary stable autoregressive models with exogenous covariates can be used to mimic nonstationary stabilising growth profiles in longitudinal data if different individuals have very different trajectories the autoregressive parameters can be interpreted as random variables varying from one individual to the next if all random effects are assumed gaussian the model will be quite easy to estimate although the marginal distributions of the observations will no longer be gaussian however this kind of model can only be used when the observations are equally spaced

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions abstract in this paper the limit of vanishing debye length in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions is studied in one dimensional case the quasi neutral limit zero debye length limit is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods our results imply that one kind of the new and interesting phenomena in semiconductor physics occurs

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

smoothing spline models with correlated random errors abstract spline smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model their performances depend greatly on the choice of smoothing parameters many methods of selecting smoothing parameters such as generalized maximum likelihood gml generalized cross validation gcv and unbiased risk ubr have been developed under the assumption of independent observations they tend to underestimate smoothing parameters when data are correlated in this article i assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters i extend the gml gcv and ubr methods to estimate the smoothing parameters and the correlation parameters simultaneously i also relate a smoothing spline model to three mixed effects models these relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction blup estimates and that the gml estimates of the smoothing parameters an

nonlinear modeling of serial immunologic data a case study abstract this article concerns the analysis of serial immunologic data from a clinical trial of immunosuppressive chemotherapy in the treatment of multiple sclerosis the goal of the analysis is to relate levels of drug dose to levels of an immunologic outcome variable i propose a new nonlinear model for the analysis of such data the model assumes that the mean function is the solution of an ordinary differential equation in time parameters of which are related to the dose via a regression function the defining differential equation is that which gives rise to the generalized logistic function a flexible form that includes a number of popular growth models we fit the model which accounts for random effects and time series autocorrelation by maximum likelihood results suggest strong treatment effects in two active drug groups and a small but significant effect in a placebo group these findings agree well with previously reported analyses of clinical outcomes from the trial an empirical comparis

bayesian semiparametric regression for longitudinal binary processes with missing data longitudinal studies with binary repeated measures are widespread in biomedical research marginal regression approaches for balanced binary data are well developed whereas for binary process data where measurement times are irregular and may differ by individuals likelihood based methods for marginal regression analysis are less well developed in this article we develop a bayesian regression model for analyzing longitudinal binary process data with emphasis on dealing with missingness we focus on the settings where data are missing at random mar which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood based inference about the marginal mean to provide maximum flexibility the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates inference is fully bayesian using simulations we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are mar longitudinal viral load data from the hiv epidemiology research study are analyzed for illustration

level sets of additive levy processes we provide a probabilistic interpretation of a class of natural capacities on euclidean space in terms of the level sets of a suitably chosen multiparameter additive levy process x we also present several probabilistic applications of the aforementioned potential theoretic connections they include areas such as intersections of levy processes and level sets as well as hausdorff dimension computations

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

shrinkage estimators for covariance matrices estimation of covariance matrices in small samples has been studied by many authors standard estimators like the unstructured maximum likelihood estimator ml or restricted maximum likelihood reml estimator can be very unstable with the smallest estimated eigenvalues being too small and the largest too big a standard approach to more stably estimating the matrix in small samples is to compute the ml or reml estimator under some simple structure that involves estimation of fewer parameters such as compound symmetry or independence however these estimators will not be consistent unless the hypothesized structure is correct if interest focuses on estimation of regression coefficients with correlated or longitudinal data a sandwich estimator of the covariance matrix may be used to provide standard errors for the estimated coefficients that are robust in the sense that they remain consistent under misspecification of the covariance structure with large matrices however the inefficiency of the sandwich estimator becomes worrisome we consider here two general shrinkage approaches to estimating the covariance matrix and regression coefficients the first involves shrinking the eigenvalues of the unstructured ml or reml estimator the second involves shrinking an unstructured estimator toward a structured estimator for both cases the data determine the amount of shrinkage these estimators are consistent and give consistent and asymptotically efficient estimates for regression coefficients simulations show the improved operating characteristics of the shrinkage estimators of the covariance matrix and the regression coefficients in finite samples the final estimator chosen includes a combination of both shrinkage approaches i e shrinking the eigenvalues and then shrinking toward structure we illustrate our approach on a sleep eeg study that requires estimation of a 24 x 24 covariance matrix and for which inferences on mean parameters critically depend on the covariance estimator chosen we recommend making inference using a particular shrinkage estimator that provides a reasonable compromise between structured and unstructured estimators

quasi neutral limit and the boundary layer problem of planck nernst poisson navier stokes equations for electro hydrodynamics abstract quasi neutral limit and the boundary layer problem of the two three dimensional incompressible planck nernst poisson navier stokes equations for electro hydrodynamics with the general mobilities of two kinds of charges and in the bounded domain is studied for the generally smooth doping profile and the physical case that the mobilities of two kinds of charges is different quasi neutral limit with a subtle boundary layer structure is rigorously proved by constructing one new weighted entropy functional coupled with multi scaling approximating expansion techniques

extremals of functionals with competing symmetries abstract we present a new method of producing optimizing sequences for highly symmetric functionals the sequences have good convergence properties built in we apply the method in different settings to give elementary proofs of some classical inequalities such as the hardy littlewood sobolev and the logarithmic sobolev inequality in their sharp form

maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix the positive definiteness constraint is the most awkward stumbling block in modelling the covariance matrix pourahmadi s 1999 unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models the new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors in this paper the maximum likelihood estimators of the parameters of a generalised linear model for the covariance matrix their consistency and their asymptotic normality are studied when the observations are normally distributed these results along with the likelihood ratio test and penalised likelihood criteria such as bic for model and variable selection are illustrated using a real dataset

existence and nonlinear stability of stationary states of the schrodinger poisson system we consider the schrodinger poisson system in the repulsive plasma physics coulomb case given a stationary state from a certain class we prove its nonlinear stability using an appropriately defined energy casimir functional as lyapunov function to obtain such states we start with a given casimir functional and construct a new functional which is in some sense dual to the corresponding energy casimir functional this dual functional has a unique maximizer which is a stationary state of the schrodinger poisson system and lies in the stability class the stationary states are parameterized by the equation of state giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels

on the schrodinger equation and the eigenvalue problem if k is thekth eigenvalue for the dirichlet boundary problem on a bounded domain in n h weyl s asymptotic formula asserts that lambda k sim c n left frac k v d right 2 n hence sum limits i 1 k lambda i sim frac nc n n 2 k frac n 2 n v d 2 n we prove that for any domain and for all sum limits i 1 k lambda i geqq frac nc n n 2 k frac n 2 n v d 2 n a simple proof for the upper bound of the number of eigenvalues less than or equal to for the operator v x defined on n n 3 in terms of int limits mathbb r n v alpha n 2 is also provided

modeling the random effects covariance matrix for longitudinal data with covariates measurement error longitudinal data occur frequently in practice such as medical studies and life sciences generalized linear mixed models glmms are commonly used to analyze such data it is typically assumed that the random effects covariance matrix is constant among subjects in these models in many situations however the correlation structure may differ among subjects and ignoring this heterogeneity can lead to biases in model parameters estimate recently lee et al developed a heterogeneous random effects covariance matrix for glmms for error free covariates covariates measured with error also happen frequently in the longitudinal data set up eg blood pressure and cholesterol level ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions in this paper we propose an approach to properly model the random effects covariance matrix based on covariates in the class of glmms where we also have covariates measured with error the resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can be easily modeled without the concern of positive definiteness of the resulting estimator the performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms of bias mean squared error and coverage rate an application of the proposed method is also provided using a longitudinal data from manitoba follow up study

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

bayesian nonparametric longitudinal data analysis abstractpractical bayesian nonparametric methods have been developed across a wide variety of contexts here we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry cs and autoregressive ar covariance structures ar structure is often specified through the use of a gaussian process gp with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart we allow for ar structure by considering a broader class of models that incorporates a dirichlet process mixture dpm over the covariance parameters of the gp we are able to take advantage of modern bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations we also take advantage of the generality of our model which provides for estimation

dynamic conditionally linear mixed models for longitudinal data we develop a new class of models dynamic conditionally linear mixed models for longitudinal data by decomposing the within subject covariance matrix using a special cholesky decomposition here dynamic means using past responses as covariates and conditional linearity means that parameters entering the model linearly may be random but nonlinear parameters are nonrandom this setup offers several advantages and is surprisingly similar to models obtained from the first order linearization method applied to nonlinear mixed models first it allows for flexible and computationally tractable models that include a wide array of covariance structures these structures may depend on covariates and hence may differ across subjects this class of models includes e g all standard linear mixed models antedependence models and vonesh carter models second it guarantees the fitted marginal covariance matrix of the data is positive definite we develop methods for bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited

modelling the random effects covariance matrix in longitudinal data a common class of models for longitudinal data are random effects mixed models in these models the random effects covariance matrix is typically assumed constant across subject however in many situations this matrix may differ by measured covariates in this paper we propose an approach to model the random effects covariance matrix by using a special cholesky decomposition of the matrix in particular we will allow the parameters that result from this decomposition to depend on subject specific covariates and also explore ways to parsimoniously model these parameters an advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix in addition the parameters resulting from this decomposition have a sensible interpretation we propose fully bayesian modelling for which a simple gibbs sampler can be implemented to sample from the posterior distribution of the parameters we illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects

the ionization conjecture in hartree fock theory we prove the ionization conjecture within the hartree fock theory of atoms more precisely we prove that if the nuclear charge is allowed to tend to infinity the maximal negative ionization charge and the ionization energy of atoms nevertheless remain bounded moreover we show that in hartree fock theory the radius of an atom properly defined is bounded independently of its nuclear charge

a simple proof of the generalized lieb thirring inequalities in one space dimension abstract the lieb thirring inequalities give a sharp upper bound for the lp norm of a function which is the pointwise sum of the squares of a finite orthonormal sequence of functions that are elements of a suitable sobolev space lt originally proven for the functions defined on the whole n dimensional euclidean space they were later extended to bounded domains and to suborthogonal sequences of functions gmt here we present a simple proof of these inequalities for bounded intervals in one space dimension utilizing simple sobolev inequalities and standard results from hilbert space theory

symmetry of extremals of functional inequalities via spectral estimates for linear operators we prove new symmetry results for the extremals of the caffarelli kohn nirenberg inequalities in any dimension larger or equal than 2 in a range of parameters for which no explicit results of symmetry were previously known

an impulsive delay differential inequality and applications an impulsive delay differential inequality is formulated in this paper an estimate of the rate of decay of solutions to this inequality is obtained it can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view as an application we consider a class of impulsive control systems with time varying delays and establish a sufficient condition to guarantee the global exponential stability it is shown that via proper impulsive control law a linear delay differential system can be exponentially stabilized even if it is initially unstable a numerical example is given to demonstrate the effectiveness of the development method

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions and the general sign changing doping profile abstract the quasi neutral limit in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions the general sign changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one dimensional case the dynamic structure stability of the solution with respect to the scaled debye length is proven by the asymptotic analysis of singular perturbation and the entropy energy method the key point of the proof is to use sufficiently the fact that the length of the boundary layer is very small in a short time period

the quantum liouville bgk equation and the moment problem abstract this work is devoted to the analysis of the quantum liouville bgk equation this equation arises in the work of degond and ringhofer on the derivation of quantum hydrodynamical models from first principles their theory consists in transposing to the quantum setting the closure strategy by entropy minimization used for kinetic equations the starting point is the quantum liouville bgk equation where the collision term is defined via a so called quantum local equilibrium defined as a minimizer of the quantum free energy under a local density constraint we then address three related problems we prove new results about the regularity of these quantum equilibria we prove that the quantum liouville bgk equation admits a classical solution and we investigate the long time behavior of the solutions the core of the proofs is based on a fine analysis of the properties of the minimizers of the free energy

a nonparametric prior for simultaneous covariance estimation in the modeling of longitudinal data from several groups appropriate handling of the dependence structure is of central importance standard methods include specifying a single covariance matrix for all groups or independently estimating the covariance matrix for each group without regard to the others but when these model assumptions are incorrect these techniques can lead to biased mean effects or loss of efficiency respectively thus it is desirable to develop methods to simultaneously estimate the covariance matrix for each group that will borrow strength across groups in a way that is ultimately informed by the data in addition for several groups with covariance matrices of even medium dimension it is difficult to manually select a single best parametric model among the huge number of possibilities given by incorporating structural zeros and or commonality of individual parameters across groups in this paper we develop a family of nonparametric priors using the matrix stick breaking process of dunson et al 2008 that seeks to accomplish this task by parameterizing the covariance matrices in terms of the parameters of their modified cholesky decomposition pourahmadi 1999 we establish some theoretic properties of these priors examine their effectiveness via a simulation study and illustrate the priors using data from a longitudinal clinical trial

an estimating equation approach to dimension reduction for longitudinal data sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data in this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace the proposed method accounts for the covariance structure within each subject and improves estimation efficiency when the covariance structure is correctly specified even if the covariance structure is misspecified our estimator remains consistent in addition our method relaxes distributional assumptions on the covariates and is doubly robust to determine the structural dimension of the central mean subspace we propose a bayesian type information criterion we show that the estimated structural dimension is consistent and that the estimated basis directions are root formula see text consistent asymptotically normal and locally efficient simulations and an analysis of the framingham heart study data confirm the effectiveness of our approach

sobolev like cones of trace class operators on unbounded domains interpolation inequalities and compactness properties abstract in this paper we extend the compactness properties for trace class operators obtained by dolbeault felmer and mayorga zambrano to a smooth unbounded domain r d d 3 we consider v a non negative potential on that blows up at infinity and the normed space h v u h 0 1 u v 2 u x 2 u x 2 v x d x a positive self adjoint trace class operator r belongs to the sobolev like cone h v 1 if i r n h v and r v i 1 i r i r v 2 where i r i n is the sequence of occupation numbers of r and i r i n l 2 is a corresponding hilbertian basis of eigenfunctions we prove that a sequence in h v 1 bounded in energy v has a subsequence that converges in trace norm this is analogous to the classical sobolev immersion h 1 l 2 we prove the existence of lower bounds for nonlinear free energy functionals and by doing so we establish lieb thirring type inequalities as well as some gagliardo nirenberg type interpolation inequalities then our compactness result is applied to minimize nonlinear free energy functionals working on h v 1

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea