classical r matrix theory for bi hamiltonian field systems this is a survey of the application of the classical r matrix formalism to the construction of infinite dimensional integrable hamiltonian field systems the main point is the study of bi hamiltonian structures appropriate constructions on poisson noncommutative and loop algebras as well as the central extension procedure are presented the theory is developed for 1 1 and 2 1 dimensional field and lattice soliton systems as well as hydrodynamic systems the formalism presented contains sufficiently many proofs and important details to make it self contained and complete the general theory is applied to several infinite dimensional lie algebras in order to construct both dispersionless and dispersive soliton integrable field systems

semiparametric modeling of repeated measurements under outcome dependent follow up in regression analysis of repeated measurements that are taken at subject specific times the availability of the outcome data may be related to the past outcome and to other measured variables that are not in the intended regression model in this paper we propose a natural extension of the semiparametric regression procedure of lin and ying j am stat assoc 2001 96 103 126 by building a class of inverse intensity rate ratio weighted estimators that accommodate such outcome dependent follow up the estimators have a closed form are radicaln consistent asymptotically normal and do not require estimation of any infinite dimensional parameters we give several simulations to demonstrate the estimator s performance and show a sensitivity study under follow up with various degrees of dependence on outcome related variables we illustrate our approach using data from a randomized health services research study with noncompliance to scheduled visits

doubly robust estimation optimally truncated inverse intensity weighting and increment based methods for the analysis of irregularly observed longitudinal data longitudinal data arising from routine follow up of patients will often have irregular measurement times existing methods for analysis include joint modelling of the outcome and measurement processes and inverse intensity weighting iiw this work extends previously proposed analysis of increments to the case of irregular follow up yielding a model for the increments that can be used as a stand alone method furthermore we propose two ways of combining the increments and iiw estimators first we use the increment model to select the truncation point for the inverse intensity weights that minimises the mean squared error of the iiw estimator second we use the increment model to augment the usual iiw estimating equations to form a doubly robust estimator we evaluate the methods through simulation and apply these to a recent study of juvenile dermatomyositis

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

three dimensional reductions of four dimensional quasilinear systems in this paper we show that four dimensional quasilinear systems of first order integrable by the method of two dimensional hydrodynamic reductions possess infinitely many three dimensional hydrodynamic reductions which are also integrable systems these three dimensional multi component integrable systems are irreducible to two dimensional hydrodynamic reductions in a generic case

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

regression analysis of longitudinal data in the presence of informative observation and censoring times longitudinal data frequently occur in many studies such as longitudinal follow up studies to develop statistical methods and theory for the analysis of these data independent or noninformative observation and censoring times are typically assumed which naturally leads to inference procedures conditional on observation and censoring times but in many situations this may not be true or realistic that is longitudinal responses may be correlated with observation times as well as censoring times this article considers the analysis of longitudinal data where these correlations may exist and proposes a joint modeling approach that uses some latent variables to characterize the correlations for inference about regression parameters estimating equation approaches are developed and both large sample and final sample properties of the proposed estimators are established in addition some graphical and numerical procedures are presented for model checking the methodology is applied to a bladder cancer stu

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

concurrent multi scale analysis of elastic composites by a multi level computational model abstract in this paper an adaptive multi level computational model is developed to comprehensively address issues of discretization and physically based modeling error in structures consisting of heterogeneous micro structures the model consists of three essential levels i a purely macroscopic domain level 0 with homogenized material parameters ii a macro micro domain level 1 with the micro domain represented by the periodic repetition of a representative volume element rve and iii purely microscopic domain level 2 where the rve ceases to exist and extended micro structural regions need to be modeled all micro structural computations of arbitrary heterogeneous domains are conducted using the adaptive voronoi cell finite element model an intermediate layer is used between the macroscopic and microscopic regions for smooth transition the level 1 domain is utilized to estimate criteria for switching from macroscopic to microscopic calculations physically based error indicators are developed for transition from macroscopic to microscopic domain statistical functions are used to assess the extent of the rve domains for non uniform micro structures for the macroscopic domains h and hp adaptations are executed using conventional error indicators based on the energy norm the numerical simulations are compared with results from pure micro mechanics and other multi level models in the literature the model is also tested for a realistic problem with macroscopic stress risers

outcome vector dependent sampling with longitudinal continuous response data stratified sampling based on summary statistics the analysis of longitudinal trajectories usually focuses on evaluation of explanatory factors that are either associated with rates of change or with overall mean levels of a continuous outcome variable in this manuscript we introduce valid design and analysis methods that permit outcome dependent sampling of longitudinal data for scenarios where all outcome data currently exist but a targeted sub study is being planned in order to collect additional key exposure information on a limited number of subjects we propose a stratified sampling based on specific summaries of individual longitudinal trajectories and we detail an ascertainment corrected maximum likelihood approach for estimation using the resulting biased sample of subjects in addition we demonstrate that the efficiency of an outcome based sampling design relative to use of a simple random sample depends highly on the choice of outcome summary statistic used to direct sampling and we show a natural link between the goals of the longitudinal regression model and corresponding desirable designs using data from the childhood asthma management program where genetic information required retrospective ascertainment we study a range of designs that examine lung function profiles over four years of follow up for children classified according to their genotype for the il 13 cytokine

a two scale deformation model for polycrystalline solids using a strongly coupled finite element methodology a two scale finite element framework for analysis of polycrystalline solids at the continuum and crystal scales is demonstrated the framework is strongly coupled in the sense that the response at the continuum scale directly bears on the response at the crystal scale and vice versa data needed at one scale from computations at the other scale are generated on the fly two important issues are addressed the projection of continuum scale motion onto crystal scale aggregates and the averaging crystal scale stresses for use at the continuum scale the framework is implemented in a scalable parallel computing environment and applied to two examples with different geometries and loading modes it is shown that combining formulations for the crystal and continuum scales can provide more detailed and accurate results in comparison to a single scale finite element approach that invokes a simpler scale linking methodology

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

towards a general asymptotic theory for cox model with staggered entry a general asymptotic theory is established for the two parameter cox score process with staggered entry data it extends in several directions the existing theory developed by sellke and siegmund slud and gu and lai an essential tool employed here is a modern empirical process theory as elucidated in a recent monograph by pollard

algebraic varieties in the birkhoff strata of the grassmannian gr 2 harrison cohomology and integrable systems the local properties of the families of algebraic subsets wg in the birkhoff strata 2g of gr 2 containing the hyperelliptic curves of genus g are studied it is shown that the tangent spaces tg for wg are isomorphic to the linear spaces of 2 coboundaries particular subsets in wg are described by the integrable dispersionless coupled kdv systems of hydrodynamical type defining a special class of 2 cocycles and 2 coboundaries in tg it is demonstrated that the blows ups of such 2 cocycles and 2 coboundaries and gradient catastrophes for associated integrable systems are interrelated

hodograph solutions of the dispersionless coupled kdv hierarchies critical points and the euler poisson darboux equation it is shown that the hodograph solutions of the dispersionless coupled kdv dckdv hierarchies describe critical and degenerate critical points of a scalar function which obeys the euler poisson darboux equation singular sectors of each dckdv hierarchy are found to be described by solutions of higher genus dckdv hierarchies concrete solutions exhibiting shock type singularities are presented

compatible poisson brackets of hydrodynamic type some general properties of compatible poisson brackets of hydrodynamic type are discussed in particular a an invariant differential geometric criterion of the compatibility based on the nijenhuis tensor which is slightly different from those existing in the literature b the lax pair with a spectral parameter governing compatible poisson brackets in the diagonalizable case c the connection of this problem with the class of surfaces in euclidean space which possess non trivial deformations preserving the weingarten operator

coisotropic deformations of algebraic varieties and integrable systems coisotropic deformations of algebraic varieties are defined as those for which an ideal of the deformed variety is a poisson ideal it is shown that coisotropic deformations of sets of intersection points of plane quadrics cubics and space algebraic curves are governed in particular by the dkp wdvv dvn d2dtl equations and other integrable hydrodynamical type systems particular attention is paid to the study of two and three dimensional deformations of elliptic curves the problem of an appropriate choice of the poisson structure is discussed

quasiclassical limit of coupled kdv equations riemann invariants and multi hamiltonian structure abstract we consider the quasiclassical limit of the first nontrivial flow in coupled kdv hierarchy written down in riemann invariants it assumes the extremely simple form r i k 1 n r k 2r i r x i i 1 n up to certain natural equivalence this turns out to be the only hydrodynamic system with n 1 compatible purely local hamiltonian structures

on hamiltonian perturbations of hyperbolic systems of conservation laws i quasi triviality of bi hamiltonian perturbations we study the general structure of formal perturbative solutions to the hamiltonian perturbations of spatially one dimensional systems of hyperbolic pdes vt v x 0 under certain genericity assumptions it is proved that any bi hamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives the main tool is in constructing the so called quasimiura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bi hamiltonian structure of hydrodynamic type the quasi triviality theorem we also describe following 35 the invariants ofsuchbi hamiltonian structures with respect to the group of miura type transformations depending polynomially on the derivatives c

on a new class of completely integrable nonlinear wave equations ii multi hamiltonian structure the multi hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed infinitely many conservation laws had earlier been obtained for these equations starting from a primary hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi hamiltonian structure are obtained and it is shown that the second hamiltonian operator can be constructed solely through a knowledge of the first hamiltonian function the recursion operator which first appears at the level of bi hamiltonian structure gives rise to an infinite sequence of conserved hamiltonians it is found that in general there exist two different infinite sequences of conserved quantities for these equations the recursion relation defining higher hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the k 1 st hamiltonian operator which depends on the kth hamiltonian function the infinite sequence of conserved hamiltonians are common to all the higher hamiltonian structures the equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri hamiltonian structure with two distinct infinite sets of conserved quantities the isothermal case of 1 is an exceptional one that requires separate treatment this corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to poisson s equation in nonlinear acoustics

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

coupled kdv equations with multi hamiltonian structures abstract we present a large class of systems of n equations which possess n 1 purely differential compatible hamiltonian structures our generic equations are isospectral to n 1 0 e i 2 i 2 n 1 0 i 2 i 2 n but our class also includes degenerate nondispersive systems which are unrelated to this linear problem embedded in this class for each n there are n distinct coupled kdv systems when n 2 our class includes 3 known equations dispersive water waves ito s equation and reduced benney s equations these equations are thus tri hamiltonian we also present 2 examples of 3 component quadri hamiltonian systems which generalise the above mentioned dispersive and nondispersive water waves

flat bidifferential ideals and semi hamiltonian pdes in this paper we consider a class of semi hamiltonian systems characterized by the existence of a special conservation law the density and the current of this conservation law satisfy a second order system of pdes which has a natural interpretation in the theory of flat bidifferential ideals the class of systems we consider contains important well known examples of semi hamiltonian systems other examples such as genus 1 whitham modulation equations for kdv are related to this class by a reciprocal transformation

estimation of local modeling error and goal oriented adaptive modeling of heterogeneous materials part ii a computational environment for adaptive modeling of heterogeneous elastic solids this paper addresses a classical and largely unsolved problem given a structural component constructed of a heterogeneous elastic material that is in equilibrium under the action of applied loads determine local micromechanical features of its response e g local stresses and displacements in or around phase boundaries or in inclusions to an arbitrary preset level of accuracy it being understood that the microstructure is a priori unknown may be randomly distributed may exist at multiple spatial scales and may contain millions even billions of microscale components the approach described in this work begins with a mathematical abstraction of this problem in which the material body is modeled as an elastic solid with highly variable possibly randomly distributed elastic properties information on the actual character of the microstructure of given material bodies is determined by computerized tomography ct imaging a procedure is given for determining the effective material properties from imaging data using either deterministic or stochastic methods an algorithm is then described for determining local quantities of interest such as average stresses on inclusion boundaries to arbitrary accuracy relative to the fine scale model a new computational environment for implementing such analyses is presented which employs parallel adaptive hp finite element methods ct interfaces automatic meshing procedures and effectively adaptive modeling schemes within the basic premises on which the approach is based results of any specified accuracy can be obtained independently of the number of microscale components and constituents the results of several numerical experiments are presented

analysis of longitudinal data with irregular outcome dependent follow up summary a frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self selected points in time as a result observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and or some auxiliary factors that are associated with the outcome if the follow up visit and outcome processes are correlated then marginal regression analyses will produce biased estimates building on the work of robins rotnitzky and zhao we propose a class of inverse intensity of visit process weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time this allows us to handle arbitrary patterns of missing data as embedded in a subject s visit process we derive the large sample distribution for our inverse visit intensity weighted estimators and investigate their finite sample behaviour by simulation our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness as percentage days homeless in the past 3 months and other auxiliary factors were recorded at follow up times that are not fixed by design

singular sector of the burgers hopf hierarchy and deformations of hyperelliptic curves we discuss the structure of shock singularities of the burgers hopf hierarchy it is shown that the set of singular solutions defines a stratification of the affine space of the flow parameters in the hierarchy the stratification is associated with the birkhoff decomposition of the grassmannian given by the set of linear spaces spanned by the hierarchy we then construct integrable hierarchy on each stratum and demonstrate that it describes a deformation of a hyperelliptic curve parametrizing the stratum the hierarchy is called the hidden burgers hopf hierarchy and we found the riemann invariant form and the hodograph solution

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimating the causal effect of zidovudine on cd4 count with a marginal structural model for repeated measures even in the absence of unmeasured confounding factors or model misspecification standard methods for estimating the causal effect of a time varying treatment on the mean of a repeated measures outcome for example gee regression may be biased when there are time dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment in contrast the recently developed marginal structural models msms can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent we describe an msm for repeated measures that parameterizes the marginal means of counterfactual outcomes corresponding to prespecified treatment regimes the parameters of msms are estimated using a new class of estimators inverse probability of treatment weighted estimators we used an msm to estimate the effect of zidovudine therapy on mean cd4 count among hiv infected men in the multicenter aids cohort study we estimated a potential expected increase of 5 4 95 per cent confidence interval 1 8 12 7 cd4 lymphocytes l per additional study visit while on zidovudine therapy we also explain the theory and implementation of msms for repeated measures data and draw upon a simple example to illustrate the basic ideas

integrable hydrodynamic chains a new approach for derivation of benney type moment chains and integrable hydrodynamic type systems is presented new integrable hydrodynamic chains are constructed all their hydrodynamical reductions are described and integrated new 2 1 integrable hydrodynamic type systems are found

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

semiparametric regression for the mean and rate functions of recurrent events the counting process with the cox type intensity function has been commonly used to analyse recurrent event data this model essentially assumes that the underlying counting process is a time transformed poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process recently pepe and cai and lawless and co workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the poisson type assumption in this paper we provide a rigorous justification of such robust procedures through modern empirical process theory furthermore we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean rate model the advantages of the robust procedures are demonstrated through simulation studies an illustration with multiple infection data taken from a clinical study on chronic granulomatous disease is also provided