shared frailty models for recurrent events and a terminal event there has been an increasing interest in the analysis of recurrent event data cook and lawless 2002 statistical methods in medical research 11 141 166 in many situations a terminating event such as death can happen during the follow up period to preclude further occurrence of the recurrent events furthermore the death time may be dependent on the recurrent event history in this article we consider frailty proportional hazards models for the recurrent and terminal event processes the dependence is modeled by conditioning on a shared frailty that is included in both hazard functions covariate effects can be taken into account in the model as well maximum likelihood estimation and inference are carried out through a monte carlo em algorithm with metropolis hastings sampler in the e step an analysis of hospitalization and death data for waitlisted dialysis patients is presented to illustrate the proposed methods methods to check the validity of the proposed model are also demonstrated this model avoids the difficulties encountered in alternative approaches which attempt to specify a dependent joint distribution with marginal proportional hazards and yields an estimate of the degree of dependence

quadratic functors on pointed categories we study polynomial functors of degree 2 called quadratic with values in the category of abelian groups ab and whose source category is an arbitrary category c with null object such that all objects are colimits of copies of a generating object e which is small and regular projective this includes all categories of models v of a pointed theory t more specifically we are interested in such quadratic functors f from c to ab which preserve filtered colimits and suitable coequalizers a functorial equivalence is established between such functors f c ab and certain minimal algebraic data which we call quadratic c modules these involve the values on e of the cross effects of f and certain structure maps generalizing the second hopf invariant and the whitehead product applying this general result to the case where e is a cogroup these data take a particularly simple form this application extends results of baues and pirashvili obtained for c being the category of groups or of modules over some ring here quadratic c modules are equivalent with abelian square groups or quadratic r modules respectively

the ternary commutator obstruction for internal crossed modules abstract in finitely cocomplete homological categories co smash products give rise to possibly higher order commutators of subobjects we use binary and ternary co smash products and the associated commutators to give characterisations of internal crossed modules and internal categories respectively the ternary terms are redundant if the category has the smith is huq property which means that two equivalence relations on a given object commute precisely when their normalisations do in fact we show that the difference between the smith commutator of such relations and the huq commutator of their normalisations is measured by a ternary commutator so that the smith is huq property itself can be characterised by the relation between the latter two commutators this allows us to show that the category of loops does not have the smith is huq property which also implies that ternary commutators are generally not decomposable into nested binary ones thus in contexts where smith is huq need not hold we obtain a new description of internal categories beck modules and double central extensions as well as a decomposition formula for the smith commutator the ternary commutator now also appears in the hopf formula for the third homology with coefficients in the abelianisation functor

ideals and clots in universal algebra and in semi abelian categories we clarify the relationship between basic constructions of semi abelian category theory and the theory of ideals and clots in universal algebra to name a few results in this frame which establish connections between hitherto separated subjects 0 regularity in universal algebra corresponds to the requirement that regular epimorphisms are normal we describe clots in categorical terms and show that ideals are images of clots under regular epimorphisms we show that the relationship between internal precrossed modules and internal reflexive graphs extends the relationship between compatible reflexive binary relations and clots

a joint model of recurrent events and a terminal event with a nonparametric covariate function we extend the shared frailty model of recurrent events and a dependent terminal event to allow for a nonparametric covariate function we include a gaussian random effect frailty in the intensity functions of both the recurrent and terminal events to capture correlation between the two processes we employ the penalized cubic spline method to describe the nonparametric covariate function in the recurrent events model we use laplace approximation to evaluate the marginal penalized partial likelihood without a closed form we also propose the variance estimates for regression coefficients numerical analysis results show that the proposed estimates perform well for both the nonparametric and parametric components we apply this method to analyze the hospitalization rate of patients with heart failure in the presence of death

regression splines in the time dependent coefficient rates model for recurrent event data many epidemiologic studies involve the occurrence of recurrent events and much attention has been given for the development of modeling techniques that take into account the dependence structure of multiple event data this paper presents a time dependent coefficient rates model that incorporates regression splines in its estimation procedure such methods would be appropriate in situations where the effect of an exposure or covariates changes over time in recurrent event data settings the finite sample properties of the estimators are studied via simulation using data from a randomized community trial that was designed to evaluate the effect of vitamin a supplementation on recurrent diarrheal episodes in small children we model the functional form of the treatment effect on the time to the occurrence of diarrhea the results describe how this effect varies over time in summary we observed a major impact of the vitamin a supplementation on diarrhea after 2 months of the dosage with the effect diminishing after the third dosage the proposed method can be viewed as a flexible alternative to the marginal rates model with constant effect in situations where the effect of interest may vary over time

loss of stability at turning points in nonlinear elliptic variational inequalities a considerable amount of work has been devoted in recent years to stationary free boundary problems in particular obstacle problems have been the subject of extensive work concerning existence estimates and regularity of the solution or of the coincidence set and occurrence of multiple solutions in 6 8 161 the authors consider obstacle problems with nonlinear forcing terms leading to multiple solutions hence to turning points when a real parameter appears in the forcing term a local study of the branches of solutions is set up the results obtained are the extension in a weaker form of those well known for equations ll 12 however some important classical questions remain open for obstacle problems

approximating eigenfunctions of fredholm operators in banach spaces abstract a singular fredholm operator a is perturbed by an operator of finite rank to obtain an invertible operator b theory previously developed for a and b in hilbert spaces is extended here to banach spaces the operator b 1 is used to construct independent elements in the null spaces n a n a2 n ak for some positive integer k and a basis for n a and n a2 the theory is used to compute approximations to eigenfunctions and generalized eigenfunctions of integral operators

higher central extensions and hopf formulae abstract higher extensions and higher central extensions which are of importance to non abelian homological algebra are studied and some fundamental properties are proven as an application a direct proof of the invariance of the higher hopf formulae is obtained

approximation of the spectrum of closed operators the determination of normal modes of a rotating basin note univ michigan dept math ann arbor mi 48109 ecole polytech ctr math appl f 91128 palaiseau france descloux j ecole prat hautes etud dept math f 75231 paris 05 france isi document delivery no le068times cited 3cited reference count 17 reference asn article 1981 004doi 10 2307 2007731 record created on 2006 08 24 modified on 2017 05 12

local piecewise polynomial projection methods for an o d e which give high order convergence at knots local projection methods which yield c sup m 1 piecewise polynomials of order m k as approximate solutions of a boundary value problem for an mth order ordinary differential equation are determined by the k linear functionals at which the residual error in each partition interval is required to vanish on we develop a condition on these k functionals which implies breakpoint superconvergence of derivatives of order less than m for the approximating piecewise polynomials the same order of superconvergence is associated with eigenvalue problems a discrete connection between two particular projectors yielding o vertical bardvertical bar sup 2k superconvergence namely a collocation at the k gauss legendre points in each partition interval and b essential least squares i e local moment methods is made by asking that this same order of superconvergence result when using collocation at k r points per interval and simultaneous local orthogonality of the residual to polynomials of order r the k r points then necessarily form a subset of the k gauss legendre points

proportional hazards models with frailties and random effects we discuss some of the fundamental concepts underlying the development of frailty and random effects models in survival one of these fundamental concepts was the idea of a frailty model where each subject has his or her own disposition to failure their so called frailty additional to any effects we wish to quantify via regression although the concept of individual frailty can be of value when thinking about how data arise or when interpreting parameter estimates in the context of a fitted model we argue that the concept is of limited practical value individual random effects frailties whenever detected can be made to disappear by elementary model transformation in consequence unless we are to take some model form as unassailable beyond challenge and carved in stone and if we are to understand the term frailty as referring to individual random effects then frailty models have no value random effects models on the other hand in which groups of individuals share some common effect can be used to advantage even in this case however if we are prepared to sacrifice some efficiency we can avoid complex modelling by using the considerable power already provided by the stratified proportional hazards model stratified models and random effects models can both be seen to be particular cases of partially proportional hazards models a view that gives further insight the added structure of a random effects model viewed as a stratified proportional hazards model with some added distributional constraints will for group sizes of five or more provide no more than modest efficiency gains even when the additional assumptions are exactly true on the other hand for moderate to large numbers of very small groups of sizes two or three the study of twins being a well known example the efficiency gains of the random effects model can be far from negligible for such applications the case for using random effects models rather than the stratified model is strong this is especially so in view of the good robustness properties of random effects models nonetheless the simpler analysis based upon the stratified model remains valid albeit making a less efficient use of resources

normalities and commutators abstract we first compare several algebraic notions of normality from a categorical viewpoint then we introduce an intrinsic description of higgins commutator for ideal determined categories and we define a new notion of normality in terms of this commutator our main result is to extend to any semi abelian category the following well known characterization of normal subgroups a subobject k is normal in a if and only if a k k

higher hopf formulae for homology via galois theory we use janelidze s categorical galois theory to extend brown and ellis s higher hopf formulae for homology of groups to arbitrary semi abelian monadic categories given such a category alpha and a chosen birkhoff subcategory beta of alpha thus we describe the barr beck derived functors of the reflector of alpha onto beta in terms of centralization of higher extensions in case alpha is the category gp of all groups and beta is the category ab of all abelian groups this yields a new proof for brown and ellis s formulae we also give explicit formulae in the cases of groups vs k nilpotent groups groups vs k solvable groups and precrossed modules vs crossed modules

on the three subobjects lemma and its higher order generalisations abstract we solve a problem mentioned in the article 1 of berger and bourn we prove that in the context of an algebraically coherent semi abelian category two natural definitions of the lower central series coincide in a first standard approach nilpotency is defined as in group theory via nested binary commutators of the form x x x in a second approach higher higgins commutators of the form x x x are used to define nilpotent objects 18 16 20 the two are known to be different in general for instance in the context of loops the definition of bruck 6 is of the former kind while the commutator associator filtration of mostovoy 27 26 and his co authors is of the latter type another example in the context of moufang loops is given in 1 in this article we show that the two streams of development agree in any algebraically coherent semi abelian category such are for instance all orzech categories of interest 31 our proof of this result is based on a higher order version of the three subobjects lemma of 8 which extends the classical three subgroups lemma from group theory to categorical algebra it says that any n fold higgins commutator k 1 k n of normal subobjects k i x may be decomposed into a join of nested binary commutators

basic reproduction ratios for almost periodic compartmental models with time delay abstract the theory of basic reproduction ratio r 0 is established for a large class of almost periodic and time delayed compartmental population models we first present some dynamical properties for linear almost periodic functional differential systems by using the product space and evolution semigroup approach we then prove that r 0 1 has the same sign as the exponential growth bound of an associated linear system as an application we apply the developed theory to an almost periodic seir model with an incubation period and obtain a threshold result on its global dynamics in terms of r 0 finally we present some numerical simulations numerical simulations indicate that prolonging the length of incubation period is beneficial for the control of the disease in addition a simple model shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one

numerical continuation methods for studying periodic travelling wave wavetrain solutions of partial differential equations abstract periodic travelling waves wavetrains are an important solution type for many partial differential equations in this paper i review the use of numerical continuation for studying these solutions i discuss the calculation of the form and stability of a given periodic travelling wave and the calculation of boundaries in a two dimensional parameter plane for wave existence and stability i also describe the automated implementation of these numerical continuation procedures via the software package wavetrain http www ma hw ac uk wavetrain i conclude by discussing ongoing work on numerical continuation methods for determining the absolute stability of periodic travelling waves

global threshold dynamics of an infection age structured sir epidemic model with diffusion under the dirichlet boundary condition abstract in this paper we are concerned with the global asymptotic behavior of an infection age structured sir epidemic model with diffusion in a general n dimensional bounded spatial domain under the homogeneous dirichlet boundary condition by using the method of characteristics we reformulate the model into a system of a reaction diffusion equation and a volterra integral equation we define the basic reproduction number r 0 by the spectral radius of a compact positive linear operator and show that if r 0 1 then the disease free steady state is globally attractive whereas if r 0 1 then a positive endemic steady state exists and the system is uniformly persistent by numerical simulation for the 2 dimensional case we show that r 0 depends on the shape of the spatial domain this result is in contrast with the case of the homogeneous neumann boundary condition in which r 0 is independent of the spatial domain

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

a comparison of frailty models for multivariate survival data this paper reviews some of the main approaches to the analysis of multivariate censored survival data such data typically have correlated failure times the correlation can be a consequence of the observational design for example with clustered sampling and matching or it can be a focus of interest as in genetic studies longitudinal studies of recurrent events and other studies involving multiple measurements we assume that the correlation between the failure or survival times can be accounted for by fixed or random frailty effects we then compare the performance of conditional and mixture likelihood approaches to estimating models with these frailty effects in censored bivariate survival data we find that the mixture methods are surprisingly robust to misspecification of the frailty distribution the paper also contains an illustrative example on the times to onset of chest pain brought on by three endurance exercise tests during a drug treatment trial of heart patients

commutator theory for loops abstract using the freese mckenzie commutator theory for congruence modular varieties as the starting point we develop commutator theory for the variety of loops the fundamental theorem of congruence commutators for loops relates generators of the congruence commutator to generators of the total inner mapping group we specialize the fundamental theorem into several varieties of loops and also discuss the commutator of two normal subloops consequently we argue that some standard definitions of loop theory such as elementwise commutators and associators should be revised and linked more closely to inner mappings using the new definitions we prove several natural properties of loops that could not be so elegantly stated with the standard definitions of loop theory for instance we show that the subloop generated by the new associators defined here is automatically normal we conclude with a preliminary discussion of abelianess and solvability in loops

topological semi abelian algebras given an algebraic theory t whose category of models is semi abelian we study the category top t of topological models of t and generalize to it most classical results on topological groups in particular top t is homological which includes barr regularity and forces the mal cev property every open subalgebra is closed and every quotient map is open we devote special attention to the hausdorff compact locally compact connected totally disconnected and profinite t algebras c 2004 elsevier inc all rights reserved

a categorical approach to commutator theory abstract we define a notion of commutator for equivalence relations in a mal cev category and show that it verifies a universal property

the spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators we are concerned with the numerical solution of the eigenvalue problem t varphi lambda varphi varphi ne 0 where t is a linear operator in a bana ch space t may represent a bounded integral operator or a closed differential operator with bounded inverse the linear operator t and its approximation t n are defined in the same space perturbation theory is then a suitable framework for our problem we present in the first part a systematic study of the various notions of convergence t n to t which imply the convergence of the eigenvalues with preservation of the multiplicities the results are then applied to practical methods for integral and differential operators in the second part we present convergence rates analytic perturbation theory is used to refine on the computed eigenelements of an integral operator and to produce localization results on the eigenelements finally superconvergence results are discussed both for integral and differential operators

a nonlocal and time delayed reaction diffusion eco epidemiological predator prey model abstract in this paper we propose and investigate a nonlocal and time delayed reaction diffusion predator prey model with disease spread in the prey which incorporates spatial heterogeneity and assimilation lag of consumed prey biomass into predator biomass the si type subsystem of prey without predator is first studied and we establish the threshold dynamics in terms of the basic reproduction number based on epidemiology then we show a series of sufficient conditions for the co existence of prey and predator species the global extinction of predator species and the global extinction of both the prey and predator species finally a special example is explored via numerical simulations where the influences of nonlocal effect spatial heterogeneity and time delay on the invasion of the predator species are probed

a semiparametric recurrent events model with time varying coefficients we consider a recurrent events model with time varying coefficients motivated by two clinical applications a random effects gaussian frailty model is used to describe the intensity of recurrent events the model can accommodate both time varying and time constant coefficients the penalized spline method is used to estimate the time varying coefficients laplace approximation is used to evaluate the penalized likelihood without a closed form the smoothing parameters are estimated in a similar way to variance components we conduct simulations to evaluate the performance of the estimates for both time varying and time independent coefficients we apply this method to analyze two data sets a stroke study and a child wheeze study

semiparametric frailty models for clustered failure time data summary we consider frailty models with additive semiparametric covariate effects for clustered failure time data we propose a doubly penalized partial likelihood dppl procedure to estimate the nonparametric functions using smoothing splines we show that the dppl estimators could be obtained from fitting an augmented working frailty model with parametric covariate effects whereas the nonparametric functions being estimated as linear combinations of fixed and random effects and the smoothing parameters being estimated as extra variance components this approach allows us to conveniently estimate all model components within a unified frailty model framework we evaluate the finite sample performance of the proposed method via a simulation study and apply the method to analyze data from a study of sexually transmitted infections sti

spectral properties of diagonally dominant infinite matrices part i on etablit des theoremes de type gersgorin pour un operateur matriciel infini non borne diagonalement dominant a agissant sur l p pour 1 p

a nonlocal and time delayed reaction diffusion model of dengue transmission a nonlocal and time delayed reaction diffusion model of dengue fever is first proposed that incorporates the aquatic stage the winged stage and the incubation periods of the dengue virus within mosquitos and hosts then the basic reproduction number r 0 is established for the model system and an explicit formula of r 0 is obtained in the case of spatially homogeneous infections it is shown that this r 0 gives the threshold dynamics in the sense that the disease free equilibrium is asymptotically stable if r 0 1 the influences of diffusion coefficients time delays and infection heterogeneity on the spread of the disease are also studied via numerical simulations it turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections

intrinsic centrality and associated classifying properties abstract the notion of central morphism is introduced in the very soft algebraic context of unital categories it reveals inside any such category an additive core which has a strong classifying potential

the computation of water waves modelled by nekrasov s equation nekrasov s integral equation describing water waves of almost extreme form is solved numerically the method consists of applying a simple quadrature rule to a rearranged version of the original equation strongly graded meshes are used to resolve an expected boundary layer in the solution for methods based on the trapezoidal rule global bifurcation theory is used to prove for fixed discretization parameter n the existence a continuous branch of positive numerical solutions these are parametrized by mu a natural parameter occurring in the original integral equation for fixed mu collective compactness arguments then prove subsequential convergence of these solutions as the mesh is refined i e as n to infty numerical experiments using higher order quadrature rules are reported these reveal that the method is capable of detecting a boundary layer and gibbs phenomenon type oscillations of maximum height about 0 37 circ in a region of width o 70 mathord left vphantom

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

3 3 lemma and protomodularity abstract the classical 3 3 lemma and snake lemma valid in any abelian category still hold in any quasi pointed the map 0 1 is a mono regular and protomodular category some applications are given in this abstract context concerning the denormalization of kernel maps and the normalization of internals groupoids i e associated crossed modules

large scale eigenvector approximation via hilbert space embedding nystrom the nystrom method approximates eigenvectors of a given kernel matrix by randomly sampling subset of data previous researches focus on good kernel approximation while the quality of eigenvector approximation is rarely explored in online eigenvector approximation method one can minimize the kernel approximation error to guarantee a good eigenvector approximation however in this work we paradoxically prove that for batch approximation methods like nystrom it is no longer true this unexpected discovery opens a question what criterion should we use in nystrom to generate a decent eigenvector approximation to address this problem we propose a novel criterion named hilbert space embedding hse nystrom criterion which directly minimizes the eigenvector approximation error the proposed hse criterion provides a general framework to approximate eigenvectors within linear time and space complexity we then show that we can rediscover many successful nystrom methods with the proposed criterion including k means nystrom and density nystrom to further demonstrate the power of our criterion we actually design a novel algorithm to approximate eigenvectors of laplacian matrices based on the proposed criterion with better accuracy among existing linear complexity methods we demonstrate the efficiency and efficacy of our proposal in numerical experiments highlightsa new criterion for nystrom method to find accurate eigenvector approximation the conventional criterion does not work well in eigenvector approximation we need to adjust kernel width together with average weight adaptively propose a new criterion to adaptively optimize the parameters efficiently

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