cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

homogeneous einstein randers metrics on symplectic groups abstract in this paper we prove that lie group sp n n 3 admits at least one family of invariant einstein randers metrics which are not naturally reductive we also give the classification of these metrics under isometries and determine their group of isometries moreover we prove that if homogeneous randers space m f with navigation data h w is berwald then m f is naturally reductive if and only if the riemannian metric m h is naturally reductive

weighted estimators for proportional hazards regression with missing covariates missing covariate data are common in epidemiologic studies and disease prevention trials in this article regression parameter estimation in the cox proportional hazards model is considered when certain covariates are observed for all study subjects and other covariate data are collected only for a subset the article presents both simple weighted and kernel assisted fully augmented weighted estimators that use the partially incomplete data nonparametrically we use nonparametric methods to estimate selection probabilities in the simple weighted estimating functions we also use nonparametric kernel smoothing techniques to estimate certain conditional expectations in fully augmented weighted estimating functions the proposed methods are nonparametric in the sense that they require neither a model for the missing data mechanism nor specification of the conditional distribution of missing covariates given observed covariates these estimators allow the missing data mechanism to depend on outcome variables

a semiparametric method for estimating population size for capture recapture experiments with random covariates in continuous time a semiparametric estimation procedure is proposed to model capture recapture data with the aim of estimating the population size for a closed population individuals covariates are possibly time dependent and missing at noncaptured times and may be measured with error a set of estimating equations ees based on covariate process and capture recapture data is constructed to estimate the relevant parameters and the population size these ees can be solved by an algorithm similar to an em algorithm simulation results show that the proposed procedures work better than the naive estimate in some cases they are even better than ideal estimates for which the true values of covariates are available for all captured subjects over the entire experimental period we apply the method to a capture recapture experiment on the bird species prinia flaviventris in hong kong

multiple closed geodesics on bumpy finsler n spheres abstract in this paper we prove that for every bumpy finsler metric f on every rationally homological n dimensional sphere s n with n 2 there exist always at least two distinct prime closed geodesics

on dually flat randers metrics abstract the notion of dually flat finsler metrics arise from information geometry in this paper we will study a special class of finsler metrics called randers metrics to be dually flat a simple characterization is provided and some non trivial explicit examples are constructed in particular we will show that the dual flatness of a randers metric always arises from that of some riemannian metric by doing some special deformations

symplectic geometry and hilbert s fourth problem inspired by hofer s definition of a metric on the space of compactly supported hamiltonian maps on a symplectic manifold this paper exhibits an area length duality between a class of metric spaces and a class of symplectic manifolds using this duality it is shown that there is a twistor like correspondence between finsler metrics on pn whose geodesics are projective lines and a class of symplectic forms on the grassmannian of 2 planes in n 1

finsler manifolds with nonpositive flag curvature and constant s curvature the flag curvature is a natural extension of the sectional curvature in riemannian geometry and the s curvature is a non riemannian quantity which vanishes for riemannian metrics there are incomplete non riemannian finsler metrics on an open subset in rn with negative flag curvature and constant s curvature in this paper we are going to show a global rigidity theorem that every finsler metric with negative flag curvature and constant s curvature must be riemannian if the manifold is compact we also study the nonpositive flag curvature case

on dually flat α β metrics abstract the dual flatness for riemannian metrics in information geometry has been extended to finsler metrics the aim of this paper is to study the dual flatness of the so called metrics in finsler geometry by doing some special deformations we will show that the dual flatness of an metric always arises from that of some riemannian metric in dimensional n 3

what is wrong with the hausdorff measure in finsler spaces we construct a class of finsler metrics in three dimensional space such that all their geodesics are lines but not all planes are extremal for their hausdorff area functionals this shows that if the hausdorff measure is used as notion of volume on finsler spaces then totally geodesic submanifolds are not necessarily minimal filling results such as those of ivanov on two dimensional minimal fillings st petersburg math j 13 2002 17 25 do not hold and integral geometric formulas do not exist on the other hand using the holmes thompson definition of volume we prove a general crofton formula for finster spaces and give an easy proof that their totally geodesic hypersurfaces are minimal c 2005 elsevier inc all rights reserved

on some explicit constructions of dually flat finsler metrics abstract by using the fundamental property of the dually flat equation we manufacture explicitly new examples of dually flat finsler metrics these metrics contain the funk metric on the unit ball

hydrodynamics of stochastic cellular automata we investigate a stochastic version of cellular automata used for simulating hydrodynamical flows e g the hpp and fhp models the extra stochasticity consists of random exchanges between neighboring cells which conserve momentum we prove that in suitable limits these models satisfy the appropriate continuous boltzmann and hydrodynamic equations the same as those conjectured for the original models except that there is no negative viscosity contribution the results are obtained by proving a very strong form of propagation of chaos and by using hilbert chapman enskog type expansions explicit proofs are presented for the stochastic hpp model

a missing composite covariate in survival analysis a case study of the chinese longitudinal health and longevity survey we estimate a cox proportional hazards model where one of the covariates measures the level of a subject s cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire a case study is presented where the sample includes partial respondents who did not answer some questionnaire items the total score takes hence the form of an interval censored variable and as a result the level of cognitive functioning is missing on some subjects we handle the partial respondents by taking a likelihood based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval estimates are obtained by an e m type algorithm that reduces to the iterative maximization of three complete log likelihood functions derived from two augmented data sets with case weights alternated with weights updating this methodology is exploited to assess the mini mental state examination index as a prognostic factor of survival in a sample of chinese older adults

proportional hazards regression with missing covariates abstract nonparametric maximum likelihood npml is used to estimate regression parameters in a proportional hazards regression model with missing covariates the npml estimator is shown to be consistent and asymptotically normally distributed under some conditions em type algorithms are applied to solve the maximization problem variance estimates of the regression parameters are obtained by a profile likelihood approach that uses em aided numerical differentiation simulation results indicate that the npml estimates of the regression parameters are more efficient than the approximate partial likelihood estimates and estimates from complete case analysis when missing covariates are missing completely at random and that the proposed method corrects for bias when the missing covariates are missing at random

likelihood based methods for missing covariates in the cox proportional hazards model problems associated with missing covariate data are well known but often ignored we present a method for estimating the parameters in the cox proportional hazards model when the missing data are missing at random mar and censoring is noninformative due to the computational burden of this method we introduce an approximation that allows us to use a weighted expectation maximization em algorithm to estimate the parameters more easily when the missing covariates are continuous rather than categorical we implement a monte carlo version of the em algorithm along with the gibbs sampler to obtain parameter estimates we also give the asymptotic distribution of these estimates the primary advantage of this method over complete case analysis is that it produces more efficient parameter estimates and corrects for bias in the mar setting to motivate the methodology we present an analysis of a phase iii melanoma clinical trial conducted by the eastern cooperative oncology group

reweighting estimators for cox regression with missing covariates missingness in covariates is a common problem in survival data in this article we propose a reweighting method for estimating the regression parameters in the cox model with missing covariates we also consider the augmented reweighting method by subtracting the projection term onto the nuisance tangent space the proposed method provides consistent and asymptotically normally distributed estimators when the missing data mechanism depends on the outcome variables as well as on the observed covariates with either monotone or arbitrary nonmonotone missingness patterns simulation results indicate that in most situations the proposed reweighting estimators are more efficient than the inverse probability weighting estimators for the regression coefficients of the missing covariates and are as efficient as or more efficient than the inverse probability weighting estimators for the regression coefficients of the completely observed covariates the simple reweighting estimators can be easily implemented in st

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

monte carlo em for missing covariates in parametric regression models we propose a method for estimating parameters for general parametric regression models with an arbitrary number of missing covariates we allow any pattern of missing data and assume that the missing data mechanism is ignorable throughout when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 we extend this method t o continuous or mixed categorical and continuous covariates and for arbitrary parametric regression models by adapting a monte carlo version of the em algorithm as discussed by wei and tanner 1990 journal of the american statistical association85 699 704 in addition we discuss the gibbs sampler for sampling from the conditional distribution of the missing covariates given the observed data and show that the appropriate complete conditionals are log concave the log concavity property of the conditional distributions will facilitate a straightforward implementation of the gibbs sampler via the adaptive rejection algorithm of gilks and wild 1992 applied statistics41 337 348 we assume the model for the response given the covariates is an arbitrary parametric regression model such as a generalized linear model a parametric survival model or a nonlinear model we model the marginal distribution of the covariates as a product of one dimensional conditional distributions this allows us a great deal of flexibility in modeling the distribution of the covariates and reduces the number of nuisance parameters that are introduced in the e step we present examples involving both simulated and real data

on a class of dually flat general α β metrics abstract in this paper we study a class of finsler metric defined by a riemannian metric a 1 form and its norm general metric we classify locally dually flat general metric when the riemannian metric is strongly dually flat and give some new examples

finsler geodesics in the presence of a convex function and their applications in this paper we obtain a result about the existence of only a finite number of geodesics between two fixed non conjugate points in a finsler manifold endowed with a convex function we apply it to randers and zermelo metrics as a by product we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime

time minimal control of dissipative two level quantum systems the generic case the objective of this article is to complete preliminary results from the work of bonnard and sugny 2009 and sugny et al 2007 concerning the time minimal control of dissipative two level quantum systems whose dynamics is governed by the lindblad equation the extremal system is described by a 3d hamiltonian depending upon three parameters we combine geometric techniques with numerical simulations to deduce the optimal solutions

hilbert isometries and maximal deviation preserving maps on jb algebras abstract in this paper we characterize the surjective linear variation norm isometries on jb algebras variation norm isometries are precisely the maps that preserve the maximal deviation the quantum analogue of the standard deviation which plays an important role in quantum statistics consequently we characterize the hilbert s metric isometries on cones in jb algebras

homogeneous randers spaces with isotropic s curvature and positive flag curvature in this paper we will give a complete classification of homogeneous randers spaces with isotropic s curvature and positive flag curvature this results in a large class of finsler spaces with non constant positive flag curvature at the final part of the paper we prove a rigidity result asserting that a homogeneous randers space with almost isotropic s curvature and negative ricci scalar must be riemannian

a jackknife estimator of variance for cox regression for correlated survival data studies in the health sciences often give rise to correlated survival data wei lin and weissfeld 1989 journal of the american statistical association 84 1065 1073 and lee wei and amato 1992 in survival analysis state of the art showed that if the marginal distributions of the correlated survival times follow a proportional hazards model then the estimates from cox s partial likelihood cox d r 1972 journal of the royal statistical society series b 24 187 220 naively treating the correlated survival times as independent give consistent estimates of the relative risk parameters however because of the correlation between survival times the inverse of the information matrix may not be a consistent estimate of the asymptotic variance wei et al 1989 and lee et al 1992 proposed a robust variance estimate that is consistent for the asymptotic variance we show that a one step jackknife estimator of variance is asymptotically equivalent to their variance estimator the jackknife variance estimator may be preferred because an investigator needs only to write a simple loop in a computer package instead of a more involved program to compute wei et al 1989 and lee et al s 1992 estimator

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

double semiparametric method for missing covariates in cox regression models the problem of nuisance covariate model specification is considered in cox regression where the maximum semiparametric likelihood method is used to handle the missing covariates a component of the covariates is modeled nonparametrically to achieve robustness against covariate model misspecification and to reduce the number of possibly intractable integrations involved in the parametric modeling of the covariates the statistical properties of the proposed method are examined it is found that in some important situations the maximum semiparametric likelihood can be applied without making any additional parametric model assumptions on covariates the proposed method can yield a more efficient estimator than the nonparametric imputation methods and does not require specification of the missingness mechanism when compared with the inverse probability weighting method a real data example is analyzed to demonstrate use of the proposed method

sharp uncertainty principles on general finsler manifolds the paper is devoted to sharp uncertainty principles heisenberg pauli weyl caffarelli kohn nirenberg and hardy inequalities on forward complete finsler manifolds endowed with an arbitrary measure under mild assumptions the existence of extremals corresponding to the sharp constants in the heisenberg pauli weyl and caffarelli kohn nirenberg inequalities fully textit characterizes the nature of the finsler manifold in terms of three non riemannian quantities namely its textit reversibility and the vanishing of the textit flag curvature and s textit curvature induced by the measure respectively it turns out in particular that the busemann hausdorff measure is the optimal one in the study of sharp uncertainty principles on finsler manifolds the optimality of our results are supported by randers type finslerian examples originating from the zermelo navigation problem

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

minimal surfaces in a randers sphere with the rotational killing vector field abstract the minimal surfaces in finsler geometry with respect to the busemann hausdorff measure and the holmes thompson measure are called bh minimal and ht minimal surfaces respectively let p 1 p 2 p 3 p 4 be the coordinates of r 4 and s 3 f be a randers sphere of flag curvature k 1 with the navigation data h w where h is the standard sphere metric and w e 0 0 p 4 p 3 0 e 1 is a killing vector field in this paper we study the rotationally invariant minimal surface in s 3 f generated by rotating the curve x s y s z s 0 in the upper half sphere of s 2 around the p 1 p 2 plane s r we first show that such a rotational bh minimal surface in s 3 f is either a great 2 sphere or the catenoid in s 3 h then we give a classification of the rotational ht minimal surfaces where we use the angle data to analyze the solutions of the system of ode that characterizes the ht minimality and prove that such a rotational ht minimal surface must be a great 2 sphere an ht minimal torus or a rotational surface of unduloid type as a special case we obtain a distinguished embedded compact ht minimal torus depending on e the completeness of these surfaces is also studied

on the energy functional on finsler manifolds and applications to stationary spacetimes in this paper we first study some global properties of the energy functional on a non reversible finsler manifold in particular we present a fully detailed proof of the palais smale condition under the completeness of the finsler metric moreover we define a finsler metric of randers type which we call fermat metric associated to a conformally standard stationary spacetime we shall study the influence of the fermat metric on the causal properties of the spacetime mainly the global hyperbolicity moreover we study the relations between the energy functional of the fermat metric and the fermat principle for the light rays in the spacetime this allows one to obtain existence and multiplicity results for light rays using the finsler theory finally the case of timelike geodesics with fixed energy is considered

some einstein randers metrics on homogeneous spaces abstract in this paper we study invariant einstein randers metrics on some homogeneous riemannian manifolds of rank 2 by finding out all the invariant killing vector fields on the corresponding homogeneous einstein riemannian manifolds we obtain a complete description of all the invariant einstein randers metrics on those homogeneous manifolds since the underlying riemannian einstein metrics are generically not diagonal this presents a large number of non riemannian homogeneous einstein randers spaces of nonconstant flag curvature

microscopic reversibility and the nonlinear einstein onsager relation in macroscopic description of nucleation we investigate the possibility of describing fluctuational decay of a metastable phase macroscopically without a detailed knowledge of the microscopic kinetics using the ideas of microscopic reversibility we construct a hydrodynamic type equation which describes the buildup of fluctuations in the region of subcritical sizes an equation of ornstein uhlenbeck type is used to bridge this equation with the one describing unstable growth of larger overcritical fluctuations an explicit time dependent solution to the proposed system of equations is derived in the spirit of the singular perturbation technique it is shown that this solution also accurately approximates the solution of the farkas becker doring master equation so that the macroscopic level of description is consistent with the underlying models

dissipation and large thermodynamic fluctuations the results of recent work of kipnis olla and varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation including non equilibrium steady states as a fluctuation dissipation hypothesis the basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation it is shown that this hypothesis leads to a nonlinear version of onsager machlup fluctuation theory that had previously been proposed by graham a direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints onsager s principle of least dissipation following graham the theory leads also to a generalized potential analogous to an equilibrium free energy for the nonequilibrium steady state and an associated static variational principle finally a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large deviations theory on a formal analogy with the results of freidlin and wentzell for finite dimensional systems

s curvature of cohomogeneity one randers spaces abstract in this paper we study s curvature of cohomogeneity one randers spaces with orbit space s 1 in particular we present an explicit coordinate free formula of s curvature in terms of some quantities which is determined by the metric and the structure of the manifold as an application we give a sufficient and necessary condition for a cohomogeneity one randers space to have almost isotropy s curvature furthermore we give some simple criterions for a cohomogeneity one randers space to be a berwald space or a douglas space

projectively flat general α β metrics with constant flag curvature abstract in this paper we study the flag curvature of a new class of finsler metrics called general metrics which are defined by a riemannian metric and a 1 form the classification of such metrics with constant flag curvature are completely determined under some suitable conditions which make them locally projectively flat as a result we construct many new projectively flat finsler metrics with flag curvature 1 0 and 1 in section 9 all of which are of singularity at some directions

estimating equations with incomplete categorical covariates in the cox model incomplete covariate data is a common occurrence in many studies in which the outcome is survival time when a full likelihood is specified a useful technique for obtaining parameter estimates is the em algorithm we propose a set of estimating equations to estimate the parameters of cox s proportional hazards model when some covariate values are missing these estimating equations can be solved by an algorithm similar to the em algorithm because of the computational burden of finding a solution to these estimating equations we propose obtaining parameter estimates via monte carlo methods asymptotic variances of the parameter estimates are also derived we present a clinical trials example with three covariates two of which have some missing values

stochastic least action principle for the incompressible navier stokes equation abstract we formulate a stochastic least action principle for solutions of the incompressible navier stokes equation which formally reduces to hamilton s principle for the incompressible euler solutions in the case of zero viscosity we use this principle to give a new derivation of a stochastic kelvin theorem for the navier stokes equation recently established by constantin and iyer which shows that this stochastic conservation law arises from particle relabelling symmetry of the action we discuss issues of irreversibility energy dissipation and the inviscid limit of navier stokes solutions in the framework of the stochastic variational principle in particular we discuss the connection of the stochastic kelvin theorem with our previous martingale hypothesis for fluid circulations in turbulent solutions of the incompressible euler equations

on the flag curvature of a class of randers metric generated from the navigation problem abstract let f x y be a randers metric of douglas type on a manifold m and v be a conformal vector field on m f let f x y be a randers metric generated from f v by solving the navigation problem f x y f x y v x 1 in this paper we establish the relationship among the flag curvature of f the flag curvature of f and the conformal vector field v see theorem 1 1

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

projectively flat randers metrics with constant flag curvature we classify locally projectively flat randers metrics with constant ricci curvature and obtain a new family of randers metrics of negative constant flag curvature

reweighting estimators for cox regression with missing covariate data analysis of insulin resistance and risk of stroke in the northern manhattan study incomplete covariates often obscure analysis results from a cox regression in an analysis of the northern manhattan study nomas to determine the influence of insulin resistance on the incidence of stroke in non diabetic individuals insulin level is unknown for 34 1 of the subjects the available data suggest that the missingness mechanism depends on outcome variables which may generate biases in estimating the parameters of interest if only using the complete observations this article aimed to introduce practical strategies to analyze the nomas data and present sensitivity analyses by using the reweighting method in standard statistical packages when the data set structure is in counting process style the reweighting estimates can be obtained by built in procedures with variance estimated by the jackknife method simulation results indicate that the jackknife variance estimate provides reasonable coverage probability in moderate sample sizes we subsequently conducted sensitivity analyses for the nomas data showing that the risk estimates are robust to a variety of missingness mechanisms at the end of this article we present the core sas and r programs used in the analysis

on general α β metrics with isotropic s curvature abstract the s curvature is an important non riemannian quantity in finsler geometry in this paper we study a class of finsler metrics called general metrics which are defined by a riemannian metric and a 1 form we characterize all of general metrics with isotropic s curvature

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

cox regression with survival time dependent missing covariate values analysis with time to event data in clinical and epidemiological studies often encounters missing covariate values and the missing at random assumption is commonly adopted which assumes that missingness depends on the observed data including the observed outcome which is the minimum of survival and censoring time however it is conceivable that in certain settings missingness of covariate values is related to the survival time but not to the censoring time this is especially so when covariate missingness is related to an unmeasured variable affected by the patient s illness and prognosis factors at baseline if this is the case then the covariate missingness is not at random as the survival time is censored and it creates a challenge in data analysis in this article we propose an approach to deal with such survival time dependent covariate missingness based on the well known cox proportional hazard model our method is based on inverse propensity weighting with the propensity estimated by nonparametric kernel regression our estimators are consistent and asymptotically normal and their finite sample performance is examined through simulation an application to a real data example is included for illustration

projectively flat finsler metrics of constant flag curvature finsler metrics on an open subset in r n with straight geodesics are said to be projective it is known that the flag curvature of any projective finsler metric is a scalar function of tangent vectors the flag curvature must be a constant if it is riemannian in this paper we discuss the classification problem on projective finsler metrics of constant flag curvature we express them by a taylor expansion or an algebraic formula many examples constructed in this paper can be used as models in finsler geometry

on the topological properties of symplectic maps in this paper we show that symplectic maps have surprising topological properties in particular we construct an interesting metric for the symplectic diffeomorphism groups which is related but not obviously to the topological properties of symplectic maps and phase space geometry we also prove a certain number of generalised symplectic fixed point theorems and give an application to a hamiltonian system

hydrodynamics for an ideal fluid hamiltonian formalism and liouville equation abstract a hamiltonian formalism for hydrodynamics of ideal fluids is developed with the help of seliger and whitham s variational principle it is shown that a density distribution function in the phase space of the mass density momentum density and energy density fields obeys a liouville equation

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

time optimal control of a self propelled particle in a spatiotemporal flow field abstractwe address a minimum time problem that constitutes an extension of the classical zermelo navigation problem in higher dimensions in particular we address the problem of steering a self propelled particle to a prescribed terminal position with free terminal velocity in the presence of a spatiotemporal flow field furthermore we assume that the norm of the rate of change of the particle s velocity relative to the flow is upper bounded by an explicit upper bound to address the problem we first employ pontryagin s minimum principle to parameterise the set of candidate time optimal control laws in terms of a parameter vector that belongs to a compact set subsequently we develop a simple numerical algorithm for the computation of the minimum time to come function that is tailored to the particular parametrisation of the set of the candidate time optimal control laws of our problem the proposed approach bypasses the task of converting the optimal control problem to a parameter optimisation proble

minimality of totally geodesic submanifolds in finsler geometry using the symplectic definition of the holmes thompson volume we prove that totally geodesic submanifolds of a finsler manifold are minimal for this volume thanks to well suited technics the minimality of totally geodesic hypersurfaces see alvarez paiva and berck in adv math 204 2 647 663 2006 and 2 dimensional totally geodesic surfaces see alvarez paiva and berck in adv math 204 2 647 663 2006 ivanov in algebra i analiz 13 1 26 38 2001 had already been proved however the corresponding statement for the hausdorff measure is known to be wrong even in the simplest case of totally geodesic 2 dimensional surfaces in a 3 dimensional finsler manifold see alvarez paiva and berck in adv math 204 2 647 663 2006

zermelo navigation on riemannian manifolds in this paper we study zermelo navigation on riemannian manifolds and use that to solve a long standing problem in finsler geometry namely the complete classification of strongly convex randers metrics of constant flag curvature

the geometry of symplectic energy non squeezing theorem which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form r2 x b2 where b2 is a 2 disc this led to hofer s discovery of symplectic capacities which give a way of measuring the size of subsets in symplectic manifolds recently hofer found a way to measure the size or energy of symplectic diffeomorphisms by looking at the total variation of their generating hamiltonians this gives rise to a bi invariant pseudo norm on the group ham m of compactly supported hamiltonian symplectomorphisms of the manifold m the deep fact is that this pseudo norm is a norm in other words the only symplectomorphism on m with zero energy is the identity map up to now this had been proved only for sufficiently nice symplectic manifolds and by rather complicated analytic arguments in this paper we consider a more geometric version of this energy which was first considered by eliashberg and hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary we prove by a simple geometric argument that both versions of energy give rise to genuine norms on all symplectic manifolds roughly speaking we show that if there were a symplectomorphism of m which had too little energy one could embed a large ball into a thin cylinder m x

twistor geometry of a pair of second order odes we discuss the twistor correspondence between path geometries in three dimensions with vanishing wilczynski invariants and anti self dual conformal structures of signature 2 2 we show how to reconstruct a system of odes with vanishing invariants for a given conformal structure highlighting the ricci flat case in particular using this framework we give a new derivation of the wilczynski invariants for a system of odes whose solution space is endowed with a conformal structure we explain how to reconstruct the conformal structure directly from the integral curves and present new examples of systems of odes with point symmetry algebra of dimension four and greater which give rise to anti self dual structures with conformal symmetry algebra of the same dimension some of these examples are 2 2 analogues of plane wave space times in general relativity finally we discuss a variational principle for twistor curves arising from the finsler structures with scalar flag curvature

multiple imputation for m regression with censored covariates we develop a new multiple imputation approach for m regression models with censored covariates instead of specifying parametric likelihoods our method imputes the censored covariates by their conditional quantiles given the observed data where the conditional quantiles are estimated through fitting a censored quantile regression process the resulting estimator is shown to be consistent and asymptotically normal and it improves the estimation efficiency by using information from cases with censored covariates compared with existing methods the proposed method is more flexible as it does not require stringent parametric assumptions on the distributions of either the regression errors or the covariates the finite sample performance of the proposed method is assessed through a simulation study and the analysis of a c reactive protein dataset in the 2007 2008 national health and nutrition examination survey this article has supplementary material online

ricci quadratic homogeneous randers spaces abstract a finsler space is called ricci quadratic if its ricci curvature r i c x y is quadratic in y it is called a berwald space if its chern connection defines a linear connection directly on the underlying manifold m in this article we prove that a homogeneous randers space is ricci quadratic if and only if it is of berwald type

solution to the quantum zermelo navigation problem the solution to the problem of finding a time optimal control hamiltonian to generate a given unitary gate in an environment in which there exists an uncontrollable ambient hamiltonian e g a background field is obtained in the classical context finding the time optimal way to steer a ship in the presence of a background wind or current is known as the zermelo navigation problem whose solution can be obtained by working out geodesic curves on a space equipped with a randers metric the solution to the quantum zermelo problem which is shown here to take a remarkably simple form is likewise obtained by finding explicit solutions to the geodesic equations of motion associated with a randers metric on the space of unitary operators the result reveals that the optimal control in a sense goes along with the wind

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

homogeneous einstein randers metrics on spheres abstract in this paper we study the homogeneous einstein randers metrics on spheres it turns out that we can find out all the homogeneous non riemannian einstein randers metrics on spheres furthermore we obtain a complete classification of such metrics under isometries using this we present a large number of homogeneous einstein randers metrics of non constant flag curvature

einstein randers metrics on some homogeneous manifolds abstract in this paper we get some new examples of non riemannian einstein randers metrics on homogeneous manifolds g h when g is either the compact simple lie group f 4 or g 2 based on the discussions associated with kahler c spaces we obtain some new einstein riemannian metrics on some homogeneous manifolds and prove that they admit non riemannian einstein randers metrics

hilbert and thompson isometries on cones in jb algebras hilbert s and thompson s metric spaces on the interior of cones in jb algebras are important examples of symmetric banach finsler spaces in this paper we characterize the hilbert s metric isometries on the interiors of cones in jbw algebras and the thompson s metric isometries on the interiors of cones in jb algebras these characterizations generalize work by bosche on the hilbert s and thompson s metric isometries on symmetric cones and work by hatori and molnar on the thompson s metric isometries on the cone of positive self adjoint elements in a unital c algebra to obtain the results we develop a variety of new geometric and jordan algebraic techniques

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

einstein riemannian metrics and einstein randers metrics on a class of homogeneous manifolds abstract in this paper we get a class of homogeneous manifolds admitting einstein riemannian metrics moreover we prove that they admit non riemannian einstein randers metrics

time minimal control of dissipative two level quantum systems the integrable case the objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two level quantum systems whose dynamics is governed by the lindblad equation we focus our analysis on the case where the extremal hamiltonian is integrable

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

augmented inverse probability weighted estimator for cox missing covariate regression summary this article investigates an augmented inverse selection probability weighted estimator for cox regression parameter estimation when covariate variables are incomplete this estimator extends the horvitz and thompson 1952 journal of the american statistical association 47 663 685 weighted estimator this estimator is doubly robust because it is consistent as long as either the selection probability model or the joint distribution of covariates is correctly specified the augmentation term of the estimating equation depends on the baseline cumulative hazard and on a conditional distribution that can be implemented by using an em type algorithm this method is compared with some previously proposed estimators via simulation studies the method is applied to a real example

auxiliary covariate data in failure time regression summary we consider the problem of missing covariate data in the context of censored failure time relative risk regression auxiliary covariate data which are considered informative about the missing data but which are not explicitly part of the relative risk regression model may be available full covariate information is available for a validation set an estimated partial likelihood method is proposed for estimating relative risk parameters this method is an extension of the estimated likelihood regression analysis method for uncensored data pepe 1992 pepe fleming 1991 a key feature of the method is that it is nonparametric with respect to the association between the missing and observed including auxiliary covariate components asymptotic distribution theory is derived for the proposed estimated partial likelihood estimator in the case where the auxiliary or mismeasured covariates are categorical asymptotic efficiencies are calculated for exponential failure times using an exponential relative risk model the estimated partial likelihood estimator compares favourably with a fully parametric maximum likelihood analysis comparisons are also made with a standard partial likelihood analysis which ignores the incomplete observations important efficiency gains can be made with the estimated partial likelihood method small sample properties are investigated through simulation studies

zermelo navigation in the quantum brachistochrone we analyse the optimal times for implementing unitary quantum gates in a constrained finite dimensional controlled quantum system the family of constraints studied is that the permitted set of time dependent hamiltonians is the unit ball of a norm induced by an inner product on we also consider a generalization of this to arbitrary norms we construct a randers metric by applying a theorem of shen on zermelo navigation the geodesics of which are the time optimal trajectories compatible with the prescribed constraint we determine all geodesics and the corresponding time optimal hamiltonian for a specific constraint on the control i e for any given value of some of the results of carlini et al are re derived using alternative methods a first order system of differential equations for the optimal hamiltonian is obtained and shown to be of the form of the euler poincar equations we illustrate that this method can form a methodology for determining which physical substrates are effective at supporting the implementation of fast quantum computation

a conditional model for incomplete covariates in parametric regression models summary incomplete covariate data arise in many data sets when the missing covariates are categorical a useful technique for obtaining parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 this method requires the estimation of many nuisance parameters for the distribution of the covariates unfortunately in data sets when the percentage of missing data is high and the missing covariate patterns are highly non monotone the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest we propose a conditional model for the covariate distribution that has several modelling advantages for the e step and provides a reduction in the number of nuisance parameters thus providing more stable estimates in finite samples we present a clinical trials example with six covariates five of which have some missing values

curvatures of homogeneous randers spaces abstract we study curvatures of homogeneous randers spaces after deducing the coordinate free formulas of the flag curvature and ricci scalar of homogeneous randers spaces we give several applications we first present a direct proof of the fact that a homogeneous randers space is ricci quadratic if and only if it is a berwald space we then prove that any left invariant randers metric on a non commutative nilpotent lie group must have three flags whose flag curvature is positive negative and zero respectively this generalizes a result of j a wolf on riemannian metrics we prove a conjecture of j milnor on the characterization of central elements of a real lie algebra in a more generalized sense finally we study homogeneous finsler spaces of positive flag curvature and particularly prove that the only compact connected simply connected lie group admitting a left invariant finsler metric with positive flag curvature is su 2

nontrivial minimal surfaces in a class of finsler spheres of vanishing s curvature abstract the minimal surface theory in finsler geometry deserves to be well developed as that in riemannian geometry in this paper we derive the mean curvature of submanifolds in a general manifold by considering the busemann hausdorff measure and holmes thompson measure respectively we then study the rotationally invariant minimal surfaces in the finsler 3 sphere endowed with an metric f k k k k k 1 where is a smooth function s 3 k is the berger sphere e 4 k 1 and k is a killing one form of constant length along the hopf fibers of s 3 we define the energy of the minimal surfaces and by using the volume ratio function introduced by the author and y b shen we give the explicit local expressions of the rotationally invariant bh minimal and ht minimal surfaces in such sphere respectively as a special case we give a detailed study of the rotationally invariant ht minimal surfaces in the 3 sphere with square metric

deformations and hilbert s fourth problem in this paper a special class of finsler metrics defined by a riemannian metric and an 1 form is studied the projectively flat metrics in dimension n ge 3 are classified by a new class of metric deformations in riemann geometry the results show that the projective flatness of such finsler metrics always arises from that of some riemannian metric

geodesics in randers spaces of constant curvature geodesies in randers spaces of constant curvature are classified randers metrics have received much attention lately as solutions to zermelo s problem of navigation largely because this navigation structure provides the frame work for a complete classification of constant flag curvature randers spaces flag curvature is the finslerian analog of riemannian sectional curvature see br04 briefly a randers metric is of constant flag curvature if and only if it solves zer melo s problem of navigation on a riemannian manifold of constant sectional cur vature under the influence of an infinitesimal homothety w see subsection 1 1 for a sketch of the navigation problem and theorem 3 for an explicit statement of the classification result the aim of this paper is to develop a geometric description of the geodesies in these spaces of constant curvature intuitively these paths minimize travel time across a riemannian landscape under windy conditions presently we will show that these curves are given by composing geodesies of the riemannian metric with the flow generated by w this claim is formalized by theorem 2 geodesies on surfaces of constant nonpositive curvature are illustrated in section 3 we then turn in section 4 to the constant flag curvature k 1 randers metrics on sn the case of the sphere is especially interesting it is possible to endow this closed manifold with a metric whose geodesies display distinctly non riemannian behaviors for example 1 a metric is projectively flat if every point admits coordinates in which the geodesies are straight lines belt r ami s theorem assures us that a riemannian metric is of constant sectional curvature if and only if it is projectively flat in contrast few randers spaces of constant flag curvature are projectively flat there are infinitely many nonisometric randers metrics of constant positive

trace formula for noisy flows a trace formula is derived for the fokker planck equation associated with ito stochastic differential equations describing noisy time continuous nonlinear dynamical systems in the weak noise limit the trace formula provides estimations of the eigenvalues of the fokker planck operator on the basis of the pollicott ruelle resonances of the noiseless deterministic system which is assumed to be non bifurcating at first order in the noise amplitude the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo energy of the onsager machlup freidlin wentzell scheme

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

a mean score method for missing and auxiliary covariate data in regression models summary we consider regression analysis when incomplete or auxiliary covariate data are available for all study subjects and in addition for a subset called the validation sample true covariate data of interest have been ascertained the term auxiliary data refers to data not in the regression model but thought to be informative about the true missing covariate data of interest we discuss a method which is nonparametric with respect to the association between available and missing data allows missingness to depend on available response and covariate values and is applicable to both cohort and case control study designs the method previously proposed by flanders greenland 1991 and by zhao lipsitz 1992 is generalised and asymptotic theory is derived our expression for the asymptotic variance of the estimator provides intuition regarding performance of the method optimal sampling strategies for the validation set are also suggested by the asymptotic results