boundary layer analysis in the semiclassical limit of a quantum drift diffusion model abstract we study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift diffusion model of a semiconductor we prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions we prove analytical estimates of the remainder terms of this asymptotic expansion and confirm by means of numerical simulations that these remainder estimates are sharp

some properties of the kaplan meier estimator for independent nonidentically distributed random variables in this paper we study the kaplan meier estimator in the case where survival and censoring times are not all i i d we prove several results which are analogous to those shown by van zuijlen in the complete data case

elliptic operators with unbounded drift coefficients and neumann boundary condition abstract we study the realization an of the operator a 1 2 du d in l 2 with neumann boundary condition where is a possibly unbounded convex open set in r n u is a convex unbounded function du x is the element with minimal norm in the subdifferential of u at x and dx c exp 2u x dx is a probability measure infinitesimally invariant for a we show that an is a dissipative self adjoint operator in l 2 log sobolev and poincare inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by an

on using stratification in the analysis of linear regression models with right censoring we study two modified synthetic data least squares estimation methods for linear regression models with right censored response variables unspecified residual distributions and random censoring variables which may not be i i d these methods are the result of an investigation into the use of stratification we conclude that stratification should be used whether or not the censoring variables are dependent on the covariates we give the asymptotic results of the estimators and numerical results

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

weak solutions to the stationary quantum drift diffusion model abstract the existence of weak solutions to the stationary quantum drift diffusion equations for semiconductor devices is investigated the proof is based on minimization procedure of non linear functional and schauder fixed point theorem furthermore the semiclassical limit e 0 from the quantum drift diffusion model to the classical drift diffusion model is discussed

generalized 3 d paving an automated quadrilateral surface mesh generation algorithm this paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three dimensional trimmed surfaces methods of calculating angles projecting elements and detecting collisions between paving boundaries for general surfaces are presented extensions of the smoothing algorithms for three dimensions are set forth advances in the use of scalar sizing functions are presented these functions can be used to better approximate internal mesh density from boundary densities and surface characteristics

residual plots for the censored data linear regression model to be consistent censored data linear regression estimators typically require a correctly specified linear regression function and independent and identically distributed errors for uncensored data one can assess these model assumptions informally by examining plots of the residuals against the independent variables or fitted values in this paper i propose plots for censored data analogous to these uncensored data residual plots one can use such plots in the same way as their uncensored data counterparts for checking model assumptions if the model assumptions are correct then the plots should exhibit a random scatter i show that the proposed plots are useful in selecting a linear regression model for the stanford heart transplant data

h morph an indirect approach to advancing front hex meshing h morph is a new automatic algorithm for the generation of a hexahedral dominant finite element mesh for arbitrary volumes the h morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra it uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh recovery techniques similar to those used in boundary constrained delaunay mesh generation are used tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed at any time during the h morph procedure a valid mixed hexahedral tetrahedral mesh is in existence within the volume the procedure continues until no tetrahedral remain within the volume or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements any remaining tetrahedral are typically towards the interior of the volume generally a less critical region for analysis transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh its ability to mesh without the need to decompose or recognize special classes of geometry and its characteristic well aligned layers of elements parallel to the boundary example test cases are presented on a variety of models

on the bipolar multidimensional quantum euler poisson system the thermal equilibrium solution and semiclassical limit abstract in this paper we establish the existence of a unique thermal equilibrium solution of the bipolar multidimensional quantum euler poisson system over the whole space r 3 and obtain the relevant semiclassical limit and a combined planck debye length limit through using energy estimating methods and a fixed point theory

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

local dual contributions representing dual surfaces for block meshing in this work we present a tool based on the new concept of local dual contributions for directly representing the topology and the approximated geometry of the dual of a block mesh this tool allows us to obtain a valid block decomposition of a given geometry without a previous discretization of its boundary specifically our tool is composed of a hierarchical scheme and a set of matching rules that explicitly insert descriptions of dual surfaces and handle their intersections that is the proposed tool generates a dual of the block mesh with intersections of the proper multiplicity without gaps and which respects the boundary features of the domain finally we present several examples that illustrate the applicability of the tool copyright 2010 john wiley sons ltd

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

censored regression local linear approximations and their applications abstract various statistical tools are available for modeling the relationship between response and covariate if the data are fully observable in the situation of censored data however those tools are no longer directly applicable this article provides an easily implemented methodology for modeling the association based on censored data the form of the regression relationship will be completely determined by the data no assumptions are made about this form basic ideas behind the methodology are to transform the observed data in an appropriate simple way and then to apply a locally weighted least squares regression the proposed estimator involves a variable bandwidth that automatically adapts to the design of the data points that the methodology is very easy to implement is illustrated by several examples including simulation studies and an analysis of the stanford heart transplant data and the primary biliary cirrhosis data several theoretical considerations are reflected in the examples fina

extended weighted log rank estimating functions in censored regression abstract in the censored regression model some regression estimators are introduced using weighted integrals of the log rank estimating functions their limiting covariance matrices do not involve the error density and can be reliably estimated inference can then be easily obtained some of these estimators have high asymptotic efficiency at some important submodels some lack of fit tests are derived that require little extra computing time these tests are asymptotically normal under the model and consistent against certain monotone or convex model misspecifications numerical studies show that for some weight functions the estimators and tests perform well implementation of the proposed procedures is discussed and illustrated in a real data example

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

existence and positivity of solutions of a fourth order nonlinear pde describing interface fluctuations we study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system in that application x lies in r but here we study primarily the periodic case x e s we establish existence uniqueness and regularity of solutions locally in time for positive initial data in h s and prove the existence of several families of lyapunov functions for the evolution from the latter we establish a sharp connection between existence globally in time and positivity preservation if o t is a maximal half open interval of existence for a positive solution of the equation with t 1 16r2 then t 03 and lim m w r exists and is constant we discuss also some explicit solutions and propose a generalization to higher dimensions 0 1994 john wiley

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

renovated scatterplots for censored data summary in simple linear regression where the response variable has been subject to right censoring censored points in the scatterplot of observed data are moved vertically to create a renovated scatterplot where the bias of censoring is removed the relationship to least squares estimation and the effect on regression diagnostics are examined in the multiple regression context

nonparametric regression estimates with censored data local linear smoothers and their applications for censored time to event data beran unpublished manuscript followed by doksum and yandell 1982 properties of regression estimates based on censored survival data and dabrowska 1987 scandinavian journal of statistics 14 181 197 suggested a nonparametric regression technique based on the kernel method to estimate the conditional survival function we propose to improve the bias term and boundary effects of their procedure by using local linear fits this is illustrated in this paper with simulated and real data moreover consistency results for the local linear based estimates of the conditional survival cumulative hazard mean and median functions are also established

face offsetting a unified approach for explicit moving interfaces dynamic moving interfaces are central to many scientific engineering and graphics applications in this paper we introduce a novel method for moving surface meshes called the face offsetting method based on a generalized huygens principle our method operates directly on a lagrangian surface mesh without requiring an eulerian volume mesh unlike traditional lagrangian methods which move each vertex directly along an approximate normal or user specified direction our method propagates faces and then reconstructs vertices through an eigenvalue analysis locally at each vertex to resolve normal and tangential motion of the interface simultaneously the method also includes techniques for ensuring the integrity of the surface as it evolves face offsetting provides a unified framework for various dynamic interface problems and delivers accurate physical solutions even in the presence of singularities and large curvatures we present the theoretical foundation of our method and also demonstrate its accuracy efficiency and flexibility for a number of benchmark problems and a real world application

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

sequential analysis for censored regression data abstract motivated by buckley and james modification of the least squares procedure for censored regression data we derive a score process that incorporates the time evolution and handles staggered entry data in a natural way by censored regression data we mean that the responses are subject to a possible right censorship such cases often arise from clinical trials and industrial life tests the score process can be interpreted as a weighted comparison of transformed survival times this is especially suitable for the accelerated failure time regression model by expressing it in an appropriate form so that the counting process and its associate martingale theory can be applied we show that the score process is approximated by a mean 0 multidimensional gaussian process a consistent estimator of its covariance matrix function is provided based on the covariance matrix estimator and the sequential test of slud and wei a repeated significance test is then proposed usefulness of the procedure is il

regression m estimators with doubly censored data the m estimators are proposed for the linear regression model with random design when the response observations are doubly censored the proposed estimators are constructed as some functional of a campbell type estimator f n for a bivariate distribution function based on data which are doubly censored in one coordinate we establish strong uniform consistency and asymptotic normality of f n and derive the asymptotic normality of the proposed regression m estimators through verifying their hadamard differentiability property as corollaries we show that our results on the proposed m estimators also apply to other types of data such as uncensored observations bivariate observations under univariate right censoring bivariate right censored observations and so on computation of the proposed regression m estimators is discussed and the method is applied to a doubly censored data set which was encountered in a recent study on the age dependent growth rate of primary breast cancer

formation of pyramid elements for hexahedra to tetrahedra transitions new algorithms are proposed for the modification of a mixed hexahedra tetrahedra element mesh to maintain compatibility by the insertion of pyramid elements several methods for generation of the pyramids are presented involving local tetrahedral transformations and or node insertion near the hex tet interface local smoothing and topological operations improve the quality of the transition region results show superior performance of the resulting elements in a commercial finite element code over non conforming interface conditions

functional form diagnostics for cox s proportional hazards model summary we propose a new type of residual and an easily computed functional form test for the cox proportional hazards model the proposed test is a modification of the omnibus test for testing the overall fit of a parametric regression model developed by stute gonzalez manteiga and presedo quindimil 1998 journal of the american statistical association93 141 149 and is based on what we call censoring consistent residuals in addition we develop residual plots that can be used to identify the correct functional forms of covariates we compare our test with the functional form test of lin wei and ying 1993 biometrika80 557 572 in a simulation study the practical application of the proposed residuals and functional form test is illustrated using both a simulated data set and a real data set

hexahedral meshing using midpoint subdivision and integer programming abstract the generation of finite element meshes of 3d hexahedral elements can be performed by subdividing the model into a number of simple bodies like hexahedra triangular prisms etc within these bodies regular or simple transition meshes can be generated in this paper a method called midpoint subdivision will be discussed which enables the user to build the model using a number of high level subregions which satisfy certain simple topological conditions these subregions can be automatically subdivided into meshes of hexahedral elements for analysis the distribution of elements within the mesh is typically controlled by specifying the division numbers of certain edges however for a given set of subregions there are a number of constraints on the edge division numbers that will yield a compatible mesh the use of integer programming will be discussed this finds the compatible division numbers which are nearest to but not less than the target values specified

regression m estimators with non i i d doubly censored data considering the linear regression model with fixed design the usual m estimator with a complete sample of the response variables is expressed as a functional of a generalized weighted bivariate empirical process and its asymptotic normality is directly derived through the hadamard differentiability property of this functional and the weak convergence of this generalized weighted empirical process the result reveals the direct relationship between the m estimator and the distribution function of the error variables in the linear model which leads to the construction of the m estimator when the response variables are subject to double censoring for this proposed regression m estimator with non i i d doubly censored data strong consistency and asymptotic normality are established

the stationary current voltage characteristics of the quantum drift diffusion model this paper is concerned with numerical algorithms for the bipolar quantum drift diffusion model for the thermal equilibrium case a quasi gradient method minimizing the energy functional is introduced and strong convergence is proved the computation of current voltage characteristics is performed by means of an extended gummel iteration it is shown that the involved fixed point mapping is a contraction for small applied voltages in this case the model equations are uniquely solvable and convergence of the proposed iteration scheme follows numerical simulations of a one dimensional resonant tunneling diode are presented the computed current voltage characteristics are in good qualitative agreement with experimental measurements the appearance of negative differential resistances is verified for the first time in a quantum drift diffusion model

existence and asymptotic behavior of multi dimensional quantum hydrodynamic model for semiconductors this paper is devoted to the study of the existence and the time asymptotic of multi dimensional quantum hydrodynamic equations for the electron particle density the current density and the electrostatic potential in spatial periodic domain the equations are formally analogous to classical hydrodynamics but differ in the momentum equation which is forced by an additional nonlinear dispersion term due to the quantum bohm potential and are used in the modelling of quantum effects on semiconductor devices we prove the local in time existence of the solutions in the case of the general nonconvex pressure density relation and large and regular initial data furthermore we propose a subsonic type stability condition related to one of the classical hydrodynamical equations when this condition is satisfied the local in time solutions exist globally in time and converge time exponentially toward the corresponding steady state since for this problem classical methods like for instance the friedrichs theory for symmetric hyperbolic systems cannot be used we investigate via an iterative procedure an extended system which incorporates the one under investigation as a special case in particular the dispersive terms appear in the form of a fourth order wave type equation

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

quantile regression under random censoring censored regression models have received a great deal of attention in both the theoretical and applied econometric literature most of the existing estimation procedures for either cross sectional or panel data models are designed only for models with fixed censoring in this paper a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed this procedure is then applied to the clad and quantile estimators of powell j econom 25 1984 303 32 1986a 143 to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring the resulting estimator is shown to have desirable asymptotic properties and performs well in a small scale simulation study

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

asymptotics for a censored generalized linear model with unknown link function for censored response variable against projected co variable a generalized linear model with an unknown link function can cover almost all existing models under censorship its special cases include the accelerated failure time model with censored data such a model in the uncensored case is called the single index model in econometrics in this paper we systematically study the asymptotic properties we derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter we also obtain the optimal convergence rate of an estimator of the unknown link function in the model

iterative partial least squares with right censored data analysis a comparison to other dimension reduction techniques summary in the linear model with right censored responses and many potential explanatory variables regression parameter estimates may be unstable or when the covariates outnumber the uncensored observations not estimable we propose an iterative algorithm for partial least squares based on the buckley james estimating equation to estimate the covariate effect and predict the response for a future subject with a given set of covariates we use a leave two out cross validation method for empirically selecting the number of components in the partial least squares fit that approximately minimizes the error in estimating the covariate effect of a future observation simulation studies compare the methods discussed here with other dimension reduction techniques data from the aids clinical trials group protocol 333 are used to motivate the methodology

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

long time behavior for a nonlinear fourth order parabolic equation we study the asymptotic behavior of solutions of the initial boundary value problem with periodic boundary conditions for a fourth order nonlinear degenerate diffusion equation with a logarithmic nonlinearity for strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity these results are derived by analyzing the equation verified by the logarithm of the solution

nearest neighbor estimation of a bivariate distribution under random censoring we consider the problem of estimating the bivariate distribution of the random vector x y when y may be subject to random censoring the censoring variable c is allowed to depend on x but it is assumed that y and c are conditionally independent given x x the estimate of the bivariate distribution is obtained by averaging estimates of the conditional distribution of y given x x over a range of values of x the weak convergence of the centered estimator multiplied by n 1 2 is obtained and a closed form expression for the covariance function of the limiting process is given it is shown that the proposed estimator is optimal in the beran sense this is similar to an optimality property the product limit estimator enjoys using the proposed estimator of the bivariate distribution an extension of the least squares estimator to censored data polynomial regression is obtained and its asymptotic normality established

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

m estimation in censored linear models summary we propose a method of obtaining an m estimator in a linear model when the responses are subject to right censoring the central limit theorem for the estimator using squared error loss i e least squares is derived using counting process martingale techniques the estimation method is applied to the stanford heart transplant data for illustration

the wasserstein gradient flow of the fisher information and the quantum drift diffusion equation we prove the global existence of non negative variational solutions to the drift diffusion evolution equation partial t u div left u mathrm d left 2 frac delta sqrt u sqrt u f right right 0 under variational boundary condition despite the lack of a maximum principle for fourth order equations non negative solutions can be obtained as a limit of a variational approximation scheme by exploiting the particular structure of this equation which is the gradient flow of the perturbed fisher information functional fancyscript f f u frac 12 int left mathrm d log u right 2 u dx int fu dx with respect to the kantorovich rubinstein wasserstein distance between probability measures we also study long time behavior of the solutions proving their exponential decay to the equilibrium state g e v characterized by delta v frac12 left mathrm d v right 2 f quad int rm e v dx int u 0 dx when the potential v is uniformly convex in this case the functional fancyscript f f coincides with the relative fisher information fancyscript f f u frac12 fancyscript i u g int left mathrm d log u g right 2u dx

some limit analysis in a one dimensional stationary quantum hydrodynamic model for semiconductors in this paper we study the steady state hydrodynamic equations for isothermal states including the quantum bohn potential the one dimensional equations for the electron current density and the particle density are coupled self consistently to the poisson equation for the electric potential the quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit the debye length quasi neutral limit and some combined limits respectively for each limit we show the strong convergence of the sequence of solutions and give the associated convergence rate

a finite element scheme with the aid of a new carving technique combined with smoothed integration abstract an efficient scheme is proposed that can generate appropriate meshes for three dimensional complex domains leading to accurate solutions in finite element analysis after preparing a structured mesh with hexahedral elements the surface information of an arbitrary domain is soaked into the mesh the elements around the surface are trimmed according to the surface information and then they are replaced by polyhedral elements while the interior of the domain remains occupied by the original hexahedral elements the scheme is further extended to manage complex domains with discontinuities in geometry and material properties such as a polycrystalline structure comprised of multiple materials or grains as well as highly curved domains with a single material subsequently the generated mesh composed of the polyhedral elements on the surface and the hexahedral elements in the interior is directly applied for finite element analysis in conjunction with smoothed integration in the strain smoothing technique because the smoothed integration does not require the shape function derivatives the efficient analysis can be conducted without explicitly defined shape functions of the polyhedral elements the smoothed integration can improve the accuracy of the numerical solutions as well the present study focuses on reporting a new idea on a finite element scheme using the polyhedral elements with the smoothed integration rather than providing a general and systematic approach however it has a great potential to deal with general and practical problems through numerical examples it is shown that the proposed scheme provides accurate solutions in a simple and efficient manner

convergent finite element discretizations of the density gradient equation for quantum semiconductors we study nonlinear finite element discretizations for the density gradient equation in the quantum drift diffusion model in particular we give a finite element description of the so called nonlinear scheme introduced by ancona we prove the existence of discrete solutions and provide a consistency and convergence analysis which yields the optimal order of convergence for both discretizations the performance of both schemes is compared numerically in particular with respect to the influence of approximate vacuum boundary conditions

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

numerical simulation of interface waves by high order spectral modeling techniques few problems in elastodynamics have a closed form analytical solution the others can be investigated with semianalytical methods but in general one is not sure whether these methods give reliable solutions the same happens with numerical techniques for instance finite difference methods solve in principle any complex problem including those with arbitrary inhomogeneities and boundary conditions however there is no way to verify the quantitative correctness of the solutions the major problems are stability with respect to material properties numerical dispersion and the treatment of boundary conditions in practice these problems may produce inaccurate solutions in this paper the study of complex problems with two different numerical grid techniques in order to cross check the solutions is proposed interface waves in particular are emphasized since they pose the major difficulties due to the need to implement boundary conditions the first method is based on global differential operators where the solution is expanded in terms of the fourier basis and chebyshev polynomials while the second is the spectral element method an extension of the finite element method that uses chebyshev polynomials as interpolating functions both methods have spectral accuracy up to approximately the nyquist wave number of the grid moreover both methods implement the boundary conditions in a natural way particularly the spectral element algorithm we first solve lamb s problem and compare numerical and analytical solutions then the problem of dispersed rayleigh waves and finally the two quarter space problem we show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect matching when these solutions do not exist the combined modeling techniques provide a powerful tool for solving complex problems in elastodynamics

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

a strengthened central limit theorem for smooth densities abstract we consider the central limit theorem for the probability density function n x of the standardized sum of independent and identically distributed random variables with finite variance and regular probability density function by showing boundedness of different convex functionals along the sequence fn we prove convergence in various norms to the normal density

development of an automatic two dimensional finite element mesh generator using quadrilateral elements and bezier curve boundary definition this paper describes the development of an automatic two dimensional quadrilateral element mesh generator the methodology is based on the looping algorithm developed in part by dr m l c sluiter bezier curves are used to define the boundaries of the parts to be meshed the required interaction by the user is reduced to specifying the boundary geometry the preferred element size and the refinement coefficient transition elements are automatically generated between regions of varying element sizes the ability to offset specified boundary curves insures well conditioned elements along the boundary meshes for several sample geometries are presented to illustrate the versatility of the mesh generator

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

a boundary collocation meshfree method for the treatment of poisson problems with complex morphologies a new meshfree method based on a discrete transformation of green s basis functions is introduced to simulate poisson problems with complex morphologies the proposed green s discrete transformation method gdtm uses source points that are located along a virtual boundary outside the problem domain to construct the basis functions needed to approximate the field the optimal number of green s functions source points and their relative distances with respect to the problem boundaries are evaluated to obtain the best approximation of the partition of unity condition a discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions a comprehensive convergence study is presented to investigate the accuracy and convergence rate of the gdtm we will also demonstrate the application of this meshfree method for simulating the conductive heat transfer in a heterogeneous materials system and the dissolved aluminum ions concentration in the electrolyte solution formed near a passive corrosion pit

all hexahedral element meshing generation of the dual mesh by recurrent subdivision abstract the domain geometry is defined by means of a closed all quadrilateral mesh the outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements following the guidelines of the outer topology the inner one is almost entirely defined several ways may be decided for certain configurations some of them requiring special considerations in order to achieve a valid fem mesh the process is entirely performed by constructing the graph theoretical dual of the hexahedral mesh this means no metric information is handled until the final positioning and smoothing steps the essential steps of this scheme are described by means of examples

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

uniform convergence of an exponentially fitted scheme for the quantum drift diffusion model we analyze an exponentially fitted finite element scheme for the unipolar quantum drift diffusion model in one dimensional space the existence of discrete solutions is shown under very mild assumptions and convergence of a subsequence is proved by compactness arguments the scheme is constructed in such a way that it reduces in the semiclassical limit to the well known scharfetter gummel discretization for the classical drift diffusion model we derive uniform error bounds which allow for the semiclassical limit on the discrete level numerical tests underlining the analytical results are presented

unconstrained plastering hexahedral mesh generation via advancing front geometry decomposition the generation of all hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem unconstrained plastering is a new method for generating all hexahedral finite element meshes on arbitrary volumetric geometries starting from an unmeshed volume boundary unconstrained plastering generates the interior mesh topology without the constraints of a pre defined boundary mesh using advancing fronts unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes each of which can be meshed with simple meshing primitives by breaking from the tradition of previous advancing front algorithms which start from pre meshed boundary surfaces unconstrained plastering demonstrates that for the tested geometries high quality boundary aligned orientation insensitive all hexahedral meshes can be generated automatically without pre meshing the boundary examples are given for meshes from both solid mechanics and geotechnical applications copyright 2009 john wiley sons ltd

automatic generation of multiblock decompositions of surfaces summary multiblock structured meshes have significant advantages over fully unstructured meshes in numerical simulation but automatically generating these meshes is considerably more difficult a method is described herein for automatically generating high quality multiblock decompositions of surfaces with boundaries controllability and flexibility are useful capabilities of the method additional alignment constraints for forcing the appearance of particular features in the decomposition can be easily handled also adjustments are made according to input metric tensor fields that describe target element size properties the general solution strategy is based around using a four way symmetry vector field called a cross field to describe the local mesh orientation on a triangulation of the surface initialisation is performed by propagating the boundary alignment constraints to the interior in a fast marching method this is similar in a way to an advancing front or paving method but much more straightforward and flexible because mesh connectivity does not have to be managed in the cross field multiblock decompositions are generated by tracing the separatrices of the cross field to partition the surface into quadrilateral blocks with square corners the final task of meshing the decomposition requires solving an integer programming problem for block division numbers copyright 2015 john wiley sons ltd

a comparison of estimators for regression with a censored response variable summary several methods of estimating parameters in a linear regression when the response variable is censored are compared the estimator of buckley james 1979 is preferred further it is shown that the strength of the regression the support and distribution of the censoring variable and the magnitude of the slope all have an effect on the relative performance of the estimators

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

a novel scheme to generate meshes with hexahedral elements and poly pyramid elements the carving technique abstract a novel scheme for three dimensional mesh generation termed the carving technique is proposed with the aid of poly pyramid elements soaking the geometry information of a given model into a regular reference mesh with brick elements the reference mesh is trimmed by the surface of the model using the marching cube algorithm the trimmed elements are reconstructed by the proposed elements which here are termed the poly pyramid elements therefore the finite element mesh is automatically generated from the surface information shape functions of the poly pyramid elements are constructed by moving least square mls approximation numerical results are presented to examine the performance of the poly pyramid elements and to demonstrate the effectiveness of the proposed scheme

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159