estimation in capture recapture models when covariates are subject to measurement errors nous considerons les problemes d estimation des modeles de capture recapture quand les covariables ou les variables auxilliaires sont mesurees avec erreur nous trouvons que l approche naive qui ignore les erreurs de mesure est inacceptable pour l estimation des parametres de regression et de la taille de la population elle donne des estimateurs biaises de manieere croissante avec l amplitude des erreurs et des intervalles de confiance fausses pour tenir compte des erreurs de mesure nous proposons un estimateur des parametres de regression par une methode de calibration et developpons des estimateurs modifies de la taille de la population une etude de simulation montre que les estimateurs resultants sont plus satisfaisant que ceux de l approche naive ou de la methode d extrapolation simulation simex des donnees de l espece d oiseau primia flaviventris a hong kong sont analysees avec et sans l hypothese d erreur de mesure pour demontrer l effet des erreurs sur les estimations

numerical optimization for symmetric tensor decomposition we consider the problem of decomposing a real valued symmetric tensor as the sum of outer products of real valued vectors algebraic methods exist for computing complex valued decompositions of symmetric tensors but here we focus on real valued decompositions both unconstrained and nonnegative for problems with low rank structure we discuss when solutions exist and how to formulate the mathematical program numerical results show the properties of the proposed formulations including one that ignores symmetry on a set of test problems and illustrate that these straightforward formulations can be effective even though the problem is nonconvex

approximation of pseudodifferential operators in absorbing boundary conditions for hyperbolic equations engquist and majda 3 proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations in the case of the wave equation this boundary condition is valid at all frequencies here least squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions it is shown that for the wave equation this approach leads to kreiss well posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of taylor and pade approximations 3 4 numerical examples indicate that this method works even more effectively for hyperbolic systems the least squares approach may be used to generate the boundary conditions automatically

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

inference for capture recapture experiments in continuous time with variable capture rates summary a two step procedure based on a partial likelihood is proposed to estimate the size of a closed population for multiple recapture studies in continuous time when the capture rates are permitted to depend on covariates associated with individuals the asymptotic and small sample properties of the resulting estimators are investigated the analysis of capture recapture experiments is often based on the assumption that capture probabilities are equal for all individuals in the population being caught it has long been recognised that this assumption is often violated indeed equal capture probability is only a convenient mathematical assumption with no empirical justification manly 1970 gilbert 1973 and carothers 1973 have shown that heterogeneity can cause substantial bias in commonly used estimators burnham overton 1978 and yip 1991 assumed a beta distribution to model the individual capture probabilities chao lee 1992 provided an estimator for a heterogeneous population using sample coverage seber 1982 and otis et al 1978 have pointed out that catchability may vary with characteristics of the individual such as age with physical conditions or with environmental factors for the discrete case with distinct capture occasions huggins 1989 used covariates to model heterogeneity a conditional argument to estimate the parameters associated with the model for the capture probabilities and a method of moments to estimate the population size here we employ a similar two step process in continuous time first using a partial likelihood applied to the counting processes of recaptures of individuals already captured to estimate the parameters in the model for the capture intensity then a method of moments to estimate the population size the work here fits into the model ih classification of pollock 1993 also lee chao 1994 recently suggested a coverage estimator for the population size with heterogeneous and time dependent and behaviour dependent capture probabilities to motivate our work consider a continuous time capture recapture experiment for a closed population of a certain type of bird where the capture intensities depend on covariates assumed to be time independent during the experimental period simulated data from a population of 50 birds with captures occurring over a two unit period where the capture intensities depend on

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

a unified parametric regression model for recapture studies with random removals in continuous time nous combinons la vraisemblance conditionnelle dans des processus de comptage avec l estimateur de horvitz thompson pour obtenir un estimateur de la taille de la population plus efficient que les estimateurs existants des suppressions aleatoires peuvent etre introduites dans le processus de recapture on presente des etudes de simulation pour determiner la performance des estimateurs proposes on donne des exemples sur une repartition d oiseaux et une petite etude de recapture de mammiferes

an optimized hybrid convolutional perfectly matched layer for efficient absorption of electromagnetic waves abstract a hybrid technique is studied in order to improve the performance of convolutional perfectly matched layer cpml in the finite difference time domain fdtd medium this technique combines the first order of higdon s annihilation equation as absorbing boundary condition abc with cpml to vanish the perfect electric conductor pec effects at the end of the cpml region an optimization algorithm is required to find optimum parameters of the proposed absorber in this investigation the particle swarm optimization pso is utilized with two separate objective functions in order to minimize the average and peak value of relative error using a standard test the overall performance of the proposed absorber is compared to the original cpml the results clearly illustrate this method provides approximately 10 db enhancements in cpml absorption error the performance memory and time requirement of the novel absorber hybrid cpml h cpml was analyzed during 2d and 3d tests and compared to most reported pmls the h cpml requirement of computer resources is similar to cpml and can simply be implemented to truncate fdtd domains furthermore an optimized set of parameters are provided to generalize the hybrid method

full likelihood inference for abundance from continuous time capture recapture data capture recapture experiments are widely used cost effective sampling techniques for estimating population sizes or abundances in biology ecology demography epidemiology and reliability studies for continuous time capture recapture data existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation the corresponding wald type confidence intervals for the abundance may have severe undercoverage and their lower limits can be below the number of individuals captured we propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood under both parametric and semiparametric intensity models we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically 2 with 1 degree of freedom simulations indicate that compared with conditional likelihood based methods the maximum full likelihood estimator has a smaller mean square error and the likelihood ratio confidence intervals often have remarkable gains in coverage probability we illustrate the advantages of the proposed approach by analysing illegal immigrant data for the netherlands and prinia flaviventris data from hong kong

an efficient algorithm for truncating spatial domain in modeling light scattering by finite difference technique the finite difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry in practice this method requires that the spatial domain for the computation of near field be truncated an absorbing boundary condition must be imposed in conjunction with this truncation the performance of this boundary condition is essential to the stability of numerical computations and the reliability of results in the present study a new boundary condition referred to as the mixed t algorithm has been developed which is a generalization of the transmitting boundary condition originally developed by liao and co workers the present algorithm does not require spatial interpolation for wave values at interior grid points in addition it produces two minima of spurious reflections at small and large incident angles allowing efficient absorption of the scattered waves at the boundary for large incident angles when the third order mixed t algorithm is used the reflection coefficient of the boundary is less than 1 for incident angles from 0 to about 70 we find that the numerical instability associated with the transmitting boundary condition is caused by the location dependent amplitude of outgoing waves in the vicinity of the boundary for this reason the mixed t algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation when the stabilized algorithm is applied the near field within the truncated domain can be computed by using single precision arithmetic without overflows for more than 105steps in the time marching iteration finally the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a tm wave excited by a sinusoidal point source simultaneous simulation of the wave propagation in small and large domains and the scattering of a tm wave by an infinite circular cylinder

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

instability of difference models for hyperbolic initial boundary value problems a th00 eory of instability is presented for finite difference models of linear hyperbolic partial differential equations in one space dimension with a boundary according to this theory instability is caused by spurious radiation of wave energy from the boundary at a numerical group velocity c 0 to make this point of view precise we first develop a rigorous description of group velocity for difference schemes and of reflection of waves at boundaries from these results we then obtain lower bounds for growth rates of unstable finite difference solution operators in l2 norms which extend earlier results due to osher and to gustafsson kreiss and sundstrom in particular we investigate l2 instability with respect to both initial and boundary data and show how they are affected by a finite versus infinite reflection coefficients and b wave radiation with c 0 versus c 0

parametric regression models for continuous time removal and recapture studies we use a class of parametric counting process regression models that are commonly employed in the analysis of failure time data to formulate the subject specific capture probabilities for removal and recapture studies conducted in continuous time we estimate the regression parameters by modifying the conventional likelihood score function for left truncated and right censored data to accommodate an unknown population size and missing covariates on uncaptured subjects and we subsequently estimate the population size by a martingale based estimating function the resultant estimators for the regression parameters and population size are consistent and asymptotically normal under appropriate regularity conditions we assess the small sample properties of the proposed estimators through monte carlo simulation and we present an application to a bird banding exercise

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

on the ideals of secant varieties to certain rational varieties abstract if x p n is a reduced and irreducible projective variety it is interesting to find the equations describing the higher secant varieties of x in this paper we find those equations in the following cases x p n 1 p n t p n is the segre embedding of the product and n is large with respect to the n i theorem 2 4 the x are some unbalanced segre veronese embeddings x is a del pezzo surface

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

singularities of linear systems and the waring problem the waring problem for homogeneous forms asks for additive decomposition of a form f into powers of linear forms a classical problem is to determine when such a decomposition is unique in this paper we answer this question when the degree of f is greater than the number of variables to do this we translate the algebraic statement into a geometric one concerning the singularities of linear systems of p with assigned singularities

stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations abstract implicit noniterative finite difference schemes have recently been developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations when applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable a stable as applied in practice the algorithms often face a severe time step restriction a major source of the difficulty is the treatment of the numerical boundary conditions one conjecture has been that unconditional stability requires implicit numerical boundary conditions an apparent counterexample was the space time extrapolation considered by gustafsson kreiss and sundstrom in this paper we examine space implicit and space time explicit extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals the results indicate that for unconditional stability with a finite number of spatial mesh intervals the numerical boundary conditions must be implicit

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

decomposition of homogeneous polynomials with low rank let f be a homogeneous polynomial of degree d in m 1 variables defined over an algebraically closed field of characteristic 0 and suppose that f belongs to the s th secant variety of the d uple veronese embedding of mathbb p m into mathbb p tiny left begin array c rm m d rm d end array right 1 but that its minimal decomposition as a sum of d th powers of linear forms m1 mr is f m 1 d cdots m r d with r s we show that if s r 2d 1 then such a decomposition of f can be split in two parts one of them is made by linear forms that can be written using only two variables the other part is uniquely determined once one has fixed the first part we also obtain a uniqueness theorem for the minimal decomposition of f if r is at most d and a mild condition is satisfied

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

the stretched mesh huygens absorbing boundary condition sm habc the huygens absorbing boundary condition habc is a new implementation of the analytical abcs which were in common use before the introduction of the perfectly matched layer pml abc in contrast to the traditional implementation the habc allows analytical abcs to be combined easily with other abcs this opens the way to combinations of two abcs where the advantages of both are preserved while their drawbacks are removed this is the case with the stretched mesh habc which relies on an analytical abc for the absorption of traveling waves and a real stretch of coordinates for the absorption of evanescent waves this paper demonstrates that such a combination can achieve a high absorption over the whole frequency spectrum and can challenge the pml abc in wave structure interaction problems

on the outflow conditions for spectral solution of the viscous blunt body problem the purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic hypersonic flow over blunt bodies governed by the compressible navier stokes equations with an emphasis motivated primarily by the use of spectral methods without any filtering the subsonic supersonic composition of the outflow boundary requires a dual boundary treatment for well posedness all compatibility relations modified to undertake the hyperbolic parabolic behaviour of the governing equations are used for the supersonic part of the outflow regarding the unknown downstream information in the subsonic region different subsonic outflow conditions in the sense of the viscous blunt body problem are examined a verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer it is demonstrated that two approaches for imposing subsonic outflow conditions namely 1 extrapolating all flow variables and 2 extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high speed flows over blunt bodies using spectral collocation methods

parametric and semiparametric models for recapture and removal studies a likelihood approach summary capture recapture processes are biased samplings of recurrent event processes which can be modelled by the andersen gill intensity model the intensity function is assumed to be a function of time covariates and a parameter we derive the maximum likelihood estimators of both the parameter and the population size and show the consistency and asymptotic normality of the estimators for both recapture and removal studies the estimators are asymptotically efficient and their theoretical asymptotic relative efficiencies with respect to the existing estimators of yip and co workers can be as large as oo the variance estimation and a numerical example are also presented

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

accurate solutions of the navier stokes equations despite unknown outflow boundary data a very common procedure when constructing boundary conditions for the time dependent navier stokes equations at artificial boundaries is to extrapolate the solution from grid points near the boundary to the boundary itself for supersonic outflow where all the characteristic variables leave the computational domain this leads to accurate results in the case of subsonic outflow where one characteristic variable enters the computational domain one cannot in general expect accurate solutions by this procedure the problem with outflow boundary operators of extrapolation type at artificial boundaries with errors in the boundary data of order one will be investigated both the problem when the artificial outflow boundary is located in essentially uniform flow and the situation when the artificial outflow boundary is located in a flow field with large gradients are discussed it will be shown that in the special case when there are large gradients tangential to the boundary extrapolation methods can be used even in the subsonic case

maximum likelihood abundance estimation from capture recapture data when covariates are missing at random in capture recapture experiments individual covariates may be subject to missingness especially when the number of captures is small when the covariate information is missing at random the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance these estimators are then used to construct wald type confidence intervals however such intervals may have seriously inaccurate coverage probabilities in this paper we propose a maximum empirical likelihood el estimation approach for the abundance in the presence of missing covariates we show that the maximum el estimator is asymptotically normal and that the el ratio statistic for the abundance has a chi square limiting distribution with one degree of freedom simulations indicate that the proposed estimator has a smaller mean square error than existing estimators and the proposed el ratio confidence interval usually has more accurate coverage probabilities than the existing wald type confidence intervals we illustrate the proposed method by analyzing data collected in hong kong for the yellow bellied prinia a bird species

varieties with minimal secant degree and linear systems of maximal dimension on surfaces abstract in this paper we prove using a refinement of terracini s lemma a sharp lower bound for the degree of higher secant varieties to a given projective variety which extends the well known lower bound for the degree of a variety in terms of its dimension and codimension in projective space moreover we study varieties for which the bound is attained proving some general properties related to tangential projections e g these varieties are rational in particular we completely classify surfaces and curves for which the bound is attained it turns out that these surfaces enjoy some maximality properties for their embedding dimension in terms of their degree or sectional genus this is related to classical beautiful results of castelnuovo and enriques that we revise here in terms of adjunction theory

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

on the identifiability of ternary forms abstract we describe a new method to determine the minimality and identifiability of a waring decomposition a of a specific form symmetric tensor t in three variables our method which is based on the hilbert function of a can distinguish between forms in the span of the veronese image of a which in general contains both identifiable and not identifiable points depending on the choice of coefficients in the decomposition this makes our method applicable for all values of the length r of the decomposition from 2 up to the generic rank a range which was not achievable before though the method in principle can handle all cases of specific ternary forms we introduce and describe it in details for forms of degree 8

the influence of open boundary conditions on the convergence to steady state for the navier stokes equations abstract the question of open boundary conditions of inflow and outflow type for the navier stokes equations and its influence on the convergence to steady state is addressed both the continuous and semi discrete problem are analysed using the energy method and the laplace transform technique the energy method is used to derive well posed boundary conditions for the continuous problem for the semi discrete problem we use the energy method to prove that by using the well posed boundary conditions for the continuous problem and adding a suitable numerical boundary condition well posedness is preserved by employing the laplace transform technique the spectra for different types of boundary conditions are obtained the spectra are analysed and it is shown how the choice of boundary conditions strongly affects the convergence to steady state one dimensional navier stokes calculations are performed and the resulting convergence rates agree well with the theoretical analysis finally the spectra obtained using inflow and outflow types of boundary conditions are compared with spectra obtained using periodic boundary conditions and the choice of a time integration method for the navier stokes equations is discussed

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

scattering of flexural waves by cavities in a plate abstract in this paper the scattering of slow flexural waves by arbitrary shaped cavities in an infinite elastic plate is studied using a combined finite element and analytical method the problem is considered as consisting of two interacting systems a bounded interior region containing all material and geometric irregularities and an unbounded exterior region the interior region is modelled by using mindlin type plate bending elements wave function expansion is used to represent the exterior region continuity of displacements and tractions are enforced at the nodes on the finite element interface with the exterior region comparison of present results for circular cavity with the analytical solution shows excellent agreement finally scattering by triangular and square shaped cavities as well as a pair of circular cavities is considered

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

nonlinear component of variance models summary general aspects of nonlinearity in the context of component of variance models are discussed and two special topics are examined in detail firstly simple procedures both formal and informal are proposed for describing departures from normal theory linear models transformation models are shown to be a special case of a more general formulation and data on blood pressure are analyzed in illustration secondly an approximate likelihood is proposed and its accurate performance is examined numerically using examples of exponential regression and the analysis of several related 2 x 2 tables in the latter example the approximate score test has improved power over the mantelhaenszel test

the coarse geometric novikov conjecture and uniform convexity abstract the coarse geometric novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero the purpose of this paper is to prove the coarse geometric novikov conjecture for spaces which admit a coarse uniform embedding into a uniformly convex banach space

stability theory of difference approximations for multidimensional initial boundary value problems an attempt is made to generalize results for arbitrary multidimensional difference schemes severe obstacles are encountered however for dissipative difference schemes the problem may be resolved

absorbing boundary conditions for the discretization schemes of the one dimensional wave equation when computing a partial differential equation it is often necessary to introduce artificial boundaries here we explain a systematic method to obtain boundary conditions for the wave equation in one dimension fitting to the discretization scheme and stable moreover we give error estimates on the reflected part

global artificial boundary conditions for computation of external flows with jets we propose new global artificial boundary conditions abcs for computation of flows with propulsive jets the algorithm is based on application of the difference potentials method dpm previously similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies the proposed modification substantially extends the applicability range of the dpm based algorithm we present the general formulation of the problem describe our numerical methodology and discuss the corresponding computational results the particular configuration that we analyze is a slender three dimensional body with boat tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack similar to the results obtained earlier for the flows around airfoils and wings current results for the jet flow case corroborate the superiority of the dpm based abcs over standard local methodologies from the standpoints of accuracy overall numerical performance and robustness

on kruskal s uniqueness condition for the candecomp parafac decomposition let x be a real valued three way array the candecomp parafac cp decomposition is written as x under bar y under bar 1 y under bar r e where y r are rank 1 arrays and e under bar is a rest term each rank 1 array is defined by the outer product of three vectors a r b r and c r i e y ijk r a i r b j r c k t these vectors make up the r columns of the component matrices a b and c if 2r 2 is less than or equal to the sum of the k ranks of a b and c then the fitted part of the decomposition is unique up to a change in the order of the rank 1 arrays and rescaling counterscaling of each triplet of vectors a r b r c r forming a rank 1 array this classical result was shown by kruskal his proof is however rather inaccessible and does not seem intuitive in order to contribute to a better understanding of cp uniqueness this paper provides an accessible and intuitive proof of kruskal s condition the proof is both self contained and compact and can easily be adapted for the complex valued cp decomposition c 2006 elsevier inc all rights reserved

issues in computational fluid dynamics code verification and validation a broad range of mathematical modeling errors of fluid flow physics and numerical approximation errors are addressed in computational fluid dynamics cfd it is strongly believed that if cfd is to have a major impact on the design of engineering hardware and flight systems the level of confidence in complex simulations must substantially improve to better understand the present limitations of cfd simulations a wide variety of physical modeling discretization and solution errors are identified and discussed here discretization and solution errors refer to all errors caused by conversion of the original partial differential or integral conservation equations representing the physical process to algebraic equations and their solution on a computer the impact of boundary conditions on the solution of the partial differential equations and their discrete representation will also be discussed throughout the article clear distinctions are made between the analytical mathematical models of fluid dynamics and the numerical models lax s equivalence theorem and its frailties in practical cfd solutions are pointed out distinctions are also made between the existence and uniqueness of solutions to the partial differential equations as opposed to the discrete equations two techniques are briefly discussed for the detection and quantification of certain types ofmore discretization and grid resolution errors less

a wavenumber based extrapolation and interpolation method for use in conjunction with high order finite difference schemes the errors incurred in using extrapolation and interpolation in large scale computations are analyzed and quantified in the wavenumber space if a large extrapolation stencil is used the errors in the low wavenumbers can be significantly reduced however the errors in the high wavenumbers are at the same time greatly increased the opposite is true if the stencil size is reduced based on the wavenumber analysis an optimized extrapolation and interpolation method is proposed the optimization is carried out over a selected band of wavenumbers it is known that extrapolation often leads to numerical instability the instability is the result of large error amplification in the high wavenumber range to reduce the tendency to trigger numerical instability it is proposed that an extra constraint be imposed on the optimized extrapolation method the added constraint aims to reduce error amplification over the high wavenumbers numerical examples are provided to illustrate that accurate and stable numerical results can be obtained in large scale simulation using a high order finite difference scheme and the proposed optimized extrapolation method when the same problems are recomputed using the familiar high order polynomials extrapolation method in the lagrange form in one case the numerical results are plagued by large errors and ultimately instability in another problem it is found that the use of the lagrange polynomials extrapolation method would lead immediately to numerical instability

estimation of population size based on additive hazards models for continuous time recapture experiments summary we use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous time capture recapture experiment and then construct a horvitz thompson type estimator for the unknown population size the resulting estimator is consistent and asymptotically normal with an easily estimated variance simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed 5 ignoring covariates would underestimate the population size and the coverage probability is poor a wildlife example is provided

on the typical rank of real bivariate polynomials abstract here we study the typical rank for real bivariate homogeneous polynomials of degree d 6 the case d 5 being settled by p comon and g ottaviani we prove that d 1 is a typical rank and that if d is odd then d 3 2 is a typical rank the comon ottaviani conjecture was later completely solved by g blekherman

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

open boundary conditions for stationary inviscid flow problems abstract the steady state problem for flow in a channel is considered very accurate open upstream and downstream boundary conditions are derived for the euler equations no data are needed at the boundaries it is enough that the upstream limit of the solution is available error estimates are derived for a simple model problem and numerical experiments verify the results for the true non linear equations newton s method is used to solve the equations the boundary conditions are given in such a form that they also can be used in connection with a time dependent procedure

an accuracy analysis of boundary conditions for the forced shallow water equations the accuracy of numerical boundary conditions for the linearized one dimensional shallow water equations is determined by extending the dispersion fourier analysis originally presented by c k chu and a sereny j comput phys 15 476 1974 accuracy is measured by calculating steady state amplitudes of incoming and outgoing numerical waves at a boundary as functions of a forcing frequency radiating closed and forced radiating boundary conditions are studied in combination with two numerical schemes the richardson sielecki explicit finite difference scheme and the galerkin finite element method with piecewise linear basis functions and crank nicolson time stepping contamination of the finite element solution with short waves is seen to vary with the choice of extraneous boundary conditions an example of l n trefethen s j comput phys 49 199 1983 interpretation of the b gustafsson h kreiss and a sundstrom math comput 26 649 1972 instability is also given for the finite element method

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

stable and accurate schemes for the compressible navier stokes equations minimal stencil width discretizations of combined mixed and non mixed second order derivatives are analyzed with respect to accuracy and stability we show that these discretizations lead to stability for cauchy problems with a careful boundary treatment we also show that the stability holds for initial boundary value problems the analysis is verified by numerical simulations of burgers and navier stokes equations in two and three space dimensions

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

weakly defective varieties a projective variety x is k weakly defective when its intersection with a general k 1 tangent hyperplane has no isolated singularities at the k 1 points of tangency if x is k defective i e if the k secant variety of x has dimension smaller than expected then x is also k weakly defective the converse does not hold in general a classification of weakly defective varieties seems to be a basic step in the study of defective varieties of higher dimension we start this classification here describing all weakly defective irreducible surfaces our method also provides a new proof of the classical terracini s classification of k defective surfaces

improved boundary conditions for viscous reacting compressible flows previous studies on physical boundary conditions for flame boundary interactions of an ideal multicomponent compressible gas have neglected reactive source terms in their boundary condition treatments by combining analyses of incompletely parabolic systems with those based on the hyperbolic euler equations a rational set of boundary conditions is determined to address this shortcoming accompanying these conditions is a procedure for implementation into a maltidimensional code in the limits of zero reaction rate or one species the boundary conditions reduce in a predictable way to cases found in the literature application is made to premixed and nonpremixed flames in one and two dimensions to establish efficacy inclusion of source terms in boundary conditions derived from characteristic analysis is essential to avoid unphysical generation of pressure and velocity gradients as well as flow reversals minor deficiencies in the boundary conditions are attributed primarily to the diffusive terms imposing vanishing diffusive boundary normal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory

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