compatibility equations of nonlinear elasticity for non simply connected bodies compatibility equations of elasticity are almost 150 years old interestingly they do not seem to have been rigorously studied to date for non simply connected bodies in this paper we derive necessary and sufficient compatibility equations of nonlinear elasticity for arbitrary non simply connected bodies when the ambient space is euclidean for a non simply connected body a measure of strain may not be compatible even if the standard compatibility equations bulk compatibility equations are satisfied it turns out that there may be topological obstructions to compatibility this paper aims to understand them for both deformation gradient f and the right cauchy green strain c ftf we show that the necessary and sufficient conditions for compatibility of deformation gradient f are the vanishing of its exterior derivative and all its periods that is its integral over generators of the first homology group of the material manifold we will show that not every non null homotopic path requires supplementary compatibility equations for f and linearized strain e we then find both necessary and sufficient compatibility conditions for the right cauchy green strain tensor c for arbitrary non simply connected bodies when the material and ambient space manifolds have the same dimensions we discuss the well known necessary compatibility equations in the linearized setting and the cesaro volterra path integral we then obtain the sufficient conditions of compatibility for the linearized strain when the body is not simply connected to summarize the question of compatibility reduces to two issues i an integrability condition which is d f dx 0 for the deformation gradient and a curvature vanishing condition for c and ii a topological condition for f dx this is a homological condition because the equation one is trying to solve takes the form d f dx for c however parallel transport is involved which means that one needs to solve an equation of the form dr ds rk where r takes values in the orthogonal group this is therefore a question about an orthogonal representation of the fundamental group which as the orthogonal group is not commutative cannot in general be reduced to a homological question

limiting distributions for l sb 1 regression estimators under general conditions it is well known that l 1 estimators of regression parameters are asymptotically normal if the distribution function has a positive derivative at 0 in this paper we derive the asymptotic distributions under more general conditions on the behavior of the distribution function near 0

riemann cartan geometry of nonlinear dislocation mechanics we present a geometric theory of nonlinear solids with distributed dislocations in this theory the material manifold where the body is stress free is a weitzenbock manifold that is a manifold with a flat affine connection with torsion but vanishing non metricity torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics using cartan s moving frames we construct the material manifold for several examples of bodies with distributed dislocations we also present non trivial examples of zero stress dislocation distributions more importantly in this geometric framework we are able to calculate the residual stress fields assuming that the nonlinear elastic body is incompressible we derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

discriminative sparsity preserving projections for image recognition previous works have demonstrated that image classification performance can be significantly improved by manifold learning however performance of manifold learning heavily depends on the manual selection of parameters resulting in bad adaptability in real world applications in this paper we propose a new dimensionality reduction method called discriminative sparsity preserving projections dspp different from the existing sparse subspace algorithms which manually construct a penalty adjacency graph dspp employs sparse representation model to adaptively build both intrinsic adjacency graph and penalty graph with weight matrix and then integrates global within class structure into the discriminant manifold learning objective function for dimensionality reduction extensive experimental results on four image databases demonstrate the effectiveness of the proposed approach we analyzed the vertex points of penalty graph using sparse representation we adaptively constructed both penalty adjacency graph and intrinsic graph our method simultaneously considered the global and local geometric structure of data

small on large geometric anelasticity in this paper we are concerned with finding exact solutions for the stress fields of nonlinear solids with non symmetric distributions of defects or more generally finite eigenstrains that are small perturbations of symmetric distributions of defects with known exact solutions in the language of geometric mechanics this corresponds to finding a deformation that is a result of a perturbation of the metric of the riemannian material manifold we present a general framework that can be used for a systematic analysis of this class of anelasticity problems this geometric formulation can be thought of as a material analogue of the classical small on large theory in nonlinear elasticity we use the present small on large anelasticity theory to find exact solutions for the stress fields of some non symmetric distributions of screw dislocations in incompressible isotropic solids

estimation of extreme conditional quantiles through power transformation the estimation of extreme conditional quantiles is an important issue in numerous disciplines quantile regression qr provides a natural way to capture the covariate effects at different tails of the response distribution however without any distributional assumptions estimation from conventional qr is often unstable at the tails especially for heavy tailed distributions due to data sparsity in this article we develop a new three stage estimation procedure that integrates qr and extreme value theory by estimating intermediate conditional quantiles using qr and extrapolating these estimates to tails based on extreme value theory using the power transformed qr the proposed method allows more flexibility than existing methods that rely on the linearity of quantiles on the original scale while extending the applicability of parametric models to borrow information across covariates without resorting to nonparametric smoothing in addition we propose a test procedure to assess the commonality of ext

nonnegative local coordinate factorization for image representation recently nonnegative matrix factorization nmf has become increasingly popular for feature extraction in computer vision and pattern recognition nmf seeks two nonnegative matrices whose product can best approximate the original matrix the nonnegativity constraints lead to sparse parts based representations that can be more robust than nonsparse global features to obtain more accurate control over the sparseness in this paper we propose a novel method called nonnegative local coordinate factorization nlcf for feature extraction nlcf adds a local coordinate constraint into the standard nmf objective function specifically we require that the learned basis vectors be as close to the original data points as possible in this way each data point can be represented by a linear combination of only a few nearby basis vectors which naturally leads to sparse representation extensive experimental results suggest that the proposed approach provides a better representation and achieves higher accuracy in image clustering

weyl geometry and the nonlinear mechanics of distributed point defects the residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry the material manifold of a solid with distributed point defects where the body is stress free is a flat weyl manifold i e a manifold with an affine connection that has non metricity with vanishing traceless part but both its torsion and curvature tensors vanish given a spherically symmetric point defect distribution we construct its weyl material manifold using the method of cartan s moving frames having the material manifold the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the euclidean ambient space in the case of incompressible neo hookean solids we calculate explicitly this residual stress field we consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere we show that the residual stress field inside the smaller ball is uniform and hydrostatic we also prove a nonlinear analogue of eshelby s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

regularized coplanar discriminant analysis for dimensionality reduction abstract the dimensionality reduction methods based on linear embedding such as neighborhood preserving embedding npe sparsity preserving projections spp and collaborative representation based projections crp try to preserve a certain kind of linear representation for each sample after projection however in the transformed low dimensional space the linear relationship between the samples may be changed which cannot make the linear representation based classifiers such as sparse representation based classifier src to achieve higher recognition accuracy in this paper we propose a new linear dimensionality reduction algorithm called regularized coplanar discriminant analysis rcda to address this problem it simultaneously seeks a linear projection matrix and some linear representation coefficients that make the samples from the same class coplanar and the samples from different classes not coplanar the proposed regularization term balances the bias from the optimal linear representation and that from the class mean to avoid overfitting the training data and overcomes the matrix singularity in solving the linear representation coefficients an alternative optimization approach is proposed to solve the rcda model experiments are done on several benchmark face databases and hyperspectral image databases and results show that rcda can obtain better performance than other dimensionality reduction methods

two dimensional supervised local similarity and diversity projection this paper presents a novel manifold learning method namely two dimensional supervised local similarity and diversity projection 2dslsdp for feature extraction the proposed method defines two weighted adjacency graphs namely similarity graph and diversity graph the affinity matrix of similarity graph is determined by the spatial relationship between vertices of this graph while affinity matrix of diversity graph is determined by the diversity information of vertices of its graph using these two graphs the proposed method constructs local similarity scatter and diversity scatter respectively a concise feature extraction criterion is then raised via minimizing the ratio of the local similarity scatter to local diversity scatter thus 2dslsdp can well preserve not only the adjacency similarity structure but also the diversity of data points which is important for the classification experiments on the ar and umist databases show the effectiveness of the proposed method

on geometric discretization of elasticity this paper presents a geometric discretization of elasticity when the ambient space is euclidean this theory is built on ideas from algebraic topology exterior calculus and the recent developments of discrete exterior calculus we first review some geometric ideas in continuum mechanics and show how constitutive equations of linearized elasticity similar to those of electromagnetism can be written in terms of a material hodge star operator in the discrete theory presented in this paper instead of referring to continuum quantities we postulate the existence of some discrete scalar valued and vector valued primal and dual differential forms on a discretized solid which is assumed to be a triangulated domain we find the discrete governing equations by requiring energy balance invariance under time dependent rigid translations and rotations of the ambient space there are several subtle differences between the discrete and continuous theories for example power of tractions in the discrete theory is written on a layer of cells with a nonzero volume we obtain the compatibility equations of this discrete theory using tools from algebraic topology we study a discrete cosserat medium and obtain its governing equations finally we study the geometric structure of linearized elasticity and write its governing equations in a matrix form we show that in addition to constitutive equations balance of angular momentum is also metric dependent all the other governing equations are topological

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

stable orthogonal local discriminant embedding for linear dimensionality reduction manifold learning is widely used in machine learning and pattern recognition however manifold learning only considers the similarity of samples belonging to the same class and ignores the within class variation of data which will impair the generalization and stableness of the algorithms for this purpose we construct an adjacency graph to model the intraclass variation that characterizes the most important properties such as diversity of patterns and then incorporate the diversity into the discriminant objective function for linear dimensionality reduction finally we introduce the orthogonal constraint for the basis vectors and propose an orthogonal algorithm called stable orthogonal local discriminate embedding experimental results on several standard image databases demonstrate the effectiveness of the proposed dimensionality reduction approach

sparsity preserving projections with applications to face recognition dimensionality reduction methods drs have commonly been used as a principled way to understand the high dimensional data such as face images in this paper we propose a new unsupervised dr method called sparsity preserving projections spp unlike many existing techniques such as local preserving projection lpp and neighborhood preserving embedding npe where local neighborhood information is preserved during the dr procedure spp aims to preserve the sparse reconstructive relationship of the data which is achieved by minimizing a l1 regularization related objective function the obtained projections are invariant to rotations rescalings and translations of the data and more importantly they contain natural discriminating information even if no class labels are provided moreover spp chooses its neighborhood automatically and hence can be more conveniently used in practice compared to lpp and npe the feasibility and effectiveness of the proposed method is verified on three popular face databases yale ar and extended yale b with promising results

continuum elasticity with topological defects including dislocations and extra matter the elasticity of continuous media with topological defects is described naturally by differential geometry since it relates metric to strain we construct a geometrical field theory identifying disclinations dislocations and extra matter defects with the curvature torsion and nonmetricity tensors respectively connection and metric are given explicitly in the presence of dislocations and extra matter the density of extra matter is a scalar source of isotropic strain described by a local length scale or gauge the logarithm of the gauge is related to the density of extra matter by a poisson equation the corresponding integral equation similar to gauss law in electrostatics measures the amount of extra matter contained inside a contour

improving generalised estimating equations using quadratic inference functions summary generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified however under such misspecification the estimator of the regression parameter can be inefficient in this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter and that remains optimal even if the working correlation structure is misspecified the idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices a representation that is valid for the working correlations most commonly used both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations this approach also provides a chi squared inference function for testing nested models and a chi squared regression misspecification test furthermore the test statistic follows a chi squared distribution asymptotically whether or not the working correlation structure is correctly specified

ensemble manifold regularization we propose an automatic approximation of the intrinsic manifold for general semi supervised learning ssl problems unfortunately it is not trivial to define an optimization function to obtain optimal hyperparameters usually cross validation is applied but it does not necessarily scale up other problems derive from the suboptimality incurred by discrete grid search and the overfitting therefore we develop an ensemble manifold regularization emr framework to approximate the intrinsic manifold by combining several initial guesses algorithmically we designed emr carefully so it 1 learns both the composite manifold and the semi supervised learner jointly 2 is fully automatic for learning the intrinsic manifold hyperparameters implicitly 3 is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption and 4 is scalable for a large number of candidate manifold hyperparameters from both time and space perspectives furthermore we prove the convergence property of emr to the deterministic matrix at rate root n extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework

a general bahadur representation of m estimators and its application to linear regression with nonstochastic designs we obtain strong bahadur representations for a general class of m estimators that satisfies sigma i psi x i theta o delta n where the x i s are independent but not necessarily identically distributed random variables the results apply readily to m estimators of regression with nonstochastic designs more specifically we consider the minimum l p distance estimators bounded influence gm estimators and regression quantiles under appropriate design conditions the error ratesobtained for the first order approximations are sharp in these cases we also provide weaker and more easily verifiable conditions that suffice for an error rate that is suboptimal but strong enough for deriving the asymptotic distribution of m estimators in a wide variety of problems

on the numerical implementation of inelastic time dependent and time independent finite strain constitutive equations in structural mechanics abstract a number of complex issues are resolved in a way that allows the incorporation of finite strain inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics without recourse to extensive continuum mechanics preliminaries an elementary time independent plasticity model an elementary time dependent creep model and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations the constitutive equations are all suitable for problems involving large deformations and finite strains the plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co rotational time derivative of the cauchy stress the viscoelastic model computes the current value of the cauchy stress from a hereditary integral of a materially invariant form of the stretching history the current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration the process of strain incrementation is examined in some depth the stretching evaluated at the mid interval and multiplied by the time step is identified as the appropriate finite strain increment to use with the selected forms of the constitutive equations discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations these rotations are used to update stresses and state variables due to rigid body rotation during the load increment comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately if not exactly for any time step and stretching this material taken collectively provides an approach to numerical implementation which is marked by its simplicity

stable local dimensionality reduction approaches dimensionality reduction is a big challenge in many areas a large number of local approaches stemming from statistics or geometry have been developed however in practice these local approaches are often in lack of robustness since in contrast to maximum variance unfolding mvu which explicitly unfolds the manifold they merely characterize local geometry structure moreover the eigenproblems that they encounter are hard to solve we propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi definite programs instead of the above mentioned eigenproblems three well known algorithms locally linear embedding lle laplacian eigenmaps le and local tangent space alignment ltsa are reinterpreted and improved within this framework several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

simple exponential family pca principal component analysis pca is a widely used model for dimensionality reduction in this paper we address the problem of determining the intrinsic dimensionality of a general type data population by selecting the number of principal components for a generalized pca model in particular we propose a generalized bayesian pca model which deals with general type data by employing exponential family distributions model selection is realized by empirical bayesian inference of the model we name the model as simple exponential family pca sepca since it embraces both the principal of using a simple model for data representation and the practice of using a simplified computational procedure for the inference our analysis shows that the empirical bayesian inference in sepca formally realizes an intuitive criterion for pca model selection a preserved principal component must sufficiently correlate to data variance that is uncorrelated to the other principal components experiments on synthetic and real data sets demonstrate effectiveness of sepca and exemplify its characteristics for model selection

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

adaptive maximum margin analysis for image recognition abstract most existing discriminant manifold learning methods aim to maximize the margin among nearby data which is determined in the high dimensional original space as such they do not necessarily best maximize the margin between different classes in the low dimensional space which is a critically important property for image classification to handle this problem we propose an adaptive maximum margin analysis amma for feature extraction amma aims to seek a projection matrix that best maximize the margin which is calculated in the low dimensional space it uses sparse representation to adaptively construct the intrinsic and penalty graphs finally an iterative algorithm is developed to solve the projection matrix extensive experimental results on several image databases illustrate the effectiveness of the proposed approach

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

a unified framework for semi supervised dimensionality reduction in practice many applications require a dimensionality reduction method to deal with the partially labeled problem in this paper we propose a semi supervised dimensionality reduction framework which can efficiently handle the unlabeled data under the framework several classical methods such as principal component analysis pca linear discriminant analysis lda maximum margin criterion mmc locality preserving projections lpp and their corresponding kernel versions can be seen as special cases for high dimensional data we can give a low dimensional embedding result for both discriminating multi class sub manifolds and preserving local manifold structure experiments show that our algorithms can significantly improve the accuracy rates of the corresponding supervised and unsupervised approaches

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

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

median regression for longitudinal data we review and compare three estimators of median regression in linear models with longitudinal data the estimators are constructed based on well known ideas of weighting decorrelating and the working assumption of independence both asymptotic efficiency calculations and finite sample monte carlo studies are used to assess the performance of these estimators we find that their relative performances depend on the nature of covariates the estimator under the working assumption of independence is computationally simple and yet has good relative performance when the covariates are invariant over time or when the within subject correlations are small its relative performance in finite samples is also found to be more favourable than suggested by the asymptotic comparisons

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

face recognition using discriminant locality preserving projections based on maximum margin criterion in this paper we propose a new discriminant locality preserving projections based on maximum margin criterion dlpp mmc dlpp mmc seeks to maximize the difference rather than the ratio between the locality preserving between class scatter and locality preserving within class scatter dlpp mmc is theoretically elegant and can derive its discriminant vectors from both the range of the locality preserving between class scatter and the range space of locality preserving within class scatter dlpp mmc can also derive its discriminant vectors from the null space of locality preserving within class scatter when the parameter of dlpp mmc approaches experiments on the orl yale feret and pie face databases show the effectiveness of the proposed dlpp mmc

trace ratio problem revisited dimensionality reduction is an important issue in many machine learning and pattern recognition applications and the trace ratio tr problem is an optimization problem involved in many dimensionality reduction algorithms conventionally the solution is approximated via generalized eigenvalue decomposition due to the difficulty of the original problem however prior works have indicated that it is more reasonable to solve it directly than via the conventional way in this brief we propose a theoretical overview of the global optimum solution to the tr problem via the equivalent trace difference problem eigenvalue perturbation theory is introduced to derive an efficient algorithm based on the newton raphson method theoretical issues on the convergence and efficiency of our algorithm compared with prior literature are proposed and are further supported by extensive empirical results

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

locally linear discriminant embedding an efficient method for face recognition in this paper an efficient feature extraction method named as locally linear discriminant embedding llde is proposed for face recognition it is well known that a point can be linearly reconstructed by its neighbors and the reconstruction weights are under the sum to one constraint in the classical locally linear embedding lle so the constrained weights obey an important symmetry for any particular data point they are invariant to rotations rescalings and translations the latter two are introduced to the proposed method to strengthen the classification ability of the original lle the data with different class labels are translated by the corresponding vectors and those belonging to the same class are translated by the same vector in order to cluster the data with the same label closer they are also rescaled to some extent so after translation and rescaling the discriminability of the data will be improved significantly the proposed method is compared with some related feature extraction methods such as maximum margin criterion mmc as well as other supervised manifold learning based approaches for example ensemble unified lle and linear discriminant analysis en ullelda locally linear discriminant analysis llda experimental results on yale and cmu pie face databases convince us that the proposed method provides a better representation of the class information and obtains much higher recognition accuracies

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

unified empirical likelihood ratio tests for functional concurrent linear models and the phase transition from sparse to dense functional data summary we consider the problem of testing functional constraints in a class of functional concurrent linear models where both the predictors and the response are functional data measured at discrete time points we propose test procedures based on the empirical likelihood with bias corrected estimating equations to conduct both pointwise and simultaneous inferences the asymptotic distributions of the test statistics are derived under the null and local alternative hypotheses where sparse and dense functional data are considered in a unified framework we find a phase transition in the asymptotic null distributions and the orders of detectable alternatives from sparse to dense functional data specifically the tests proposed can detect alternatives of n order when the number of repeated measurements per curve is of an order larger than n 0 with n being the number of curves the transition points 0 for pointwise and simultaneous tests are different and both are smaller than the transition point in the estimation problem simulation studies and real data analyses are conducted to demonstrate the methods proposed

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

on spatial and material covariant balance laws in elasticity this paper presents some developments related to the idea of covariance in elasticity the geometric point of view in continuum mechanics is briefly reviewed building on this regarding the reference configuration and the ambient space as riemannian manifolds with their own metrics a lagrangian field theory of elastic bodies with evolving reference configurations is developed it is shown that even in this general setting the euler lagrange equations resulting from horizontal referential variations are equivalent to those resulting from vertical spatial variations the classical green naghdi rivilin theorem is revisited and a material version of it is discussed it is shown that energy balance in general cannot be invariant under isometries of the reference configuration which in this case is identified with a subset of r 3 transformation properties of balance of energy under rigid translations and rotations of the reference configuration is obtained the spatial covariant theory of elasticity is also revisited the transformation of balance of energy under an arbitrary diffeomorphism of the reference configuration is obtained and it is shown that some nonstandard terms appear in the transformed balance of energy then conditions under which energy balance is materially covariant are obtained it is seen that material covariance of energy balance is equivalent to conservation of mass isotropy material doyle ericksen formula and an extra condition that we call configurational inviscidity in the last part of the paper the connection between noether s theorem and covariance is investigated it is shown that the doyleericksen formula can be obtained as a consequence of spatial covariance of lagrangian density similarly it is shown that the material doyle ericksen formula can be obtained from material covariance of lagrangian density 2006 american institute of physics doi 10 1063 1 2190827

learning with ell 1 graph for image analysis the graph construction procedure essentially determines the potentials of those graph oriented learning algorithms for image analysis in this paper we propose a process to build the so called directed 1 graph in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its 1 norm driven reconstruction from the remaining samples and the noise then a series of new algorithms for various machine learning tasks e g data clustering subspace learning and semi supervised learning are derived upon the 1 graphs compared with the conventional k nearest neighbor graph and ball graph the 1 graph possesses the advantages 1 greater robustness to data noise 2 automatic sparsity and 3 adaptive neighborhood for individual datum extensive experiments on three real world datasets show the consistent superiority of 1 graph over those classic graphs in data clustering subspace learning and semi supervised learning tasks

design sensitivity analysis in large deformation elasto plastic and elasto viscoplastic problems implicit time integration algorithm derived by simo for his large deformation elasto plastic constitutive model is generalized for the case of isotropy and associative flow rule towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters combining it with the general formulation of design sensitivity analysis dsa for non linear finite element transient equilibrium problem we come at a numerically efficient closed form finite element formulation of dsa for large deformation elasto plastic and elasto viscoplastic problems with various types of design variables material constants shape parameters the paper handles several specific issues like the use of a non algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change computational examples demonstrate abilities of the formulation and quality of results copyright 2005 john wiley sons ltd

maximal linear embedding for dimensionality reduction over the past few decades dimensionality reduction has been widely exploited in computer vision and pattern analysis this paper proposes a simple but effective nonlinear dimensionality reduction algorithm named maximal linear embedding mle mle learns a parametric mapping to recover a single global low dimensional coordinate space and yields an isometric embedding for the manifold inspired by geometric intuition we introduce a reasonable definition of locally linear patch maximal linear patch mlp which seeks to maximize the local neighborhood in which linearity holds the input data are first decomposed into a collection of local linear models each depicting an mlp these local models are then aligned into a global coordinate space which is achieved by applying mds to some randomly selected landmarks the proposed alignment method called landmarks based global alignment lga can efficiently produce a closed form solution with no risk of local optima it just involves some small scale eigenvalue problems while most previous aligning techniques employ time consuming iterative optimization compared with traditional methods such as isomap and lle our mle yields an explicit modeling of the intrinsic variation modes of the observation data extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm

robust and efficient estimation with weighted composite quantile regression abstract in this paper we introduce a weighted composite quantile regression cqr estimation approach and study its application in nonlinear models such as exponential models and arch type models the weighted cqr is augmented by using a data driven weighting scheme with the error distribution unspecified the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator mle for a variety of error distributions including the normal mixed normal student s t cauchy distributions etc we also suggest an algorithm for the fast implementation of the proposed methodology simulations are carried out to compare the performance of different estimators and the proposed approach is used to analyze the daily s p 500 composite index which verifies the effectiveness and efficiency of our theoretical results

a geometric structure preserving discretization scheme for incompressible linearized elasticity abstract in this paper we present a geometric discretization scheme for incompressible linearized elasticity we use ideas from discrete exterior calculus dec to write the action for a discretized elastic body modeled by a simplicial complex after characterizing the configuration manifold of volume preserving discrete deformations we use hamilton s principle on this configuration manifold the discrete euler lagrange equations are obtained without using lagrange multipliers the main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field we explicitly derive the governing equations for the two dimensional case where the discrete spaces for the displacement field are constructed by p 1 polynomials over primal meshes for incompressibility constraint p 0 polynomials over dual meshes for the kinetic energy and p 1 polynomials over support volumes for the elastic energy and the discrete space of the pressure field is constructed by p 0 polynomials over primal meshes we test the efficiency and robustness of this geometric scheme using some numerical examples in particular we do not see any volume locking and or checkerboarding of pressure in our numerical examples this suggests that our choice of discrete solution spaces is compatible

a riemannian approach to reduced plate shell and rod theories abstract we derive a dimensionally reduced limit theory for an n dimensional nonlinear elastic body that is slender along k dimensions the starting point is to view an elastic body as an n dimensional riemannian manifold together with a not necessarily isometric w 1 2 immersion in n dimensional euclidean space the equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics the dimensionally reduced limit theory views the elastic body as a k dimensional riemannian manifold along with an isometric w 2 2 immersion in n dimensional euclidean space and linear data in the normal directions the equilibrium configuration minimizes a functional depending on the average covariant derivatives of the linear data the dimensionally reduced limit is obtained using a convergence approach the limit includes as particular cases plate shell and rod theories it applies equally to standard elasticity and to incompatible elasticity thus including as particular cases so called non euclidean plate shell and rod theories

a non greedy algorithm for l1 norm lda recently l1 norm based discriminant subspace learning has attracted much more attention in dimensionality reduction and machine learning however most existing approaches solve the column vectors of the optimal projection matrix one by one with greedy strategy thus the obtained optimal projection matrix does not necessarily best optimize the corresponding trace ratio objective function which is the essential criterion function for general supervised dimensionality reduction in this paper we propose a non greedy iterative algorithm to solve the trace ratio form of l1 norm based linear discriminant analysis we analyze the convergence of our proposed algorithm in detail extensive experiments on five popular image databases illustrate that our proposed algorithm can maximize the objective function value and is superior to most existing l1 lda algorithms

covariance in plasticity covariance is imposed to the second law of thermodynamics and consequences are shown for elastic perfectly plastic bodies in this setting pointwise balances of standard and configurational action

statistical inference in a growth curve quantile regression model for longitudinal data this article describes a polynomial growth curve quantile regression model that provides a comprehensive assessment about the treatment effects on the changes of the distribution of outcomes over time the proposed model has the flexibility as it allows the degree of a polynomial to vary across quantiles a high degree polynomial model fits the data adequately yet it is not desirable due to the complexity of the model we propose the model selection criterion based on an empirical loglikelihood that consistently identifies the optimal degree of a polynomial at each quantile after the parsimonious model is fitted to the data the hypothesis test is further developed to evaluate the treatment effects by comparing the growth curves it is shown that the proposed empirical loglikelihood ratio test statistic follows a chi square distribution asymptotically under the null hypothesis various simulation studies confirm that the proposed test successfully detects the difference between the curves across quantiles when the empirical loglikelihood is employed we incorporate the within subject correlation commonly existing in longitudinal data and gain estimation efficiency of the quantile regression parameters in the growth curve model the proposed process is illustrated through the analysis of randomized controlled longitudinal depression data

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

optimal mean two dimensional principal component analysis with f norm minimization our method simultaneously optimizes the projection matrix and mean in the criterion objective our method directly considers the reconstruction errors of data while most existing l1 norm 2dpca methods do not our method is not only robust but also retains 2dpcas desirable properties such as rotational invariance we solve the solution by a non greedy algorithm which has closed form solution and good convergence two dimensional principal component analysis 2dpca employs the squared f norm as distance metric for feature extraction and is widely used in the field of pattern analysis and recognition especially face image analysis but it is sensitive to the presence of outliers due to the fact that squared f norm remarkably enlarges the role of outliers in the criterion function to handle this problem we propose a robust formulation for 2dpca namely optimal mean 2dpca with f norm minimization omf 2dpca in omf 2dpca distance in spatial dimensions attribute dimensions is measured in f norm while the summation over different data points uses 1 norm moreover we center the data using the optimized mean rather than the fixed mean this helps further improve robustness of our method to solve omf 2dpca we propose a fast iterative algorithm which has a closed form solution in each iteration experimental results on face image databases illustrate its effectiveness and advantages

objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses abstract computational techniques which preserve the objectivity of incremental constitutive relations for finite elastic or inelastic materials for finite time steps during which the material elements may undergo finite rotations are presented these techniques are useful in finite deformation finite rotations and finite strain computational analysis of two as well as three dimensional solids and structures

chern simons terms in metric affine space time bianchi identities as euler lagrange equations the metric affine gauge theory of gravity encompasses a space time with the following geometrical fields coframe metric g and an independent linear connection within this geometrical framework all four forms b dc are constructed which qualify as boundary terms for a gauge lagrangian that is they are gl 4 r scalars as well as exact forms derived from chern simons type three forms c the result of our search is summarized in eq 4 20 the translational piece dctt is new the boundary terms effectively serve as lagrangians for the bianchi identities of nonmetricity torsion and curvature in the canonical formalism the normal parts of the chern simons three forms represent generating functions that are capable of generating new ashtekar type variables eventually the bach lanczos identity is generalized to the metric affine space time

semiparametric estimation in general repeated measures problems summary the paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function special cases in our approach include marginal models for longitudinal or clustered data conditional logistic regression for matched case control studies multivariate measurement error models generalized linear mixed models with a semiparametric component and many others we propose profile kernel and backfitting estimation methods for these problems derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient although generally not true it transpires that with our methods profiling and backfitting are asymptotically equivalent we also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm the methods proposed are evaluated by using simulation studies and applied to the kenya haemoglobin data

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

the anelastic ericksen problem universal eigenstrains and deformations in compressible isotropic elastic solids the elastic ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain energy density functions in the compressible case ericksen showed that only homogeneous deformations are possible here we solve the anelastic version of the same problem that is we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain energy density functions anelasticity is described by finite eigenstrains in a nonlinear solid these eigenstrains can be modelled by a riemannian material manifold whose metric depends on their distribution in this framework we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations deformations with covariantly constant deformation gradients we prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains we show that in a simply connected body for any distribution of universal eigenstrains the material manifold is a symmetric riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero stress

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

locality preserved maximum information projection dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze in this paper we propose an essentially linear projection technique called locality preserved maximum information projection lpmip to identify the underlying manifold structure of a data set lpmip considers both the within locality and the between locality in the processing of manifold learning equivalently the goal of lpmip is to preserve the local structure while maximize the out of locality global information of the samples simultaneously different from principal component analysis pca that aims to preserve the global information and locality preserving projections lpps that is in favor of preserving the local structure of the data set lpmip seeks a tradeoff between the global and local structures which is adjusted by a parameter alpha so as to find a sub space that detects the intrinsic manifold structure for classification tasks computationally by constructing the adjacency matrix lpmip is formulated as an eigenvalue problem lpmip yields orthogonal basis functions and completely avoids the singularity problem as it exists in lpp further we develop an efficient and stable lpmip qr algorithm for implementing lpmip especially on high dimensional data set theoretical analysis shows that conventional linear projection methods such as weighted pca maximum margin criterion mmc linear discriminant analysis lda and lpp could be derived from the lpmip framework by setting different graph models and constraints extensive experiments on face digit and facial expression recognition show the effectiveness of the proposed lpmip method

bayesian latent variable models for median regression on multiple outcomes souvent il est impossible de mesurer une reponse d interet et on doit necessairement faire appel a des grandeurs accessoires multiples qu on suppose independantes conditionnellement aux valeurs de la variable latente et des covariables observees de facon typique les modeles en variable latente supposent que les residuees sont gaussions cet article propose une regression bayesienne modelisant la mediane et qui dispense d hypothese sur les distributions des residus en s appuyant sur une approximation basee sur les quartiles pour traiter de la dependance intra sujet les quartiles de la reponse des variables de remplacement sont liees a des distributions normales sous jacentes dependant d une variable latente normale la structure de covariance gaussienne qui en resulte simplifie l interpretatin et l ajustement sans limiter les distributions marginales des variables de remplacement pour les calculs des distributions a posteriori nous proposons un algorithme de chaine de markov monte carlo les methodes sont appliquees sont appliquees pour d une etude de toxicologie genetique aux dosages par electrophorese sur cellule unique essai cornet

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

non negative patch alignment framework in this paper we present a non negative patch alignment framework npaf to unify popular non negative matrix factorization nmf related dimension reduction algorithms it offers a new viewpoint to better understand the common property of different nmf algorithms although multiplicative update rule mur can solve npaf and is easy to implement it converges slowly thus we propose a fast gradient descent fgd to overcome the aforementioned problem fgd uses the newton method to search the optimal step size and thus converges faster than mur experiments on synthetic and real world datasets confirm the efficiency of fgd compared with mur for optimizing npaf based on npaf we develop non negative discriminative locality alignment ndla experiments on face image and handwritten datasets suggest the effectiveness of ndla in classification tasks and its robustness to image occlusions compared with representative nmf related dimension reduction algorithms

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

empirical likelihood and quantile regression in longitudinal data analysis we propose a novel quantile regression approach for longitudinal data analysis which naturally incorporates auxiliary information from the conditional mean model to account for within subject correlations the efficiency gain is quantified theoretically and demonstrated empirically via simulation studies and the analysis of a real dataset

rapid and brief communication local structure based supervised feature extraction in the past few years the computer vision and pattern recognition community has witnessed the rapid growth of a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel feature extraction method called locally discriminating projection ldp ldp utilizes class information to guide the procedure of feature extraction in ldp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the similarity has several good properties which help to discover the true intrinsic structure of the data and make ldp a robust technique for the classification tasks we compare the proposed ldp approach with lpp as well as other feature extraction methods such as pca and lda on the public available data sets feret and ar experimental results suggest that ldp provides a better representation of the class information and achieves much higher recognition accuracies