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

a validated information criterion to determine the structural dimension in dimension reduction models summary a crucial component of performing sufficient dimension reduction is to determine the structural dimension of the reduction model we propose a novel information criterion based method for this purpose a special feature of which is that when examining the goodness of fit of the current model one needs to perform model evaluation by using an enlarged candidate model althoughtheproceduredoesnotrequireestimationundertheenlargedmodelofdimensionk 1 the decision as to how well the current model of dimensionk fits relies on the validation provided by the enlarged model thus we call this procedure the validated information criterion vic k our method is different from existing information criterion based model selection methods it breaks free from dependence on the connection between dimension reduction models and their corresponding matrix eigenstructures which relies heavily on a linearity condition that we no longer assume we prove consistency of the proposed method and its finite sample performance is demonstrated numerically

non standard contact conditions in generalized continua microblock contact model for a cosserat body abstract generalized continuum theories involve non standard boundary conditions that are associated with the additional kinematic variables introduced in those theories e g higher gradients of the displacement field or additional kinematic degrees of freedom accordingly formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and or for the respective generalized tractions in this paper we address several related open problems namely how to enhance the classic contact conditions to include the effects of the additional kinematic variables how to link the enhanced contact model to the underlying microstructure of the solid and how to do it in a consistent manner as a first step towards a new class of contact models for generalized continua a microblock contact model is derived for a cosserat solid based on simple micromechanical considerations to illustrate the non trivial effects introduced by the non standard boundary conditions the problem of compression of an infinite strip with nonaligned microblocks is considered and the analytical solution is derived for the corresponding boundary layers a hertz like contact problem is also solved numerically with the focus on non standard features of the solution and on the related size effects

a peridynamic model for plasticity micro inertia based flow rule entropy equivalence and localization residuals this article presents a non ordinary state based peridynamic pd model for thermo visco plasticity that incorporates a microinertia driven dynamic flow rule in addition to the three displacement degrees of freedom the model assigns to each particle an internal degree of freedom namely the equivalent plastic strain the flow rule itself is in the form of an integro differential micro force balance written in terms of appropriate pd states associated with micro stresses corresponding to the internal degree of freedom an equation for entropy balance adapted to the pd setup is also proposed along with the internal energy equivalence we exploit a notion of equivalence of the local entropy production for the constitutive modelling of the force states as we also demonstrate the pd model naturally accounts for the localization residual terms in the local balances for internal energy and entropy originally conceived of by edelen and co workers nearly half a century ago as a source of nonlocal interaction the model is numerically implemented for the problem of impact between two 4340 steel plates and the results show that the model provides information on nontrivial effects of micro inertia on the plastic flow and temperature generation by incorporating a classical damage model in the pd set up we also discuss an extension of the approach for ductile failure and report on the numerical results against tension test on an a440 steel plate with holes c 2017 elsevier b v all rights reserved

on theoretical and numerical methods in the theory of porous media based on polar and non polar elasto plastic solid materials the consideration of saturated and non saturated porous solid materials as for instance soil concrete sinter materials polymeric and metallic foams temperate ice living tissues etc naturally falls into the category of multiphase materials which can be described by use of a macroscopic continuum mechanical approach within the well founded framework of the theory of porous media tpm in the present contribution granular elasto plastic porous solid skeletons frictional materials are taken into consideration where regardless of whether or not the solid is fluid saturated or empty localization phenomena can occur as a result of local concentrations of plastic strains as a consequence of localization phenomena the numerical solution of the governing equations generally reveals an ill posed problem in particular the shear band width strongly depends on the mesh size of the finite element discretization by the fact that each mesh refinement leads to a decrease of the shear band width until one obtains a singular surface in the present article it is shown that the inclusion of fluid viscosity in the saturated case and the inclusion of micropolar grain rotations both in the saturated and in the non saturated case leads to a regularization of the shear band problem on the other hand the inclusion of micropolar degrees of freedom in the sense of the cosserat brothers additionally allows for the determination of the local average grain rotations the numerical examples are solved by use of finite element discretization techniques where in particular the computation of shear band localization phenomena is carried out by the example of the well known geotechnical slope failure problem and two additional academic problems which clearly demonstrate the efficiency of the proposed procedure

strong orthogonal arrays and associated latin hypercubes for computer experiments this paper introduces constructs and studies a new class of arrays called strong orthogonal arrays as suitable designs for computer experiments a strong orthogonal array of strength t enjoys better space filling properties than a comparable orthogonal array in all dimensions lower than t while retaining the space filling properties of the latter in t dimensions latin hypercubes based on strong orthogonal arrays of strength t are more space filling than comparable orthogonal array based latin hypercubes in all g dimensions for any 2 g t 1 copyright 2013 oxford university press

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

micropolar hyper elastoplasticity constitutive model consistent linearization and simulation of 3d scale effects summary a computational model for micropolar hyperelastic based finite elastoplasticity that incorporates isotropic hardening is developed the basic concepts of the non linear micropolar kinematic framework are reviewed and a thermodynamically consistent constitutive model that features neo hooke type elasticity and generalized von mises plasticity is described the integration of the constitutive initial value problem is carried out by means of an elastic predictor plastic corrector algorithm which retains plastic incompressibility the solution procedure is developed carefully and described in detail the consistent material tangent is derived the micropolar constitutive model is implemented in an implicit finite element framework the numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented the results of the finite element simulations demonstrate i that the methodology is capable of capturing the size effect in three dimensional elastoplastic solids in the finite strain regime ii that the formulation possesses a regularizing effect in the presence of strain localization and iii that asymptotically quadratic convergence rates of the newton raphson procedure are achieved throughout this paper effort is made to present the developments as a direct extension of standard finite deformation computational plasticity copyright 2012 john wiley sons ltd

on sliced inverse regression with high dimensional covariates sliced inverse regression is a promising method for the estimation of the central dimension reduction subspace cdr space in semiparametric regression models it is particularly useful in tackling cases with high dimensional covariates in this article we study the asymptotic behavior of the estimate of the cdr space with high dimensional covariates that is when the dimension of the covariates goes to infinity as the sample size goes to infinity strong and weak convergence are obtained we also suggest an estimation procedure of the bayes information criterion type to ascertain the dimension of the cdr space and derive the consistency a simulation study is conducted

characterization of the asymptotic distribution of semiparametric m estimators this paper develops a concrete formula for the asymptotic distribution of two step possibly non smooth semiparametric m estimators under general misspecification our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature the first stage nonparametric estimation may depend on finite dimensional parameters we characterize 1 conditions under which the first stage estimation of nonparametric components do not affect the asymptotic distribution 2 conditions under which the asymptotic distribution is affected by the derivatives of the first stage nonparametric estimator with respect to the finite dimensional parameters and 3 conditions under which one can allow non smooth objective functions our framework is illustrated by applying it to three examples 1 profiled estimation of a single index quantile regression model 2 semiparametric least squares estimation under model misspecification and 3 a smoothed matching estimator 2010 elsevier b v all rights reserved

tree based methods for individualized treatment regimes individualized treatment rules recommend treatments on the basis of individual patient characteristics a high quality treatment rule can produce better patient outcomes lower costs and less treatment burden if a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight it is crucial that it be interpretable clinicians may be unwilling to implement models they do not understand and black box models may not be useful for guiding future research the canonical example of an interpretable prediction model is a decision tree we propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees the class of rules we consider is interpretable but expressive a novel feature of this problem is that the learning task is unsupervised as the optimal treatment for each patient is unknown and must be estimated the proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments we illustrate it using data from a study of major depressive disorder

space filling properties of good lattice point sets we study space filling properties of good lattice point sets and obtain some general theoretical results we show that linear level permutation does not decrease the minimum distance for good lattice point sets and we identify several classes of such sets with large minimum distance based on good lattice point sets some maximin distance designs are also constructed

residual weighted learning for estimating individualized treatment rules abstractpersonalized medicine has received increasing attention among statisticians computer scientists and clinical practitioners a major component of personalized medicine is the estimation of individualized treatment rules itrs recently zhao et al proposed outcome weighted learning owl to construct itrs that directly optimize the clinical outcome although owl opens the door to introducing machine learning techniques to optimal treatment regimes it still has some problems in performance 1 the estimated itr of owl is affected by a simple shift of the outcome 2 the rule from owl tries to keep treatment assignments that subjects actually received 3 there is no variable selection mechanism with owl all of them weaken the finite sample performance of owl in this article we propose a general framework called residual weighted learning rwl to alleviate these problems and hence to improve finite sample performance unlike owl which weights misclassification errors by clinical outcom

efficient estimation in sufficient dimension reduction we develop an efficient estimation procedure for identifying and estimating the central subspace using a new way of parameterization we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model this conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound the resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace we conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods

calibrating parametric subject specific risk estimation for modern evidence based medicine decisions on disease prevention or management strategies are often guided by a risk index system for each individual the system uses his her baseline information to estimate the risk of experiencing a future disease related clinical event such a risk scoring scheme is usually derived from an overly simplified parametric model to validate a model based procedure one may perform a standard global evaluation via for instance a receiver operating characteristic analysis in this article we propose a method to calibrate the risk index system at a subject level specifically we developed point and interval estimation procedures for t year mortality rates conditional on the estimated parametric risk score the proposals are illustrated with a dataset from a large clinical trial with post myocardial infarction patients

theory and numerics of ductile micropolar elastoplastic damage the aim of this work is to extend an isotropic elastoplastic damage concept for ductile materials within a generalized micropolar continuum framework the underlying motivation is on the one hand to model softening behaviour by damage evolution and on the other hand to regularize the impending loss of ellipticity which results in strong mesh dependence of localization computations to this end the classical displacement field is supplemented by an independent rotation field to yield an enhanced continuum for the model originally proposed by lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity special emphasis is directed towards the numerical implementation of the constitutive model within the framework of finite element analysis of inelastic boundary value problems to compare damage evolution and standard strain softening the results are contrasted to the outcome of an analysis with the micropolar version of the classical von mises model thereby the intriguing correspondence of strain softening and damage evolution is highlighted additionally several planar micropolar finite element formulations are derived within mixed variational principles to enhance the poor performance of the standard bilinear displacement and rotation expansions used so far in the literature the merits of these new element developments are demonstrated for the example of localization within a compression problem

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

greedy outcome weighted tree learning of optimal personalized treatment rules summary we propose a subgroup identification approach for inferring optimal and interpretable personalized treatment rules with high dimensional covariates our approach is based on a two step greedy tree algorithm to pursue signals in a high dimensional space in the first step we transform the treatment selection problem into a weighted classification problem that can utilize tree based methods in the second step we adopt a newly proposed tree based method known as reinforcement learning trees to detect features involved in the optimal treatment rules and to construct binary splitting rules the method is further extended to right censored survival data by using the accelerated failure time model and introducing double weighting to the classification trees the performance of the proposed method is demonstrated via simulation studies as well as analyses of the cancer cell line encyclopedia ccle data and the tamoxifen breast cancer data

orthogonal and nearly orthogonal designs for computer experiments we introduce a method for constructing a rich class of designs that are suitable for use in computer experiments the designs include latin hypercube designs and two level fractional factorial designs as special cases and fill the vast vacuum between these two familiar classes of designs the basic construction method is simple building a series of larger designs based on a given small design if the base design is orthogonal the resulting designs are orthogonal likewise if the base design is nearly orthogonal the resulting designs are nearly orthogonal we present two generalizations of our basic construction method the first generalization improves the projection properties of the basic method the second generalization gives rise to designs that have smaller correlations sample constructions are presented and properties of these designs are discussed

strong orthogonal arrays of strength two plus strong orthogonal arrays were recently introduced and studied in he and tang biometrika100 2013 254 260 as a class of space filling designs for computer experiments to enjoy the benefits of better space filling properties when compared to ordinary orthogonal arrays strong orthogonal arrays need to have strength three or higher which may require run sizes that are too large for experimenters to afford to address this problem we introduce a new class of arrays called strong orthogonal arrays of strength two plus these arrays while being more economical than strong orthogonal arrays of strength three still enjoy the better two dimensional space filling property of the latter among the many results we have obtained on the characterizations and constructions of strong orthogonal arrays of strength two plus worth special mention is their intimate connection with second order saturated designs

counting process based dimension reduction methods for censored outcomes we propose counting process based dimension reduction methods for right censored survival data semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model our methods address two limitations of existing approaches first using the counting process formulation they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace second the nonparametric estimation involved adapts to the structural dimension so our methods circumvent the curse of dimensionality asymptotic normality is established for the estimators we propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace numerical studies suggest that our new approaches exhibit significantly improved performance the methods are implemented in the formula see text package formula see text

a semiparametric approach to dimension reduction we provide a novel and completely different approach to dimension reduction problems from the existing literature we cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations viewing this problem from the new angle allows us to derive a rich class of estimators and obtain the classical dimension reduction techniques as special cases in this class the semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact the common assumption of linearity and or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression the semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example this article has online supplementary material

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

doubly robust learning for estimating individualized treatment with censored data individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit when the clinical outcome of interest is survival time estimation is often complicated by censoring we develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data to adjust for censoring we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model but not both the method is shown to be fisher consistent when either model is correct furthermore we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule we illustrate the proposed methods using simulation study and data from a phase iii clinical trial on non small cell lung cancer

on partial sufficient dimension reduction with applications to partially linear multi index models partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest which includes dimension reduction as its special case when the predictors in the remaining part are constants in this article we propose a novel method to conduct partial dimension reduction estimation for predictors of primary interest without assuming that the remaining predictors are categorical to this end we first take the dichotomization step such that any existing approach for partial dimension reduction estimation can be employed then we take the expectation step to integrate over all the dichotomic predictors to identify the partial central subspace as an example we use the partially linear multi index model to illustrate its applications for semiparametric modeling simulations and real data examples are given to illustrate our methodology

construction of 2 m4 n designs via a grouping scheme on developpe une methode pour grouper les 2 k 1 effets factoriels dans un plan factoriel a deux niveaux dans des ensembles disjoints mutuellement s t st ou st est l interaction generalisee des effets s et t comme application on construit des tableaux orthogonaux oa 2 k 2 m 4 n 2 de taille 2 k m contraintes avec 2 niveaux et n contraintes avec 4 niveaux satisfaisant m 3n 2 k 1 et de puissance 2 le nombre maximum de contraintes avec 4 niveaux dans la construction ne peut plus etre ameliore dans ce sens le schema de groupement qu on donne est optimal on discute les avantages de la presente approche par rapport a d autres methodes de construction

a regression tree approach to identifying subgroups with differential treatment effects in the fight against hard to treat diseases such as cancer it is often difficult to discover new treatments that benefit all subjects for regulatory agency approval it is more practical to identify subgroups of subjects for whom the treatment has an enhanced effect regression trees are natural for this task because they partition the data space we briefly review existing regression tree algorithms then we introduce three new ones that are practically free of selection bias and are applicable to data from randomized trials with two or more treatments censored response variables and missing values in the predictor variables the algorithms extend the guide approach by using three key ideas i treatment as a linear predictor ii chi squared tests to detect residual patterns and lack of fit and iii proportional hazards modeling via poisson regression importance scores with thresholds for identifying influential variables are obtained as by products a bootstrap technique is used to construct confidence intervals for the treatment effects in each node the methods are compared using real and simulated data