some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

implicit algorithm for finite deformation hypoelastic viscoplasticity in fcc metals an implicit objective stress update algorithm is proposed for a hypoelastic viscoplastic model a thermal dynamic yield function which is derived based on the thermal activation analysis and dislocation interaction mechanisms is used along with the consistency approach and the framework of additive viscoplasticity in deriving the proposed model for fcc metals the corotational formulation approach is utilized in developing the proposed model in the finite deformation field for the case of the newton raphson iteration method a new expression for the consistent algorithmic tangent stiffness matrix of rate dependent metals is derived by direct linearization of the stress update algorithm finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program abaqus numerical implementation for a simple tensile problem is used for validating the material parameters of the ofhc copper under low and high strain rates and temperatures the numerical results of the adiabatic true stress true strain curves compare very well with the experimental data the effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh independent results copyright 2006 john wiley sons ltd

generalized linear array models with applications to multidimensional smoothing summary data with an array structure are common in statistics and the design or regression matrix for analysis of such data can often be written as a kronecker product factorial designs contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models in such a setting we develop an arithmetic of arrays which allows us to define the expectation of the data array as a sequence of nested matrix operations on a coefficient array we show how this arithmetic leads to low storage high speed computation in the scoring algorithm of the generalized linear model we refer to a generalized linear array model and apply the methodology to the smoothing of multidimensional arrays we illustrate our procedure with the analysis of three data sets mortality data indexed by age at death and year of death spatially varying microarray background data and disease incidence data indexed by age at death year of death and month of death

the ubiquitous kronecker product abstract the kronecker product has a rich and very pleasing algebra that supports a wide range of fast elegant and practical algorithms several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future first the application areas where kronecker products abound are all thriving these include signal processing image processing semidefinite programming and quantum computing second sparse factorizations and kronecker products are proving to be a very effective way to look at fast linear transforms researchers have taken the kronecker methodology as developed for the fast fourier transform and used it to build exciting alternatives third as computers get more powerful researchers are more willing to entertain problems of high dimension and this leads to kronecker products whenever low dimension techniques are tensored together

two stress update algorithms for large strains accuracy analysis and numerical implementation two algorithms for the stress update i e time integration of the constitutive equation in large strain solid mechanics are compared from an analytical point of view the order of the truncation error associated to the numerical integration is deduced for each algorithm a priori using standard numerical analysis this accuracy analysis has been performed by means of a convected frame formalism which also allows a unied derivation of both algorithms in spite of their inherent dierences then the two algorithms are adapted from convected frames to a xed cartesian frame and implemented in a small strain nite element code the implementation is validated by means of a set of simple deformation paths simple shear extension extension and compression extension and rotation and two benchmark tests in non linear mechanics the necking of a circular bar and a shell under ring loads in these numerical tests the observed order of convergence is in very good agreement with the theoretical order of convergence thus corroborating the accuracy analysis 1997 john wiley sons ltd

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

a novel non linearly explicit second order accurate l stable methodology for finite deformation hypoelastic hypoelasto plastic structural dynamics problems a novel non linearly explicit second order accurate l stable computational methodology for integrating the non linear equations of motion without non linear iterations during each time step and the underlying implementation procedure is described emphasis is placed on illustrative non linear structural dynamics problems employing both total updated lagrangian formulations to handle finite deformation hypoelasticity hypoelasto plasticity models in conjunction with a new explicit exact integration procedure for a particular rate form constitutive equation illustrative numerical examples are shown to demonstrate the robustness of the overall developments for non linear structural dynamics applications

weak sharpness for gap functions in vector variational inequalities abstract in this paper characterizations of the set of solutions for vvi are presented by using scalarization approaches the set of solutions of vvi is shown to be the set of weak sharpness for gap functions of some scalarization of vvi and for gap functions of vvi under semi strong monotonicity some examples are given to illustrate these results

an extension of 3 d procedure to large strain analysis of shells abstract a numerical stress integration procedure for general 3 d large strain problems in inelasticity based on the total formulation and the governing parameter method gpm is extended to shell analysis the multiplicative decomposition of the deformation gradient is adopted with the evaluation of the deformation gradient practically in the same way as in a general 3 d material deformation the calculated trial elastic logarithmic strains are transformed to the local shell cartesian coordinate system and the stress integration is performed according to the gpm developed for small strain conditions the consistent tangent matrix is calculated as in case of small strain deformation and then transformed to the global coordinate system a specific step in the proposed procedure is the updating of the left elastic green lagrangian deformation tensor namely after the stresses are computed the principal elastic strains and the principal vectors corresponding to the stresses at the end of time step are determined in this way the shell conditions are taken into account appropriately for the next step some details are given for the stress integration in case of thermoplastic and creep material model numerical examples include bulging of plate plastic thermoplastic and creep models for metal and necking of a thin sheet comparison of solutions with those available in the literature and with solutions using other type of finite elements demonstrates applicability efficiency and accuracy of the proposed procedure

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

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

spline based meshfree method summary in the present work the spline based meshfree method sbmfm is presented the sbmfm uses spline basis functions for field variables and boundary representation because of the inherent properties of splines that is nurbs nonuniform rational b splines the analysis domain used in the sbmfm has its own parametric domain unlike the classical concepts in the computer aided design cad community in which the nurbs patches are used to model the body the nurbs patch is treated as a background mesh in the present work the real analysis domain is created by trimming operation so that the domain boundaries are described by spline curves only on a single nurbs patch building the geometry in this way enables a convenient boundary representation of the domains because direct manipulation of spline curves becomes possible from a deformation point of view the mesh distortion problem is effectively avoided even if the analysis domain undergoes a large deformation in the sbmfm boundary spline curves freely move with complete independence from the quadrilateral background nurbs patch the so called element connectivity is unnecessary for geometry description in this paper geometrically nonlinear problems are considered implementation strategy is presented and the effectiveness of the present sbmfm is shown through various numerical examples copyright 2012 john wiley sons ltd

linear models for field trials smoothing and cross validation abstract spatial methods for the analysis of agricultural field experiments are represented here as smoothing methods applied simultaneously with the estimation of treatment effects selection of both the form of the smoother and the degree of smoothing required may be based on cross validation particular emphasis is placed in this paper on generalized least squares estimation ion linear models but the principle applies quite generally keywords agricultural field experiments generalized least squares incomplete block designs neighbour methods papadakis method recovery of inter block formation smoothing and spatial models

adapting broyden method to handle linear constraints imposed via lagrange multipliers various non linear equation solvers are adapted to handle linear constraints via the lagrange multiplier technique this adaptation process turns out to be quite straightforward for newton raphson methods and rank two quasi newton methods bfgs and dfp but rather more involved for broyden method in fact two broyden methods can be obtained the standard one and a modified one better adapted to the lagrange multiplier environment some numerical examples are used to assess the relative performance of the various adapted solvers these tests illustrate the superiority of the modified broyden method over the standard one

conditional transformation models the ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables this goal is however seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not aected by the regressors the underlying reason for such a restriction is the assumption of additivity of signal and noise we propose to relax this common assumption in the framework of transformation models the novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables these transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts e g the continuous ranked probability score the corresponding estimated conditional distribution functions are consistent based on applications from dierent domains we show that these conditional transformation models are useful for describing possible heteroscedasticity comparing spatially varying distributions identifying extreme events deriving prediction intervals and selecting variables beyond mean regression eects an empirical investigation based on a heteroscedastic varying coecient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more benecial than kernel based non parametric approaches or parametric generalised additive models for location scale and shape

formulation of an implicit algorithm for finite deformation viscoplasticity abstract within the framework of additive plasticity an objective stress update algorithm has been proposed the procedure is implemented in such way that the extension from a standard small strain fe code to the finite strain range is straightforward and objectivity can be retained for any choice of the intermediate configuration the additional computational cost only includes some geometrical manipulations for the newton raphson iteration method a closed form solution of the consistent tangent is derived by direct linearization of the stress update algorithm numerical examples show a quadratic rate of convergence with the proposed viscoplastic model the analysis of a tensile test first shows a shear band with a finite thickness independent of the finite element size at large deformation the shear band pattern transforms into a necking failure mode as a second example a thin sheet tensile test is analyzed a necking failure mode leads to global softening even though locally the material is still hardening although viscoplastic regularization is used the results still show a mesh dependence for deformations over 40

modelling and smoothing parameter estimation with multiple quadratic penalties summary penalized likelihood methods provide a range of practical modelling tools including spline smoothing generalized additive models and variants of ridge regression selecting the correct weights for penalties is a critical part of using these methods and in the single penalty case the analyst has several well founded techniques to choose from however many modelling problems suggest a formulation employing multiple penalties and here general methodology is lacking a wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimise kw 1 2 xp a y k 2 o p m i 1 iip 0 s i p p is a parameter vector x a design matrix si a non negative definite coefficient matrix defining the i th penalty with associated smoothing parameter ii w a diagonal weight matrix y a vector of data or pseudodata and o an overall smoothing parameter included for reasons of computational efficiency this paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross validation to this problem and how this allows non linear generalized linear and linear models to be fitted using multiple penalties substantially increasing the scope of penalized modelling methods examples of non linear modelling generalized additive modelling and anisotropic smoothing are given

modelling covariance structure in bivariate marginal models for longitudinal data summary it can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case due to the correlations arising between multiple responses the positive definiteness constraint and the high dimensionality are further obstacles in covariance modelling in this paper we develop a data based method by which the parametersinthecovariancematricesarereplacedbyunconstrainedandinterpretableparameterswith reduced dimensions the maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures

modulation models for seasonal time series and incidence tables we model monthly disease counts on an age time grid using the two dimensional varying coefficient poisson regression since the marginal profile of counts shows a very strong and varying annual cycle sine and cosine regressors model periodicity but their coefficients are allowed to vary smoothly over the age and time plane the coefficient surfaces are estimated using a relatively large tensor product b spline basis smoothness is tuned using difference penalties on the rows and columns of the tensor product coefficients heavy over dispersion occurs making it impossible to use akaike s information criterion or bayesian information criterion based on a poisson likelihood it is handled by selective weighting of part of the data and by the use of extended quasi likelihood very efficient computation is achieved with fast array algorithms the model is applied to monthly deaths due to respiratory diseases for u s females during 1959 1998 and for ages 51 100

modelling function valued stochastic processes with applications to fertility dynamics summary we introduce a simple and interpretable model for functional data analysis for situations where the observations at each location are functional rather than scalar this new approach is based on a tensor product representation of the function valued process and utilizes eigenfunctions of marginal kernels the resulting marginal principal components and product principal components are shown to have nice properties given a sample of independent realizations of the underlying function valued stochastic process we propose straightforward fitting methods to obtain the components of this model and to establish asymptotic consistency and rates of convergence for the estimates proposed the methods are illustrated by modelling the dynamics of annual fertility profile functions for 17 countries this analysis demonstrates that the approach proposed leads to insightful interpretations of the model components and interesting conclusions

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

modeling and testing differential item functioning in unidimensional binary item response models with a single continuous covariate a functional data analysis approach differential item functioning dif referring to between group variation in item characteristics above and beyond the group level disparity in the latent variable of interest has long been regarded as an important item level diagnostic the presence of dif impairs the fit of the single group item response model being used and calls for either model modification or item deletion in practice depending on the mode of analysis methods for testing dif with continuous covariates rather than categorical grouping variables have been developed however they are restrictive in parametric forms and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates in the current study we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate which is then approximated by a two dimensional smoothing spline the accuracy and precision of the proposed procedure is evaluated via monte carlo simulations if anchor items are available we proposed an extended model that simultaneously estimates item characteristic functions icfs for anchor items icfs conditional on the covariate for non anchor items and the latent variable density conditional on the covariate all using regression splines a permutation dif test is developed and its performance is compared to the conventional parametric approach in a simulation study we also illustrate the proposed semiparametric dif testing procedure with an empirical example

fast bivariate p splines the sandwich smoother national science foundation dms 0805975 national institutes of health r01 ns060910 national center for research resources ul1 rr024996 national natural science foundation of china 11201390

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

finite strain plasticity in convected frames a rate type formulation of quasi static boundary value problems using convected material frames is proposed and an associated method of numerical solution is derived two numerical problems are presented the first deals with a significant validation example the second with a necking bifurcation analysis