continuum modeling of the mechanical and thermal behavior of discrete large structures in the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss like repetitive structures once the actual structure is specified the construction procedure can be outlined by the following three steps a all sets of parallel members are identified b unidirectional effective continuum properties are derived for each of these sets and c orthogonal transformations are finally used to determine the contribution of each set to the overall effective continuum properties of the structure here the properties includes mechanical stiffnesses thermal coefficients of thermal expansions and material densities once expanded descriptions of the steps b and c are done the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods

on the thermally induced bistability of composite cylindrical shells for morphing structures abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable cylindrical panels polynomial discretisations of the displacements field are used to predict stable shapes geometry and other aspects of the nonlinear structural behaviour in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional shell lamination theory with sanders nonlinear strains is developed and presented an investigation on the relative importance of different nonlinear strain terms is shown to provide useful insight into the applicability of common assumptions about shell kinematics in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics is carried out using a set of in house m atlab routines for numerical continuation results are compared with detailed finite elements analysis throughout the course of the paper

bootstrapping a regression equation some empirical results abstract the bootstrap like the jackknife is a technique for estimating standard errors the idea is to use monte carlo simulation based on a nonparametric estimate of the underlying error distribution the main object of this article is to present the bootstrap in the context of an econometric equation describing the demand for energy by industry as it turns out the conventional asymptotic formulas for estimating standard errors are too optimistic by factors of nearly three when applied to a particular finite sample problem in a simpler context this finding can be given a mathematical proof

variational principles in dissipative electro magneto mechanics a framework for the macro modeling of functional materials summary this paper presents a general framework for the macroscopic continuum based formulation and numerical implementation of dissipative functional materials with electro magneto mechanical couplings based on incremental variational principles we focus on quasi static problems where mechanical inertia effects and time dependent electro magnetic couplings are a priori neglected and a time dependence enters the formulation only through a possible rate dependent dissipative material response the underlying variational structure of non reversible coupled processes is related to a canonical constitutive modeling approach often addressed to so called standard dissipative materials it is shown to have enormous consequences with respect to all aspects of the continuum based modeling in macroscopic electro magnetomechanics at first the local constitutive modeling of the coupled dissipative response i e stress electric and magnetic fields versus strain electric displacement and magnetic induction is shown to be variational based governed by incremental minimization and saddle point principles next the implications on the formulation of boundary value problems are addressed which appear in energy based formulations as minimization principles and in enthalpy based formulations in the form of saddle point principles furthermore the material stability of dissipative electro magneto mechanics on the macroscopic level is defined based on the convexity concavity of incremental potentials we provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation such as formulation of constitutive update algorithms and finite element solvers from the viewpoint of constitutive modeling including the understanding of the stability in coupled electro magneto mechanics an energy based formulation is shown to be the canonical setting from the viewpoint of the computational convenience an enthalpy based formulation is the most convenient setting a numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials copyright 2011 john wiley sons ltd received 1 october 2010 revised 15 december 2010 accepted 15 december 2010

sample size and power calculations for correlations between bivariate longitudinal data the analysis of a baseline predictor with a longitudinally measured outcome is well established and sample size calculations are reasonably well understood analysis of bivariate longitudinally measured outcomes is gaining in popularity and methods to address design issues are required the focus in a random effects model for bivariate longitudinal outcomes is on the correlations that arise between the random effects and between the bivariate residuals in the bivariate random effects model we estimate the asymptotic variances of the correlations and we propose power calculations for testing and estimating the correlations we compare asymptotic variance estimates to variance estimates obtained from simulation studies and compare our proposed power calculations for correlations on bivariate longitudinal data to power calculations for correlations on cross sectional data

the foppl von karman equations for plates with incompatible strains we provide a derivation of the foppl von karman equations for the shape of and stresses in an elastic plate with incompatible or residual strains these might arise from a range of causes inhomogeneous growth plastic deformation swelling or shrinkage driven by solvent absorption our analysis gives rigorous bounds on the convergence of the three dimensional equations of elasticity to the low dimensional description embodied in the plate like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves it also formalizes a procedure that can be used to derive other low dimensional descriptions of active materials with complex non euclidean geometries

sample size calculations for evaluating mediation this paper presents sample size calculations for testing the mediation of the effect of a primary predictor by an intermediate variable this problem is related to validating surrogate markers and to testing the effect of a primary predictor in the presence of confounders for those problems proposals for sample size calculation exist in the literature and can be adapted to the problem of mediation methods based on the variance inflation factor in linear regression provide exact sample size calculations for the linear model and approximations for the logistic poisson and cox models we propose another procedure based on simulation of the underlying data structure with applications to the logistic and cox models for the poisson model a new analytic method is also proposed the behavior of the different proposals is investigated by means of simulation studies copyright 2008 john wiley sons ltd

sample size determination for hierarchical longitudinal designs with differential attrition rates we consider the problem of sample size determination for three level mixed effects linear regression models for the analysis of clustered longitudinal data three level designs are used in many areas but in particular multicenter randomized longitudinal clinical trials in medical or health related research in this case level 1 represents measurement occasion level 2 represents subject and level 3 represents center the model we consider involves random effects of the time trends at both the subject level and the center level in the most common case we have two random effects constant and a single trend at both subject and center levels the approach presented here is general with respect to sampling proportions number of groups and attrition rates over time in addition we also develop a cost model as an aid in selecting the most parsimonious of several possible competing models i e different combinations of centers subjects within centers and measurement occasions we derive sample size requirements i e power characteristics for a test of treatment by time interaction s for designs based on either subject level or cluster level randomization the general methodology is illustrated using two characteristic examples

power calculations for general linear multivariate models including repeated measures applications abstract recently developed methods for power analysis expand the options available for study design we demonstrate how easily the methods can be applied by 1 reviewing their formulation and 2 describing their application in the preparation of a particular grant proposal the focus is a complex but ubiquitous setting repeated measures in a longitudinal study describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis discussion of the example also highlights issues that typically must be considered in designing a study first we discuss the motivation for using detailed power calculations focusing on multivariate methods in particular second we survey available methods for the general linear multivariate model glmm with gaussian errors and recommend those based on f approximations the treatment includes coverage of the multivariate and univariate approaches to repeated measures manova anova multivariate regression and

bootstrap bartlett adjustment in seemingly unrelated regression abstract seemingly unrelated regression sur is a method introduced by zellner 1962 for estimating several regression equations simultaneously a common and important problem in econometrics this article considers hypothesis testing in sur using the log likelihood ratio llr test although the asymptotic distribution of this statistic is well known substantial departures occur in samples of the size commonly employed by economists significance levels given by the use of this asymptotic distribution are too low sometimes by an order of magnitude leading to the rejection of too many true null hypotheses a common approach to this problem is to use a bartlett 1937 adjustment to the llr statistic in which the test statistic is multiplied by a factor derived from second order asymptotics before it is referred to the asymptotic 2 q distribution this article proposes that the bartlett adjustment factor be computed using efron s bootstrap 1979 1982 in the cases examined this leads to more accu

multiparameter actuation for shape control of bistable composite plates this paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects starting with a von karman plate kinematics and an energetic formulation a discrete intrinsic nonlinear model in terms of curvatures only is deduced the model has 3 degrees of freedom namely the components of the symmetric curvature tensor which is supposed to be uniform in space despite of this rough assumption the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code literature results about the bistable behavior of isotropic plates under a single parameter loading are extended to the orthotropic case with two loading parameters in light of a global stability analysis and a phase portrait as a function of the inelastic curvatures we study possible actuation techniques for controlling the transition of the plate between its two stable configurations we show that with a suitable two parameter actuation it is possible to get a controlled quasi static transition avoiding any instability phenomenon numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

periodicity repetitions and orbits of an automatic sequence we revisit a technique of s lehr on automata and use it to prove old and new results in a simple way we give a very simple proof of the 1986 theorem of honkala that it is decidable whether a given k automatic sequence is ultimately periodic we prove that it is decidable whether a given k automatic sequence is overlap free or squarefree or cubefree etc we prove that the lexicographically least sequence in the orbit closure of a k automatic sequence is k automatic and use this last result to show that several related quantities such as the critical exponent irrationality measure and recurrence quotient for sturmian words with slope a have automatic continued fraction expansions if a does

multistable composite plates with piecewise variation of lay up in the planform abstract the non linear out of plane displacements of partially unsymmetric laminates are modelled using both finite element analysis and an analytical method attention is focused on the effects that thermal stresses have on the potential multiple shapes of a composite structure the paper extends previous analytical models which could only take into account free free boundary conditions the shape functions that model the out of plane displacements are modified to include variations of the curvatures within the domain the new analytical formulation is compared with literature and finite element analysis for a square plate and then it is tested for laminates with piecewise variation of lay up in the planform the results are validated against finite element analysis and experimental tests and a good correlation is obtained finally a parametric study is made on the effect of changing the fibres orientation and the laminate thickness the results confirm that it is possible to introduce bi stable composites within structures to obtain systems that are both flexible and stiff depending on the loading environment

multivariate test power approximations for balanced linear mixed models in studies with missing data multilevel and longitudinal studies are frequently subject to missing data for example biomarker studies for oral cancer may involve multiple assays for each participant assays may fail resulting in missing data values that can be assumed to be missing completely at random catellier and muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies they suggested modifying the degrees of freedom for both the hotelling lawley trace f statistic and its null case reference distribution we propose parallel adjustments to approximate power for this multivariate test in studies with missing data the power approximations use a modified non central f statistic which is a function of i the expected number of complete cases ii the expected number of non missing pairs of responses or iii the trimmed sample size which is the planned sample size reduced by the anticipated proportion of missing data the accuracy of the method is assessed by comparing the theoretical results to the monte carlo simulated power for the catellier and muller multivariate test over all experimental conditions the closest approximation to the empirical power of the catellier and muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases the utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study we describe how to implement the method using standard commercially available software products and give example code copyright 2015 john wiley sons ltd

a new method for choosing sample size for confidence interval based inferences scientists often need to test hypotheses and construct corresponding confidence intervals in designing a study to test a particular null hypothesis traditional methods lead to a sample size large enough to provide sufficient statistical power in contrast traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval with either approach a sample size so large as to waste resources or introduce ethical concerns is undesirable this work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals we focus on situations which involve a fixed unknown scalar parameter representing the true state of nature the width of the confidence interval is defined as the difference between the random upper and lower bounds an event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori an event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds an event rejection is said to occur if the confidence interval excludes the null value of the parameter in our opinion scientists often implicitly seek to have all three occur width validity and rejection new results illustrate that neglecting rejection or width and less so validity often provides a sample size with a low probability of the simultaneous occurrence of all three events we recommend considering all three events simultaneously when choosing a criterion for determining a sample size we provide new theoretical results for any scalar mean parameter in a general linear model with gaussian errors and fixed predictors convenient computational forms are included as well as numerical examples to illustrate our methods

adjusting power for a baseline covariate in linear models the analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research with gaussian errors adding random covariates does not change either the theory or the computations of general linear model data analysis however adding random covariates does change the theory and computation of power analysis many data analysts fail to fully account for this complication in planning a study we present our results in five parts i a review of published results helps document the importance of the problem and the limitations of available methods ii a taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem iii we describe how random covariates introduce the need to consider quantiles and conditional values of power iv we provide new exact and approximate methods for power analysis of a range of multivariate models with a gaussian baseline covariate for both small and large samples the new results apply to the hotelling lawley test and the four tests in the univariate approach to repeated measures unadjusted huynh feldt geisser greenhouse box the techniques allow rapid calculation and an interactive graphical approach to sample size choice v calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods we particularly recommend using quantile power with a new satterthwaite style approximation

an incremental variational formulation of dissipative magnetostriction at the macroscopic continuum level this paper outlines a new variational based modeling and computational implementation of macroscopic continuum magneto mechanics involving non linear inelastic material behavior with a special focus on dissipative magnetostriction it is based on a constitutive variational principle that optimizes a generalized incremental work function with respect to the internal state variables in an incremental setting at finite time steps this variational problem defines a quasi hyper magnetoelastic potential for the stresses and the magnetic induction and incorporates energy storage as well as dissipative mechanisms the existence of this potential further allows the incremental boundary value problem of quasi static inelastic magneto mechanics to be recast into a principle of stationary incremental energy the second focus of this paper is on the careful construction of the energy storage and dissipation functions for the model problem of hysteretic magnetostriction at the macroscopic level it is then demonstrated that the proposed model is capable of predicting the ferromagnetic and field induced strain hysteresis curves characteristic of magnetostrictive material response in good agreement with experiments the numerical solution of the coupled non linear boundary value problem is based on a monolithic multi field finite element implementation as a consequence of the proposed incremental variational principle the discretization of the multi field problem appears in a compact symmetric format in this sense the proposed formulation provides a canonical framework for the simulation of boundary value problems in dissipative magnetostriction at the macro level the performance of the proposed algorithm is tested by application to relevant numerical examples

tristability of thin orthotropic shells with uniform initial curvature composite shells show a rich multistable behaviour of interest for the design of shape changing morphing structures previous studies have investigated how the initial shape determines the shell

a characterization of power free morphisms abstract a word is called kth power free if it does not contain any non empty factor uk a morphism is kth power free if it preserves kth power free words a morphism is power free if it is kth power free for every k 1 we show that it is decidable whether a morphism is power free more precisely we prove that a morphism h is power free iff h is a square free morphism and for each letter a the image h a2 is cube free

a rayleigh ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions abstract to overcome the lack of a more general method for free vibration analysis of trapezoidal plates a computationally efficient and highly accurate rayleigh ritz approach with the newly developed orthogonal plate functions is proposed to solve these problems with any combination of clamped simply supported and free edge support conditions the deflection of the plate is approximated by a set of two dimensional orthogonal plate functions generated using the gram schmidt procedure which expresses the entire plate domain into two implicitly related variables in the present paper the effects of the fibre orientation on the vibrational behaviour of the plates are considered the numerical results for isotropic and anisotropic trapezoidal plates are presented where possible the numerical results are verified with other existing values in the literature

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

bistable plates for morphing structures a refined analytical approach with high order polynomials abstract the multistability of composite thin structures has shown potential for morphing applications the present work combines a ritz model with path following algorithms to study bistable plates behaviour classic low order ritz models predict stable shapes geometry with reasonable accuracy however they may fail when modelling other aspects of the elastic structural behaviour a refined higher order model is here presented in order to improve the inherently poor conditioning properties of ritz approximations of slender structures a non dimensional version of classical plate lamination theory with von karman nonlinear strains is developed and presented in the current approach we continue numerical solutions in parameter space that is we path follow equilibrium configurations as the control parameter varies find stable and unstable configurations and identify bifurcations the numerics are carried out using a set of in house matlab routines for numerical continuation the increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour finally the complex experimentally observed snap through geometry is captured analytically for the first time results are validated against finite elements analysis throughout the course of the paper

a unified approach to power calculation and sample size determination for random regression models the underlying statistical models for multiple regression analysis are typically attributed to two types of modeling fixed and random the procedures for calculating power and sample size under the fixed regression models are well known however the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution this paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables numerical examples are provided to illustrate the usefulness of the proposed method and monte carlo simulation studies are also conducted to assess the accuracy the results show that the proposed method performs well for various model specifications and explanatory variable distributions

non axisymmetric bending of thin annular plates due to circumferentially distributed moments abstract the non linear deformation of a thin annular plate subjected to circumferentially distributed bending moments is studied a von karman plate model is adopted to formulate the equations of motion free free boundary conditions have been applied at both inner and outer edges the matrix formulation of the differential quadrature method is used to discretise and solve the governing equations linear analysis predicts that the annular disk deforms axisymmetrically into a spherical dome however the proposed non linear analysis shows that a symmetry breaking bifurcation may occur after which the linear solution becomes unstable and the plate transitions into a non axisymmetric cylindrical deformation this is the case when at least one of two parameters reaches a critical value these parameters are the non dimensionalised ratio between applied moment and bending stiffness and the ratio between inner and outer radius furthermore it is noted that free free boundary conditions and circumferentially distributed bending moments do not break the circular symmetry of the annular disk hence the principal axes of curvature in the deformed configuration do not have a preferred orientation therefore the present work describes a shell possessing infinite identical equilibria having different yet no favoured direction and hence links to previous researches on neutrally stable structures

analytical investigation of structurally stable configurations in shape memory alloy actuated plates strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface like engineering structures shape memory alloys smas are active materials that provide a significant amount of strain under large stresses a characteristic of great utility in such morphing structures in this work an analytical approach to approximate the deformation of plates with sma constituents is developed via the rayleigh ritz method an additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field the total potential energy is then calculated using the displacement field loading conditions and constitutive relations for the plate layer s composed of sma wire meshes dense sma films and or elastic material the unknown coefficients are then found via minimization of the total potential energy this approach provides closed form expressions for the approximate deformation of the plates including multistable configurations the response of circular sma based plates is studied herein the results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate gaussian curvature is determined by the direction of the temperature gradient an alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape the obtained closed form expressions show good agreement with detailed non linear finite element analysis simulations the proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of sma based plates under given loading conditions knowledge of such stable configurations is very valuable in the design of sma based morphing structures c 2015 elsevier ltd all rights reserved

discrete approximations of the foppl von karman shell model from coarse to more refined models abstract the problem of deducing from the foppl von karman energy functional a sequence of reduced discrete models having few degrees of freedom is analyzed similar discrete models have been recently intensively studied to analyze the multistable behavior of shallow shells the bifurcations of composite laminates under temperature loads or the wrinkling in soft tissues in particular three relevant examples are discussed and compared among them where the curvature is assumed uniform linearly and quadratically varying through the shell while the uniform curvature assumption dates back to mansfield 1962 linear variations of the shell curvatures can describe smooth transitions between everted configurations while quadratic variations can account for the usually disregarded bending boundary conditions for their deduction we revisit the maxwell mohr method accordingly a sequence of auxiliary elliptic problems of plane elasticity is solved to determine the statically unknown membranal stresses this is a key ingredient for the presented models to compare extremely well with finite element approximations or with literature models with far more degrees of freedom

some results on k power free morphisms one way to generate infinite k power free words is to iterate a k power free morphism that is a morphism that preserves finite k power free words we first prove that the monoid of k power free endomorphisms on an alphabet containing at least three letters is not finitely generated test sets for k power free morphisms that is the sets t such that a morphism f is k power free if and only if f t is k power free give characterizations of these morphisms in the case of binary morphisms and k 3 we prove that a set t of cube free words is a test set for cube freeness if and only if it contains 12 particular factors consequently a morphism f on a b is cube free if and only if f aabbababbabbaabaababaabb is cube free length 24 is optimal another consequence is an unpublished result of leconte a binary morphism is cube free if and only if the images of all cube free words of length 7 are cube free when k3 we show that no finite test set exists for morphisms defined on an alphabet containing at least three letters in the last part we show that to generate an infinite cube free word by iterating a morphism we do not necessarily need a cube free morphism we give a new characterization of some morphisms that generate infinite cube free words

a powerful abelian square free substitution over 4 letters in 1961 paul erdos posed the question whether abelian squares can be avoided in arbitrarily long words over a finite alphabet an abelian square is a non empty word uv where u and v are permutations anagrams of each other the case of the four letter alphabet s 4 a b c d turned out to be the most challenging and remained open until 1992 when the author presented an abelian square free a 2 free endomorphism g 8 5 of s 4 the size of this g 8 5 i e g 8 5 abcd is equal to 4x85 uniform modulus until recently all known methods for constructing arbitrarily long a 2 free words on s 4 have been based on the structure of g 8 5 and on the endomorphism g 9 8 of s 4 found in 2002 in this paper a great many new a 2 free endomorphisms of s 4 are reported the sizes of these endomorphisms range from 4x102 to 4x115 importantly twelve of the new a 2 free endomorphisms of modulus m 109 can be used to construct an a 2 free commutatively functional substitution s 1 0 9 of s 4 with 12 image words for each letter the properties of s 1 0 9 lead to a considerable improvement for the lower bound of the exponential growth of c n i e of the number of a 2 free words over 4 letters of length n it is obtained that c n b 5 email protected n with b 12 1 m 1 02306 originally in 1998 carpi established the exponential growth of c n by showing that c n b email protected n with b 2 1 9 t 2 1 9 8 5 3 8 5 1 000021 where t 85 3 85 is the modulus of the substitution that he constructs starting from g 8 5

effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells multistable shells are thin walled structures that have more than one stable state of self stress we consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a foppl von karman analytical model by employing a rayleigh ritz approach we identify stable shapes from local minima in the strain energy formulation and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion an effect not directly answered in the literature systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs for typical cap like shells it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases i e when boundary movements in plane are resisted but when their rotations are not however for certain other shapes and large in plane stiffness values bistability can be enhanced by resisting but not entirely preventing edge rotations our predictions are furnished as detailed regime maps of the critical geometry which are accurately correlated against finite element analysis furthermore the suitabilities of single degree of freedom models for which solutions are achieved in closed form are evaluated and compared to our more accurate predictions

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

a two scale finite element relaxation analysis of shear bands in non convex inelastic solids small strain theory for standard dissipative materials abstract we propose a fundamentally new approach to the treatment of shear band localizations in strain softening elastic plastic solids at small strains based on energy minimization principles associated with micro structure developments the point of departure is a general internal variable formulation that determines the inelastic response as a standard dissipative medium consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasihyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables the existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments in finite elasticity furthermore localization phenomena are interpreted as micro structure developments on multiple scales associated with non convex incremental stress potentials in analogy to elastic phase decomposition problems these micro structures can be resolved by the relaxation of non convex energy functionals based on a convexification of the stress potential the relaxed problem provides a well posed formulation for a mesh objective analysis of localizations as close as possible to the non convex original problem we develop based on an approximated rank one convexification of the incremental stress potential a computational two scale procedure for a mesh objective treatment of localization problems it constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the micro shearing of a rank one laminate aligned to the shear band this problem is sufficiently robust with regard to applications to large scale inhomogeneous deformation processes of elastic plastic solids the performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which illustrate the mesh independence of the results

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

approximate power for repeated measures anova lacking sphericity abstract violation of sphericity of covariance across repeated measures inflates type i error rates in univariate repeated measures analysis of variance hence the use of geisser greenhouse or huynh feldt is now common to provide improved type i error rate with nonsphericity no method has been available to compute power a convenient method is suggested for approximating power and test size under nonsphericity new approximations are suggested for a a weighted sum of independent noncentral 2 s b the trace of a noncentral wishart or pseudo wishart matrix c the expected values of and and d the noncentral test statistic whether corrected or uncorrected the new approximations are extensions of the work of box 1954a b and satterthwaite 1941 the method performed well when evaluated against published and new simulations

statistical tests with accurate size and power for balanced linear mixed models the convenience of linear mixed models for gaussian data has led to their widespread use unfortunately standard mixed model tests often have greatly inflated test size in small samples many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model alternately stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures unirep multirep even in small samples an appropriate unirep or multirep test always controls test size and has a good power approximation in sharp contrast to mixed model tests hence mixed model tests should never be used when one of the unirep tests uncorrected huynh feldt geisser greenhouse box conservative or multirep tests wilks hotelling lawley roy s pillai bartlett apply convenient methods give exact power for the uncorrected and box conservative tests simulations demonstrate that new power approximations for all four unirep tests eliminate most inaccuracy in existing methods in turn free software implements the approximations to give a better choice of sample size two repeated measures power analyses illustrate the methods the examples highlight the advantages of examining the entire response surface of power as a function of sample size mean differences and variability

power analyses for correlations from clustered study designs power analysis constitutes an important component of modern clinical trials and research studies although a variety of methods and software packages are available almost all of them are focused on regression models with little attention paid to correlation analysis however the latter is arguably a simpler and more appropriate approach for modelling concurrent events especially in psychosocial research in this paper we discuss power and sample size estimation for correlation analysis arising from clustered study designs our approach is based on the asymptotic distribution of correlated pearson type estimates although this asymptotic distribution is easy to use in data analysis the presence of a large number of parameters creates a major problem for power analysis due to the lack of real data to estimate them by introducing a surrogacy type assumption we show that all nuisance parameters can be eliminated making it possible to perform power analysis based only on the parameters of interest simulation results suggest that power and sample size estimates obtained under the proposed approach are robust to this assumption copyright 2005 john wiley sons ltd

power and sample size calculations for multivariate linear models with random explanatory variables this article considers the problem of power and sample size calculations for normal outcomes within the framework of multivariate linear models the emphasis is placed on the practical situation that not only the values of response variables for each subject are just available after the observations are made but also the levels of explanatory variables cannot be predetermined before data collection using analytic justification it is shown that the proposed methods extend the existing approaches to accommodate the extra variability and arbitrary configurations of the explanatory variables the major modification involves the noncentrality parameters associated with the f approximations to the transformations of wilks likelihood ratio pillai trace and hotelling lawley trace statistics a treatment of multivariate analysis of covariance models is employed to demonstrate the distinct features of the proposed extension monte carlo simulation studies are conducted to assess the accuracy using a child s intellectual development model the results update and expand upon current work in the literature

a practical approach to computing power for generalized linear models with nominal count or ordinal responses data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models many current proposals for dealing with binary ordinal or count outcomes are conceptually or computationally demanding limited in terms of accommodating covariates and or have not been extensively assessed for accuracy assuming moderate sample sizes here we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non continuous outcome the model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters the variance covariance matrix resulting from this fit is then used in conjunction with an established non central chi square approximation to the distribution of the wald statistic alternatively the model can be re fit under the null hypothesis to approximate power based on the likelihood ratio statistic we provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates relative to prior proposals the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing we illustrate the method for a variety of outcome types and covariate patterns using simulations to demonstrate its accuracy for realistic sample sizes

power calculation for overall hypothesis testing with high dimensional commensurate outcomes the complexity of system biology means that any metabolic genetic or proteomic pathway typically includes so many components e g molecules that statistical methods specialized for overall testing of high dimensional and commensurate outcomes are required while many overall tests have been proposed very few have power and sample size methods we develop accurate power and sample size methods and software to facilitate study planning for high dimensional pathway analysis with an account of any complex correlation structure between high dimensional outcomes the new methods allow power calculation even when the sample size is less than the number of variables we derive the exact finite sample and approximate non null distributions of the univariate approach to repeated measures test statistic as well as power equivalent scenarios useful to generalize our numerical evaluations extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large we derive a minimum set of constants and parameters sufficient and practical for power calculation using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin b6 deficiency helps illustrate the practical value of the new results free software implementing the power and sample size methods applies to a wide range of designs including one group pre intervention and post intervention comparisons multiple parallel group comparisons with one way or factorial designs and the adjustment and evaluation of covariate effects