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

analysis of covariance using the rank transformation the rank transformation refers to the replacement of data by their ranks with a subsequent analysis using the usual normal theory procedure but calculated on the ranks rather than on the data rank transformation procedures have previously been shown by the authors to have properties of robustness and power in both regression and analysis of variance it seems natural to consider the use of the rank transformation in analysis of covariance which is a combination of regression and analysis of variance in this paper the rank transformation approach to analysis of covariance is presented and examined comparisons are made with the rank transformation procedure given by quade 1967 journal of the american statistical association 62 1187 1200 and some standard data sets are used to compare the results of these two procedures a monte carlo simulation study examines the behavior of these methods under the null hypothesis and under alternative hypotheses with both normal and nonnormal distributions all results are compared with the usual analysis of covariance procedure on the basis of robustness and power

a finite element method for stability problems in finite elasticity in this paper a finite element method is developed to treat stability problems in finite elasticity for this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches these results can then be used to derive an efficient numerical scheme for the computation of singular points

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

a robust riks like path following method for strain actuated snap through phenomena in soft solids abstract in this paper a practical and robust riks like path following method is developed to automatically trace the nonlinear equilibrium path for initial finite strain induced snap through phenomena in soft solids the deformation gradient is decomposed into an elastic part and an initial strain part where the initial strain is characterized through a prescribed pattern tensor and an unknown strain factor describing the magnitude in the non linear finite element fe solution scheme an equivalent body force proportional to the increment of the strain factor is derived which varies in each iteration step due to its dependence on deformed configuration and stress both the displacement and the strain factor increments are introduced as unknowns in the linearized equation which permits to predict the critical equilibrium states before and after the snap through several examples with various configurations and strain histories are constructed including multilayer beams and film substrate systems which demonstrate the effectiveness and robustness of the algorithm to capture the strain induced snap through phenomena

estimation of error rates in discriminant analysis with selection of variables accurate estimation of misclassification rates in discriminant analysis with selection of variables by for example a stepwise algorithm is complicated by the large optimistic bias inherent in standard estimators such as those obtained by the resubstitution method application of a bootstrap adjustment can reduce the bias of the resubstitution method however the bootstrap technique requires the variable selection procedure to be repeated many times and is therefore difficult to compute in this paper we propose a smoothed estimator that requires relatively little computation and which on the basis of a monte carlo sampling study is found to perform generally at least as well as the bootstrap method

on the spatial formulation of anisotropic multiplicative elasto plasticity abstract this contribution aims at a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto plasticity embedded in the well established framework of non standard dissipative materials we adopt as a key ingredient the introduction of additional symmetric arguments typically structural tensors into the relevant scalar valued isotropic tensor functions on this basis the fundamental covariance relation leads us to a formulation which allows itself to be set up directly in terms of spatial arguments and thus guarantees a convenient implementation within a finite element setting

the effects of measurement error in response variables and tests of association of explanatory variables in change models biomedical studies often measure variables with error examples in the literature include investigation of the association between the change in some outcome variable blood pressure cholesterol level etc and a set of explanatory variables age smoking status etc typically one fits linear regression models to investigate such associations with the outcome variable measured with error a problem occurs when we include the baseline value of the outcome variable as a covariate in such instances one can find a relationship between the observed change in the outcome and the explanatory variables even when there is no association between these variables and the true change in the outcome variable we present a simple method of adjusting for a common measurement error bias that tends to be overlooked in the modelling of associations with change additional information for example replicates instrumental variables is needed to estimate the variance of the measurement error to perform this bias correction

smoothed additive estimators for non error rates in multiple discriminant analysis abstract a generalization of smoothed additive estimators for non error rates to the case of more than two groups is discussed several properties the smoothing should have are shown to be satisfied the problem of choosing a smoothing parameter is considered and a parameter choice depending on the sample is proposed in simulation experiments with normal uniform and discrete distributions the smoothed additive estimators with fixed and variable smoothing parameter are compared to the leaving one out method and the resubstitution method with respect to bias and variance

the limiting distribution of least squares in an errors in variables regression model abstract there is a substantial literature concerning linear regression when some of the predictors independent variables are measured with error such models are of importance in econometrics instrumental variables models psychometrics correction for attenuation models of change and in instrumental calibration studies in medicine and industry recent theoretical work concerning maximum likelihood estimation in such models appears in healy 1980 fuller 1980 and anderson 1984 while reilly and patino leal 1981 take a bayesian approach in an applied context an investigator may either overlook the measurement errors in the predictors or choose the classical ordinary least squares ols estimator of the parameters because of its familiarity and ease of use certainly the methodology of classical least squares theory confidence intervals multiple comparisons tests of hypotheses residual analysis is considerably more developed than the corresponding errors in variables methodology particularly in samples of moderate size in this paper it is shown that under reasonable regularity conditions such linear combinations are jointly asymptotically normally distributed

application of material forces to hyperelastostatic fracture mechanics i continuum mechanical setting the concern of this work is a consequent exploitation of the notion of material forces for the application within hyperelastostatic fracture mechanics contrary to physical forces material forces act on the material manifold thus essentially representing the tendency of defects like cracks or inclusions to move relative to the ambient material based on the formulation of the appropriate quasi static balance laws in the material space we aim at a fresh look onto classical aspects of hyperelastostatic fracture mechanics operating throughout within the geometrically nonlinear setting we emphasize on the one hand the duality of the direct and the inverse motion description and on the other hand we re establish the classical path integrals from elementary equilibrium considerations in the material space

proper metrics for clinical trials transformations and other procedures to remove non normality effects a simulation study was performed to study the effects of non normality and to examine procedures to ameliorate possible loss of power when data are incorrectly assumed to be normally distributed it was found that only distributions with high asymmetry or heavy tails seriously affect the t test the box cox likelihood ratio test appears to have some advantages over the others but this must be offset by the greater complexity in making the results understandable to non statisticians the variability in outcomes with the different procedures demonstrates the importance of specifying such procedures a priori

an evaluation of smoothed classification error rate estimators this article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution leave one out and bootstrap estimators smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing an algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector using the criterion of unconditional mean squared error this particular smoothed estimator called the ns method appears to offer a reasonable alternative to existing nonparametric estimators

on the determination of strength of belief for decision support under uncertainty part ii fusing strengths of belief the problem of decision making under uncertainty is described and the difficulty of comparing actions with uncertain outcomes is noted we discuss the role of valuation functions which convert an uncertain outcome into a single representative value and hence aid in the comparison of uncertain alternatives the need for information about the strength of belief that a given outcome will occur is pointed out we then look at various methods for obtaining this information we consider in particular detail the situation in which the strength of belief is dependent on the outcome payoff

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

decision making on the sole basis of statistical likelihood this paper presents a new axiomatic decision theory for choice under uncertainty unlike bayesian decision theory where uncertainty is represented by a probability function in our theory uncertainty is given in the form of a likelihood function extracted from statistical evidence the likelihood principle in statistics stipulates that likelihood functions encode all relevant information obtainable from experimental data in particular we do not assume any knowledge of prior probabilities consequently a bayesian conversion of likelihoods to posterior probabilities is not possible in our setting we make an assumption that defines the likelihood of a set of hypotheses as the maximum likelihood over the elements of the set we justify an axiomatic system similar to that used by von neumann and morgenstern for choice under risk our main result is a representation theorem using the new concept of binary utility we also discuss how ambiguity attitudes are handled applied to the statistical inference problem our theory suggests a novel solution the results in this paper could be useful for probabilistic model selection

a bayesian study of the error in variables model this article presents the results of a study of the functional case of the problem of parameter estimation when there is error in all the variables there is consequently no distinction between independent and dependent variables posterior probability density functions are developed for the parameters with both linear and nonlinear and possibly multiple relations among the true values of the variables there is no distinction between models that are linear or nonlinear in the parameters the results are equivalent to generalizations of the work of some previous authors but lead to new and efficient algorithms for finding point estimates and their precisions for most of the results the error covariance matrix is assumed known though a case is treated where it is known except for a scalar multiplier the results are also shown to be valid if the covariance matrix is singular geometric interpretations are described

on the continuity of the concave integral whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set if so the hahn banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it we refer to such representation as a dual representation dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity

continental scale relationship between bankfull width and drainage area for single thread alluvial channels we explore the bankfull width wbf versus drainage area ada relationship across a range of climatic and geologic environments and ask 1 is the relationship between ln wbf and ln ada best described by a linear function and 2 can a reliable relationship be developed for predicting wbf with ada as the only independent variable the principal data set for this study was compiled from regional curve studies and other reports that represent 1018 sites 1 m wbf 110 m and 0 50 km2 ada 22 000 km2 in the continental united states two additional data sets were used for validation after dividing the data into small medium and large size basins which respectfully correspond to ada 4 95 km2 4 95 km2 ada 337 km2 and ada 337 km2 regression lines from each data set were compared using one way analysis of covariance ancova a second ancova was performed to determine if mean annual precipitation p is an extraneous factor in the wbf versus ada relationship the ancova results reveal that using ada alone does not yield a reliable wbf versus ada relationship that is applicable across a wide range of environments and that p is a significant extraneous factor in the relationship considering data for very small basins ada 0 49 km2 and very large basins ada 1 0 105 km2 we conclude that a two segment linear model is the most probable form of the ln wbf versus ln ada relationship this study provides useful information for building complex multivariate models for predicting wbf

average effects based on regressions with a logarithmic link function a new approach with stochastic covariates researchers often use regressions with a logarithmic link function to evaluate the effects of a treatment on a count variable in order to judge the average effectiveness of the treatment on the original count scale they compute average treatment effects which are defined as the average difference between the expected outcomes under treatment and under control current practice is to evaluate the expected differences at every observation and use the sample mean of these differences as a point estimate of the average effect the standard error for this average effect estimate is based on the implicit assumption that covariate values are fixed i e do not vary across different samples in this paper we present a new way of analytically computing average effects based on regressions with log link using stochastic covariates and develop new formulas to obtain standard errors for the average effect in a simulation study we evaluate the statistical performance of our new estimator and compare it with the traditional approach our findings suggest that the new approach gives unbiased effect estimates and standard errors and outperforms the traditional approach when strong interaction and or a skewed covariate is present

mass and volume specific views on thermodynamics for open systems a general framework for the thermodynamics of open systems is presented the theory is fundamentally based on the generalized balance of mass which is enhanced by additional surface flux and volume source terms the presentation highlights the influence of the enhanced mass balance on the remaining balance equations to clarify the impact of the variable reference density we introduce the notions of volume specific and mass specific formats particular attention is drawn to the fact that the mass specific balance equations are free from explicit open system contributions they resemble the classical balance equations and can thus be evaluated in complete analogy to the closed system case restrictions for the constitutive equations follow from the second law of thermodynamics as illustrated for the particular model problem of thermo hyperelasticity

qualitative decision theory from savage s axioms to nonmonotonic reasoning this paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible in the scope of artificial intelligence contrary to classical approaches to decision theory we try to rank acts without resorting to any numerical representation of utility or uncertainty and without using any scale on which both uncertainty and preference could be mapped our approach is a variant of savage s where the setting is finite and the strict preference on acts is a partial order it is shown that although many axioms of savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts the approach is inconsistent with a probabilistic representation of uncertainty the latter leads to the kind of paradoxes encountered in the theory of voting it is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty originally due to lewis and usual in nonmonotonic reasoning our axiomatic investigation thus provides decision theoretic foundations to the preferential inference of lehmann and colleagues however the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions although their basic principles look sound this paper points out some limitations of purely ordinal approaches to savage like decision making under uncertainty in perfect analogy with similar difficulties in voting theory

on concavity and supermodularity abstract concavity and supermodularity are in general independent properties a class of functionals defined on a lattice cone of a riesz space has the choquet property when it is the case that its members are concave whenever they are supermodular we show that for some important riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the choquet property we extend in this way the results of choquet g choquet theory of capacities ann inst fourier grenoble 5 1953 1954 131 295 and konig h konig the sub super additivity assertion of choquet studia math 157 2003 171 197

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

on the integral representation of g expectations with terminal constraints abstract in this paper we study the integral representation of g expectations with two kinds of terminal constraints and obtain the corresponding necessary and sufficient conditions

variable selection in canonical discriminant analysis for family studies summary in family studies canonical discriminant analysis can be used to find linear combinations of phenotypes that exhibit high ratios of between family to within family variabilities but with large numbers of phenotypes canonical discriminant analysis may overfit to estimate the predicted ratios associated with the coefficients obtained from canonical discriminant analysis two methods are developed one is based on bias correction and the other based on cross validation because the cross validation is computationally intensive an approximation to the cross validation is also developed furthermore these methods can be applied to perform variable selection in canonical discriminant analysis the proposed methods are illustrated with simulation studies and applications to two real examples

strain measures integrability condition and frame indifference in the theory of oriented media this paper is concerned with the appropriate choice of state variables within the continuum model or oriented media it is shown that residual deformation strain and wryness can be considered as such quantities the compatibility conditions for them are derived which make the inverse problem of determining the displacement and director triad fields well posed the principle of frame indifference justifies the use of these quantities as state variables in the free energy density governing and constitutive equations are studied in detail a comparison with the continuum model of crystals with continuously distributed dislocations is provided

fdr control with pseudo gatekeeping based on a possibly data driven order of the hypotheses we propose a multiple testing procedure controlling the false discovery rate the procedure is based on a possibly data driven ordering of the hypotheses which are tested at the uncorrected level q until a suitable number is not rejected when the order is data driven larger effect sizes are considered first therefore selecting more interesting hypotheses with larger probability the proposed procedure is valid under independence for the test statistics we also propose a modification which makes our procedure valid under arbitrary dependence it is shown in simulation that we compare particularly well when the sample size is small we conclude with an application to identification of molecular signatures of intracranial ependymoma the methods are implemented in an r package somemtp freely available on cran

hyperelastic internal balance by multiplicative decomposition of the deformation gradient the multiplicative decomposition of the deformation gradient bf f hat bf f bf f is often used in finite deformation continuum mechanics as a basis for treating mechanical effects including plasticity biological growth material swelling and notions of material morphogenesis evolution rules for the particular effect from this list are then posed for f the tensor hat bf f is then invoked to describe a subsequent elastic accommodation and a hyperelastic framework is put in place for its determination using an elastic energy density function say w hat bf f as a constitutive specification here we explore the theory that emerges if both f and hat bf f are governed by hyperelastic criteria thus we consider energy densities w hat bf f bf f the decomposition of f is itself determined by energy minimization and the variation associated with the multiplicative decomposition gives a tensor relation that is interpreted as an internal balance requirement our initial development purposefully proceeds with minimal presumptions on the kinematic interpretation of the factors in the deformation gradient decomposition connections are then made to treatments that ascribe particular kinematic properties to the decomposition factors the theory of structured deformations is especially significant in this regard such theories have broad utility in describing certain substructural reconfigurations in solids to demonstrate in the context of the present variational treatment we consider a boundary value problem that involves an imposed twist if the twist is small then the minimizer is classically smooth at larger values of twist the energy minimizer exhibits a non smooth deformation that localizes slip at a singular surface

finite element formulations for hyperelastic transversely isotropic biphasic soft tissues abstract this paper presents a finite element model for the three dimensional 3 d nonlinear analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions a biphasic continuum description is used to represent the soft tissue as a two phase mixture of incompressible inviscid fluid and a hyperelastic transversely isotropic solid alternate mixed penalty and velocity pressure finite element formulations are used to solve the nonlinear biphasic governing equations including the effects of a strain dependent permeability and a hyperelastic solid phase under finite deformation the resulting first order nonlinear system of equations are discretized in time using an implicit finite difference scheme and solved using the newton raphson method a significant contribution of this work is the implementation and testing of a biphasic description with a transversely isotropic hyperelastic solid phase this description considers a helmholtz free energy function of five invariants of the cauchy green deformation tensor and the preferred direction of the material allowing for asymmetric behavior in tension and compression an exponential form is suggested and a set of material parameters is identified to represent the response of soft tissues in ranges of deformation and stress observed experimentally after demonstrating the behavior of this constitutive model in simple tension and compression a sample problem of unconfined compression is used to further validate the finite element implementation

cross validation the jackknife and the bootstrap excess error estimation in forward logistic regression abstract given a prediction rule based on a set of patients what is the probability of incorrectly predicting the outcome of a new patient call this probability the true error an optimistic estimate is the apparent error or the proportion of incorrect predictions on the original set of patients and it is the goal of this article to study estimates of the excess error or the difference between the true and apparent errors i consider three estimates of the excess error cross validation the jackknife and the bootstrap using simulations and real data the three estimates for a specific prediction rule are compared when the prediction rule is allowed to be complicated overfitting becomes a real danger and excess error estimation becomes important the prediction rule chosen here is moderately complicated involving a variable selection procedure based on forward logistic regression

a review of some statistical methods for covariance analysis of categorical data three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis the three methods considered are randomization model nonparametric procedures maximum likelihood logistic regression and weighted least squares analysis of correlated marginal functions a fourth heuristic approach the unweighted linear model analysis is an approximate procedure but it is easy to implement the assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales attention is given to computational differences but it is shown that the methods lead to similar results for analogous problems it is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

on configurational forces in multiplicative elastoplasticity abstract the main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity this nowadays well established approach which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement is adopted as a paradigm for the general modelling of finite inelasticity the overall motion in space is throughout assumed to be compatible and sufficiently smooth according to the underlying configurations namely the material and the spatial configuration as well as what we call the intermediate configuration different representations of balance of linear momentum are set up for the static case the underlying flux terms are thereby identified as stress tensors of piola and cauchy type and are assumed to derive from a free energy density function thus taking hyperelastic formats moreover the incorporated source terms namely the configurational volume forces are identified by comparison arguments these quantities include gradients of distortions as well as dislocation density tensors in particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration as a result configurational volume forces which are settled in the intermediate configuration embody non vanishing dislocation density tensors while their material counterparts directly incorporate non vanishing gradients of distortions this fundamental property enables us to recover the celebrated peach koehler force for finite inelasticity acting on a single dislocation from the intermediate configuration volume forces

on the determination of the crystal reference in nonlinear continuum theory of dislocations the paper is concerned with the determination of the anholonomic crystal reference from the given elastic strain metric and dislocation density cartan torsion the incompatible inverse elastic deformation is shown to satisfy a system of linear first order differential equations the integrability condition requires that the curvature of the crystal connection should vanish the equivalent system of equations and integrability condition for the inverse elastic rotation are also obtained formulae for the inverse elastic deformation and the inverse elastic rotation in form of tensor series are derived the dual problem of determining the plastic deformation and the plastic rotation from the plastic strain and the dislocation density is solved in a similar manner a linearization procedure is carried out and a comparison with kroner s theory is provided

measurement error and ancova functional and structural relationship approaches this article discusses alternative procedures to the standardf test for ancova in case the covariate is measured with error both a functional and a structural relationship approach are described examples of both types of analysis are given for the simple two group design several cases are discussed and special attention is given to issues of model identifiability an approximate statistical test based on the functional relationship approach is described on the basis of monte carlo simulation results it is concluded that this testing procedure is to be preferred to the conventionalf test of the ancova null hypothesis it is shown how the standard null hypothesis may be tested in a structural relationship approach it is concluded that some knowledge of the reliability of the covariate is necessary in order to obtain meaningful results

nonconvex model of material growth mathematical theory the model of volumetric material growth is introduced in the framework of finite elasticity the new results obtained for the model are presented with complete proofs the state variables include the deformations temperature and the growth factor matrix function the existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown the mathematical results can be applied to a wide class of growth models in mechanics and biology

nonparametric analysis of covariance for comparing change in randomized studies with baseline values subject to error summary change from baseline to a follow up examination can be compared among two or more randomly assigned treatment groups by using analysis of variance on the change scores however a generally more sensitive powerful test can be performed using analysis of covariance anova on the follow up data with the baseline data as a covariate this approach is not without potential problems though the assumption of ordinary ancova of normally distributed errors is speculative for many variables employed in biomedical research furthermore the baseline values are inevitably random variables and often are measured with error this report investigates in this situation the validity and relative power of the ordinary ancova test and two asymptotically distribution free alternative tests one based on the rank transformation and the other based on the normal scores transformation the procedures are illustrated with data from a clinical trial normal and several nonnormal distributions as well as varying degree of variable error are studied by monte carlo methods the normal scores test is generally recommended for statistical practice consider the situation frequently occurring in clinical trials and other biomedical studies where two or more groups are selected at random from the same population and assessed for some variable of interest at the time of randomization assume that the statistical question is whether there is a significant difference among the groups in terms of the distribution of the variable at some time subsequent to randomization a statistical test of the hypothesis of no difference among groups at follow up could be based on the follow up data only since the groups differ only at random at baseline however it may not be efficient to ignore the baseline data feldt 1958 compared three approaches to data analysis stratifying the baseline data and using two way analysis of variance anova using analysis of covariance ancova on the follow up data with the baseline data a covariate and using anova on the change scores he found that ancova is generally the most efficient powerful of these approaches some problems occur in applying ancova in this situation however first the variable of interest at baseline will inevitably be random not fixed by the experimenter this is termed subject variability second the ascertainment of the variable may be subject to error this error can be measurement error or intrasubject error or both measurement error can be due to instrument imprecision or human inability to accurately read an instrument such as a sphygmomanometer or both intrasubject error can arise from diurnal or other short term variability of a physiologic variable such as blood pressure subsequently any of these types of variability will

on efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance in randomized clinical trials measurements are often collected on each subject at a baseline visit and several post randomization time points the longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points liang and zeger 2000 sankhy the indian journal of statistics series b 62 134 148 propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization if the baseline value is subject to missingness the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance the efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values and for the pre post design decreases with the absolute correlation between baseline and postbaseline values

a general framework for the numerical solution of problems in finite elasto plasticity this article discusses a general framework for the analysis of initial boundary value problems of rate independent finite elasto plasticity based on the theory of green and naghdi a constitutive model is developed within the context of the above theory employing generalized measures of lagrangian strain and work conjugate measures of stress computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential algebraic equations of plastic flow representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations

comparison of least squares and errors in variables regression with special reference to randomized analysis of covariance abstract in an errors in variables regression model the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter we explore the conjecture that when the least squares estimate is consistent for a linear combination of the regression parameter it will be preferred to an errors in variables estimate at least asymptotically the conjecture is false in general but it is true for some important classes of problems one such problem is a randomized two group analysis of covariance upon which we focus

theory and finite element formulation of rubberlike membrane shells using principal stretches a theory of rubberlike membrane shells undergoing large elastic deformations is derived the stresses are deduced from ogden s material law which is formulated in terms of the principal values of the right stretch tensor incompressibility is fulfilled exactly using the plane stress constraint furthermore a finite element formulation of the membrane theory is given the use of the tangential stiffness matrix derived analytically provides a quadratically convergent solution process several numerical examples show the robustness of the developed finite element

fuzzy linear regression using rank transform method in regression analysis the rank transform rt method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers in this paper we construct a so called level fuzzy regression model based on the resolution identity theorem and apply rt method to this model fuzzy regression models with crisp input fuzzy output and fuzzy input fuzzy output are investigated to show the effectiveness of the proposed method to compare its effectiveness with existing methods we introduce a new performance measure in addition we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

on policy capturing with fuzzy measures policy capturing methods generally apply linear regression analysis to model human judgment in this paper we examine the application of fuzzy set and fuzzy measure theories to obtain subjective descriptions of cue importance for policy capturing at the heart of the approach is a method of learning fuzzy measures the shapley values associated with the fuzzy measures provide a basis for comparison with the results of linear regression however the fuzzy measure theoretical approach provides additional insight into interaction effects corresponding to the nonlinear noncompensatory nature of the underlying decision model to illustrate the methodology we estimated the importance of factors and the interactions among them that influence decisions related to strategic investments in telecommunications infrastructure and compared the results from the fuzzy approach to those obtained from traditional statistical methods

some unexamined aspects of analysis of covariance in pretest posttest studies summary the use of an analysis of covariance ancova model in a pretest posttest setting deserves to be studied separately from its use in other non pretest posttest settings for pretest posttest studies the following points are made in this article a if the familiar change from baseline model accurately describes the data generating mechanism for a randomized study then it is impossible for unequal slopes to exist conversely if unequal slopes exist then it implies that the change from baseline model as a data generating mechanism is inappropriate an alternative data generating model should be identified and the validity of the ancova model should be demonstrated b under the usual assumptions of equal pretest and posttest within subject error variances the ratio of the standard error of a treatment contrast from a change from baseline analysis to that from ancova is less than 21 2 c for an observational study it is possible for unequal slopes to exist even if the change from baseline model describes the data generating mechanism d adjusting for the pretest variable in observational studies may actually introduce bias where none previously existed

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

symmetric upper probabilities as a first step toward developing statistical models based on upper and lower probabilities we study upper probabilities and upper expectations on the unit interval that are symmetric by which we mean invariant with respect to equimeasurability these upper probabilities are generalizations of uniform probability measures we give some characterizations of these upper probabilities specifically we show that symmetry of the upper expectation functional is equivalent to the underlying set of densities being closed under majorization we also show that a function is the upper distribution for a symmetric upper probability if and only if its lower graph is star shaped with respect to the origin and to the point 1 1 we derive inner and outer approximations to symmetric classes of probabilities based on the upper probability the class of symmetric upper expectations that are completely determined by their values on the indicator functions is characterized we provide a geometric characterization of a hierarchy of upper probabilities including fine s generalized upper probabilities and 2 alternating choquet capacities in particular we establish a 1 1 correspondence between symmetric 2 alternating capacities and nonincreasing density functions we prove that undominated generalized upper probabilities do not exist in the symmetric case examples from robust statistics are considered an example is given that shows that symmetry of upper probabilities does not imply symmetry of upper expectations a corollary is that symmetry of the choquet integral does not imply symmetry of the upper expectation functional

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

low dimensional adaptive texture feature vectors from class distance and class difference matrices in many popular texture analysis methods second or higher order statistics on the relation between pixel gray level values are stored in matrices a high dimensional vector of predefined nonadaptive features is then extracted from these matrices identifying a few consistently valuable features is important as it improves classification reliability and enhances our understanding of the phenomena that we are modeling whatever sophisticated selection algorithm we use there is a risk of selecting purely coincidental good feature sets especially if we have a large number of features to choose from and the available data set is limited in a unified approach to statistical texture feature extraction we have used class distance and class difference matrices to obtain low dimensional adaptive feature vectors for texture classification we have applied this approach to four relevant texture analysis methods the new adaptive features outperformed the classical features when applied to the most difficult set of 45 brodatz texture pairs class distance and difference matrices also clearly illustrated the difference in texture between cell nucleus images from two different prognostic classes of early ovarian cancer for each of the texture analysis methods one adaptive feature contained most of the discriminatory power of the method

a nonlinear finite element model for the stress analysis of soft solids with a growing mass abstract the paper presents a new finite element fe model for the stress analysis of soft solids with a growing mass based on the work of lubarda and hoger 2002 contrary to the traditional numerical methods emphasizing on the influence of growth on constitutive equations an equivalent body force is firstly detected which is resulted from the linearization of the nonlinear equation and acts as the driver for material growth in the numerical aspect in the algorithm only minor correction on the traditional tangent modulus is needed to take the growth effects into consideration and its objectivity could be guaranteed comparing with the traditional method to solve the resulted equation in time domain both explicit and implicit integration algorithms are developed where the growth tensor is updated as an internal variable of gauss point the explicit updating scheme shows higher efficiency while the implicit one seems to be more robust and accurate the algorithm validation and its good performance are demonstrated by several two dimensional examples including free growth constrained growth and stress dependent growth

tests of significance using regression models for ordered categorical data regression models of the type proposed by mccullagh 1980 journal of the royal statistical society series b 42 109 142 are a general and powerful method of analyzing ordered categorical responses assuming categorization of an unknown continuous response of a specified distribution type tests of significance with these models are generally based on likelihood ratio statistics that have asymptotic chi 2 distributions therefore investigators with small data sets may be concerned with the small sample behavior of these tests in a monte carlo sampling study significance tests based on the ordinal model are found to be powerful but a modified test procedure using an f distribution with a finite number of degrees of freedom for the denominator is suggested such that the empirical significance level agrees more closely with the nominal significance level in small sample situations we also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression we illustrate the model with two data sets one from a study investigating the relationship between phosphorus in soil and plant available phosphorus in corn grown in that soil and the other from a clinical trial comparing analgesic drugs

probabilistic sophistication and multiple priors we show that under fairly mild conditions a maximin expected utility preference relation is probabilistically sophisticated if and only if it is subjective expected utility this abstract was borrowed from another version of this item

choquet representability of submodular functions let omega be an arbitrary set equipped with an algebra mathcal a subseteq 2 omega and let f b mathcal a rightarrow mathbb r be a functional defined on the set b mathcal a of bounded measurable functions x omega rightarrow mathbb r we provide necessary and sufficient conditions for a submodular functional f to be representable as a choquet integral from standard properties of the choquet integral the functional f should be positively homogeneous and constant additive our first result shows that these two properties together with submodularity characterize a subadditive choquet integral when omega is finite in the general case f is a subadditive choquet integral if and only if it satisfies the three previous properties together with sup norm continuity this result provides another characterization of subadditive choquet integrals different from the seminal paper by schmeidler proc am math soc 97 2 255 261 1986 that relies on comonotonic additivity

material growth in thermoelastic continua theory algorithmics and simulation a theoretical formulation of stress induced volumetric material growth in thermoelastic continua is developed material growth is regulated by a three surface activation criterion and corresponding flow rules a simple model is proposed based on this formulation and its algorithmic implementation including a method for solving the underlying differential algebraic equations for growth is examined in the context of an implicit finite element method selected numerical simulations are presented that showcase the predictive capacity of the model for both soft and hard biomaterials

some characterizations of strongly subadditive discounting functions the aim of this paper is to characterize some parameters which measure the force of discount in a discounting function the instantaneous discount rate and the geometric mean of a discounting function and relate them with the strong subadditivity and the so called subadditivity of second order we distinguish two intertemporal choice frameworks depending on the consideration of time as an interval or both as an interval and a delay and we establish some necessary and sufficient conditions to identify strongly subadditive and subadditive of second order discounting functions

on the application of multi step integration methods to infinitesimal elastoplasticity this article proposes an implicit algorithm for time integration of the differential algebraic equations of small deformation elastoplasticity in strain space the algorithm employs a two step backwards differentiation formula and a standard operator split procedure second order accuracy and non linear stability are established under appropriate constitutive restrictions the algorithm is implemented for the model of j2 plasticity and numerical simulations are conducted that illustrate its applicability and accuracy

a continuum theory of surface growth a continuum theory of surface growth in deformable bodies is presented the theory employs a decomposition of the deformation and growth processes which leads to a well posed set of governing equations it is argued that an evolving reference configuration is required to track the material points in the body the balance laws are formulated with respect to a non inertial frame of reference which is used to track the motion of the body a one dimensional example problem is included to showcase the predictive capacity of the theory

decision making with monotone lower probabilities of infinite order fabrice properties of convex and monotone capacities of infinite order in polish spaces are studied and used to justify the representation of certain situations of imprecise risk imprecisely known probabilities by lower probabilities which are monotone of infinite order decision making with imprecise risk is then modeled and linear utility theory is shown to be generalizable to the case of imprecise risk

union intersection rank tests for ordered alternatives in anocova abstract for an analysis of covariance model pertaining to completely randomized as well as complete block designs based on the union intersection principle a general class of permutationally distribution free rank tests for the ordered alternative problem is considered the theory is supplemented by numerical studies

on the comparison of two approaches to compute material forces for inelastic materials application to single slip crystal plasticity abstract the main goal of this contribution is the application of the material force method to dissipative materials whereby special emphasis is placed on the application to crystal plasticity balance equations on the material manifold as e g the material motion balance of momentum generally necessitate the computation of the spatial gradient of additional internal degrees of freedom or rather internal variables we therefore focus in this work on the comparison of two different numerical approaches to compute these gradient fields within a finite element setting namely a node point based and an integration point based formulation several numerical examples underline that the latter framework which is the convenient numerically comparatively cheap and well established approach in computational inelasticity turns out to be sufficiently accurate for the problem at hand

should baseline be a covariate or dependent variable in analyses of change from baseline in clinical trials in randomized clinical trials a pre treatment measurement is often taken at baseline and post treatment effects are measured at several time points post baseline say t 1 t at the end of the trial it is of interest to assess the treatment effect based on the mean change from baseline at the last time point t we consider statistical methods for i a point estimate and 95 per cent confidence interval for the mean change from baseline at time t for each treatment group and ii a p value and 95 per cent confidence interval for the between group difference in the mean change from baseline the manner in which the baseline responses are used in the analysis influences both the accuracy and the efficiency of items i and ii in this paper we will consider the ancova approach with change from baseline as a dependent variable and compare that with a constrained longitudinal data analysis clda model proposed by liang and zeger sankhya indian j stat ser b 2000 62 134 148 in which the baseline is modeled as a dependent variable in conjunction with the constraint of a common baseline mean across the treatment groups some drawbacks of the ancova model and potential advantages of the clda approach are discussed and illustrated using numerical simulations copyright 2009 john wiley sons ltd

what determines the shape of the probability weighting function under uncertainty decision weights are an important component in recent theories of decision making under uncertainty to better explain these decision weights a two stage approach has been proposed first the probability of an event is judged and then this probability is transformed by the probability weighting function known from decision making under risk we extend the two stage approach by allowing the probability weighting function to depend on the type of uncertainty using this more general approach properties of decision weights can be attributed to properties of probability judgments and or to properties of probability weighting we present an empirical study that shows that it is indeed necessary to allow the probability weighting function to be source dependent the analysis includes an examination of properties of the probability weighting function under uncertainty that have not been considered yet

ambiguity in the small and in the large this paper considers local and global multiple prior representations of ambiguity for preferences that are i monotonic ii bernoullian that is admit an affine utility representation when restricted to constant acts and iii locally lipschitz continuous we do not require either certainty independence or uncertainty aversion we show that the set of priors identified by ghirardato maccheroni and marinacci s 2004 unambiguous preference relation can be characterized as a union of clarke differentials we then introduce a behavioral notion of locally better deviation at an act and show that it characterizes the clarke differential of the preference representation at that act these results suggest that the priors identified by these preference statements are directly related to local optimizing behavior

a kinematically and thermodynamically consistent volumetric growth model based on the stress free configuration a continuum volumetric growth theory is presently elaborated based on the stress free configuration the total deformation gradient is the composition of a growth mapping followed by an elastic mapping ensuring the compatibility of the body a measure of the growth rate fully lying in the stress free configuration is elaborated and the balance of momentum accounting for mass changes due to growth is written in the same configuration highlighting measures of kinematic incompatibilities an eshelby stress is identified as the driving force for growth in the sense that it appears as the true dissipative thermodynamic force conjugated to the growth rate examples of incompatible cylindrical growth with residual stress generation and tumor growth with mechanics coupled to diffusion of nutrients illustrate the proposed theory

methods for assessing difference between groups in change when initial measurement is subject to intra individual variation statistical analysis of difference between groups in change for some variable adjusting for initial value is complicated by the presence of intra individual variation in that variable we estimate here the asymptotic bias that results from calculating the adjusted between group difference by ordinary least squares ols from observed data we also present explicit formulae that use the ols estimates the difference between treatment groups in mean initial values and a measure of the intra individual variation to compute a corrected estimator and its variance alternatively we can use ols on transformed data to obtain unbiased estimates in which we replace initial observed values by conditional stein estimates of true values we illustrate the results with data from an observational study and a clinical trial

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

analysis of covariance in parallel group clinical trials with pretreatment baselines analysis of covariance ancova techniques are often employed in the analysis of clinical trials to try to account for the effects of varying pretreatment baseline values of an outcome variable on posttreatment measurements of the same variable baseline measurements of outcome variables are typically random variables which violates the usual ancova assumption that covariate values are fixed therefore the usual ancova hypothesis tests of treatment effects may be invalid and the ancova slope parameter estimator biased for this application we show however that if the pretreatment posttreatment measurements have a bivariate normal distribution then i the ancova model with residual error independent of the covariate is a valid expression of the relationship between pretreatment and posttreatment measurements ii the usual fixed covariate analysis ancova estimates of the slope parameter and treatment effect contrasts are unbiased and iii the usual ancova treatment effect contrast t tests are valid significance tests for treatment effects moreover as long as the magnitudes of the treatment effects do not depend on the true pretreatment value of the outcome variable the true slope parameter must lie in the interval 0 1 and the ancova model has a clear interpretation as an adjustment based on between and within subject variability to an analysis of variance model applied to the posttreatment pretreatment differences

on the mechanics of solids with a growing mass a general constitutive theory of the stress modulated growth of biomaterials is presented with a particular accent given to pseudo elastic soft living tissues the governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics the multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic transversely isotropic and orthotropic biomaterials an explicit representation of the growth part of the deformation gradient is given in each case which leads to an effective incremental formulation in the analysis of the stress modulated growth process the rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function physically appealing structures of the stress dependent evolution equations for the growth induced stretch ratios are proposed