the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

d optimum designs for heteroscedastic linear models abstract the methods of optimum experimental design are applied to models in which the variance as well as the mean is a parametric function of explanatory variables extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions or the parameters of only one function are of interest the theory also applies whether the mean and variance are functions of the same variables or of different variables although the mathematical foundations differ the example studied is a second order two factor response surface for the mean with a parametric nonlinear variance function the theory is used both for constructing designs and for checking optimality a major potential for application is to experimental design in off line quality control

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

an efficient staggered time marching procedure for porodynamics the present work proposes a novel time marching procedure which is designed for the dynamic simulation of the coupled two phase biot equations considering the displacement pressure u p formulation the new approach provides unconditional stability and excellent efficiency due to the staggered character of the temporal discretization where equilibrium is established at time t for the u group of governing equations and at time t t for the p group of governing equations the resulting systems of equations have an improved format and can be factorized solved at significantly less computational effort when compared to standard approaches such as the generalized newmark scheme in addition the resulting new systems of equations are characterized by considerably lower condition numbers reducing correlated numerical issues unconditional stability is achieved by a consistent manipulation of the mass and compressibility matrix of the model which causes virtually no computational overhead as a byproduct of the altered compressibility matrix the method is capable of simulating incompressible and impermeable phenomena without the need for any further feats the newly developed time marching technique is implemented and tested considering different benchmark problems for comparison the commonly used newmark scheme is also applied and both direct lu decomposition and iterative gmres linear solvers are employed in order to assess the efficiency of the new technique

brauer t tuples two non isomorphic finite groups form a brauer pair if there exist a bijection for the conjugacy classes and a bijection for the irreducible characters that preserve all the character values and the power map generalizing the definition of a brauer pair we introduce the notion of a brauer t tuple we show that brauer t tuples exist for any t 2

character tables of p groups with derived subgroup of prime order iii abstract two character tables of finite groups are isomorphic if there exist a bijection for the irreducible characters and a bijection for the conjugacy classes that preserve all the character values we give necessary and sufficient conditions for two finite groups to have isomorphic character tables in the case of finite p groups with derived subgroup of order p we show that the character tables can be classified by equivalence classes of certain homomorphisms of abelian p groups

iterative dynamic analysis of linear and nonlinear fully saturated porous media considering edge based smoothed meshfree techniques abstract in this work smoothed meshfree methods are firstly applied to numerically analyze nonlinear pore dynamic models a weakened weak formulation based on the edges of triangular cells obtained by a delaunay triangulation is considered here framing the so called edge based smoothed domains the meshfree shape functions are computed by the radial point interpolation method considering the t6 scheme for the shape function support domains enhanced procedures to compute the mass compressibility and coupling matrices of the pore dynamic model are discussed which are consistent with the computation of the stiffness and permeability matrices as well as internal force vectors in case of nonlinear analyses of the edge based smoothed domain formulation and that consider finer local integration techniques at lower computational costs rendering more accurate and efficient procedures two numerical formulations are considered here to analyze the time domain nonlinear coupled system of equations that arises once the spatial discretization is accomplished the standard newmark newton raphson method and an alternative iterative coupling approach in this iterative approach each phase of the coupled problem is treated separately uncoupling the governing equations of the model thus smaller and better conditioned systems of equations are obtained rendering more attractive techniques a relaxation parameter is introduced in order to improve the efficiency of the iterative coupling procedure and an expression to compute optimal values for the relaxation parameter is discussed at the end of the paper numerical examples are presented illustrating the effectiveness and potentialities of the proposed methodologies

optimal designs for quantile regression models despite their importance optimal designs for quantile regression models have not been developed so far in this article we investigate the d optimal design problem for nonlinear quantile regression analysis we provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally d optimal designs the results are illustrated determining locally bayesian and standardized maximin d optimal designs for quantile regression analysis in the michaelis menten and emax model which are widely used in such important fields as toxicology pharmacokinetics and dose response modeling

robust discrimination designs we study the construction of experimental designs the purpose of which is to aid in the discrimination between two regression models each of which might be only approximately specified a rough description of our approach is that we impose neighbourhood structures on each regression response and determine the members of these neighbourhoods which are least favourable in the sense of minimizing the kullback leibler divergence designs are obtained which maximize this minimum divergence both static and sequential approaches are studied we then consider sequential designs whose purpose is initially to discriminate but which move their emphasis towards efficient estimation or prediction as one model becomes favoured over the other

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

locally d optimal designs based on a class of composed models resulted from blending emax and one compartment models a class of nonlinear models combining a pharmacokinetic compartmental model and a pharmacodynamic emax model is introduced the locally d optimal ld design for a 4 parameter composed model is found to be a saturated 4 point uniform ld design with the two boundary points of the design space in the ld design support for a 5 parameter composed model a su cient condition for the ld design to require the minimum number of sampling time points is derived robust ld designs are also investigated for both models it is found that an ld design with k parameters is equivalent to an ld design with k i1 parameters if the linear parameter in the two composed models is a nuisance parameter assorted examples of ld designs are presented research supported by national science foundation nsf grants dms 0103727 dms 0603761 and national institutes of health nih grant p50 at00155 jointly supported by national center for complementary and alternative medicine the o ce of dietary supplements the o ce of research on women s health and national institute of general medicine any opinions flndings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re ect the views of the nsf and the nih

on the number of support points of maximin and bayesian optimal designs we consider maximin and bayesian d optimal designs for nonlinear regression models the maximin criterion requires the specification of a region for the nonlinear parameters in the model while the bayesian optimality criterion assumes that a prior for these parameters is available on interval parameter spaces it was observed empirically by many authors that an increase of uncertainty in the prior information i e a larger range for the parameter space in the maximin criterion or a larger variance of the prior in the bayesian criterion yields a larger number of support points of the corresponding optimal designs in this paper we present analytic tools which are used to prove this phenomenon in concrete situations the proposed methodology can be used to explain many empirically observed results in the literature moreover it explains why maximin d optimal designs are usually supported at more points than bayesian d optimal designs

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

optimal designs for the emax log linear and exponential models we derive locally d and edp optimal designs for the exponential log linear and three parameter emax models for each model the locally d and ed p optimal designs are supported at the same set of points while the corresponding weights are different this indicates that for a given model d optimal designs are efficient for estimating the smallest dose that achieves 100p of the maximum effect in the observed dose range conversely ed p optimal designs also yield good d efficiencies we illustrate the results using several examples and demonstrate that locally d and ed p optimal designs for the emax log linear and exponential models are relatively robust with respect to misspecification of the model parameters

robustness of design in dose response studies summary we construct experimental designs for dose response studies the designs are robust against possibly misspecified link functions for this they minimize the maximum meansquared error of the estimated dose required to attain a response in 100p of the target population here p might be one particular value p d 0 5 corresponds to ed50 estimation or it might range over an interval of values of interest the maximum of the mean squared error is evaluated over a kolmogorov neighbourhood of the fitted link both the maximum and the minimum must be evaluated numerically the former is carried out by quadratic programming and the latter by simulated annealing

a characterization of optimal designs for observational studies summary an empirical investigation of the effects of a treatment is an observational study if it involves the comparison of treated and control groups that were not formed by randomization in such studies treated and control groups may differ systematically with respect to pretreatment measures or covariates and addressing these pre treatment differences is a central concern matching and subclassification are two standard methods of adjusting for observed pretreatment differences they may be used alone e g cochran 1968 or in conjunction with analytical or model based adjustments e g rubin 1973 1979 holford 1978 rosenbaum and rubin 1984 section 3 3 and rosenbaum 1987 1988a in particular rubin s simulation studies suggest that model based adjustments applied to matched or subclassified samples are more robust than model based adjustments applied to unmatched samples the purpose of this paper is to identify the structure of an optimal subclassification i e one in which the treated and control subjects in the same subclass are on average as similar as possible with respect to observed covariates it turns out that this structure is simple and intuitive while adjustments may control imbalances in observed covariates they cannot

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

designing experiments with respect to standardized optimality criteria we introduce a new class of standardized optimality criteria which depend on standardized covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces

model robust designs for quantile regression we give methods for the construction of designs for regression models when the purpose of the investigation is the estimation of the conditional quantile function and the estimation method is quantile regression the designs are robust against misspecified response functions and against unanticipated heteroscedasticity the methods are illustrated by example and in a case study in which they are applied to growth charts

groups of prime power order with derived subgroup of prime order abstract the paper classifies up to isomorphism those groups of prime power order whose derived subgroups have prime order

optimal designs for dose finding studies understanding and properly characterizing the dose response relationship is a fundamental step in the investigation of a new compound be it a herbicide or fertilizer a molecular entity an environmental toxin or an industrial chemical in this article we investigate the problem of deriving efficient designs for the estimation of target doses in the context of clinical dose finding we propose methods to determine the appropriate number and actual levels of the doses to be administered to patients as well as their relative sample size allocations more specifically we derive local optimal designs that minimize the asymptotic variance of the minimum effective dose estimate under a particular dose response model we investigate the small sample properties of these designs together with their sensitivity to a misspecification of the true parameter values and of the underlying dose response model through simulation finally we demonstrate that the designs derived for a fixed model are rather sensitive

robust and efficient designs for the michaelis menten model for the michaelis menten model we determine designs that maximize the minimum of the d efficiencies over a certain interval for the nonlinear parameter the best two point designs can be found explicitly and a characterization is given when these designs are optimal within the class of all designs in most cases of practical interest the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter the results are illustrated and applied in an example of a hormone receptor assay

a geometric approach to optimal design for one parameter non linear models summary a geometric framework for constructing optimal bayesian designs and maximin designs for non linear models with a single unknown parameter and a prior distribution on that parameter which is restricted in that it comprises exactly two points of support is presented the approach is illustrated by means of selected examples involving logistic regression and the simple exponential model and its applicability to the construction of optimal designs for models with uncontrolled variation and to model robust designs is also demonstrated in addition the method is shown to provide some valuable insights into the general properties of optimal bayesian designs for non linear models

a stabilized central difference scheme for dynamic analysis summary in this work a new unconditionally stable time marching procedure for dynamic analyses is presented the scheme is derived from the standard central difference approximation with stabilization being provided by a consistent perturbation of the original problem because the method only involves constitutive variables that are already available from computations at previous time steps iterative procedures are not required to establish equilibrium when nonlinear models are focused allowing more efficient analyses to be obtained the theoretical properties of the proposed scheme are discussed taking into account standard stability and accuracy analyses indicating the excellent performance of the new technique at the end of the contribution representative nonlinear numerical examples are studied further illustrating the effectiveness of the new technique numerical results obtained by the standard central difference procedure and the implicit constant average acceleration method are also presented along the text for comparison copyright 2015 john wiley sons ltd

computer aided blocking of factorial and response surface designs we consider the problem of blocking response surface and factorial designs when block sizes are prespecified often rendering standard approaches inapplicable a generalization of harville s 1974