spherical codes generated by binary partitions of symmetric pointsets several constructions are presented by which spherical codes are generated from groups of binary codes in the main family of constructions the codes are generated from equally spaced symmetric pointsets on the real line the main ideas are code concatenation and set partitioning extensive tables are presented for spherical codes in dimension n spl les 24

a characterization of hybridized mixed methods for second order elliptic problems in this paper we give a new characterization of the approximate solution given by hybridized mixed methods for second order self adjoint elliptic problems we apply this characterization to obtain an explicit formula for the entries of the matrix equation for the lagrange multiplier unknowns resulting from hybridization we also obtain necessary and sufficient conditions under which the multipliers of the raviart thomas and the brezzi douglas marini methods of similar order are identical

using a dpg method to validate dma experimental calibration of viscoelastic materials abstract a discontinuous petrov galerkin dpg method is used to solve the time harmonic equations of linear viscoelasticity it is based on a broken primal variational formulation which is very similar to the classical primal variational formulation used in galerkin methods but has additional interface variables at the boundaries of the mesh elements both the classical and broken formulations are proved to be well posed in the infinite dimensional setting and the resulting discretization is proved to be stable a full h p convergence analysis is also included and the analysis is verified using computational simulations the method is particularly useful as it carries its own natural arbitrary p a posteriori error estimator which is fundamental for solving problems with localized solution features this proves to be useful when validating calibration models of dynamic mechanical analysis dma experiments indeed different dma experiments of epoxy and silicone resins were successfully validated to within 5 of the quantity of interest using the numerical method

a construction for constant composition codes by employing the residue polynomials we give a construction of constant composition codes this construction generalizes the one proposed by xing 2002 it turns out that when d 3 this construction gives a lower bound of constant composition codes improving the one by luo 2003 for some case moreover for d 3 we give a lower bound on maximal size of constant composition codes in particular our bound for d 5 gives the best possible size of constant composition codes up to magnitude

on the constructions of constant weight codes two methods of constructing binary constant weight codes from 1 codes over gf q and 2 constant weight codes over gf q are presented several classes of binary optimum constant weight codes are derived from these methods in general we show that binary optimum constant weight codes which achieve the johnson bound can be constructed from optimum codes over gf q which achieve the plotkin bound finally several classes of optimum constant weight codes over gf q are constructed

superconvergence in a dpg method for an ultra weak formulation abstract in this work we study a dpg method for an ultra weak variational formulation of a reaction diffusion problem we improve existing a priori convergence results by sharpening an approximation result for the numerical flux by duality arguments we show that higher convergence rates for the scalar field variable are obtained if the polynomial order of the corresponding approximation space is increased by one furthermore we introduce a simple elementwise postprocessing of the solution and prove superconvergence numerical experiments indicate that the obtained results are valid beyond the underlying model problem

linear size optimal q ary constant weight codes and constant composition codes an optimal constant composition or constant weight code of weight w has linear size if and only if its distance d is at least 2w 1 when d 2w the determination of the exact size of such a constant composition or constant weight code is trivial but the case of d 2w 1 has been solved previously only for binary and ternary constant composition and constant weight codes and for some sporadic instances this paper provides a construction for quasicyclic optimal constant composition and constant weight codes of weight w and distance 2w 1 based on a new generalization of difference triangle sets as a result the sizes of optimal constant composition codes and optimal constant weight codes of weight w and distance 2w 1 are determined for all such codes of sufficiently large lengths this solves an open problem of etzion the sizes of optimal constant composition codes of weight w and distance 2w 1 are also determined for all w 6 except in two cases

a first order system least squares method for the helmholtz equation we present a first order system least squares fosls method for the helmholtz equation at high wave number k which always leads to a hermitian positive definite algebraic system by utilizing a non trivial solution decomposition to the dual fosls problem which is quite different from that of the standard finite element methods we give an error analysis to the h p version of the fosls method where the dependence on the mesh size h the approximation order p and the wave number k is given explicitly in particular under some assumption of the boundary of the domain the l 2 norm error estimate of the scalar solution from the fosls method is shown to be quasi optimal under the condition that k h p is sufficiently small and the polynomial degree p is at least o log k numerical experiments are given to verify the theoretical results

an analysis of the practical dpg method we give a complete error analysis of the discontinuous petrov galerkin dpg method accounting for all the approximations made in its practical implementation specifi cally we consider the dpg method that uses a trial space consisting of polynomials of degree p on each mesh element earlier works showed that there is a trial to test operator t which when applied to the trial space defines a test space that guarantees stability in dpg formulations this operator t is local it can be applied element by element however an infinite dimensional problem on each mesh element needed to be solved to apply t in prac tical computations t is approximated using polynomials of some degree r p on each mesh element we show that this approximation maintains optimal convergence rates provided that r 2 p n where n is the space dimension two or more for the laplace equation we also prove a similar result for the dpg method for linear elasticity remarks on the conditioning of the stiffness matrix in dpg methods are also included

estimates on the size of symbol weight codes the study of codes for powerline communications has garnered much interest over the past decade various types of codes such as permutation codes frequency permutation arrays and constant composition codes have been proposed over the years in this paper we study a type of code called bounded symbol weight codes which was first introduced by versfeld in 2005 and a related family of codes that we term constant symbol weight codes we provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes we also give direct and recursive constructions of codes for certain parameters

construction of dpg fortin operators for second order problems abstract the use of ideal optimal test functions in a petrov galerkin scheme guarantees the discrete stability of the variational problem however in practice the computation of the ideal optimal test functions is computationally intractable in this paper we study the effect of using approximate practical test functions on the stability of the dpg discontinuous petrov galerkin method and the change in stability between the ideal and practical cases is analyzed by constructing a fortin operator we highlight the construction of an optimal dpg fortin operator for h 1 and h div spaces the continuity constant of the fortin operator is a measure of the loss of stability between the ideal and practical dpg methods we take a two pronged approach first we develop a numerical procedure to estimate an upper bound on the continuity constant of the fortin operator in terms of the inf sup constant h of an auxiliary problem second we construct a sequence of approximate fortin operators and exactly compute the continuity constants of the approximate operators which provide a lower bound on the exact fortin continuity constant our results shed light not only on the change in stability by using practical test functions but also indicate how stability varies with the approximation order p and the enrichment order p the latter has important ramifications when one wishes to pursue local h p adaptivity

three new families of zero difference balanced functions with applications zero difference balanced zdb functions integrate a number of subjects in combinatorics and algebra and have many applications in coding theory cryptography and communications engineering in this paper three new families of zdb functions are presented the first construction gives zdb functions defined on the abelian groups gf q1 gf qk with new and flexible parameters the other two constructions are based on 2 cyclotomic cosets and yield zdb functions on bbzn with new parameters the parameters of optimal constant composition codes optimal and perfect difference systems of sets obtained from these new families of zdb functions are also summarized

a discontinuous petrov galerkin method with lagrangian multipliers for second order elliptic problems we present a discontinuous petrov galerkin dpg method for the finite element discretization of second order elliptic boundary value problems the novel approach emanates from a one element weak formulation of the differential problem this procedure which is typical of discontinuous galerkin dg methods is based on introducing variables defined in the interior and on the boundary of the element the interface variables are suitable lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivative thus providing the proper connection between neighboring elements the internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size in the sole lagrangian multipliers a stability and convergence analysis of the novel formulation is carried out and its connection with mixed hybrid and dg methods is explored numerical tests on several benchmark problems are included to validate the convergence performance and the flux conservation properties of the dpg method

low order dpg fem for an elliptic pde this paper introduces a novel lowest order discontinuous petrovgalerkin dpg finite element method fem for the poisson model problem the ultra weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest order raviartthomas test functions this lowest order discretization for the poisson model problem allows for a direct proof of the discrete infsup condition and a complete apriori and aposteriori error analysis numerical experiments investigate the performance of the method and underline the quasi optimal convergence

zero difference balanced functions with new parameters and their applications as an optimal combinatorial object zero difference balanced zdb functions introduced by ding in 2008 are a generalization of the well known perfect nonlinear functions zdb functions have received much attention in recent years due to its important applications in coding theory and sequence design one objective of this paper is to present a construction of zdb functions based on a kind of generalized cyclotomy it generates zdb functions over cyclic group with new parameters which can not be produced by earlier constructions another objective of this paper is to employ these zdb functions to obtain at the same time 1 optimal constant composition codes 2 perfect difference systems of sets and 3 optimal frequency hopping sequences all with new parameters

bounds and constructions for ternary constant composition codes the problem of determining the maximum size of a ternary code is considered under the restriction that each symbol should appear a given number of times in each codeword upper and lower bounds on the size of such codes under the hamming metric are discussed where the lower bounds follow from constructions of good codes some of the results are obtained by explicitly finding codes by computer search a table of exact values and best known bounds on the maximum size for codes of length at most 10 is presented

quaternary constant composition codes with weight 4 and distances 5 or 6 the sizes of optimal constant composition codes cccs of weight 3 have been determined by chee ge and ling with four cases in doubt group divisible codes gdcs played an important role in their constructions in this paper we study the problem of constructing optimal quaternary cccs with hamming weight 4 and minimum distances 5 or 6 through gdcs and room square approaches the problem is solved leaving only five lengths undetermined previously the results on the sizes of such quaternary cccs were scarce

covariate imbalance and random allocation in clinical trials a model is developed to estimate the effect of covariate imbalance on the size of a test of treatment efficacy in randomized clinical trials comparing two treatments when dispersion parameters are known it is concluded that tests of homogeneity on the covariates should not be performed that covariate imbalance is just as much a problem for large studies as for small ones in terms of effect on size and that the effect of correlation between covariates and measures of efficacy is more complex than has previously been suggested the best way to adjust for covariate imbalance is by an analysis of covariance

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

a priori and computable a posteriori error estimates for an hdg method for the coercive maxwell equations abstract in this paper we present and analyze a hybridizable discontinuous galerkin hdg method for a mixed curl curl formulation of the steady state coercive maxwell equations with a discrete sobolev embedding type estimates for the discontinuous polynomials we provide a priori error estimates for the electric field and the lagrange multiplier in the energy norm with the smooth or minimal regularity assumption on the exact solution we have optimal convergence rate for the electric field and the lagrange multiplier in the energy norm the a priori error estimate for the electric field in the l 2 norm is also obtained by the duality argument and the approximation is also optimal for the electric field in the l 2 norm moreover by employing suitable helmholtz decompositions of the error together with the upper bound estimate for the lagrange multiplier we provide a computable residual based a posteriori error estimator which is derived based on the error measured in terms of a mesh dependent energy norm the efficiency of the a posteriori error estimator is also established three dimensional numerical results testing the performance of the a priori and a posteriori error estimates for the maxwell equations are given

the dpg method for the stokes problem we discuss well posedness and convergence theory for the dpg method applied to a general system of linear partial differential equations pdes and specialize the results to the classical stokes problem the stokes problem is an iconic troublemaker for standard bubnov galerkin methods if discretizations are not carefully designed they may exhibit non convergence or locking by contrast dpg does not require us to treat the stokes problem in any special manner we illustrate and confirm our theoretical convergence estimates with numerical experiments

construction of dpg fortin operators revisited abstract we construct a general family of dpg fortin operators for the exact energy spaces defined on a tetrahedral element

a robust dpg method for convection dominated diffusion problems ii adjoint boundary conditions and mesh dependent test norms we introduce a dpg method for convection dominated diffusion problems the choice of a test norm is shown to be crucial to achieving robust behavior with respect to the diffusion parameter demkowicz and heuer 2011 18 we propose a new inflow boundary condition which regularizes the adjoint problem allowing the use of a stronger test norm the robustness of the method is proven and numerical experiments demonstrate the method s robust behavior

a family of optimal constant composition codes constant composition codes are a special class of constant weight codes with very strong constraints it is hard to construct optimal constant composition codes there are only a few classes of such optimal codes in the literature in this correspondence a family of optimal ternary constant composition codes is constructed from a class of newly discovered perfect nonlinear functions this class of codes is related to a new family of skew hadamard difference sets which are the only examples of such difference sets discovered in the last seventy years

new lower bounds for constant weight codes some new lower bounds are given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance 4 and constant weight w in a number of cases the results significantly improve on the best bounds previously known

analysis and application of an equivalent berenger s pml model abstract the perfectly matched layer pml is a technique initially proposed by berenger for solving unbounded electromagnetic problems with the finite difference time domain method in this work we first formulate an equivalent pml model from the original berenger pml model in the corner region and then establish its stability we further develop a discontinuous galerkin method to solve this pml model and discrete stability similar to the continuous case is proved to demonstrate the absorbing property of this pml model we apply it to simulate wave propagation in metamaterials

construction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshes abstract given a sequence of finite element spaces which form a de rham sequence we will construct dual representations of these spaces with associated differential operators which connect these spaces such that they also form a de rham sequence the dual representations also need to satisfy the de rham sequence on the domain boundary the matrix which converts primal representations to dual representations the hodge matrix is the mass or gram matrix it will be shown that a bilinear form of a primal and a dual representation is equal to the vector inner product of the expansion coefficients degrees of freedom of both representations this leads to very sparse system matrices even for high order methods the differential operators for dual representations will be defined vector operations grad curl and div for primal and dual representations are both topological and do not depend on the metric i e the size and shape of the mesh or the order of the numerical method derivatives are evaluated by applying sparse incidence and inclusion matrices to the expansion coefficients of the representations as illustration of the use of dual representations the method will be applied to i a mixed formulation for the poisson problem in 3d ii it will be shown that this approach allows one to preserve the equivalence between dirichlet and neumann problems in the finite dimensional setting and iii the method will be applied to the approximation of grad div eigenvalue problem on affine and non affine meshes

an absolutely stable discontinuous galerkin method for the indefinite time harmonic maxwell equations with large wave number this paper develops and analyzes an interior penalty discontinuous galerkin ipdg method using piecewise linear polynomials for the indefinite time harmonic maxwell equations with the impedance boundary condition in the three dimensional space the main novelties of the proposed ipdg method include the following first the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field second the penalty parameters are taken as complex numbers of negative imaginary parts for the differential problem we prove that the sesquilinear form associated with the maxwell problem satisfies a generalized weak stability i e inf sup condition for star shaped domains such a generalized weak stability readily infers wave number explicit a priori estimates for the solution of the maxwell problem which plays an important role in the error analysis for the ipdg method for the proposed ipdg metho

regression to the mean for nonnormal populations summary regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have upon remeasurement values nearer to the population mean for the normal distribution simple expressions for estimates of the magnitude of this effect are available many biological variables however are not normally distributed estimates for regression to the mean for nonnormal data are given based on edgeworth series and saddlepoint approximations

analysis of the dpg method for the poisson equation we give an error analysis of the recently developed dpg method applied to solve the poisson equation and a convection diffusion problem we prove that the method is quasioptimal error estimates in terms of both the mesh size h and the polynomial degree p for various element shapes can be derived from our results results of extensive numerical experiments are also presented

a numerical study of the pollution error and dpg adaptivity for long waveguide simulations abstract high frequency wave propagation has many important applications in acoustics elastodynamics and electromagnetics unfortunately the finite element discretization for these problems suffers from significant numerical pollution errors that increase with the wavenumber it is critical to control these errors to obtain a stable and accurate method we study the effect of pollution for very long waveguide problems in the context of robust discontinuous petrov galerkin dpg finite element discretizations our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the dpg method while phase errors appear less significant we report results for 3d vectorial time harmonic maxwell problems in waveguides with more than 8000 wavelengths our results corroborate previous analysis for the galerkin discretization of the helmholtz operator by melenk and sauter 2011 additionally we discuss adaptive refinement strategies for multi mode fiber waveguides where the propagating transverse modes must be resolved sufficiently our study shows the applicability of the dpg error indicator to this class of problems finally we illustrate the importance of load balancing in these simulations for distributed memory parallel computing

the dpg methodology applied to different variational formulations of linear elasticity abstract the flexibility of the dpg methodology is exposed by solving the linear elasticity equations under different variational formulations including some with non symmetric functional settings different infinite dimensional trial and test spaces the family of formulations presented is proved to be mutually ill or well posed when using traditional energy spaces on the whole domain moreover they are shown to remain well posed when using broken energy spaces and interface variables four variational formulations are solved in 3d using the dpg methodology numerical evidence is given for both smooth and singular solutions and the expected convergence rates are observed

repeated measures in clinical trials analysis using mean summary statistics and its implications for design this paper explores the use of simple summary statistics for analysing repeated measurements in randomized clinical trials with two treatments quite often the data for each patient may be effectively summarized by a pre treatment mean and a post treatment mean analysis of covariance is the method of choice and its superiority over analysis of post treatment means or analysis of mean changes is quantified as regards both reduced variance and avoidance of bias using a simple model for the covariance structure between time points quantitative consideration is also given to practical issues in the design of repeated measures studies the merits of having more than one pre treatment measurement are demonstrated and methods for determining sample sizes in repeated measures designs are provided several examples from clinical trials are presented and broad practical recommendations are made the examples support the value of the compound symmetry assumption as a realistic simplification in quantitative planning of repeated measures trials the analysis using summary statistics makes no such assumption however allowance in design for alternative non equal correlation structures can and should be made when necessary

constant composition codes as subcodes of cyclic codes constant composition codes are codes where the frequency distribution of the elements in a codeword is the same for all codewords in this paper three classes of constant composition codes are constructed these codes are subcodes of cyclic codes which have few weights occurring among the codewords the new codes are excellent asymptotically compared to the previously best known constant composition codes

optimal constant composition codes from zero difference balanced functions constant composition codes are a special class of constant weight codes and include permutation codes as a subclass they have applications in communications engineering in this correspondence a generic construction of optimal constant composition codes using zero difference balanced functions is introduced it generalizes the earlier construction of optimal constant composition codes employing perfect nonlinear functions in addition two classes of optimal constant composition codes with new parameters are reported

a new construction of zero difference balanced functions and its applications in this paper a new construction of zero difference balanced functions defined on is given where is an odd positive integer based on the generic constructions proposed by ding optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero difference balanced functions constructed in this paper

a low order discontinuous petrov galerkin method for the stokes equations this paper introduces a low order discontinuous petrov galerkin dpg finite element method fem for the stokes equations the ultra weak formulation utilizes piecewise constant and affine ansatz functions and piecewise affine and discontinuous lowest order raviart thomas test search functions this low order discretization for the stokes equations allows for a direct proof of the discrete inf sup condition with explicit constants the general framework of carstensen et al siam j numer anal 52 3 1335 1353 2014 then implies a complete a priori and a posteriori error analysis of the dpg fem in the natural norms numerical experiments investigate the performance of the method and underline its quasi optimal convergence

robust dpg method for convection dominated diffusion problems we propose and analyze a discontinuous petrov galerkin dpg method for convection dominated diffusion problems that provides robust l 2 error estimates for the field variables which are quasi optimal in the energy norm a key feature of the method is to construct test functions defined by a variational formulation with bilinear form test norm specifically designed for the goal of robustness a main theoretical ingredient is a stability analysis of the adjoint problem numerical experiments underline our theoretical results and in particular confirm robustness of the dpg method for well chosen test norms

methods for assessing whether change depends on initial value statistical analysis of whether the change in a variable depends on its initial value in clinical trials and other studies is complicated by the phenomenon of regression to the mean we review this problem and examine some approaches for handling it macgregor s log log plot fails to correct for the regression effect while oldham s method of plotting the change against the average of initial and final values is shown to give misleading results when the effect of treatment varies between subjects or when subjects are selected for study if their initial observations fall above or below a specified cut off point these results are illustrated by computer simulations we prefer the use of blomqvist s method of correcting the association between change and initial value to allow for the regression effect

nonlinear discontinuous petrov galerkin methods the discontinuous petrov galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper its lowest order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation a reduced formulation and a weighted nonlinear least squares method quasi optimal a priori and reliable and efficient a posteriori estimates are obtained for the abstract nonlinear dpg framework for the approximation of a regular solution the variational model example allows for a built in guaranteed error control despite inexact solve the subtle uniqueness of discrete minimizers is monitored in numerical examples

some new classes of zero difference balanced functions zero difference balanced zdb functions were introduced recently by ding for the construction of optimal constant composition codes and optimal and perfect difference systems of sets they are closely related to partitioned difference families in this paper we present generic constructions of zdb functions from functions with difference balanced property in particular two classes of zdb functions with new and flexible parameters are reported employing these new zdb functions we obtain at the same time optimal 1 constant composition codes 2 constant weight codes and 3 perfect difference systems of sets all with new and flexible parameters

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

group divisible codes and their application in the construction of optimal constant composition codes of weight three the concept of group divisible codes a generalization of group divisible designs with constant block size is introduced in this paper this new class of codes is shown to be useful in recursive constructions for constant weight and constant composition codes large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant composition codes of weight three and specified distance leaving only four cases undetermined previously the sizes of constant composition codes of weight three were known only for those of sufficiently large length

the double adaptivity paradigm how to circumvent the discrete inf sup conditions of babuska and brezzi abstract we present an efficient implementation of the double adaptivity algorithm of cohen et al 2012 within the setting of the petrov galerkin method with optimal test functions we apply this method to the ultraweak variational formulation of a general linear variational problem discretized with the standard galerkin finite element method as an example we demonstrate the feasibility of the method in the context of the convection dominated diffusion problem the presented ideas however apply to virtually any well posed system of first order partial differential equations including singular perturbation problems

wavenumber explicit analysis of a dpg method for the multidimensional helmholtz equation we study the properties of a novel discontinuous petrov galerkin dpg method for acoustic wave propagation the method yields hermitian positive definite matrices and has good pre asymptotic stability properties numerically we find that the method exhibits negligible phase errors otherwise known as pollution errors even in the lowest order case theoretically we are able to prove error estimates that explicitly show the dependencies with respect to the wavenumber the mesh size h and the polynomial degree p but the current state of the theory does not fully explain the remarkably good numerical phase errors theoretically comparisons are made with several other recent works that gave wave number explicit estimates numerically comparisons are made with the standard finite element method and its recent modification for wave propagation with clever quadratures the new dpg method is designed following the previously established principles of optimal test functions in addition to the nonstandard test functions in this work we also use a nonstandard wave number dependent norm on both the test and trial space to obtain our error estimates

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

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

constructions of ternary constant composition codes with weight three we consider the problem of determining the maximum size of a ternary code with constant composition and hamming weight three we give several constructions of codes having maximum size and we also present an improvement of the johnson 1962 bound the results presented solve the problem for all lengths when d 3 as well as for lengths 7 11 and all even lengths when d 4

upper bounds for constant weight codes let a n d w denote the maximum possible number of codewords in an n d w constant weight binary code we improve upon the best known upper bounds on a n d w in numerous instances for n spl les 24 and d spl les 12 which is the parameter range of existing tables most improvements occur for d 8 10 where we reduce the upper bounds in more than half of the unresolved cases we also extend the existing tables up to n spl les 28 and d spl les 14 to obtain these results we develop new techniques and introduce new classes of codes we derive a number of general bounds on a n d w by means of mapping constant weight codes into euclidean space this approach produces among other results a bound on a n d w that is tighter than the johnson bound a similar improvement over the best known bounds for doubly constant weight codes studied by johnson and levenshtein is obtained in the same way furthermore we introduce the concept of doubly bounded weight codes which may be thought of as a generalization of the doubly constant weight codes subsequently a class of euclidean space codes called zonal codes is introduced and a bound on the size of such codes is established this is used to derive bounds for doubly bounded weight codes which are in turn used to derive bounds on a n d w we also develop a universal method to establish constraints that augment the delsarte inequalities for constant weight codes used in the linear programming bound in addition we present a detailed survey of known upper bounds for constant weight codes and sharpen these bounds in several cases all these bounds along with all known dependencies among them are then combined in a coherent framework that is amenable to analysis by computer this improves the bounds on a n d w even further for a large number of instances of n d and w

on constant composition codes over z sub q a constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword in this correspondence we give a lower bound for the maximum size of the q ary constant composition codes with minimum distance at least 3 this bound is asymptotically optimal and generalizes the graham sloane bound for binary constant weight codes in addition three construction methods of constant composition codes are presented and a number of optimum constant composition codes are obtained by using these constructions

convergence rates of the dpg method with reduced test space degree this paper presents a duality theorem of the aubin nitsche type for discontinuous petrov galerkin dpg methods this explains the numerically observed higher convergence rates in weaker norms considering the specific example of the mild weak or primal dpg method for the laplace equation two further results are obtained first the dpg method continues to be solvable even when the test space degree is reduced provided it is odd second a non conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree

nonparametric regression to the mean available data may reflect a true but unknown random variable of interest plus an additive error which is a nuisance the problem in predicting the unknown random variable arises in many applied situations where measurements are contaminated with errors it is known as the regression to the mean problem there exists a well known solution when both the distributions of the true underlying random variable and the contaminating errors are normal this solution is given by the classical regression to the mean formula which has a data shrinkage interpretation we discuss the extension of this solution to cases where one or both of these distributions are unknown and demonstrate that the fully nonparametric case can be solved for the case of small contaminating errors the resulting nonparametric regression to the mean paradigm can be implemented by a straightforward data sharpening algorithm that is based on local sample means asymptotic justifications and practical illustrations are provided

low order discontinuous petrov galerkin finite element methods for linear elasticity this paper analyzes lowest order discontinuous petrov galerkin dpg finite element methods fem for the navier lame equations with different norms and side restrictions the focus is on the direct proof of a discrete inf sup condition for a low order test search space the low order finite element spaces in the ultraweak formulation involve the piecewise constant and affine ansatz functions and discontinuous piecewise affine test functions in two and three space dimensions with neumann boundary conditions or the pure dirichlet problem those lowest order discretizations for linear elasticity allow for a direct proof of the discrete inf sup condition and a complete a priori and a posteriori error analysis which is robust in the incompressible limit as lambda rightarrow infty numerical experiments with uniform and adaptive mesh refinements investigate lambda robustness and confirm that one scheme is locking free

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

a posteriori error control for dpg methods a combination of ideas in least squares finite element methods with those of hybridized methods recently led to discontinuous petrov galerkin dpg finite element methods they minimize a residual inherited from a piecewise ultraweak formulation in a nonstandard locally computable dual norm this paper establishes a general a posteriori error analysis for the natural norms of the dpg schemes under conditions equivalent to a priori stability estimates it is proven that the locally computable residual norm of any discrete function is a lower and an upper error bound up to explicit data approximation errors the presented abstract framework for a posteriori error analysis applies to known dpg discretizations of laplace and lame equations and to a novel dpg method for the stress velocity formulation of stokes flow with symmetric stress approximations since the error control does not rely on the discrete equations it applies to inexactly computed or otherwise perturbed solutions within the discrete space

an adaptive characteristic petrov galerkin finite element method for convection dominated linear and nonlinear parabolic problems in one space variable a new adaptive finite element method for convection dominated problems is presented a special feature of the method is that it is based on a petrov galerkin scheme for spatial approximation at a typical time step which employs test functions chosen so that the approximate solution coincides with the exact solution at the nodes of finite element grid this procedure makes possible the derivation of truly local a posteriori error estimates and a very effective solver numerical examples are discussed which illustrate the efficiency and effectively of the method

combinatorial constructions of optimal constant composition codes constant composition codes cccs are a special class of constant weight codes they include permutation codes as a subclass in this correspondence a link between cccs and generalized double resolvable packing designs is developed and used to construct several infinite series of optimal cccs

breaking spaces and forms for the dpg method and applications including maxwell equations discontinuous petrov galerkin dpg methods are made easily implementable using broken test spaces i e spaces of functions with no continuity constraints across mesh element interfaces broken spaces derivable from a standard exact sequence of first order unbroken sobolev spaces are of particular interest a characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces this technique is used to provide a complete error analysis of dpg methods for maxwell equations with perfect electric boundary conditions the technique also permits considerable simplifications of previous analyses of dpg methods for other equations reliability and efficiency estimates for an error indicator also follow finally the equivalence of stability for various formulations of the same maxwell problem is proved including the strong form the ultraweak form and various forms in between

a class of discontinuous petrov galerkin methods part i the transport equation considering a simple model transport problem we present a new finite element method while the new method fits in the class of discontinuous galerkin dg methods it differs from standard dg and streamline diffusion methods in that it uses a space of discontinuous trial functions tailored for stability the new method unlike the older approaches yields optimal estimates for the primal variable in both the element size h and polynomial degree p and outperforms the standard upwind dg method

importance of symbol equity in coded modulation for power line communications the use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system in this paper we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code s performance against permanent narrowband noise as a result we define a new class of codes namely equitable symbol weight codes which are optimal with respect to this measure

fully discrete dpg methods for the kirchhoff love plate bending model abstract we extend the analysis and discretization of the kirchhoff love plate bending problem from fuhrer et al in press in two aspects first we present a well posed formulation and quasi optimal dpg discretization that include the gradient of the deflection second we construct fortin operators that prove the well posedness and quasi optimal convergence of lowest order discrete schemes with approximated test functions for both formulations our results apply to the case of non convex polygonal plates where shear forces can be less than l 2 regular numerical results illustrate expected convergence orders

high order polygonal discontinuous petrov galerkin polydpg methods using ultraweak formulations abstract this work represents the first endeavor in using ultraweak formulations to implement high order polygonal finite element methods via the discontinuous petrov galerkin dpg methodology ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space while most of the trial space can be chosen as copies of l 2 discretizations that have no need to be continuous across adjacent elements additionally the test spaces are broken along the mesh interfaces this allows one to construct conforming polygonal finite element methods termed here as polydpg methods by defining most spaces by restriction of a bounding triangle or box to the polygonal element the only variables that require nontrivial compatibility across elements are the so called interface or skeleton variables which can be defined directly on the element boundaries unlike other high order polygonal methods polydpg methods do not require ad hoc stabilization terms thanks to the crafted stability of the dpg methodology a proof of convergence of the form h p is provided and corroborated through several illustrative numerical examples these include polygonal meshes with n sided convex elements and with highly distorted concave elements as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid since polydpg methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes this work is also accompanied by an open source polydpg software supporting polygonal and conventional elements

algebraic constructions of constant composition codes constant composition codes are a special class of constant weight codes they include permutation codes as a subclass in this correspondence two classes of optimal constant composition codes are constructed both constructions employ perfect nonlinear functions but they are different

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

cyclotomic constructions of zero difference balanced functions with applications based on a recent work of ding wang and xiong we present some cyclotomic constructions of zero difference balanced zdb functions which interpret the previous construction proposed by cai zeng helleseth tang and yang the resulted zdb functions can be used to generate optimal constant composition codes and perfect difference systems of sets with new parameters

note on discontinuous trace approximation in the practical dpg method we analyze a non conforming dpg method with discontinuous trace approximation for the poisson problem in two and three space dimensions we show its well posedness and quasi optimal convergence in the principal unknown numerical experiments confirming the theory have been presented previously

a primal dpg method without a first order reformulation abstract we show that it is possible to apply the dpg methodology without reformulating a second order boundary value problem into a first order system by considering the simple example of the poisson equation the result is a new weak formulation and a new dpg method for the poisson equation which has no numerical trace variable but has a numerical flux approximation on the element interfaces in addition to the primal interior variable

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

the pbd closure of constant composition codes we show an interesting pairwise balanced design pbd closure result for the set of lengths of constant composition codes whose distance and size meet certain conditions a consequence of this pbd closure result is that the size of optimal constant composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code as an application the sizes of several infinite families of optimal constant composition codes are derived in particular the problem of determining the size of optimal constant composition codes having distance four and weight three is solved for all lengths sufficiently large this problem was previously unresolved for odd lengths except for lengths seven and eleven

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

a lower bound for ternary constant weight codes we derive a lower bound for ternary constant weight codes with minimum hamming distance three the bound is similar to a bound for binary constant weight codes with minimum distance four described by graham and sloane 1980 it improves upon the gilbert 1952 bound and coincides asymptotically with the johnson 1962 bound for fixed weight as the codeword length tends to infinity

high rate self synchronizing codes self synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error tolerant self synchronizing codes may be realized as cosets of linear codes ideally difference systems of sets should sacrifice as few bits as possible for a given code length alphabet size and error tolerance capability however it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low in fact the majority of known optimal difference systems of sets are for exceptionally noisy channels requiring a substantial amount of bits for synchronization to address this problem we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent our constructions utilize optimal difference systems of sets as ingredients and when applied carefully generate asymptotically optimal ones with higher information rates we also give direct constructions for optimal difference systems of sets with high information rates and error tolerance that generate binary and ternary self synchronizing codes

orientation embedded high order shape functions for the exact sequence elements of all shapes a unified construction of high order shape functions is given for all four classical energy spaces h1 h curl h div and l2 and for elements of all shapes segment quadrilateral triangle hexahedron tetrahedron triangular prism and pyramid the discrete spaces spanned by the shape functions satisfy the commuting exact sequence property for each element the shape functions are conforming hierarchical and compatible with other neighboring elements across shared boundaries so they may be used in hybrid meshes expressions for the shape functions are given in coordinate free format in terms of the relevant affine coordinates of each element shape the polynomial order is allowed to differ for each separate topological entity vertex edge face or interior in the mesh so the shape functions can be used to implement local p adaptive finite element methods each topological entity may have its own orientation and the shape functions can have that orientation embedded by a simple permutation of arguments

a lower bound for a n 4 w corresp an explicit lower bound is given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance four and constant weight w

an adaptive dpg method for high frequency time harmonic wave propagation problems abstract the discontinuous petrov galerkin dpg method for high frequency wave propagation problems is discussed the dpg method with its attractive uniform mesh and wavenumber independent pre asymptotic stability property allows for a fully automatic adaptive h p algorithm that can be initiated from very coarse meshes moreover dpg always delivers a hermitian positive definite system suggesting the use of the conjugate gradient algorithm for its solution we present a new iterative solution scheme which capitalizes on these attractive properties of dpg this novel solver is integrated within the adaptive procedure by constructing a two grid like preconditioner for the conjugate gradient method that exploits information from previous meshes the construction of our preconditioner is discussed and its efficacy is illustrated with an example of a 2d acoustics problem our results show that the proposed iterative algorithm converges at a rate independent of the mesh and the wavenumber

analysis of non conforming dpg methods on polyhedral meshes using fractional sobolev norms abstract the work is concerned with two problems a analysis of a discontinuous petrov galerkin dpg method set up in fractional energy spaces b use of the results to investigate a non conforming version of the dpg method for general polyhedral meshes we use the ultraweak variational formulation for the model laplace equation the theoretical estimates are supported with 3d numerical experiments