choice of column scores for testing independence in ordered 2 x k contingency tables the numerous statistical methods for testing no association between a binary response rows and k ordered categories columns group naturally into two classes those that require preassigned numerical column scores and those that do not an example of the former would be a logistic regression analysis and of the latter would be a wilcoxon rank sum test in this paper we demonstrate that the perceived advantage of not preassigning scores is illusory we do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate our recommendations are to assign reasonable column scores whenever possible and to consider equally spaced scores when the choice is not apparent midranks as scores should always be examined for their appropriateness before a rank test is applied

recovery type superconvergence and a posteriori error estimates for control problems governed by stokes equations in this paper we derive recovery type superconvergence analysis and a posteriori error estimates for the finite element approximation of the distributed optimal control governed by stokes equations we obtain superconvergence results and asymptotically exact a posteriori error estimates by applying two recovery methods which are the patch recovery technique and the least squares surface fitting method our results are based on some regularity assumption for the stokes control problems and are applicable to the first order conforming finite element method with regular but nonuniform partitions

a hierarchical clustering algorithm based on fuzzy graph connectedness many clustering methods have been proposed in the area of data mining but only few of them focused on the incremental databases in this paper an algorithm for hierarchical clustering based on fuzzy graph connectedness algorithm fhc is investigated the presented algorithm applies fuzzy set theory to hierarchical clustering method so as to discover clusters with arbitrary shape it first partitions the data sets into several sub clusters using a partitioning method and then constructs a fuzzy graph of sub clusters by analyzing the fuzzy connectedness degree among sub clusters by computing the cut graph the connected components of the fuzzy graph can be obtained hence resulting the desired clustering the algorithm can be performed in high dimensional data sets finding clusters of arbitrary shapes such as the spherical linear elongated or concave ones also rendered in this research is the incremental algorithm ifhc applicable to periodically incremental environments not only can fhc and ifhc handle data with numerical attributes but categorical attributes can be dealt with as well the results of our experimental study for data sets with arbitrary shape and size are very encouraging the experimental study in web log files is also conducted that can help discover the user access patterns efficiently the investigation demonstrates that the proposed method generates better quality clusters than traditional algorithms and scales up well for large databases

a posteriori error estimates for control problems governed by stokes equations in this paper we derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the stokes equations we obtain a posteriori error estimators for both the state and the control approximation in the l2 norm and the h1 norm these estimates can be used to construct reliable adaptive finite element approximation for the control problems

analysis and finite element approximation of an optimal control problem in electrochemistry with current density controls an optimal control problem for impressed cathodic systems in electrochemistry is studied the control in this problem is the current density on the anode a matching objective functional is considered we first demonstrate the existence and uniqueness of solutions for the governing partial differential equation with a nonlinear boundary condition we then prove the existence of an optimal solution next we derive a necessary condition of optimality and establish an optimality system of equations finally we define a finite element algorithm and derive optimal error estimates

ritz galerkin approximation of the time optimal boundary control problem for parabolic systems with dirichlet boundary conditions this paper deals with ritz galerkin approximations of the following two problems i boundary value problems with l 2 boundary data given in the form of dirichlet boundary conditions ii time optimal control problems for parabolic systems with control acting on the boundary in both cases optimal rates of convergence of approximation are obtained also the specialization is considered to approximating with nonconformal elements which are not required to satisfy boundary conditions corresponding rates of convergence are also proved

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part 1 a smooth problem and globally quasi uniform meshes a class of a posteriori estimators is studied for the error in the maximum norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems the meshes are unstructured and in particular it is not assumed that there are any known superconvergent points the estimators are based on averaging operators which are approximate gradients recovered gradients which are then compared to the actual gradient of the approximation on each element conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large in a controlled fashion to be detailed below compared to the size of the elements

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

on asymptotic power and efficiency of tests of independence in contingency tables with ordered classifications abstract asymptotic power formulas for tests of independence against simple association models in i j contingency tables with ordered categories are presented yates s score correlation test and spearman s tied rank correlation test are compared with a likelihood ratio test proposed by s j haberman for testing independence in log linear models with ordered classifications asymptotic power and relative efficiencies are derived under local alternatives that need not be included in the likelihood model assumed by haberman s procedure some computations for real and fictitious data are presented

the analysis of contingency tables preface contingency tables and the chi square test 2 x 2 contingency tables r x c contingency tables multidimensional tables log linear models for contingency table linear logistic models contingency tables with ordered categories some special types of contingency tables appendices percentage points of the chi squared distribution computer software for fitting log linear and logistic models reference index

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

analysis of some finite elements for the stokes problem we study some finite elements which are used in the approximation of the stokes problem so as to obtain error estimates of optimal order resume nous etudions deux elements finis utilises pour l approximation du probleme de stokes et obtenons des estimations d erreur d ordre optimal

superconvergence of finite element approximations for the stokes problem by projection methods this paper derives a general superconvergence result for finite element approximations of the stokes problem by using projection methods proposed and analyzed recently by wang j math study 33 2000 pp 229 243 for the standard galerkin method the superconvergence result is based on some regularity assumption for the stokes problem and is applicable to any finite element method with regular but nonuniform partitions the method is proved to give a convergent scheme for certain finite element spaces which fail to satisfy the well known uniform inf sup condition of brezzi and babuska

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part ii the piecewise linear case we extend results from part i about estimating gradient errors elementwise a posteriori given there for quadratic and higher elements to the piecewise linear case the key to our new result is to consider certain technical estimates for differences in the error e x 1 e x 2 rather than for e x itself we also give a posteriori estimators for second derivatives on each element

efficiency robust tests for survival or ordered categorical data summary the selection of a single method of analysis is problematic when the data could have been generated by one of several possible models we examine the properties of two tests designed to have high power over a range of models the first one the maximum efficiency robust test mert uses the linear combination of the optimal statistics for each model that maximizes the minimum efficiency the second procedure called the mx uses the maximum of the optimal statistics both approaches yield efficiency robust procedures for survival analysis and ordinal categorical data guidelines for choosing between them are provided

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

local a posteriori error estimates for convex boundary control problems in this paper we derive some improved a posteriori error estimates for finite element approximation of neumann boundary control problems we first establish local upper a posteriori error estimates for both the state and the control approximation of the general convex boundary control problems we then derive local upper and lower a posteriori error estimates for a class of control problems that frequently appear in applications

finite dimensional approximation of a class of constrained nonlinear optimal control problems an abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed nonlinearities occur in both the objective functional and the constraints the framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces an approximate problem posed on finite dimensional spaces together with a number of hypotheses concerning the two problems the framework is used to show that optimal solutions exist to show that lagrange multipliers may be used to enforce the constraints to derive an optimality system from which optimal states and controls may be deduced and to derive existence results and error estimates for solutions of the approximate problem the abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods the first involves the von k arm an plate equations of nonlinear elasticity the second the ginzburg landau equations of superconductivity and the third the navier stokes equations for incompressible viscous flows

a posteriori error estimates for some model boundary control problems in this paper we derive a posteriori error estimates for the finite element approximation of quadratic optimal boundary control problems we derive a posteriori error estimates for both the state and the control approximation on polygonal domains such estimates which are apparently not available in the literature can be used to construct reliable adaptive finite element approximation schemes for the control problems

superconvergence properties of optimal control problems an optimal control problem for a two dimensional 2 d elliptic equation is investigated with pointwise control constraints this paper is concerned with discretization of the control by piecewise constant functions the state and the adjoint state are discretized by linear finite elements approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state it is proved that these approximations have convergence order h2