analysis of rank measures of association for ordinal data from longitudinal studies abstract consideration is given to longitudinal data settings in which an ordinal response variable is observed at two or more visits for each subject in two or more ordered groups with at least moderately large sample sizes e g overall n 40 rank measures of association between group and response are constructed at each time and the covariance matrix of these measures is also estimated variation among the rank measures of association is then analyzed through weighted least squares methods with weights based on the estimated covariance matrix such methods permit evaluation of group visit interaction as well as other effects of interest extensions of this type of analysis to situations with stratification or concomitant variables or missing data are also considered examples are provided for illustrative purposes

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

analysing repeated measurements with possibly missing observations by modelling marginal distributions suppose that subjects are observed repeatedly over a common set of time points with possibly time dependent covariates and possibly missing observations at each time point we model the marginal distribution of the response variable and the effect of the covariates on that distribution using a class of quasi likelihood models studied in mccullagh and nelder no parametric model of dependence of the repeated observations of the subject is assumed for large samples the quasi likelihood estimates of the time specific regression coefficients over the set of predetermined time points are shown to be approximately jointly normal this coupled with various inference procedures provides a global picture about the effects of the covariates on the response variable over the entire study period a lack of fit test for testing the adequacy of the assumed quasi likelihood model is also provided all the methods considered here are illustrated with real life examples

a generalized estimating equations approach for testing ordered group effects with repeated measurements in repeated measures studies we are often interested in comparing group effects in which groups are associated with a certain order relation we propose testing procedures for ordered group effects using the generalized estimating equations gee approach of liang and zeger 1986 biometrika 73 13 22 the order constrained gee estimators of group effects are approximated by the isotonic regression of the unconstrained gee estimators based on these constrained estimators we construct test statistics for detecting ordered group effects the limiting distributions of the test statistics are mixtures of chi square distributions a monte carlo experiment shows improved performances of the proposed tests over the usual chi square tests in detecting ordered group effects the proposed test procedures are illustrated by familial polyposis supplementation trial data

distributed exponential finite time coordination of multi agent systems containment control and consensus in this paper exponential finite time coordination problems of multi agent systems are investigated including containment control and consensus the theoretical basis is that a class of nonlinear systems has favourable finite time convergence characteristic for the objective of containment control the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time for the objective of consensus a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time the distinguished features of this paper lie in the following two points 1 a smaller settling time of the lyapunov function is obtained which manifests in a faster convergence rate than the traditional one and 2 the weakly connected topology considered in this paper is more general than the o

analysis of mixed finite elements methods for the stokes problem a unified approach we develop a method for the analysis of mixed finite element methods for the stokes problem in the velocity pressure formulation a technical macroelement condition which is sufficient for the classical babuska brezzi inequality to be valid is introduced using this condition we are able to verify the stability and optimal order of convergence of several known mixed finite element methods

modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions abstractthis paper addresses the modulus consensus in a network of singularly perturbed systems all of which own multi time scales characteristics the interactions among the agents are collaborat

general methods for analysing repeated measures we present an overview of issues and methods for analysing repeated measures of a continuous random variable we discuss modelling the mean vector and covariance structure statistical efficiency regression diagnostics and discrepancies between longitudinal and cross sectional methods we illustrate key points with examples and discuss areas requiring further development

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

a mixed finite element method for approximating incompressible materials a mixed finite element method is proposed for approximating the deformation u of a plane incompressible material satisfying the condition det nabla u 1 for piecewise linear shape functions it is proved that the discrete solutions exist and converge with nearly quasi optimal rates in l infty the corresponding nonlinear system is iteratively solved by a multigrid method

finite time weighted average consensus with respect to a monotonic function and its application abstract the consensus state is an important and fundamental quantity for consensus problems of multi agent systems which indicates where all the dynamical agents reach in this paper weighted average consensus with respect to a monotonic function which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values is studied for a group of kinematic agents with time varying topology by constructing a continuous nonlinear distributed protocol such a consensus problem can be solved in finite time even though the time varying topology involves unconnected graphs then the distributed protocol is employed to compute the maximum likelihood estimation of unknown parameters over sensor networks compared with the existing results the estimate scheme proposed here may reduce the costs of data communication storage memory book keeping and computational overheads

rank based regression with repeated measurements data summary a rank based regression method is proposed for repeated measurements data it is a generalisation of the classical wilcoxon mann whitney rank statistic for independent observations the method is valid under a weak condition on the error terms that can accommodate certain heteroscedasticity and within subject dependency the asymptotic normality of the proposed estimator is proved using empirical process theory a variance estimator shown to be consistent is also constructed the proposed method is illustrated using data from a clinical trial on treating labour pain robustness and efficiency of the estimator is demonstrated in simulation studies

nonlinear finite time bipartite consensus protocol for multi agent systems associated with signed graphs in this paper finite time multi agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative a nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time if the signed graph is structurally balanced then the final consensus states of all agents are the same in modulus but not in sign otherwise if the signed graph is structurally unbalanced then the states of all agents converge to zero moreover the final consensus states of agents can be provided uniformly regarding a signed average quantity that depends on both the initial states of agents and the topology structure of the whole multi agent network numerical simulations illustrate that the protocol is effective in achieving the finite time consensus of agents under signed graphs and can particularly solve the finite time average consensus problem of agents when their associated graph has all positive edge weights

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

analysis of repeated categorical data using generalized estimating equations moment methods for analysing repeated binary responses have been proposed by liang and zeger and extended by prentice and zhao and prentice in these estimating equations models are proposed for the correlation between the repeated binary responses we extend liang and zeger s method to models for the correlation between repeated nominal or ordinal categorical responses in particular when the repeated responses are binary our methods reduce to liang and zeger s method our method is illustrated with two datasets one dataset contains repeated observations of self assessment of arthritis an ordered variable with three categories collected during a randomized comparative study of alternative treatments of patients with rheumatoid arthritis the second dataset is a longitudinal study of the health effects of air pollution in which the repeated ordered multinomial response is the wheezing status no wheeze wheeze with cold wheeze apart from cold of a child at ages 9 10 11 and 12 years

a survey of models for repeated ordered categorical response data we survey models for analysing repeated observations on an ordered categorical response variable the models presented are univariate models that permit correlation among repeated measurements the models describe simultaneously the dependence of marginal response distributions on values of explanatory variables and on the occasion of response we present models for three transformations of the response distribution cumulative logits adjacent category logits and the mean for scores assigned to response categories we discuss three methods for fitting the models maximum likelihood weighted least squares and semi parametric weighted least squares is easily implemented with sas as illustrated with a study designed to compare a drug with a placebo for the treatment of insomnia

some test statistics for use in multistate survival analysis summary some current nonparametric methods related to the log rank test are extended to cover ordered categories of response e g response no change progression and to incorporate information on duration of response as an example data from a protocol for the treatment of advanced breast cancer are analysed the powers of several tests for this special case of multistate survival data are compared by monte carlo simulation for both small and moderate samples from exponential and weibull distributions

median regression for longitudinal data we review and compare three estimators of median regression in linear models with longitudinal data the estimators are constructed based on well known ideas of weighting decorrelating and the working assumption of independence both asymptotic efficiency calculations and finite sample monte carlo studies are used to assess the performance of these estimators we find that their relative performances depend on the nature of covariates the estimator under the working assumption of independence is computationally simple and yet has good relative performance when the covariates are invariant over time or when the within subject correlations are small its relative performance in finite samples is also found to be more favourable than suggested by the asymptotic comparisons

on the convergence of the bilinear velocity constant pressure finite element method in viscous flow abstract in this paper we show that the standard isoparametric q 1 q 0 velocity pressure finite element method for solving viscous flow problems leads to a fully and optimally convergent sequence of approximations if an appropriate quadrangulation of the domain is used

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

computing for incomplete repeated measures summary repeated measures experiments involve two or more intended measurements per subject if the within subjects design is the same for each subject and no data are missing then the analysis is relatively simple and there are readily available programs that do the analysis automatically however if the data are incomplete and do not have the same arrangement for each subject then the analysis becomes much more difficult beginning with procedures that are not optimal but are comparatively simple we discuss unbalanced linear model analysis and then normal maximum likelihood ml procedures included are ml and reml restricted maximum likelihood estimators for the mixed model and also estimators for a model that allows arbitrary within subject covariance matrices the objective is to give procedures that can be implemented with available software

brief paper target containment control of multi agent systems with random switching interconnection topologies in this paper the distributed containment control is considered for a second order multi agent system guided by multiple leaders with random switching topologies the multi leader control problem is investigated via a combination of convex analysis and stochastic process the interaction topology between agents is described by a continuous time irreducible markov chain a necessary and sufficient condition is obtained to make all the mobile agents almost surely asymptotically converge to the static convex leader set moreover conditions on the tracking estimation are provided for the convex target set determined by moving multiple leaders

two sample asymptotically distribution free tests for incomplete multivariate observations abstract asymptotically distribution free tests for equality of two multivariate distributions based on censored observations are proposed by choosing appropriate test scores we obtain the multivariate versions of the gehan and log rank tests an important application of the proposed tests is in the area in which multiple observations are collected on study subjects some of whom may have missing observations the patterns of missing observations are allowed to differ for the two groups to be compared these tests are particularly useful for longitudinal studies for example the analysis of repeated measurements and growth curves real examples are also provided for illustration

compatibility condition and existence results in discrete finite incompressible elasticity abstract a theory on the existence of solutions of the discretized equilibrium equations in incompressible finite elasticity is given a compatibility condition between the space of displacements and the space of pressures is introduced and is studied in a particular case of finite element spaces using q 1 and q 0 isoparametric elements an original assembling of these elements is presented which leads to discrete spaces satisfying the compatibility condition

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

numerical solution of problems in incompressible finite elasticity by augmented lagrangian methods ii three dimensional problems in a first paper siam j appl math 42 1982 pp 400 429 we introduced an augmented lagrangian methodology for solving equilibrium problems in incompressible finite elasticity and then applied it to the solution of several two dimensional and axisymmetric test problems in this second paper we extend our methods to the solution of genuine three dimensional problems actually using these augmented lagrangian techniques we can reduce the solution of these complicated nonlinear nonconvex problems to the solution of a sequence of linear problems and also to the solution of a sequence of minimization problems for convex functionals on convex sets the capabilities of our methods are illustrated by the results of numerical experiments

robust finite time containment control for high order multi agent systems with matched uncertainties under directed communication graphs abstractin this paper we study the robust finite time containment control problem for a class of high order uncertain nonlinear multi agent systems modelled as high order integrator systems with bounded matched uncertainties when relative state information between neighbouring agents is available an observer based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite time containment control problem under general directed communication graphs when only relative output information is available robust exact differentiators and high order sliding mode controllers are employed together with the distributed finite time observers it is shown that robust finite time containment control can still be achieved in this situation an application in the coordination of multiple non holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies

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

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

some large sample distribution free estimators and tests for multivariate partially incomplete data from two populations the most common instance of multivariate observations is the case of repeated measures over time the two most widely used methods for the analysis of k repeated measures for two groups are the k degrees of freedom d f t2 manova f test and the within subjects 1 degree of freedom anova f test both require complete samples from normally distributed populations in this paper i describe alternative k and 1 d f distribution free procedures which allow for randomly missing observations these include a large sample analysis of means the wei and lachin multivariate wilcoxon test with estimates of the mann whitney parameter and a multivariate hodges lehmann location shift estimator based on the multivariate u statistic of wei and johnson each of these methods provides a distribution free k variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences these tests include the k d f omnibus t2 like test 1 d f tests of restricted hypotheses such as the wei lachin multivariate one sided test of stochastic ordering and the test of general association based on a minimum variance generalized least squares gls estimate of the average group difference i then describe covariate stratified adjusted gls estimates and tests of group differences this approach also provides tests of homogeneity interaction for within subjects and between subjects effects i illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients stratified by sex such analyses provide an overall distribution free summary estimate and test of the treatment effect obtained by combining the group differences over both time repeated measures and strata

existence and approximation results for nonlinear mixed problems application to incompressible finite elasticity this paper considers the problems of minimizing gateaux differentiable functionals over subsets of real banach spaces defined by a non linear equality constraint the existence of a lagrange multiplier is proved together with approximation results on the constrained subset provided a nonlinear compatibility condition generalizing the classical inf sup condition is satisfied these ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

diamond elements a finite element discrete mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity we present a finite element discretization scheme for the compressible and incompressible elasticity problems that possess the following properties i the discretization scheme is defined on a triangulation of the domain ii the discretization scheme is defined and is identical in all spatial dimensions iii the displacement field converges optimally with mesh refinement and iv the inf sup condition is automatically satisfied the discretization scheme is motivated both by considerations of topology and analysis and it consists of the combination of a certain mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures rigorous proofs of the satisfaction of the inf sup condition are presented for the problem of linearized incompressible elasticity we additionally show that the discretization schemes can be given a compelling interpretation in terms of discrete differential operators in particular we develop a discrete analogue of the classical tensor differential complex in terms of which the discrete and continuous boundary value problems are formally identical we also present numerical tests that demonstrate the dimension independent scope of the scheme and its good performance in problems of finite elasticity

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

analyzing repeated measures on generalized linear models via the bootstrap the analysis of longitudinal data for which the response variables have nonnormal error distributions previously has been complex and or dependent on restrictive assumptions in this paper simple methods are introduced for the class of generalized linear models glms regressions are fit to the data at each observation time functions of the resulting coefficients may be bootstrapped or the coefficients combined through closed form estimation of their covariances application is made to a data set on xerophthalmia in indonesian children

group sequential large sample t2 like chi2 tests for multivariate observations in many studies a k degree of freedom large sample 2 test is used to assess the effect of treatment on a multivariate response such as an omnibus t2 like test of a difference between two treatment groups in any of k repeated measures alternately a k df 2 test may be used to test the equality of k 1 groups in a single outcome measure jennison and turnbull biometrika 1991 78 133 141 describe group sequential 2 and f tests for normal errors linear models and proschan follmann and geller statist med 1994 13 1441 1452 describe group sequential tests for k 1 group comparisons these methods apply to sequences of statistics that can be characterized as having an independent increments variance covariance structure thus simplifying the computation of the sequential variance covariance matrix and the resulting sequential test boundaries however many commonly used statistics do not share this structure including a liang zeger biometrika 1986 73 13 22 gee longitudinal analysis with an independence working correlation structure and a wei lachin j amer statist assoc 1984 79 653 661 multivariate wilcoxon rank test among others for such analyses this paper describes the computation of group sequential boundaries for the interim analysis of emerging results using k df tests that are expressed as quadratic forms in a statistics vector that is distributed as multivariate normal at least asymptotically we derive the elements of the covariance matrix of multiple successive k df 2 statistics based on established theorems on the distribution of quadratic forms this covariance matrix is estimated by augmenting the data from the successive interim analyses into a single analysis from which the component sequential tests and their variance covariance matrix can then be extracted boundary values for the sequential statistics can then be computed using the method of slud and wei j amer statist assoc 1982 77 862 868 or using the spending function of lan and demets biometrika 1983 70 659 663 with a surrogate measure of information an example is presented using the analysis of repeated cholesterol measurements in a clinical trial copyright 2003 john wiley sons ltd

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

sample size estimation for gee method for comparing slopes in repeated measurements data sample size calculation is an important component at the design stage of clinical trials controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed up for measurements at intervals across a treatment period of fixed duration in studies with repeated measurements one of the popular primary interests is the comparison of the rates of change in a response variable between groups statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly in this paper we propose to use the generalized estimating equation gee method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator since the sample size formula is based on asymptotic theory we investigate the performance of the estimated sample size in practical settings through simulations

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

numerical models of steady rolling for non linear viscoelastic structures in finite deformations a lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented these laws are expressed by a non linear differential equation governing the evolution of an internal variable then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics a finite element approximation and a solution technique of the algebraic system is proposed the eiimination of the internal variable allows one to keep an elastic like algorithm with an independent solution of the viscoelastic equation numerical tests show the feasibility and the efficiency of the proposed methods in large three dimensional situations

a nonparametric smoothing method for assessing gee models with longitudinal binary data studies involving longitudinal binary responses are widely applied in the health and biomedical sciences research and frequently analyzed by generalized estimating equations gee method this article proposes an alternative goodness of fit test based on the nonparametric smoothing approach for assessing the adequacy of gee fitted models which can be regarded as an extension of the goodness of fit test of le cessie and van houwelingen biometrics 1991 47 1267 1282 the expectation and approximate variance of the proposed test statistic are derived the asymptotic distribution of the proposed test statistic in terms of a scaled chi squared distribution and the power performance of the proposed test are discussed by simulation studies the testing procedure is demonstrated by two real data

procedures for comparing samples with multiple endpoints summary five procedures are considered for the comparison of two or more multivariate samples these procedures include a newly proposed nonparametric rank sum test and a generalized least squares test also considered are the following tests ordinary least squares hotelling s p and a bonferroni per experiment error rate approach applications are envisaged in which each variable represents a qualitatively different measure of response to treatment the null hypothesis of no treatment difference is tested with power directed towards alternatives in which at least one treatment is uniformly better than the others in all simulations the nonparametric procedure provided relatively good power and accurate control over the size of the test and is recommended for general use alternatively the generalized least squares procedure may also be useful with normally distributed data in moderate or large samples a convenient expression for this procedure is obtained and its asymptotic relative efficiency with respect to the ordinary least squares test is evaluated clinical trials are often conducted for the purpose of evaluating the relative efficacy of two or more modes of therapy when the therapies are administered to independent groups and efficacy is measured on the basis of a single response variable appropriate parametric and nonparametric one way analysis of variance anova procedures and their properties are well known often however efficacy is measured by more than one variable although univariate methods for assessing each characteristic individually are useful in this setting there is often the additional need for a single overall objective probability statement that addresses the question of whether or not the experimental therapy is efficacious this need is particularly acute when the medical question is controversial and the sample size is small although a large literature exists on the comparison of multivariate samples the procedures tend to be infrequently used in practice as pointed out by meier 1975 p 523 the standard analysis for the comparison of two multivariate samples which is based on hotelling s t2 statistic addresses somewhat the wrong question and consequently has very poor power for the alternatives of primary interest specifically the t2 procedure addresses the question are one or more of the treatments different making no distinction between variables that change favorably and variables that change unfavorably a second approach would be to assign per experiment error rates to each of the univariate tests by using bonferroni s inequality i e by multiplying each univariate p value by the number of variables studied the desired overall probability statement is then given by the minimum of the per experiment univariate p values although this approach may be useful in some settings it may lack power for alternatives in which most or all measures of efficacy are improved this will be of particular concern when the number k of endpoints studied is large relative to sample size in fact statistical significance will not be possible in some instances this problem will be exacerbated when the measures of efficacy are highly

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

convergence analysis of directed signed networks via an m matrix approach abstractthis paper aims at solving convergence problems on directed signed networks with multiple nodes where interactions among nodes are described by signed digraphs the convergence analysis is

nonparametric methods for analyzing incomplete nondecreasing repeated measurements in comparing the effectiveness of two treatments suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject a class of univariate one sided global asymptotically distribution free tests is proposed to test the equality of the two treatments the test procedures allow different patterns of missing observations in the two groups to be compared although the missing data mechanism is required to be independent of the observations in each treatment group test based point and interval estimators of the global treatment difference are given multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study the proposed methods are illustrated by an example from a bladder cancer study

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

a comparison of the generalized estimating equation approach with the maximum likelihood approach for repeated measurements liang and zeger proposed an extension of generalized linear models to the analysis of longitudinal data their approach is closely related to quasi likelihood methods and can handle both normal and non normal outcome variables such as poisson or binary outcomes their approach however has been applied mainly to non normal outcome variables this is probably due to the fact that there is a large class of multivariate linear models available for normal outcomes such as growth models and random effects models furthermore there are many iterative algorithms that yield maximum likelihood estimators mles of the model parameters the multivariate linear model approach based on maximum likelihood ml estimation specifies the joint multivariate normal distribution of outcome variables while the approach of liang and zeger based on the quasi likelihood specifies only the marginal distributions in this paper i compare the approach of liang and zeger and the ml approach for the multivariate normal outcomes i show that the generalized estimating equation gee reduces to the score equation only when the data do not have missing observations and the correlation is unstructured in more general cases however the gee estimation yields consistent estimators that may differ from the mles that is the gee does not always reduce to the score equation even when the outcome variables are multivariate normal i compare the small sample properties of the gee estimators and the mles by means of a monte carlo simulation study

semi parametric and non parametric methods for the analysis of repeated measurements with applications to clinical trials techniques applicable for the analysis of longitudinal data when the response variable is non normal are not nearly as comprehensive as for normally distributed outcomes however there have been several recent developments semi parametric and non parametric methodology for the analysis of repeated measurements is reviewed the commonly encountered design in which for each subject one assesses a univariate response variable at multiple fixed time points is considered the types of outcomes considered include binary ordered categorical and continuous but extremely non normal response variables all of the methods considered allow for incomplete data due to the occurrence of missing observations in addition discrete and or continuous covariates which may be time dependent are accommodated by some of the approaches the methods are demonstrated using data from three clinical trials

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

automatically inf sup compliant diamond mixed finite elements for kirchhoff plates we develop a mixed finite element approximation scheme for kirchhoff plate theory based on the reformulation of kirchhoff plate theory of ortiz and morris 1 in this reformulation the moment equilibrium problem for the rotations is in direct analogy to the problem of incompressible two dimensional elasticity this analogy in turn opens the way for the application of diamond approximation schemes hauret et al 2 to kirchhoff plate theory we show that a special class of meshes derived from an arbitrary triangulation of the domain the diamond meshes results in the automatic satisfaction of the corresponding inf sup condition for kirchhoff plate theory the attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests we also provide a reinterpretation of the diamond approximation scheme for kirchhoff plate theory within the framework of discrete mechanics in this interpretation the discrete moment equilibrium problem is formally identical to the classical continuous problem and the two differ only in the choice of differential structures it also follows that the satisfaction of the inf sup condition is a property of the cohomology of a certain discrete transverse differential complex this close connection between the classical inf sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems