a posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions in this paper we shall derive a posteriori error estimates in the l 1 norm for upwind finite volume schemes for the discretization of nonlinear conservation laws on unstructured grids in multi dimensions this result is mainly based on some fundamental a priori error estimates published in a recent paper by c chainais hillairet the theoretical results are confirmed by numerical experiments

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

an application of maximum likelihood and generalized estimating equations to the analysis of ordinal data from a longitudinal study with cases missing at random data are analysed from a longitudinal psychiatric study in which there are no dropouts that do not occur completely at random a marginal proportional odds model is fitted that relates the response severity of side effects to various covariates two methods of estimation are used generalized estimating equations gee and maximum likelihood ml both the complete set of data and the data from only those subjects completing the study are analysed for the completers only data the gee and ml analyses produce very similar results these results differ considerably from those obtained from the analyses of the full data set there are also marked differences between the results obtained from the gee and ml analysis of the full data set the occurrence of such differences is consistent with the presence of a non completely random dropout process and it can be concluded in this example that both the analyses of the completers only and the gee analysis of the full data set produce misleading conclusions about the relationships between the response and covariates

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

risk averse pde constrained optimization using the conditional value at risk uncertainty is inevitable when solving science and engineering application problems in the face of uncertainty it is essential to determine robust and risk averse solutions in this work we consider a class of pde constrained optimization problems in which the pde coefficients and inputs may be uncertain we introduce two approximations for minimizing the conditional value at risk cvar for such pde constrained optimization problems these approximations are based on the primal and dual formulations of cvar for the primal problem we introduce a smooth approximation of cvar in order to utilize derivative based optimization algorithms and to take advantage of the convergence properties of quadrature based discretizations for this smoothed cvar we prove differentiability as well as consistency of our approximation for the dual problem we regularize the inner maximization problem rigorously derive optimality conditions and demonstrate the consistency of our approximation furthermore we propose a

modelling progression of cd4 lymphocyte count and its relationship to survival time the purpose of this article is to model the progression of cd4 lymphocyte count and the relationship between different features of this progression and survival time the complicating factors in this analysis are that the cd4 lymphocyte count is observed only at certain fixed times and with a high degree of measurement error and that the length of the vector of observations is determined in part by the length of survival if probability of death depends on the true unobserved cd4 lymphocyte count then the survival process must be modelled wu and carroll 1988 biometrics 44 175 188 proposed a random effects model for two sample longitudinal data in the presence of informative censoring in which the individual effects included only slopes and intercepts we propose methods for fitting a broad class of models of this type in which both the repeated cd4 lymphocyte counts and the survival time are modelled using random effects these methods permit us to estimate parameters describing the progression of cd4 lymphocyte count as well as the effect of differences in the cd4 trajectory on survival we apply these methods to results of aids clinical trials

error estimates for a finite difference scheme associated with hamilton jacobi equations on a junction this paper is concerned with monotone time explicit finite difference schemes associated with first order hamilton jacobi equations posed on a junction they extend the schemes recently introduced by costeseque lebacque and monneau 2013 to general junction conditions on the one hand we prove the convergence of the numerical solution towards the viscosity solution of the hamilton jacobi equation as the mesh size tends to zero for general junction conditions on the other hand we derive optimal error estimates of order delta x frac 1 2 in l loc infty for junction conditions of optimal control type at least if the flux is strictly limited

dynamic multi source x ray tomography using a spacetime level set method a novel variant of the level set method is introduced for dynamic x ray tomography the target is allowed to change in time while being imaged by one or several source detector pairs at a relatively high frame rate the algorithmic approach is motivated by the results in 22 showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography furthermore defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here the tomographic reconstruction is found as a minimizer of a nonlinear functional the functional contains a regularization term penalizing the l 2 norms of up to n derivatives of the reconstruction the case n 1 is shown to be equivalent to a convex tikhonov problem that has a unique minimizer for n 2 the existence of a minimizer is proved under certain assumptions on the signal to noise ratio and the size of the regularization parameter numerical examples with both simulated and measured dynamic x ray data are included and the proposed method is found to yield reconstructions superior to standard methods such as fbp or non negativity constrained tikhonov regularization and favorably comparable to those of total variation regularization furthermore the methodology can be adapted to a wide range of measurement arrangements with one or more x ray sources

robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions a simulation study repeated measurements of surrogate markers are frequently used to track disease progression but these series are often prematurely terminated due to disease progression or death analysing such data through standard likelihood based approaches can yield severely biased estimates if the censoring mechanism is non ignorable motivated by this problem we have proposed the bivariate joint multivariate random effects jmre model which has shown that when correctly specified it performs well in terms of bias reduction and precision the bivariate jmre model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers evolution are linked through a multivariate normal distribution of random effects as in every parametric model robustness under violations of its distributional assumptions is of great importance in this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy tailed distribution two skewed distributions or a mixture of two normal distributions moreover we generated data where level 1 errors or residuals in the survival part of the model follow a skewed distribution further sensitivity analysis on the effects of reduced sample size increased level 1 variances and altered fixed effects values was also performed we found that fixed effects estimates are almost unaffected but their standard errors ses may be underestimated especially under heavily skewed distributions the proposed model seems robust enough but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation

breather and soliton wave families for the sine gordon equation the approach of steuerwaldlamb for obtaining exact solutions of the sinegordon equation is further developed through transformations by means of which complicated solutions of the corresponding odes are obtained without any explicit integration polynomial and nonpolynomial transformations are discussed and several of them are used to obtain breather and soliton solutions of the sinegordon equation the obtained solutions are discussed from the point of view of the electrodynamics of the long josephson junction

an engquist osher type scheme for conservation laws with discontinuous flux adapted to flux connections we consider scalar conservation laws with the spatially varying flux h x f u 1 h x g u where h x is the heaviside function and f and g are smooth nonlinear functions adimurthi mishra and veerappa gowda j hyperbolic differ equ 2 2005 pp 783 837 pointed out that such a conservation law admits many l 1 contraction semigroups one for each so called connection a b here we define entropy solutions of type a b involving kruzkov type entropy inequalities that can be adapted to any fixed connection a b it is proved that these entropy inequalities imply the l 1 contraction property for l infty solutions in contrast to the piecewise smooth setting of adimurthi mishra and veerappa gowda for a fixed connection these entropy inequalities include a single adapted entropy of the type used by audusse and perthame proc roy soc edinburgh sect a 135 2005 pp 253 265 we prove convergence of a new difference scheme that approximates entropy solutions of type a b for any connection a b if a few parameters are varied the scheme relies on a modification of the standard engquist osher flux is simple as no 2 times2 riemann solver is involved and is designed such that the steady state solution connecting a to b is preserved in contrast to most analyses of similar problems our convergence proof is not based on the singular mapping or compensated compactness methods but on standard spatial variation estimates away from the flux discontinuity some numerical examples are presented

finite volume schemes for locally constrained conservation laws this paper is devoted to the numerical analysis of the road traffic model proposed by colombo and goatin j differ equ 234 2 654 675 2007 the model involves a standard conservation law supplemented by a local unilateral constraint on the flux at the point x 0 modelling a road light a toll gate etc we first show that the problem can be interpreted in terms of the theory of conservation laws with discontinuous flux function as developed by adimurthi et al j hyperbolic differ equ 2 4 783 837 2005 and burger et al siam j numer anal 47 3 1684 1712 2009 we reformulate accordingly the notion of entropy solution introduced by colombo and goatin j differ equ 234 2 654 675 2007 and extend the well posedness results to the l framework then starting from a general monotone finite volume scheme for the non constrained conservation law we produce a simple scheme for the constrained problem and show its convergence the proof uses a new notion of entropy process solution numerical examples modelling a green wave are presented

impact of missing data due to drop outs on estimators for rates of change in longitudinal studies a simulation study many cohort studies and clinical trials are designed to compare rates of change over time in one or more disease markers in several groups one major problem in such longitudinal studies is missing data due to patient drop out the bias and efficiency of six different methods to estimate rates of changes in longitudinal studies with incomplete observations were compared generalized estimating equation estimates gee proposed by liang and zeger 1986 unweighted average of ordinary least squares olse of individual rates of change uwls weighted average of olse wls conditional linear model estimates cle a covariate type estimates proposed by wu and bailey 1989 random effect re and joint multivariate re jmre estimates the latter method combines a linear re model for the underlying pattern of the marker with a log normal survival model for informative drop out process the performance of these methods in the presence of missing data completely at random mcar at random mar and non ignorable nim were compared in simulation studies data for the disease marker were generated under the linear random effects model with parameter values derived from realistic examples in hiv infection rates of drop out assumed to increase over time were allowed to be independent of marker values or to depend either only on previous marker values or on both previous and current marker values under macr all six methods yielded unbiased estimates of both group mean rates and between group difference however the cross sectional view of the data in the gee method resulted in seriously biased estimates under mar and nim drop out process the bias in the estimates ranged from 30 per cent to 50 per cent the degree of bias in the gee estimates increases with the severity of non randomness and with the proportion of mar data under mcar and mar all the other five methods performed relatively well re and jmre estimates were more efficient that is had smaller variance than uwls wls and cl estimates under nim wls and particularly re estimates tended to underestimate the average rate of marker change bias approximately 10 per cent under nim uwls cl and jmre performed better in terms of bias 3 5 per cent with the jmre giving the most efficient estimates given that markers are key variables related to disease progression missing marker data are likely to be at least mar thus the gee method may not be appropriate for analysing such longitudinal marker data the potential biases due to incomplete data require greater recognition in reports of longitudinal studies sensitivity analyses to assess the effect of drop outs on inferences about the target parameters are important

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

a theory of l 1 dissipative solvers for scalar conservation laws with discontinuous flux we propose a general framework for the study of l1 contractive semigroups of solutions to conservation laws with discontinuous flux u t mathfrak f x u x 0 qquad mathfrak f x u left begin array ll f l u x 0 end array right quad quad quad rm cl where the fluxes fl fr are mainly assumed to be continuous developing the ideas of a number of preceding works baiti and jenssen in j differ equ 140 1 161 185 1997 towers in siam j numer anal 38 2 681 698 2000 towers in siam j numer anal 39 4 1197 1218 2001 towers et al in skr k nor vidensk selsk 3 1 49 2003 adimurthi et al in j math kyoto university 43 1 27 70 2003 adimurthi et al in j hyperbolic differ equ 2 4 783 837 2005 audusse and perthame in proc roy soc edinburgh a 135 2 253 265 2005 garavello et al in netw heterog media 2 159 179 2007 burger et al in siam j numer anal 47 1684 1712 2009 we claim that the whole admissibility issue is reduced to the selection of a family of elementary solutions which are piecewise constant weak solutions of the form c x c l11 left x 0 right we refer to such a family as a germ it is well known that cl admits many different l1 contractive semigroups some of which reflect different physical applications we revisit a number of the existing admissibility or entropy conditions and identify the germs that underly these conditions we devote specific attention to the vanishing viscosity germ which is a way of expressing the condition of diehl j hyperbolic differ equ 6 1 127 159 2009 for any given germ we formulate germ based admissibility conditions in the form of a trace condition on the flux discontinuity line x 0 in the spirit of vol pert math ussr sbornik 2 2 225 267 1967 and in the form of a family of global entropy inequalities following kruzhkov math ussr sbornik 10 2 217 243 1970 and carrillo arch ration mech anal 147 4 269 361 1999 we characterize those germs that lead to the l1 contraction property for the associated admissible solutions our approach offers a streamlined and unifying perspective on many of the known entropy conditions making it possible to recover earlier uniqueness results under weaker conditions than before and to provide new results for other less studied problems several strategies for proving the existence of admissible solutions are discussed and existence results are given for fluxes satisfying some additional conditions these are based on convergence results either for the vanishing viscosity method with standard viscosity or with specific viscosities adapted to the choice of a germ or for specific germ adapted finite volume schemes

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

pattern mixture models for multivariate incomplete data with covariates pattern mixture models stratify incomplete data by the pattern of missing values and formulate distinct models within each stratum pattern mixture models are developed for analyzing a random sample on continuous variables y 1 y 2 when values of y 2 are nonrandomly missing methods for scalar y 1 and y 2 are here generalized to vector y 1 and y 2 with additional fixed covariates x parameters in these models are identified by alternative assumptions about the missing data mechanism models may be underidentified in which case additional assumptions are needed just identified or overidentified maximum likelihood and bayesian methods are developed for the latter two situations using the em and sem algorithms direct and interactive simulation methods the methods are illustrated on a data set involving alternative dosage regimens for the treatment of schizophrenia using haloperidol and on a regression example sensitivity to alternative assumptions about the missing data mechanism is assessed and the new methods are compared with complete case analysis and maximum likelihood for a probit selection model

linearly divergent treatment effects in clinical trials with repeated measures efficient analysis using summary statistics in many randomized clinical trials with repeated measures of a response variable one anticipates a linear divergence over time in the difference between treatments this paper explores how to make an efficient choice of analysis based on individual patient summary statistics with the objective of estimating the mean rate of treatment divergence the simplest choice of summary statistic is the regression coefficient of response on time for each subject slope the gains in statistical efficiency imposed by adjusting for the observed pre treatment levels or even better the estimated intercepts are clarified in the process we develop the optimal linear summary statistic for any repeated measures design with assumed known covariance structure and shape of true mean treatment difference over time statistical power considerations are explored and an example from an asthma trial is used to illustrate the main points

discrimination power of measures for nonlinearity in a time series the performance of a number of different measures of nonlinearity in a time series is compared numerically their power to distinguish noisy chaotic data from linear stochastic surrogates is determined by monte carlo simulation for a number of typical data problems the main result is that the ratings of the different measures vary from example to example it therefore seems preferable to use an algorithm with good overall performance that is higher order autocorrelations or nonlinear prediction errors

adaptation and its impact on the dynamics of a system of three competing populations abstract we investigate how the adaptation of the competition coefficients of the competing populations for the same limited resource influences the system dynamics in the regions of the parameter space where chaotic motion of shilnikov kind exists we present results for two characteristic values of the competition coefficient adaptation factor the first value 0 05 belongs to the small interval of possible negative values of for this a transition to chaos by period doubling bifurcations occurs and a window of periodic motion exists between the two regions of chaotic motion with increasing the system becomes more dissipative and the number of the windows of periodic motion increases when 1 0 a region of transient chaos is observed after the last window of periodic motion we verify the picture of the system dynamics by power spectra histograms and autocorrelations and calculate the lyapunov exponents and kaplan yorke dimension finally we discuss the eligibility of the investigated system for a topological analysis

higher order regularization based image restoration with automatic regularization parameter selection abstract poisson and multiplicative rayleigh noises often appear in medical imaging such as x ray images positron emission tomography and ultrasound images in this study we propose novel variational models for removing poisson multiplicative rayleigh noise we make use of hybrid higher order total variation as the regularization terms of our proposed models to eliminate staircasing artifacts we also adopt the spatially adaptive parameter technique to adequately smooth homogenous regions while preserving the edges the spatially adaptive parameter selection is closely related to local constraints through a local expected value estimator we provide a convergence analysis including the existence and uniqueness of solution and the first order optimality conditions we apply the alternating direction method of multipliers for solving the proposed models numerical experiments demonstrate that our models exhibit a better performance than that of state of the art models in terms of edge preservation smoothness of the homogenous regions and various quality measures

first order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality so called elliptic mpecs are formulated in reflexive banach spaces with the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures variational analytic concepts are both applied and further developed the paper is split into two main parts the first part concerns the derivation of conditions in which the lower level state constraints are assumed to be polyhedric sets this part is then completed by two examples the latter of which involves pointwise bilateral bounds on the gradient of the state the second part focuses on an important nonpolyhedric example namely when the lower level state constraints are presented by pointwise bounds on the euclidean norm of the gradient of the state a formula for the second order mosco epiderivative of the indicator function for this convex set is derived this result is then used to demonstrate the hadamard directional differentiability of the solution mapping of the variational inequality which then leads to the derivation of explicit strong stationarity conditions for this problem

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

a simulation study of estimators for rates of change in longitudinal studies with attrition many longitudinal studies and clinical trials are designed to compare rates of change over time in one or more outcome variables in several groups most such studies have incomplete data because some patients drop out before completing the study the missing data may induce bias and inefficiency in naive estimates of important parameters this paper uses monte carlo methods to compare the bias and efficiency of several two stage estimators of the effect of treatment on the mean rate of change when the missing data arise from one of four processes we also study the validity of confidence intervals and the power of hypothesis tests based on these estimates and their standard errors in general the weighted least squares estimator does relatively well as does an analysis of covariance type estimator proposed by wu et al the best estimates of variance components are based on complete cases or maximum likelihood

population dynamics in presence of state dependent fluctuations we discuss a model of a system of interacting populations for the case when i the growth rates and the coefficients of interaction among the populations depend on the populations densities and ii the environment influences the growth rates and this influence can be modelled by a gaussian white noise the system of model equations for this case is a system of stochastic differential equations with i deterministic part in the form of polynomial nonlinearities and ii state dependent stochastic part in the form of multiplicative gaussian white noise we discuss both the cases when the formal integration of the stochastic differential equations leads i to integrals of ito kind or ii to integrals of stratonovich kind the systems of stochastic differential equations are reduced to the corresponding fokker planck equations for the ito case and for the case of 1 population analytic results are obtained for the stationary p d f of the population density for the case of more than one population and for both the ito case and stratonovich case the detailed balance conditions are not satisfied as a result the exact analytic solutions of the corresponding fokker planck equations for the stationary p d f s for the population densities are not known we obtain approximate solutions for this case by the method of adiabatic elimination

existence uniqueness and stability of solutions of generalized tikhonov phillips functionals abstract the tikhonov phillips method is widely used for regularizing ill posed inverse problems mainly due to the simplicity of its formulation as an optimization problem the use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety of other methods which can be considered as variants of the traditional tikhonov phillips method of order zero such is the case for instance of the tikhonov phillips method of order one the total variation regularization method etc in this article we find sufficient conditions on the penalizers in generalized tikhonov phillips functionals which guarantee existence uniqueness and stability of the minimizers the particular cases in which the penalizers are given by the bounded variation norm by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators are studied several examples are presented and a few results on image restoration are shown

extended simplest equation method for nonlinear differential equations abstract the modified simplest equation method to look for the exact solutions of the nonlinear differential equations is presented our approach is applied to search for the exact solutions of the sharma tasso olver and the burgers huxley equations the new exact solutions of these equations are obtained

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

optimal profiles in a phase transition model with a saturating flux abstract it is well known that for the allen cahn equation the minimizing transition in an infinite cylinder r is one dimensional and unique up to a translation in the first variable we analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase separation model with a saturating flux this amounts to consider transitions in the space of bv functions as we consider the area integral instead of the dirichlet energy to penalize the creation of wild interfaces

error estimate for godunov approximation of locally constrained conservation laws we consider a model of traffic flow with unilateral constraint on the flux introduced by colombo and goatin j differential equations 234 2007 pp 654 675 for which the convergence of numerical approximation using monotone finite volume schemes has been performed by andreianov goatin and seguin numer math 115 2010 pp 609 645 we derive for this problem a new rm bv estimate and make use of it to provide an error estimate for the godunov approximation of the problem of order h 1 3 that is improved into the optimal order h 1 2 under a reasonable assumption numerical experiments are then provided to illustrate the optimality of the result

existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity the inverse balancing method for the determination of the necessary conditions of existence of solitary solutions to mth order differential equations with nth order polynomial nonlinearity is presented in this paper it is shown that the order of possible solitary solutions does not increase if orders of the differential equation and the polynomial nonlinearity increase furthermore the relationships between the order of the solitary solution and the order of the equation and the nonlinearity are given in the explicit form

a note on the bias of estimators with missing data it is well known that many standard analyses including maximum likelihood estimation and the generalized estimating equation approach liang and zeger 1986 biometrika 73 13 22 can result in biased estimation when there are missing observations in such cases it is of interest to calculate the magnitude of the bias incurred under specific assumptions about the process generating the full data and the nonresponse mechanism in this paper we give a condition that identifies the limit in probability of estimators that are solutions of estimating equations computed from the incomplete data with discrete data this condition suggests a simple algorithm to compute the asymptotic bias of these estimators that can be easily implemented with existing statistical software we illustrate our approach with asthma prevalence data in children

solitary wave solutions for nonlinear partial differential equations that contain monomials of odd and even grades with respect to participating derivatives the method of simplest equation is applied to nonlinear pdes the pdes contain monomials of odd and even order with respect to derivatives solitary wave solutions are studied numerous examples of the methodology are presented we apply the method of simplest equation for obtaining exact solitary traveling wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives we consider first the general case of presence of monomials of the both odd and even grades and then turn to the two particular cases of nonlinear equations that contain only monomials of odd grade or only monomials of even grade the methodology is illustrated by numerous examples

estimation and comparison of changes in the presence of informative right censoring conditional linear model a general linear regression model for the usual least squares estimated rate of change slope on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups two noniterative estimators for the group slope means the linear minimum variance unbiased lmvub estimator and the linear minimum mean squared error lmmse estimator are proposed under this conditional model in realistic situations we illustrate that the lmvub and lmmse estimators derived under a simple linear regression model are quite competitive compared to the pseudo maximum likelihood estimator pmle derived by modeling the censoring probabilities generalizations to polynomial response curves and general linear models are also described

on boundary detachment phenomena for the total variation flow with dynamic boundary conditions abstract we combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions we analyze the behavior of facets at the parts of the boundary where these conditions are imposed we devote particular attention to the radially symmetric data we observe that the boundary layer detachment actually can happen at concave parts of the boundary

a well posed conservation law with a variable unilateral constraint this paper considers the cauchy problem for a conservation law with a variable unilateral constraint its motivation being for instance the modeling of a toll gate along a highway this problem is solved by means of nonclassical shocks and its well posedness is proved then the solutions so obtained are shown to coincide with the limits of the classical solutions to suitable conservation laws with discontinuous flux function that approximate the constrained problem

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method in this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies

a test of the missing data mechanism for repeated categorical data due to the occurrence of missing observations longitudinal data are rarely balanced and complete weighted least squares analyses described by grizzle starmer and koch 1969 biometrics 25 489 504 have been developed for the analysis of incomplete longitudinal categorical data stanish gillings and koch 1978 biometrics 34 305 317 woolson and clarke 1984 journal of the royal statistical society series a 147 87 99 however all these analyses have assumed that missing observations are missing completely at random in the sense of rubin 1976 biometrika 63 581 592 when the occurrence of missing observations is related to the unobserved response values these analyses may result in biased results in this paper we develop a simple and practical test of the missing mechanism in incomplete repeated categorical data the proposed test is an extension of the test of little 1988 journal of the american statistical association 83 1198 1202 and uses a test criterion given in general form by wald the test is illustrated using data from a longitudinal investigation of obesity in school age children

new class of running wave solutions of the 2 1 dimensional sine gordon equation a new class of running wave solutions of the 2 1 dimensional sine gordon equation is investigated the obtained waves require two spatial dimensions for their propagation i e they generalize solutions of the 2 0 dimensional sine gordon equation the parameters of the waves strongly depend on the wave amplitude and there exist forbidden areas for the wavenumber and frequency the obtained solutions describe a new class of josephson waves whose velocity is smaller than the swihart velocity if omega 0 the running waves are reduced to the self consistent phase current and magnetic field distributions in a large two dimensional josephson junction the self restriction coefficient for the josephson current corresponding to one of the structures is calculated

on nonlinear population waves we discuss a model system of partial differential equations for description of the spatio temporal dynamics of interacting populations we are interested in the waves caused by migration of the populations we assume that the migration is a diffusion process influenced by the changing values of the birth rates and coefficients of interaction among the populations for the particular case of one population and one spatial dimension the general model is reduced to analytically tractable pde with polynomial nonlinearity up to 4th order we investigate this particular case and obtain two kinds of solutions i approximate solution for small value of the ratio between the coefficient of diffusion and the wave velocity and ii exact solutions which describe nonlinear kink and solitary waves in an appropriate phase space the kinks correspond to a connection between two states represented by a saddle point and a stable node finally we derive conditions for the asymptotic stability of the obtained solutions

modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations we discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities as simplest equation we use differential equation for a special function that contains as particular cases trigonometric and hyperbolic functions as well as the elliptic function of weierstrass and jacobi we show that for this case the studied class of nonlinear partial differential equations can be reduced to a system of two equations containing polynomials of the unknown functions this system may be further reduced to a system of nonlinear algebraic equations for the parameters of the solved equation and parameters of the solution any nontrivial solution of the last system leads to a traveling wave solution of the solved nonlinear partial differential equation the methodology is illustrated by obtaining solitary wave solutions for the generalized korteweg devries equation and by obtaining solutions of the higher order korteweg devries equation

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

traveling waves and statistical distributions connected to systems of interacting populations we discuss the following two issues from the dynamics of interacting populations i density waves for the case or negligible random fluctuations of the population densities ii probability distributions connected to the model equations for spatially averaged population densities for the case of significant random fluctuations of the independent quantity that can be associated with the population density for the case of issue i we consider model equations containing polynomial nonlinearities such nonlinearities arise as a consequence of interaction among the populations for the case of large population densities or as a result of a taylor series expansion for the case of small density of interacting populations by means of the modified method of the simplest equation we obtain exact traveling wave solutions of the model equations and these solution for the case of issue ii we discuss model equations of the fokker planck kind for the evolution of the statistical distributions of population densities we derive a few stationary distributions for the population density and calculate the expected exit time associated with the extinction of the studied population

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

statistical distributions connected to motion of substance in a channel of a network abstract we discuss a model of motion of substance through the nodes of a channel of a network the channel can be modeled by a chain of urns where each urn can exchange substance with the neighboring urns in addition the urns can exchange substance with the network nodes and the extension of the model with respect to the previous research is that we consider also the possibility for exchange of substance among the urns and the environment of the network we consider stationary regime of motion of substance through a finite channel stationary regime of exchange of substance along the chain of urns and obtain a class of statistical distributions for the substance in the channel our attention is concentrated on this class of distributions and we show that for the case of finite channel the class of distributions contains as particular cases truncated versions of the families of distributions of katz ord kemp etc several characteristics of the obtained class of distributions are calculated the theory for the case of chain containing infinite number of urns is presented in the appendix

nonlinear stochastic partial differential equations with singular diffusivity and gradient stratonovich noise abstract we study existence and uniqueness of a variational solution in terms of stochastic variational inequalities svi to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative stratonovich gradient type noise we derive a commutator relation for the unbounded noise coefficients in terms of a geometric killing vector condition the drift term is given by the total variation flow respectively by a singular p laplace type operator we impose nonlinear zero neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise this solves an open problem posed in barbu et al 2013 7 and barbu and rockner 2015 10

application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring we apply parametric empirical bayes inference of morris7 to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative that is the length of time the subjects participate in the study is associated with level of the study variable ignoring such an association can result in a biased estimate of rate of change the proposed method provides estimates of rate of change for individual subjects as well as for the entire group adjusted for informative right censoring the method is considered more robust than those based on a specific parametric model for the censoring distribution under non informative right censoring these estimators of slopes are equivalent to the bayes estimators derived by fearn 11 we illustrate the method with an example involving renal transplant data we evaluate the method s performance through a simulation study

upper bounds on convective heat transport in a rotating fluid layer of infinite prandtl number case of intermediate taylor numbers by means of the howard busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a heated from below layer of fluid of infinite prandtl number rotating with a constant angular velocity about the vertical axis we consider the region of intermediate taylor numbers alpha41 ta alpha61 where alpha 1 is the wave number connected to the 1 alpha solution of the variational problem the studied optimum fields possess a three layer or four layer structure in addition to the internal intermediate and boundary layers ekman layers could arise between the intermediate and boundary ones for the discussed interval of taylor numbers the intermediate layers do not expand in the direction of the internal layers we present an asymptotic theory for the case of the fluid layer with rigid lower boundary and stress free upper boundary we use an improved solution of the euler lagrange equations of the variational problem for the intermediate sublayer of the optimum field this solution leads also to correction of the thicknesses of the boundary layers and to lowering of the upper bounds on the convective heat transport for the cases of fluid layer with stress free or with rigid boundaries thus the known upper bounds for these cases can be treated as upper bounds on the upper bounds on the convective heat transport for the case of the fluid layer with stress free boundaries the four layer optimum fields leads to bounds on the convective heat transport which change from r 1 3 at the lower boundary of their interval of validity to values slightly large than r 2 7 near the upper boundary of the interval of validity finally we discuss the area of application of the obtained bounds with respect to the taylor number ta and rayleigh number r

modified method of simplest equation and its application to nonlinear pdes abstract we search for traveling wave solutions of the class of pdes p 1 n 1 a p q p q t p r 2 n 2 b r q q t r s 1 n 3 c s q s q x s u 2 n 4 d u q q x u f q 0 where a p q b r q c s q d u q and f q are polynomials of q the basis of the investigation is a modification of the method of simplest equation the equations of bernoulli riccati and the extended tanh function equation are used as simplest equations the obtained general results are illustrated by obtaining exact solutions of versions of the generalized kuramoto sivashinsky equation reaction diffusion equation with density dependent diffusion and the reaction telegraph equation

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