analysis of the parareal time parallel time integration method the parareal algorithm is a method to solve time dependent problems parallel in time it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time in this paper the relation of the parareal algorithm to space time multigrid and multiple shooting methods is first briefly discussed the focus of the paper is on new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals and linear convergence for unbounded intervals

composite linear models for incomplete multinomial data a composite linear model clm is a matrix model for incomplete multinomial data a clm provides a unified approach for maximum likelihood inference which is applicable to a wide variety of problems involving incomplete multinomial data by formulating a model as a clm one can simplify computation of maximum likelihood estimates and asymptotic standard errors as an example we use clm to test marginal homogeneity for ordered categories subject to both ignorable and non ignorable missing data mechanisms

a non hopfian almost convex group in this article we prove that an isometric multiple hnn extension of a group satisfying the falsification by fellow traveler property is almost convex as a corollary wise s example of a cat 0 non hopfian group is almost convex

rewriting systems in sufficiently large artin tits groups abstract a conjecture of dehornoy claims that given a presentation of an artin tits group every word that represents the identity can be transformed into the trivial word using the braid relations together with certain rules between pairs of words that are not both positive that can be derived directly from the braid relations as well as free reduction but without introducing trivial factors s s 1 or s 1 s this conjecture is known to be true for artin tits groups of spherical type or of fc type we prove the conjecture for artin tits groups of sufficiently large type

adjustment for non differential misclassification error in the generalized linear model it is well known that estimates of association between an outcome variable and a set of categorical covariates some of which are measured with misclassification tend to be biased upon application of the usual methods of estimation that ignore the classification error we propose a method to adjust for misclassification in covariates when one applies the generalized linear model in the case where one can observe some true covariates only through surrogates we combine a latent class analysis with the approach to incorporate multiple surrogates into the model we include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution we provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework

small cancellation theory and automatic groups part ii the main results obtained in part i can be rephrased in the language of root systems and euclidean planar tessellations as saying that finite a1 x a1 and a 2 piecewise euclidean abbreviated pe complexes of non positive curvature have automatic fundamental groups a 2 dimensional complex is a a 1 a1 respectively a2 pe complex if every 2 cell can be identified with a unit square resp equilateral triangle in the euclidean plane in such a way that the induced metrics agree on intersections such a complex has non positive curvature if the link of each vertex contains no circuits without backtracking of length less than 2 n here we prove using similar techniques that finite 2 complexes modelled on the other two root systems b 2 and g2 corresponding to tessellations by 45 right angle triangles and by 30 60 right angle triangles also have automatic fundamental groups theorems 2 3 and 3 2 to be precise

nonparametric regression estimates using misclassified binary responses summary for random design nonparametric regression in the case that the responses are binary and subject to misclassification the performance of the kernel estimator is investigated the kernel estimator is generally biased for the local proportion to adjust for the bias the double sampling scheme of tenenbein 1970 1971 is considered a plugged in kernel estimator and an imputed kernel estimator which adjust for the effect of misclassification on the kernel estimator are proposed and their asymptotic mean squared errors are analysed the plugged in kernel estimator is better than the simple kernel estimator which uses only the data without misclassification in the validation subsample in the sense of having smaller asymptotic mean squared error however the imputed kernel estimator has smaller asymptotic variance if the misclassification probabilities are constant then the two proposed estimators have the same asymptotic bias in this case the imputed kernel estimator is always better than the plugged in kernel estimator for general misclassification probabilities the asymptotic biases of the two proposed estimators are not comparable in magnitude however our simulation results demonstrate that even when the misclassification probabilities are not constant the imputed kernel estimator is still better for reasonable sample sizes

bounded rank subgroups of coxeter groups artin groups and one relator groups with torsion we obtain a number of results regarding the freeness of subgroups of coxeter groups artin groups and one relator groups with torsion in the case of coxeter groups we also obtain results on quasiconvexity and subgroup separability

rapid decay and baum connes for large type artin groups we prove that many artin groups of large type satisfy the rapid decay property including all those of extra large type for many of these including all 3 generator groups of extra large type a result of lafforgue applies to show that the groups satisfy the baum connes conjecture without coefficients our proof of rapid decay combines elementary analysis with combinatorial techniques and relies on properties of geodesic words in artin groups of large type that were observed in earlier work by two of the authors of this current article

bayesian analysis of multivariate probit models with surrogate outcome data a new class of parametric models that generalize the multivariate probit model and the errors in variables model is developed to model and analyze ordinal data a general model structure is assumed to accommodate the information that is obtained via surrogate variables a hybrid gibbs sampler is developed to estimate the model parameters to obtain a rapidly converged algorithm the parameter expansion technique is applied to the correlation structure of the multivariate probit models the proposed model and method of analysis are demonstrated with real data examples and simulation studies

small cancellation groups and translation numbers in this paper we prove that c 4 t 4 p c 3 t 6 p and c 6 p small cancellation groups are translation discrete in the strongest possible sense and that in these groups for any g and any n there is an algorithm deciding whether or not the equation xn g has a solution there is also an algorithm for calculating for each g the maximum n such that g is an n th power of some element we also note that these groups cannot contain isomorphic copies of the group of p adic fractions and so in particular of the group of rational numbers besides we show that for c 4 t 4 and c 3 t 6 groups all translation numbers are rational and have bounded denominators

hyperbolic groups and their quotients of bounded exponents in 1987 gromov conjectured that for every non elementary hyperbolic group g there is an n n g such that the quotient group g gn is infinite the article confirms this conjecture in addition a description of finite subgroups of g gn is given it is proven that the word and conjugacy problem are solvable in g gn and that k 1g k 1 the proofs heavily depend upon prior authors results on the gromov conjecture for torsion free hyperbolic groups and on the burnside problem for periodic groups of even exponents

estimating odds ratios adjusting for misclassification in alzheimer s disease risk factor assessment epidemiological studies of alzheimer s disease and dementia are often two phase studies including a screening phase and a clinical assessment phase it is common to interview a relative of the subject at each of these phases to obtain information about the subject s exposure to risk factors this can result in a misclassification error when assessing risk factors as the two responses of the relative often differ this is especially a problem for risk factors involving life style and family history which cannot be confirmed using the subject s medical records a naive analysis using data from each phase separately would give two different estimates of the odds ratio both estimates could be biased in this paper we extend the estimation methods adjusting for misclassification developed by liu and liang to data collected through two phase sampling we first use a latent class analysis and the em algorithm to estimate the misclassification parameters we then derive the maximum pseudo likelihood estimators conditional on the misclassification parameters to estimate the odds ratios accounting for the complex sampling study design we propose to use the jack knife estimator for estimation of the variances we apply the above method to data collected in the indianapolis ibadan dementia study to estimate the odds ratio for smoking adjusting for misclassification error

complex hyperbolic hyperplane complements we study spaces obtained from a complete finite volume complex hyperbolic n manifold m by removing a compact totally geodesic complex n 1 submanifold s the main result is that the fundamental group of m setminus s is relatively hyperbolic relative to fundamental groups of the ends of m setminus s and m setminus s admits a complete finite volume a regular riemannian metric of negative sectional curvature it follows that for n 1 the fundamental group of m setminus s satisfies mostow type rigidity has solvable word and conjugacy problems has finite asymptotic dimension and rapid decay property satisfies borel and baum connes conjectures is co hopf and residually hyperbolic has no nontrivial subgroups with property t and has finite outer automorphism group furthermore if m is compact then the fundamental group of m setminus s is biautomatic and satisfies strong tits alternative

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

computing the geometric intersection number of curves the geometric intersection number of a curve on a surface is the minimal number of self intersections of any homotopic curve i e of any curve obtained by continuous deformation given a curve c represented by a closed walk of length at most e on a combinatorial surface of complexity n we describe simple algorithms to 1 compute the geometric intersection number of c in o n e2 time 2 construct a curve homotopic to c that realizes this geometric intersection number in o n e4 time and 3 decide if the geometric intersection number of c is zero i e if c is homotopic to a simple curve in o n e log e time the algorithms for 2 and 3 are restricted to orientable surfaces but the algorithm for 1 is also valid on non orientable surfaces to our knowledge no exact complexity analysis had yet appeared on those problems an optimistic analysis of the complexity of the published algorithms for problems 1 and 3 gives at best a o n g2e2 time complexity on a genus g surface without boundary no polynomial time algorithm was known for problem 2 for surfaces without boundary interestingly our solution to problem 3 provides a quasi linear algorithm to a problem raised by poincare more than a century ago finally we note that our algorithm for problem 1 extends to computing the geometric intersection number of two curves of length at most e in o n e2 time

structural inference in transition measurement error models for longitudinal data we propose a new class of models transition measurement error models to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error we show that the response variable conditional on the error prone covariate follows a complex transition mixed effects model the naive model obtained by ignoring the measurement error correctly specifies the transition part of the model but misspecifies the covariate effect structure and ignores the random effects we next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes we show that the naive estimator of the regression coefficient of the error prone covariate is attenuated while the naive estimators of the regression coefficients of the past responses are generally inflated we then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method in view of the multidimensional integration required by full maximum likelihood estimation an em algorithm is developed to calculate maximum likelihood estimators in which monte carlo simulations are used to evaluate the conditional expectations in the e step we evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease an additional simulation study shows that the bayesian information criterion bic performs well in choosing the correct transition orders of the models

conditional resampling for misclassified multinomial data with applications to sampling inspection a conditional resampling methodology is proposed for improving the estimators of multinomial classification probabilities in the presence of a fallible classifier the unbiased estimator requires knowledge of the misclassification error rates which are obtained by resampling from the initial sample and applying an infallible classifier tenenbein s double sampling methodology resamples randomly from the initial sample we show that substantial gains in efficiency are obtainable if instead of simple random resampling different resampling rates are allowed for the fallibly determined classes in the initial sample in most situations this resampling methodology is neither more difficult nor more expensive than the double sampling methodology a very promising area of application of the proposed methodology is sampling inspection in quality control where products can either be classified quickly by inspectors or by a more thorough perhaps destructive inspection

determining the value of additional surrogate exposure data for improving the estimate of an odds ratio we consider the design of both cohort and case control studies in which an initial stage 1 sample of complete data on an error free disease indicator d a correct gold standard dichotomous exposure measurement x and an error prone exposure measurement z are available we calculate the amount of additional information on the odds ratio relating d to x that one can obtain from a second stage 2 sample of measurements only on d and z if one allows for differential measurement error in z there is often little advantage in having more than four times as much data in stage 2 data as in stage 1 with the assumption that a non differential measurement error model is reasonable larger amounts of stage 2 data can be useful simulations indicate that stage 1 samples of modest size 50 cases in case control studies and 50 failures in cohort studies yield sufficiently reliable estimates of needed parameters to assist in determining an appropriate size for the stage 2 sample these ideas apply in settings either where the amount of stage 1 data is limited and fixed by external constraints or where one has gathered stage 1 data in advance to avoid collecting superfluous stage 2 data

an algorithm with polylog parallel complexity for solving parabolic partial differential equations the standard numerical algorithms for solving parabolic partial differential equations are inherently sequential in the time direction this paper describes an algorithm for the time accurate solution of certain classes of parabolic partial differential equations that can be parallelized in both time and space it has a serial complexity that is proportional to the serial complexities of the best known algorithms the algorithm is a variant of the multigrid waveform relaxation method where the scalar ordinary differential equations that make up the kernel of computation are solved using a cyclic reduction type algorithm experimental results obtained on a massively parallel multiprocessor are presented

artin groups and infinite coxeter groups if the associated coxeter group 7 is finite for the braid group b the associated coxeter group is the symmetric group s brieskorn and saito 4 and independently deligne 6 have investigated artin groups of finite type in 1969 garside 7 solved the conjugacy problem for braid groups brieskorn this work was supported by nsf grants mcs 7902512 and mcs 7703452 the authors would like to thank the referee for an extremely careful reading of the paper and many helpful sugges tions

testing hypotheses with binary data subject to misclassification errors analysis and experimental design summary consider a binary random variable having outcomes subject to misclassification errors where the probabilities of misclassification errors depend on outcome the asymptotic relative efficiencies are derived for comparing two binomial populations comparing stratified binomial populations and for paired comparisons the probabilities of misclassification can vary with strata or be different for each pair the criterion for optimum experimental designs is shown to be the ratio of the asymptotic relative efficiency to expected cost per observation this criterion implies that mixtures of different experiments can never be optimal a number of experimental strategies is discussed

finite grobner shirshov bases for plactic algebras and biautomatic structures for plactic monoids this paper shows that every plactic algebra of finite rank admits a finite grobner shirshov basis the result is proved by using the combinatorial properties of young tableaux to construct a finite complete rewriting system for the corresponding plactic monoid which also yields the corollaries that plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right fp fp also answering a question of zelmanov we apply this rewriting system and other techniques to show that plactic monoids of finite rank are biautomatic

convergence analysis for three parareal solvers we analyze in this paper the convergence properties of the parareal algorithm for the symmetric positive definite problem mathbf u a mathbf u g the coarse propagator mathcal g is fixed to the backward euler method and three time integrators are chosen for the mathcal f propagator the trapezoidal rule the third order diagonal implicit runge kutta rk dirk method and the fourth order gauss rk method it is well known that the parareal euler algorithm using the backward euler method for mathcal f and mathcal g converges rapidly but less is known when one uses for mathcal f the trapezoidal rule or the fourth order gauss rk method especially when the mesh ratio j delta t delta t is small we show that for a specified lambda max the maximal eigenvalue of a or its upper bound there exists some critical j rm cri such that the parareal solvers derived from these three choices of mathcal f converge as fast as parareal euler provided j geq j rm cri

acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure abstract the paper presents the development and investigation of an adaptive smoothing as procedure in conjunction with the full multigrid full approximation storage method the latter has been previously implemented by the authors 1 for the incompressible navier stokes equations in conjunction with the artificial compressibility method and forms the basis for investigating the current as approach the principle of adaptive smoothing is to exploit the nonuniform convergence behavior of the numerical solution during the iterations to reduce the size of the computational domain and subsequently to reduce the total computing time the implementation of the as approach is investigated in conjunction with three different adaptivity criteria for two and three dimensional incompressible flows furthermore a dynamic procedure henceforth labeled dynamic adaptivity for defining variably the as parameters during the computation is also proposed and its performance is investigated in contrast to as with constant parameters henceforth labeled static adaptivity both static and dynamic adaptivity can provide similar acceleration but the latter additionally provides more stable numerical solutions and also requires less experimentation for optimizing the performance of the method numerical experiments are presented for attached and separated flows around airfoils as well as for three dimensional flow in a curved channel for external flows the as performs better when it is applied in all grid levels of the multigrid method while for internal flows the best performance is achieved when as is applied in the finest grid only overall the results show that substantial acceleration of multigrid computations can be achieved by using adaptive smoothing

tadpole labelled oriented graph groups and cyclically presented groups abstract we study a class of labelled oriented graph log group where the underlying graph is a tadpole graph we show that such a group is the natural hnn extension of a cyclically presented group and investigate the relationship between the log group and the cyclically presented group we relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented group implies solvability of the conjugacy problem for the log group in the case where the label on the tail of the log spells a positive word in the vertices in the circuit we show that the logs and groups coincide with those considered by szczepanski and vesnin we obtain new presentations for these cyclically presented groups and show that the groups of fibonacci type introduced by johnson and mawdesley are of this form these groups generalise the fibonacci groups and the sieradski groups and have been studied by various authors we continue these investigations using small cancellation and curvature methods to obtain results on hyperbolicity automaticity sq universality and solvability of decision problems

rational subgroups of biautomatic groups centralizers of finite subsets in biautomatic groups are them selves biautomatic every polycyclic subgroup of a biautomatic group is abelian by finite

multigrid method based on a space time approach with standard coarsening for parabolic problems in this work a space time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions in particular an adaptive smoothing strategy based on the degree of anisotropy of the discrete operator on each grid level is the basis of the proposed multigrid algorithm local fourier analysis is used for the selection of the crucial parameter defining such an adaptive smoothing approach central differences are used to discretize the spatial derivatives and both implicit euler and crank nicolson schemes are considered for approximating the time derivative for the solution of the second order scheme we apply a double discretization approach within the space time multigrid method the good performance of the method is illustrated through several numerical experiments

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

the triviality problem for profinite completions we prove that there is no algorithm that can determine whether or not a finitely presented group has a non trivial finite quotient indeed this property remains undecidable among the fundamental groups of compact non positively curved square complexes we deduce that many other properties of groups are undecidable for hyperbolic groups there cannot exist algorithms to determine largeness the existence of a linear representation with infinite image over any infinite field or the rank of the profinite completion

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

fourier mode analysis of multigrid methods for partial differential equations with random coefficients partial differential equations with random coefficients appear for example in reliability problems and uncertainty propagation models various approaches exist for computing the stochastic characteristics of the solution of such a differential equation in this paper we consider the spectral expansion approach this method transforms the continuous model into a large discrete algebraic system we study the convergence properties of iterative methods for solving this discretized system we consider one level and multi level methods the classical fourier mode analysis technique is extended towards the stochastic case this is done by taking the eigenstructure into account of a certain matrix that depends on the random structure of the problem we show how the convergence properties depend on the particulars of the algorithm on the discretization parameters and on the stochastic characteristics of the model numerical results are added to illustrate some of our theoretical findings

garside groups are strongly translation discrete abstract in this paper we show that all garside groups are strongly translation discrete that is the translation numbers of non torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r it is a consequence of the inequality inf s g inf s g n n inf s g 1 for a positive integer n and an element g of a garside group g where inf s denotes the maximal infimum for the conjugacy class we prove the inequality by studying the semidirect product g n z g n of the infinite cyclic group z and the cartesian product g n of a garside group g which turns out to be a garside group we also show that the root problem in a garside group g can be reduced to a conjugacy problem in g n hence the root problem is solvable for garside groups

average case complexity and decision problems in group theory abstract we investigate the average case complexity of decision problems for finitely generated groups in particular the word and membership problems using our recent results on generic case complexity we show that if a finitely generated group g has word problem solvable in subexponential time and has a subgroup of finite index which possesses a non elementary word hyperbolic quotient group then the average case complexity of the word problem of g is linear time uniformly with respect to the collection of all length invariant measures on g this results applies to many of the groups usually studied in geometric group theory for example all braid groups b n all groups of hyperbolic knots many coxeter groups and all artin groups of extra large type

hyperplane complements of large type let f2 be an open convex subset of a finite dimensional real vectorspace v and m a collection of linear hyperplanes we shall suppose that m is locally finite on f2 this means that each point of f2 has a neighborhood meeting only finitely many hyperplanes in m as in 2 chap 5 f2 is partitioned by m in facets recalling that a plinth is a codimension 2 facet we shall say that m is of large type on f2 if for each plinth p its multiplicity m m p c m 3 the main result of the paper is the following

an isoperimetric inequality for artin groups of finite type we show that artin groups of finite type satisfy a quadratic isoperimetric inequality moreover we describe an explicit algorithm to solve the word problem in quadratic time

high order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems high mixed order finite difference discretization of optimality systems arising from elliptic nonlinear constrained optimal control problems are discussed for the solution of these systems an efficient and robust multigrid algorithm is presented theoretical and experimental results show the advantages of higher order discretization and demonstrate that the proposed multigrid scheme is able to solve efficiently constrained optimal control problems also in the limit case of bang bang control

a space time multigrid method for parabolic partial differential equations we consider the solution of parabolic partial differential equations pdes in standard time stepping techniques multigrid can be used as an iterative solver for the elliptic equations arising at each discrete time step by contrast the method presented in this paper treats the whole of the space time problem simultaneously thus the multigrid operations of smoothing and coarse grid correction are defined on all of the space time variables of a given grid level the method is characterized by a coarsening strategy with prolongation and restriction operators which depend at each grid level on the degree of anisotropy of the discretization stencil numerical results for the one and two dimensional heat equations are presented and are shown to agree closely with predictions from fourier mode analysis

variance estimation for epidemiologic effect estimates under misclassification this paper presents basic methods for construction of variance estimators for epidemiologic effect estimates when adjusting for misclassification methods are described for differential and non differential misclassification and for external and internal estimates of classification rates the methods take account of sampling variability in both the observed data and the estimated classification rates the methods are illustrated in a case control analysis of the association of antibiotic use during pregnancy with sudden infant death syndrome

a general approach to categorical data analysis with missing data using generalized linear models with composite links a general approach for analyzing categorical data when there are missing data is described and illustrated the method is based on generalized linear models with composite links the approach can be used among other applications to fill in contingency tables with supplementary margins fit loglinear models when data are missing fit latent class models without or with missing data on observed variables fit models with fused cells including many models from genetics and to fill in tables or fit models to data when variables are more finely categorized for some cases than others both newton like and em methods are easy to implement for parameter estimation

parabolic subgroups of artin groups abstract let a be an artin system for x we denote by a x the subgroup of a generated by x such a group is called a parabolic subgroup of a we reprove van der lek s theorem a parabolic subgroup of an artin group is an artin group we give an algorithm which decides whether two parabolic subgroups of an artin group are conjugate let a be a finite type artin group and let a x be a parabolic subgroup with connected associated coxeter graph the quasi centralizer of a x in a is the set of in a such that x 1 x we prove that the commensurator of a x in a is equal to the normalizer of a x in a and that this group is generated by a x and the quasi centralizer of a x in a moreover if a x is not of type d l l 4 and l even then this group is generated by a x and the centralizer of a x in a

a new index of fit based on mixture methods for the analysis of contingency tables summary a framework based on mixture methods is proposed for evaluating goodness of fit in the analysis of contingency tables for a given model h applied to a contingency table p we consider the two point mixture p 1 r i1 ri2 with 7r the mixing proportion o r 1 and hi and i2 the tables of probabilities for each latent class or component in the unstructured approach recommended here the mixture model applies h to hi but does not impose any restrictions on i2 a contingency table p can generally be represented as such a two point mixture for an interval of 7r values we define our index of lack of fit ir to be the smallest such 7r i e 7r is the fraction of the population that cannot be described by model h this approach can be contrasted with the structured approach that applies model h to both h and i2 and leads to conventional latent class models when h is the hypothesis of independence the case where h is the hypothesis of row column independence and p is a two way contingency table is covered in detail but the procedure is quite general

thick metric spaces relative hyperbolicity and quasi isometric rigidity we study the geometry of non relatively hyperbolic groups generalizing a result of schwartz any quasi isometric image of a non relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup this implies that a group being relatively hyperbolic with non relatively hyperbolic peripheral subgroups is a quasi isometry invariant as an application artin groups are relatively hyperbolic if and only if freely decomposable we also introduce a new quasi isometry invariant of metric spaces called metrically thick which is sufficient for a metric space to be non hyperbolic relative to any non trivial collection of subsets thick finitely generated groups include mapping class groups of most surfaces outer automorphism groups of most free groups certain artin groups and others non uniform lattices in higher rank semisimple lie groups are thick and hence non relatively hyperbolic in contrast with rank one which provided the motivating examples of relatively hyperbolic groups mapping class groups are the first examples of non relatively hyperbolic groups having cut points in any asymptotic cone resolving several questions of drutu and sapir about the structure of relatively hyperbolic groups outside of group theory teichmuller spaces for surfaces of sufficiently large complexity are thick with respect to the weil peterson metric in contrast with brock farb s hyperbolicity result in low complexity

corrected score estimation in the proportional hazards model with misclassified discrete covariates we consider cox proportional hazards regression when the covariate vector includes error prone discrete covariates along with error free covariates which may be discrete or continuous the misclassification in the discrete error prone covariates is allowed to be of any specified form building on the work of nakamura and his colleagues we present a corrected score method for this setting the method can handle all three major study designs internal validation design external validation design and replicate measures design both functional and structural error models and time dependent covariates satisfying a certain localized error condition we derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix we present the results of a finite sample simulation study under weibull survival with a single binary covariate having known misclassification rates the performance of the method described here was similar to that of related methods we have examined in previous works specifically our new estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study our method generally performed well in these simulations the new estimator has a broader range of applicability than many other estimators proposed in the literature including those described in our own earlier work in that it can handle time dependent covariates with an arbitrary misclassification structure we illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer

analysis of a multigrid strokes solver model problem analysis or local mode analysis is used to investigate the two level convergence rates for multigrid strokes solvers the solvers are based on the discretization on the staggered grid and the distributive relaxation of the continuity equation the influence of the grid geometry is analyzed by also considering the poisson equation on the semistaggered grid various grid transfer operators are compared for an isotropic h x h y discretization simple tranfer operators are sufficient to obtain optimal rates but not in the anisotropic case the theoretical results are compared with observed multigrid convergence rates

maximum likelihood estimation and model selection in contingency tables with missing data abstract in many studies the values of one or more variables are missing for subsets of the original sample this article focuses on the problem of obtaining maximum likelihood estimates mle for the parameters of log linear models under this type of incomplete data the appropriate systems of equations are presented and the expectation maximization em algorithm dempster laird and rubin 1977 is suggested as one of the possible methods for solving them the algorithm has certain advantages but other alternatives may be computationally more effective tests of fit for log linear models in the presence of incomplete data are considered the data from the protective services project for older persons blenkner bloom and nielsen 1971 blenkner bloom and weber 1974 are used to illustrate the procedures discussed in the article

on the order of prolongations and restrictions in multigrid procedures abstract it is well known in the world of multigrid that the order of the prolongation and the order of the restriction in a multigrid method should satisfy certain conditions a rule of thumb is that the sum of the orders of the prolongation and of the restriction should at least be equal to the order of the differential equation solved in this note we show the correctness of this rule we notice that we have to distinguish between low frequency and high frequency orders for the transfer operators for the restriction the low frequency order is related with its accuracy whereas for the interpolation operator both orders are related with the accuracy of the result of the interpolation if an interpolation rule leaves all polynomials of degree k 1 invariant then both the low and the high frequency order are equal to k it is the high frequency order that plays a role in the above mentioned rule of thumb

conjugacy in artin groups of extra large type abstract we describe a constructive cubic time solution to the conjugacy problem in artin groups of extra large type which was proved soluble in those groups in 2 we use results from 7 6 that characterise geodesic words in those groups as well as the description of conjugacy between elements involving three or more generators that is given in 2

analysis of a new space time parallel multigrid algorithm for parabolic problems we present and analyze a new space time parallel multigrid method for parabolic equations the method is based on arbitrarily high order discontinuous galerkin discretizations in time and a finite element discretization in space the key ingredient of the new algorithm is a block jacobi smoother we present a detailed convergence analysis when the algorithm is applied to the heat equation and determine asymptotically optimal smoothing parameters a precise criterion for semi coarsening in time or full coarsening and give an asymptotic two grid contraction factor estimate we then explain how to implement the new multigrid algorithm in parallel and show with numerical experiments its excellent strong and weak scalability properties

locally optimal design for comparing two probabilities from binomial data subject to misclassification optimal experimental designs are found for estimating the difference 1 2 of two population probabilities using measuring instruments possibly subject to known error rates the available experiments considered are to measure for i 1 or 2 the outcome of a trial on the population i without error or with error or with error with the possibility of checking either positive or negative responses given that the cost per observation depends on which experiment is carried out an asymptotically locally optimal allocation is derived in terms of results of elfving which provide a simple geometrical solution

new estimates for multilevel algorithms including the v cycle the purpose of this paper is to provide new estimates for certain multilevel algorithms in particular we are concerned with the simple additive multilevel algorithm discussed recently together with j xu and the standard v cycle algorithm with one smoothing step per grid we shall prove that these algorithms have a uniform reduction per iteration independent of the mesh sizes and number of levels even on nonconvex domains which do not provide full elliptic regularity for example the theory applies to the standard multigrid vcycle on the l shaped domain or a domain with a crack and yields a uniform convergence rate we also prove uniform convergence rates for the multigrid v cycle for problems with nonuniformly refined meshes finally we give a new multigrid approach for problems on domains with curved boundaries and prove a uniform rate of convergence for the corresponding multigrid v cycle algorithms

on the hyperbolicity of small cancellation groups and one relator groups in the article a result relating to maps finite planar connected and simply connected 2 complexes that satisfy a c p t it is shown that a finitely generated onerelator group g whose reduced relator r is of the form r at0at1 atn 1 where the words ti are distinct and have no occurrences of the letter a 1 is not hyperbolic if and only if one has in the free group that 1 n 2 and t0t 1 1 is a proper power 2 n 3 and for some i it is true with subscripts mod 3 that tit 1 i 1tit 1 i 2 1 3 n 4 and for some i it is true with subscripts mod 4 that tit 1 i 1ti 2t 1 i 3 1

on correcting for misclassification in twin studies and other matched pair studies in twin studies and other matched pair studies of the effect of a k level risk factor on disease risk one must estimate the proportion of pairs in each of k2 possible pair categories of which k k 1 categories represent discordant pairs in particular for a binary factor one must estimate proportions within two discordant pair categories and the variances of functions of these estimates this paper shows how to do so when misclassification is present and stable estimates of the classification rates are available unlike methods that estimate only the discordance ratio one can use the methods presented here to improve estimates of epidemiologic effects

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

hierarchical log linear models not preserved by classification error abstract a model of bross 1954 for classification error in 2 2 contingency tables is extended to higher dimensional tables it is known mote and anderson 1965 that the usual hypothesis tests of independence for a sampled two dimensional table have the nominal significance level in the presence of misclassification a simple criterion is given to determine which hierarchical log linear models in higher dimensional tables do not share this property that is are not preserved by classification error

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

regression models for choice based samples with misclassification in the response variable abstract in this paper we provide a general framework to deal with the presence of misclassification in the response variable in choice based samples the contaminated data sampling distribution is written as a function of the error free conditional distribution of the dependent variable given the covariates and the conditional misclassification probabilities of the observable variable of interest given its latent values we propose an extension of imbens econometrica 60 1992 1187 efficient generalized method of moments to estimate this model and outline a specification test to detect the presence of this sort of measurement error the performance of both the estimators and the test is investigated in a monte carlo simulation study which shows very encouraging results

metric systolicity and two dimensional artin groups we introduce the notion of metrically systolic simplicial complexes we study geometric and large scale properties of such complexes and of groups acting on them geometrically we show that all two dimensional artin groups act geometrically on metrically systolic complexes as direct corollaries we obtain new results on two dimensional artin groups and all their finitely presented subgroups we prove that the conjugacy problem is solvable and that the dehn function is quadratic we also show several large scale features of finitely presented subgroups of two dimensional artin groups lying background for further studies concerning their quasi isometric rigidity

precision of double sampling estimators for comparing two probabilities summary it is assumed that both error prone and error free observations can be made on a binary response the second type being more expensive in double sampling error prone observations are made on all sample units and for a random subsample error free observations are made as well tenenbein 1970 studied allocation of units in double sampling for estimating a single probability we consider double sampling for comparing two probabilities for different cost ratios for error prone versus error free observations and for fixed total cost we assess how the large sample variance of the log odds ratio estimator varies with the proportion of units subject to both error prone and error free observation we determine the optimal double sampling proportion and the possible gain from using double sampling versus single sampling in which only error free observations are made

log linear models for doubly sampled categorical data fitted by the em algorithm abstract double sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log linear models the framework described can be applied to experiments with any number of factors and measurement devices maximum likelihood estimation via the em algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters

rigorous quantitative analysis of multigrid i constant coefficients two level cycle with l 2 norm exact numerical convergence factors for any multigrid cycle can be predicted by local mode fourier analysis for general linear elliptic partial differential equation pde systems with piecewise smooth coefficients in general domains discretized by uniform grids it is proved that in the limit of small meshsizes these predicted factors are indeed obtained provided the cycle is supplemented with a proper processing at and near the boundaries that processing it is proved costs negligible extra computer work apart from mode analysis a coarse grid approximation cga condition is introduced which is both necessary and sufficient for the multigrid algorithm to work properly the present part studies the l 2 convergence in one cycle for equations with constant coefficients in the sequel brandt rigorous quantitative analysis of multigrid ii extensions and practical implications manuscript extensions are discussed to many cycles asymptotic convergence to more levels with arbitrary cycle ty

generic case complexity decision problems in group theory and random walks abstract we give a precise definition of generic case complexity and show that for a very large class of finitely generated groups the classical decision problems of group theory the word conjugacy and membership problems all have linear time generic case complexity we prove such theorems by using the theory of random walks on regular graphs

the equation xp yq zr and groups that act freely on l trees let g be a finitely generated group that acts freely on a lambda tree where lambda is an ordered abelian group and let x y z be elements in g we show that if x p y q z r with integers p q r geq 4 then x y and z commute

multilevel and latent variable modeling with composite links and exploded likelihoods composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models applications considered include survival or duration models models for rankings small area estimation with census information models for ordinal responses item response models with guessing randomized response models unfolding models latent class models with random effects multilevel latent class models models with log normal latent variables and zero inflated poisson models with random effects some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation

algorithms versus models for analyzing data that contain misclassification errors espeland and hui 1987 biometrics 43 1001 1012 propose a methodology for analysing epidemiologic data contaminated by misclassification they explicate their algorithm by a data set concerning cervical cancer and circumcision we reanalyse these data using a conditional independence assumption different from theirs and reach radically different conclusions espeland and hui s methodology is a form of correlation analysis we propose an alternative methodology based on the logic of regression analysis