the topology of deformation spaces of kleinian groups let m be a compact hyperbolizable 3 manifold with nonempty incompressible boundary and let ah 1 m denote the space of conjugacy classes of discrete faithful representations of 1 m i nto psl 2 c the components of the interior mp 1 m of ah 1 m as a subset of the appropriate representation variety are enumerated by the spacea m of marked homeomorphism types of oriented compact irreducible 3 manifolds homotopy equivalent to m in this paper we give a topological enumeration of the components of the closure of mp 1 m and hence a conjectural topological enumeration of the components of ah 1 m we do so by characterizing exactly which changes of marked homeomorphism type can occur in the algebraic limit of a sequence of isomorphic freely indecomposable kleinian groups we use this enumeration to exhibit manifolds m for which ah 1 m has inflnitely many components in this paper we begin a study of the global topology of deformation spaces of kleinian groups the basic object of study is the space ah 1 m of marked hyperbolic 3 manifolds homotopy equivalent to a flxed compact 3manifold m the interior mp 1 m of ah 1 m is very well understood due to work of ahlfors bers kra marden maskit sullivan and thurston in particular the components ofmp 1 m are enumerated by topological data namely the set a m of marked compact oriented irreducible 3 manifolds homotopy equivalent to m while each component is parametrized by analytic data coming from the conformal boundaries of the hyperbolic 3 manifolds thurston s ending lamination conjecture provides a conjectural classiflcation for elements of ah 1 m by data which are partially topologi

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

hyperbolic cone manifolds short geodesics and schwarzian derivatives given a geometrically finite hyperbolic cone manifold with the cone singularity sufficiently short we construct a one parameter family of cone manifolds decreasing the cone angle to zero we also control the geometry of this one parameter family via the schwarzian derivative of the projective boundary and the length of closed geodesics

nonparametric estimation of a multivariate distribution in the presence of censoring summary this paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right censored a distinction is made between what we term homogeneous and heterogeneous censoring it is shown how a multivariate empirical survivor function must be constructed in order to be considered a nonparametric maximum likelihood estimate of the underlying survivor function a closed form solution similar to the product limit estimate of kaplan and meier is possible with homogeneous censoring but an iterative method such as the em algorithm is required with heterogeneous censoring an example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables this anomaly is shown to disappear if

self bumping of deformation spaces of hyperbolic 3 manifolds let n be a hyperbolic 3 manifold and b a component of the interior of ah 1 n the space of marked hyperbolic 3 manifolds homotopy equivalent to n we will give topological conditions on n sufficient to give b such that for every sufficiently small neighbourhood v of v b is disconnected this implies that b is not a manifold with boundary

the non holonomic mechanics abstract two approaches for the study of mechanical systems with non holonomic constraints are presented d alembertian mechanics and variational vakonomic mechanics the first one is equivalent to the d alembert principle and the second comes from a variational principle in order to develop the two approaches d alembertian and vakonomic trajectories are introduced a generalized version of the classical liouville theorem for the conservation of volume is proved in the context of d alembertian mechanics a characterization for the notions of regular and singular curves is presented the flow corresponding to the regular vakonomic trajectories is hamiltonian

tameness persists in weakly type preserving strong limits we show that if a weakly type preserving sequence of tame hyperbolic 3 manifolds converges strongly then the limit is tame as a first corollary we observe that we can replace the assumption of strong convergence with algebraic convergence in most cases as a second corollary we observe that given a finitely generated geometrically finite kleinian group tame groups are dense in the boundary of its quasiconformal deformation space in most cases

reml and ml estimation for clustered grouped survival data clustered grouped survival data arise naturally in clinical medicine and biological research for example in a randomized clinical trial the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters however it is sometimes impossible or too expensive to monitor the experimental subjects continuously the subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale with such a design researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster namely the intracluster correlation this paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation time dependent covariates can be accommodated in the proposed model and the estimation procedure will not be further complicated with large cluster sizes the proposed method is applied to the data from the diabetic retinopathy study the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes associated retinopathy the intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed results from a simulation study of the proposed method are also presented

dynamic convexity for natural thermostatted systems abstract natural thermostatted systems are mechanical systems whose lagrangian is the difference of a kinetic and a potential energy subjected to the nonholonomic constraint of a constant kinetic energy when any two points of the configuration space are joined by a thermostatted motion we say that the system is dynamically convex a thermostatted charged particle on the plane with a constant electric field is not a dynamically convex system we prove a general sufficient condition for dynamic convexity from which whole classes of examples are easily constructed

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

singular surfaces mod 2 homology and hyperbolic volume i if m is a simple closed orientable 3 manifold such that 1 m contains a genus g surface group and if h 1 m 2 has rank at least 4g 1 we show that m contains an embedded closed incompressible surface of genus at most g as an application we show that if m is a closed orientable hyperbolic 3 manifold of volume at most 3 08 then the rank of h 1 m 2 is at most 6

growth rates _ homology and volumes of hyperbolic 3 manifolds it is shown that if m is a closed orientable irreducible 3 manifold and n is a nonnegative integer and if h 1 m z p has rank n 2 for some prime p then every n generator subgroup of 1 m has infinite index in 1 m and is in fact contained in infinitely many finite index subgroups of 1 m this result is used to estimate the growth rates of the fundamental group of a 3 manifold in terms of the rank of the z p homology

bayesian models for multivariate current status data with informative censoring des donnees multivariees d etat consistent en un ensemble d indicatrices associees a la realisation de plusieurs evenements au moment d un examen nous nous interessons aux inferences sur les distributions jointes des temps d evenements les methodes conventionnelles d analyse des donnees de durees multiples ne peuvent etre utilisees parce que tous les temps d evenements sont censures et la censure peut etre informative nous prenons en compte la correlation des temps d evenements chez un sujet au moyen d une variable latente propre au sujet conditionnellement a laquelle les divers temps d evenements sont supposes independants nous supposons egalement que chaque evenement contribue independamment au risque de censure des fonctions en escalier non parametriques sont utilisees pour caracteriser les distributions de base des differents temps d evenements et des temps d examen les covariables et les effets specifiques du sujet sont incorpores grace au modele lineaire generalise un algorithme de monte carlo par chaines de markov est decrit pour l estimation des distributions a posteriori des inconnues les methodes sont illustrees par une application sur des donnees de sites multiples de tumeurs dans une etude de carcinogenicite animale

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

topological tameness of margulis spacetimes we show that margulis spacetimes without parabolic holonomy elements are topologically tame a margulis spacetime is the quotient of the 3 dimensional minkowski space by a free proper isometric action of the free group of rank geq 2 we will use our particular point of view that the margulis spacetime is a manifold with boundary with an bbb r sf p 3 structure in an essential way the basic tools are a bordification by a closed bbb r sf p 2 surface with free holonomy group and the work of goldman labourie and margulis on geodesics in the margulis spacetimes and 3 manifold topology

shrinkwrapping and the taming of hyperbolic 3 manifolds we introduce a new technique for finding cat 1 surfaces in hyperbolic 3 manifolds we use this to show that a complete hyperbolic 3 manifold with finitely generated fundamental group is geometrically and topologically tame

multiple bumping of components of deformation spaces of hyperbolic 3 manifolds let m be a hyperbolizable 3 manifold with nonempty incompressible boundary of negative euler characteristic suppose that b 1 b k is a collection of components of the interior of the space of complete marked hyperbolic 3 manifolds homotopy equivalent to m such that for any i j inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i we prove that there is a geometrically finite hyperbolic structure on int m which is in the closure of each b i moreover we show that this structure can be constructed so as to admit quasiconformal deformations which also lie in the closure of every b i

on continuous extensions of grafting maps the definition of the grafting operation for quasifuchsian groups is extended by bromberg preprint to all b groups in this paper we show that the extended grafting maps behave as continuous maps for every sequence which converges standardly to a boundary group although the maps are not continuous in general as a consequence of this result we extend goldman s grafting theorem for quasifuchsian groups to all boundary b groups

ranks of mapping tori via the curve complex is generated by nielsen transformations this isequivalent to requiring that our two generating sets for g are related by asequence of the following moves 1 if a6 bare generators replace awith ab 2 if a6 bare generators switch their places in the ordering 3 if ais a generator replace it with a

approximation by maximal cusps in boundaries of deformation spaces of kleinian groups let m be a compact oriented irreducible atoroidal 3 manifold with nonempty boundary let cc0 m denote the space of convex cocompact kleinian groups uniformizing m we show that any kleinian group in the boundary of cc0 m whose limit set is the whole sphere can be approximated by maximal cusps density of maximal cusps on the boundary of schottky space is derived as a corollary we further show that maximal cusps are dense in the boundary of the quasiconformal deformation space of any geometrically finite hyperbolic 3 manifold with connected conformal boundary

cusps are dense we show cusps are dense in bers boundary for teichmuller space the proof rests on an estimate for the algebraic effect of a unit quasiconformal deformation supported in the thin part of a hyperbolic riemann surface

ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3 manifolds we show that geometrically finite kleinian groups are dense in the boundary of the quasiconformal deformation space of any geometrically finite kleinian group

a multiple imputation approach for clustered interval censored survival data multivariate interval censored failure time data arise commonly in many studies of epidemiology and biomedicine analysis of these type of data is more challenging than the right censored data we propose a simple multiple imputation strategy to recover the order of occurrences based on the interval censored event times using a conditional predictive distribution function derived from a parametric gamma random effects model by imputing the interval censored failure times the estimation of the regression and dependence parameters in the context of a gamma frailty proportional hazards model using the well developed em algorithm is made possible a robust estimator for the covariance matrix is suggested to adjust for the possible misspecification of the parametric baseline hazard function the finite sample properties of the proposed method are investigated via simulation the performance of the proposed method is highly satisfactory whereas the computation burden is minimal the proposed method is also applied to the diabetic retinopathy study drs data for illustration purpose and the estimates are compared with those based on other existing methods for bivariate grouped survival data

connectivity of the space of ending laminations we prove that for any closed surface of genus at least four and any punctured surface of genus at least two the space of ending laminations is connected a theorem of e klarreich 28 theorem 1 3 implies that this space is homeomorphic to the gromov boundary of the complex of curves it follows that the boundary of the complex of curves is connected in these cases answering the conjecture of p storm other applications include the rigidity of the complex of curves and connectivity of spaces of degenerate kleinian groups

the visual core of a hyperbolic 3 manifold in this note we introduce the notion of the visual core of a hyperbolic 3 manifold n bf h 3 gamma and explore some of its basic properties we investigate circumstances under which the visual core cal v n of a cover n bf h 3 gamma of n embeds in n via the usual covering map pi n rightarrow n we go on to show that if the algebraic limit of a sequence of isomorphic kleinian groups is a generalized web group then the visual core of the algebraic limit manifold embeds in the geometric limit manifold finally we discuss the relationship between the visual core and klein maskit combination along component subgroups

ends of hyperbolic 3 manifolds let n h3 f be a hyperbolic 3 manifold which is homeomorphic to the interior of a compact 3 manifold we prove that n is geometrically tame as a consequence we prove that f s limit set l is either the entire sphere at infinity or has measure zero we also prove that n s geodesic flow is ergodic if and only if lf is the entire sphere at infinity department of mathematics stanford university stanford california 94305 current address department of mathematics university of michigan ann arbor michigan 48109 e mail address dick canary math lsa umich edu this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 06 utc all use subject to http about jstor org terms

on ahlfors finiteness theorem abstract ahlfors finiteness theorem and its two complements namely the area inequalities of bers and the finiteness of the cusps due to sullivan are some of the central results in the modern theory of kleinian groups their proofs are analytic whereas their conclusions have a geometric flavor in this paper we have attempted to explain the topological and group theoretic genesis of these theorems our approach is based on a relative version of the theorem a finitely generated 3 manifold groups is finitely presented due to scott and shalen

geometrical finiteness for hyperbolic groups abstract in this paper we give an account of the notion of geometrical finiteness as applied to discrete groups acting on hyperbolic space of any dimension we prove the equivalence of various definitions of geometrical finiteness and describe the geometry of fundamental domains we give a complete account of when dirichiet domains are finite sided

quasiconformal homeomorphisms and dynamics ii structural stability implies hyperbolicity for kleinian groups sous groupe de psl 2 c familles holomorphes d homeomorphismes de c lemme champs de ligne invariants familles holomorphes de groupes abstraitement isomorphes car finiment genere la stabilite structurelle implique geometriquement fini ou rigide theoreme a avec paraboles stabilite structurelle au sens de la dynamique differentiable

algebraic limits of kleinian groups which rearrange the pages of a book in this paper we give examples of two new phenomena in kleinian groups we rst exhibit a sequence of homeomorphic marked hyperbolic 3 manifolds whose algebraic limit is not homeomorphic to any element in the sequence we then use this construction to exhibit situations where the space of convex co compact representations of a given 3 manifold group has many components but its closure is connected let m be a compact irreducible oriented 3 manifold and let d 1 m denote the space of all discrete faithful representations of 1 m into psl2 c a sequence of representations n d 1 m converging to d 1 m gives rise to a sequence n n h n 1 m of hyperbolic 3 manifolds each of which is homotopy equivalent to m the sequence n n is said to converge algebraically to n h 1 m see 7 13 14 for more information about algebraic convergence of kleinian groups in many situations see 1 6 15 24 25 27 it has been shown that n n must be homeomorphic to n for all large enough n and we had suspected that this would always be the case in this paper we give a collection of examples where n n is not homeomorphic to n for any n our sequences are quite well behaved the n 1 m are convex co compact and mutually quasiconformally conjugate and the algebraic limit 1 m is geometrically nite in our examples m is obtained by gluing a collection of i bundles to a solid torus along a family of parallel annuli these manifolds are particularly simple examples of books of i bundles see 9 where to explain the terminology one should think of the solid torus as the binding and the i bundles

exotic projective structures and quasi fuchsian space ii let p s be the space of projective structures on a closed surface s of genus g 1 and let q s be the subset of p s of projective structures with quasi fuchsian holonomy it is known that q s consists of infinitely many connected components in this article we show that the closure of any exotic component of q s is not a topological manifold with boundary and that any two components of q s have intersecting closures

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

logistic regression survival analysis and the kaplan meier curve abstract we discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data these techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors an example is given that demonstrates the increased structure that can be seen in a parametric analysis as compared with the nonparametric kaplan meier survival curves in fact the logistic regression estimates are closely related to kaplan meier curves and approach the kaplan meier estimate as the number of parameters grows large

a flexible model for multivariate interval censored survival times with complex correlation structure we focus on the analysis of multivariate survival times with highly structured interdependency and subject to interval censoring such data are common in developmental genetics and genetic epidemiology we propose a flexible mixed probit model that deals naturally with complex but uninformative censoring the recorded ages of onset are treated as possibly censored ordinal outcomes with the interval censoring mechanism seen as arising from a coarsened measurement of a continuous variable observed as falling between subject specific thresholds this bypasses the requirement for the failure times to be observed as falling into non overlapping intervals the assumption of a normal age of onset distribution of the standard probit model is relaxed by embedding within it a multivariate box cox transformation whose parameters are jointly estimated with the other parameters of the model complex decompositions of the underlying multivariate normal covariance matrix of the transformed ages of onset become possible the new methodology is here applied to a multivariate study of the ages of first use of tobacco and first consumption of alcohol without parental permission in twins the proposed model allows estimation of the genetic and environmental effects that are shared by both of these risk behaviours as well as those that are specific

critical exponent and displacement of negatively curved free groups we study the action of the fundamental group of a negatively curved 3manifold m on the universal cover m of m in particular we consider the ergodicity properties of the action and the distances by which points of m are displaced by elements of first we prove a displacement estimate for a general n dimensional manifold with negatively pinched curvature and free fundamental group this estimate is given in terms of the critical exponent

generalized survival models for correlated time to event data our aim is to develop a rich and coherent framework for modeling correlated time to event data including 1 survival regression models with different links and 2 flexible modeling for time dependent and nonlinear effects with rich postestimation we extend the class of generalized survival models which expresses a transformed survival in terms of a linear predictor by incorporating a shared frailty or random effects for correlated survival data the proposed approach can include parametric or penalized smooth functions for time time dependent effects nonlinear effects and their interactions the maximum penalized marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty or random effects the optimal smoothing parameters for the penalized marginal likelihood estimation can be automatically selected by a likelihood based cross validation criterion for models with normal random effects gauss hermite quadrature can be used to obtain the cluster level marginal likelihoods the akaike information criterion can be used to compare models and select the link function we have implemented these methods in the r package rstpm2 simulating for both small and larger clusters we find that this approach performs well through 2 applications we demonstrate 1 a comparison of proportional hazards and proportional odds models with random effects for clustered survival data and 2 the estimation of time varying effects on the log time scale age varying effects for a specific treatment and two dimensional splines for time and age

the classification of punctured torus groups thurston s ending lamination conjecture proposes that a flnitely generated kleinian group is uniquely determined up to isometry by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends we present a proof of this conjecture for punctured torus groups these are free two generator kleinian groups with parabolic commutator which should be thought of as representations of the fundamental group of a punctured torus as a consequence we verify the conjectural topological description of the deformation space of punctured torus groups including bers conjecture that the quasi fuchsian groups are dense in this space and prove a rigidity theorem two punctured torus groups are quasi conformally conjugate if and only if they are topologically conjugate

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

regression analysis of multivariate grouped survival data multivariate failure time data arise when each study subject may experience several types of event or when there are clusterings of observational units such that failure times within the same cluster are correlated the failure times are often subject to interval grouping or have truly discrete measurements in this paper the marginal distribution for each discrete failure time variable is formulated by a grouped data version of the proportional hazards model while the dependence structure is unspecified generalized estimating equations in the spirit of liang and zeger 1986 biometrika 73 13 22 are proposed to estimate the regression parameters and survival probabilities the resulting estimators are consistent and asymptotically normal robust estimators for the limiting covariance matrices are constructed simulation studies demonstrate that the asymptotic approximations are adequate for practical use and that ignoring the intracluster dependence in the variance covariance estimation would lead to invalid statistical inference a psychological experiment is provided for illustration

the classification of kleinian surface groups ii the ending lamination conjecture thurston s ending lamination conjecture states that a hyperbolic 3manifold n with nitely generated fundamental group is uniquely determined by its topological type and its end invariants in this paper we prove this conjecture for kleinian surface groups the general case when n has incompressible ends relative to its cusps follows readily the main ingredient is a uniformly bilipschitz model for the quotient of h 3 by a kleinian surface group

cannon thurston maps for surface groups we prove the existence of cannon thurston maps for simply and doubly degenerate surface kleinian groups as a consequence we prove that connected limit sets of nitely generated kleinian groups are locally connected

cores of hyperbolic 3 manifolds and limits of kleinian groups troels jorgensen conjectured that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic kleinian groups agree if there are no new parabolics in the algebraic limit we prove that this conjecture holds in most cases in particular we show that it holds when the domain of discontinuity of the algebraic limit of such a sequence is non empty we further show with the same assumptions that the limit sets of the groups in the sequence converge to the limit set of the algebraic limit as a corollary we verify the conjecture for finitely generated kleinian groups which are not non trivial free products of surface groups and infinite cyclic groups these results are extensions of similar results for purely loxodromic groups thurston previously established these results in the case when the kleinian groups are freely indecomposable using different techniques from ours ohshika has proven versions of these results for purely loxodromic function groups

reduction of constrained mechanical systems and stability of relative equilibria a mechanical system with perfect constraints can be described under some mild assumptions as a constrained hamiltonian system m h d w m thephase space is a symplectic manifold h thehamiltonian a smooth function onm d theconstraint submanifold a submanifold ofm andw theprojection bundle a vector sub bundle oft d m the reduced tangent bundle alongd we prove that when these data satisfy some suitable conditions the time evolution of the system is governed by a well defined differential equation ond we define constrained hamiltonian systems with symmetry and prove a reduction theorem application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane two other simple examples show that constrained mechanical systems with symmetry may have an attractive or repulsive set of relative equilibria

pseudo maximum likelihood estimation the asymptotic distribution gong and samaniego 1981 define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates this note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

modeling clustered discrete or grouped time survival data with covariates summary we have developed methods for modeling discrete or grouped time right censored survival data collected from correlated groups or clusters we assume that the marginal hazard of failure for individual items within a cluster is specified by a linear log odds survival model and the dependence structure is based on a gamma frailty model the dependence can be modeled as a function of cluster level covariates likelihood equations for estimating the model parameters are provided generalized estimating equations for the marginal hazard regression parameters and pseudolikelihood methods for estimating the dependence parameters are also described data from two clinical trials are used for illustration purposes

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

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided

examples of relative deformation spaces that are not locally connected we provide an infinite family of pared manifolds with the property that the relative deformation spaces of hyperbolic structures on these manifolds are not locally connected this is a natural extension of the recent result of bromberg that shows the space of kleinian punctured torus groups is not locally connected