thermodynamics dimension and the weil petersson metric in this paper we study branched coverings of metrized simplicial trees f t t which arise from polynomial maps f c c with disconnected julia sets we show that the collection of all such trees up to scale forms a contractible space ptd compactifying the moduli space of polynomials of degree d that f records the asymptotic behavior of the multipliers of f and that any meromorphic family of polynomials over can be completed by a unique tree at its central fiber in the cubic case we give a combinatorial enumeration of the trees that arise and show that pt3 is itself a tree resume dans ce travail nous etudions des revetements ramifies d arbres metriques simpliciaux f t t qui sont obtenus a partir d applications polynomiales f c c possedant un ensemble de julia non connexe nous montrons que la collection de tous ces arbres a un facteur d echelle pres forme un espace contractile ptd qui compactifier l espace des modules des polynomes de degre d nous montrons aussi que f enrigistre le comportement asymptotique des multiplicateurs de f et que tout famille meromorphe de polynomes definis sur peut etre completee par un unique arbre comme sa fibre centrale dans le cas cubique nous donnons une enumeration combinatoire des arbres ainsi obtenus et montrons que pt3 est lui meme un arbre

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

dense subgroups of n dimensional mobius groups we will derive a new discreteness condition for n dimensional mobius subgroups as well as obtain some results concerning classification of such groups we will also discuss dense subgroups of n dimensional mobius groups the main result is that any dense group of an n dimensional mobius group contains a dense subgroup which is generated by at most n elements if n geq 2

holomorphic motions and teichmuller spaces we prove an equivariant form of slodkowski s theorem that every holomorphic motion of a subset of the extended complex plane c extends to a holomorphic motion of c as a consequence we prove that every holomorphic map of the unit disc into teichmuller space lifts to a holomorphic map into the space of beltrami forms we use this lifting theorem to study the teichmuller metric

survival curve estimation for informatively coarsened discrete event time data interval censored or more generally coarsened event time data arise when study participants are observed at irregular time periods and experience the event of interest in between study observations such data are often analysed assuming non informative censoring which can produce biased results if the assumption is wrong this paper extends the standard approach for estimating survivor functions to allow informatively interval censored data by incorporating various assumptions about the censoring mechanism into the model we include a bayesian extension in which final estimates are produced by mixing over a distribution of assumed censoring mechanisms we illustrate these methods with a natural history study of hiv infected individuals using assumptions elicited from an aids expert

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

a modified secant method for unconstrained optimization abstract in this study a modification of the classical secant method for solving nonlinear univariate and unconstrained optimization problems based on the development of the cubic approximation is presented the iteration formula including an approximation of the third derivative of f x by using the taylor series expansion is derived the performance of the new method is analyzed in terms of the number of iterations in comparison with the secant methods using six test functions

random walks kleinian groups and bifurcation currents let be a holomorphic family of representations of a finitely generated group g into psl 2 parameterized by a complex manifold we define a notion of bifurcation current in this context that is a positive closed current on describing the bifurcations of this family of representations in a quantitative sense it is the analogue of the bifurcation current introduced by demarco for holomorphic families of rational mappings on 1 our definition relies on the theory of random products of matrices so it depends on the choice of a probability measure on g

dependent competing risks and summary survival curves summary in many contexts where there is interest in inferring the marginal distribution of a survival time t subject to censoring embodied in a latent waiting time c the times t and c may not be independent this paper presents a new class of nonparametric assumptions on the conditional distribution of t given c and shows how they lead to consistent generalizations of the kaplan meier 1958 survival curve estimator the new survival curve estimators are used under weak assumptions to construct bounds on the marginal survival which can be much narrower than those of peterson 1976 in stratified populations where t and c are independent only within strata examples indicate that the kaplan meier estimator is often approximately consistent

bounds on net survival probabilities for dependent competing risks bounds on the marginal survival function based on data from a competing risks experiment are obtained these bounds require an investigator to specify a range of possible concordances for the times to occurrences of the competing risks these bounds are tighter than those of peterson 1976 proceedings of the national academy of sciences 73 11 13

a second derivative free modified secant like method with order 2 732 for unconstrained optimization abstract a second derivative free modified secant like method for solving univariate and unconstrained optimization problems is presented the new method is proved to have convergence order of 2 732 which is better than the convergence order of 2 414 of the method proposed recently by kahya e kahya modified secant type methods for unconstrained optimization appl math comput 181 2006 1349 1356 numerical examples are also provided which show that the new method is better than the old one

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

discussion of the frangakis and rubin article in clinical survival studies conducted in the united states rich data are frequently available on variables recording time to drop out and the evolution over time of a patient s clinical signs symptoms and laboratory measurements motivated by a greek study frangakis and rubin fr consider estimation of a marginal survival curve under a double sampling design from severely impoverished reduced data that included none of the aforementioned variables due to confidentiality restrictions to make our discussion relevant to settings with and without confidentiality restrictions we shall consider survival curve estimation both from rich data that includes the aforementioned variables and from reduced data that does not let t l and c be continuous failure dropout and administrative censoring times respectively with time measured from date of enrollment the goal is to estimate the cumulative net marginal hazard of failure a t fj at u du and the survival function s t e a t under a double sampling design in which a subset of the dropouts is followed up in a secondphase sample in their analysis fr assumed a all dropouts had the same chance of being selected into the second stage sample b all dropouts selected into the second phase had their censoring indicator a 6 t c and their minimum x min t c of censoring and failure successfully ascertained and c c was independent of underlying variables such as t and l it was necessary for fr to impose these assumptions because fr s estimator of a t is inconsistent unless a c hold in practice one or more of assumptions a c may often fail to hold for instance in the first paragraph of their section 5 fr noted it will often happen that a subset of the dropouts pursued in the second phase will fail to have x i ascertained violating assumption b fr recommend that members of this subset be treated in the analysis as having been administratively censored however were this recommendation to be followed fr s survival estimator would be inconsistent and could be severely biased if the number of secondstage subjects who do not have x i ascertained is large assumption a will be false if a potentially more efficient design has been employed in which subjects who dropped out early are oversampled in the second phase assumption c will be false when there are secular trends in the distribution of t as was the case during the 1980s and 1990s for the survival time t of aids patients if only assumption a were false then as fr note identification of a t could be restored by addition of the known second phase sampling probabilities to fr s reduced data however when assumptions b and or c are false both additional assumptions and rich data are required to restore identification in this discussion we make the following points first we show in section 4 that if assumptions a c hold then i when only the reduced data are available for analysis fr s estimator is algebraically identical to the efficient inverse prow ability weighted ipw estimator but ii when rich data are available fr s estimator is inefficient for this case we provide in section 8 a locally semiparametric efficient lse estimator of s t that exploits the information in the rich data second we consider the more realistic setting in which i fr s estimator is inconsistent because one or more of assumptions a c fail to hold and ii rich data are available in sections 6 and 7 we derive doubly robust lse survival curve estimators under the assumption that the missingness process is ignorable in summary we describe aspects of a powerful methodology for the analysis of doubly sampled censored survival data that can resolve the three principal problems left open by fr i how to construct locally lse estimators of s t when fr s assumptions a c hold and as would typically be the case in the united states rich data are available for analysis ii how to construct lse doubly robust estimators of s t when fr s assumptions b and or c fail but missingness remains ignorable and iii how to conduct a sensitivity analysis when missingness may be nonignorable this methodology is in effect a subset of the general theory developed in robins and rotnitzky 1992 robins 1993a b robins rotnitzky and scharfstein 1999 and scharfstein rotnitzky and robins 1999a for the analysis of semiand nonparametric rightcensored data models specialized to the case of doubly sampled censored survival data because of space limitations our resolution of problem iii will be described elsewhere in order to successfully exploit our general theory in the context of doubly sampled data an additional problem must be faced specifically in this context the distribution of the censoring variable has both discrete and continuous components as a result none of the estimators of s t previously proposed in the aforementioned papers are directly applicable in section 6 and the appendix we provide a survival estimator that allows for a mixed discrete and continuous censor

non realizability and ending laminations proof of the density conjecture we give a complete proof of the bers sullivan thurston density conjecture in the light of the ending lamination theorem it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds the ending invariants are either riemann surfaces or filling laminations supporting masur domain measured laminations and satisfying some mild additional conditions with any set of ending invariants we associate a sequence of geometrically finite hyperbolic manifolds and prove that this sequence has a convergent subsequence we derive the necessary compactness theorem combining the rips machine with non existence results for certain small actions on real trees of free products of surface groups and free groups we prove then that the obtained algebraic limit has the desired conformal boundaries and the property that none of the filling laminations is realized by a pleated surface in order to be able to apply the ending lamination theorem we have to prove that this algebraic limit has the desired topological type and that these non realized laminations are ending laminations that this is the case is the main novel technical result of this paper loosely speaking we show that a filling masur domain lamination which is not realized is an ending lamination

regression survival analysis with an assumed copula for dependent censoring a sensitivity analysis approach summary in clinical studies when censoring is caused by competing risks or patient withdrawal there is always a concern about the validity of treatment effect estimates that are obtained under the assumption of independent censoring because dependent censoring is nonidentifiable without additional information the best we can do is a sensitivity analysis to assess the changes of parameter estimates under different assumptions about the association between failure and censoring this analysis is especially useful when knowledge about such association is available through literature review or expert opinions in a regres sion analysis setting the consequences of falsely assuming independent censoring on parameter estimates are not clear neither the direction nor the magnitude of the potential bias can be easily predicted we provide an approach to do sensitivity analysis for the widely used cox proportional hazards models the joint distribution of the failure and censoring times is assumed to be a function of their marginal dis tributions this function is called a copula under this assumption we propose an iteration algorithm to estimate the regression parameters and marginal survival functions simulation studies show that this algorithm works well we apply the proposed sensitivity analysis approach to the data from an aids clinical trial in which 27 of the patients withdrew due to toxicity or at the request of the patient or investigator

julia fatou sullivan theory for real one dimensional dynamics our aim is to show that the julia fatou sullivan structure theory for the dynamics of rational maps is also valid for smooth endomorphisms of the circle and of the interval under extremely mild smoothness and non flatness conditions in order to stress the similarity between real and complex one dimensional dynamics let us recall the main results from the fatou julia sullivan theory if f is a rational map then there is a dynamical decomposition of the riemann sphere into the disjoint union of two totally invariant i e both forward and backward invariant sets j f f f here f f is the domain of normality of the family of iterates of f and is called the fatou set its complement which is called the julia set off is a compact set which contains all the complications of the dynamics off the connected components of the open set f f are mapped onto each other by f hence the orbit of a component of f f is the union of some components of f f julia proved in the beginning of the century that if a component of f f is periodic and contains an attracting periodic point then the orbit of this component must contain a critical point sullivan in the remarkable paper su showed via quasi conformal deformations that the components are eventually periodic and fall into finitely many orbits let n be either the circle s j or a compact interval of the real line and f n n be a smooth endomorphism a critical point of f is a point where the derivative vanishes a critical point is non flat if some higher derivative is non zero a critical point is an inflection point if it has a neighbourhood where f is monotone otherwise it is called a turning point assume f is not a homeomorphism i f f is a homeomorphism then these maps correspond to degree 1 rational maps of the riemann sphere and the situation is

modified secant type methods for unconstrained optimization for solving nonlinear univariate and unconstrained optimization problems newton method is an important and basic method which convergences quadratically in this paper we suggest a family of three new modifications of the classical secant method where the iteration formula including an approximation of f x k is satisfied by a recursive scheme the efficiencies of the new methods are analyzed in terms of the most popular and widely used criterion the number of iterations in comparison with the newton and secant methods using six test functions

estimates of marginal survival for dependent competing risks based on an assumed copula summary when time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product limit estimators which assume independent censoring if no assumption about the relationship between the two times is made the marginal survival functions are not identifiable a natural function that defines the association between the two random variables is the copula we show that if this function is known then the competing risks data are sufficient to identify the marginal survival functions and construct a suitable estimator this estimator is consistent and reduces to the kaplan meier estimator when death and censoring times are independent this statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks

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

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

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

coarsening at random in general sample spaces and random censoring in continuous time heitjan and rubin proposed a concept coarsening at random generalizing rubin s theory of missing at random their analysis was done in discrete sample spaces we propose a generalization to general sample spaces among heitjan and rubin s applications was right censoring in survival analysis we discuss the application of the generalized theory to various censoring patterns in continuous time and connect to the modern theory of random censoring

estimation of the failure time distribution in the presence of informative censoring we present a method for estimating the survival curve of a continuous failure time random variable from right censored data our method allows adjustment for informative censoring due to measured prognostic factors for time to event and censoring while simultaneously quantifying the sensitivity of the inference to residual dependence between failure and censoring due to unmeasured factors we present the results of a simulation study and illustrate our approach using data from the aids clinical trial group 175 study

open sets of maximal dimension in complex hyperbolic quasi fuchsian space let pi 1 be the fundamental group of a closed surface sigma of genus g 1 one of the fundamental problems in complex hyperbolic geometry is to find all discrete faithful geometrically finite and purely loxodromic representations of pi 1 into su 2 1 the triple cover of the group of holomorphic isometries of h c 2 in particular given a discrete faithful geometrically finite and purely loxodromic representation rho 0 of pi 1 can we find an open neighbourhood of rho 0 comprising representations with these properties we show that this is indeed the case when rho 0 preserves a totally real lagrangian plane

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

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

slicing skinning and grafting we prove that a bers slice is never algebraic meaning that its zariski closure in the character variety has strictly larger dimension a corollary is that skinning maps are never constant the proof uses grafting and the theory of complex projective structures

prym varieties and teichmuller curves this paper gives a uniform construction of infinitely many primitive teichmuller curves v mg for g 2 3 and 4

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

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

dimension and rigidity of quasi fuchsian representations let fo c so n 1 n 2 be a cocompact lattice and p fo f be an injective representation into a convex cocompact discrete isometric subgroup of a noncompact rank 1 symmetric space the hausdorff dimension 6 f of the limit set of f p fo satisfies 6 f 6 fo n 1 we prove that equality holds if and only if p is a fuchsian representation i e f preserves a totally geodesic copy of hri in hr this generalizes the result of 2 and settles a question raised by tukia 43 p 428 actually we prove a more general result in the context of variable negative curvature strikingly there are no quasi fuchsian representations at least for the lower codimensional case in complex hyperbolic geometry that is for a cocompact lattice fo c su n 1 n 2 and an injective representation p fo su m 1 n m 2n 1 with f p fo convex cocompact we prove that one always has 6 f 6 fo and moreover f must stabilize a totally geodesic copy of h in h this can be viewed as a global generalization of goldman and millson s local rigidity theorem see 20 another global generalization was obtained by k corlette 5 various other related rigidity results are also obtained

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

inference in randomized studies with informative censoring and discrete time to event endpoints summary in this article we present a method for estimating and comparing the treatment specific distributions of a discrete time to event variable from right censored data our method allows for 1 adjustment for informative censoring due to measured prognostic factors for time to event and censoring and 2 quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors we develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia we perform a simulation study to assess the practical performance of our methodology

invariant peano curves of expanding thurston maps we consider thurston maps i e branched covering maps f s 2 s 2 that are post critically finite in addition we assume that f is expanding in a suitable sense it is shown that each sufficiently high iterate f f n of f is semi conjugate to z d s 1 s 1 where d deg f more precisely for such an f we construct a peano curve s 1 s 2 onto such that f z z d for all z s 1

affine action and margulis invariant abstract in this paper we show that two zariski dense subgroups consisting of hyperbolic elements in so n 1 n r 2n 1 with the same marked margulis invariant are conjugate we also consider in affine deformations an analogue of quasifuchsian deformation of fuchsian groups

doubly robust estimation of the area under the receiver operating characteristic curve in the presence of verification bias the area under the receiver operating characteristic curve auc is a popular summary measure of the efficacy of a medical diagnostic test to discriminate between healthy and diseased subjects a frequently encountered problem in studies that evaluate a new diagnostic test is that not all patients undergo disease verification because the verification test is expensive invasive or both furthermore the decision to send patients to verification often depends on the new test and on other predictors of true disease status in such cases usual estimators of the auc based on verified patients only are biased in this article we develop estimators of the auc of markers measured on any scale that adjust for selection to verification these estimators adjust for measured patient covariates and diagnostic test results and also for an assumed degree of residual selection bias they can then be used in a sensitivity analysis to examine how the auc estimates change when different plausible degrees of residual asso

on the discreteness criterion in sl 2 c in tukia and wang math scand 91 214 220 2002 the authors conjectured that a non elementary subgroup in sl 2 c containing parabolic and elliptic elements is discrete if and only if each two generator subgroup generated by a parabolic and an elliptic element is discrete the purpose of this paper is to give an affirmative answer to this question

foliations of hilbert modular surfaces the hilbert modular surface xd is the moduli space of abelian varieties a with real multiplication by a quadratic order of discriminant d 1 the locus where a is a product of elliptic curves determines a finite union of algebraic curves xd 1 xd in this paper we show the lamination xd 1 extends to an essentially unique foliation fd of xd by complex geodesics the geometry of fd is related to teichm uller theory holomorphic motions polygonal billiards and lattes rational maps we show every leaf of fd is either closed or dense and compute its holonomy we also introduce refinements tn i of the classical modular curves on xd leading to an explicit description of xd 1

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

area distortion of quasiconformal mappings in recent years quasiconformal mappings have been an efficient tool in the study of dynamical systems of the complex plane we show here that in turn methods or ideas from dynamical systems can be used to solve a number of open questions in the theory of planar quasiconformal mappings it has been known since the work of ahlfors a and mori mo that k quasiconformal mappings are locally h51der continuous with exponent 1 k the function

inference for cumulative incidence functions with informatively coarsened discrete event time data we consider the problem of comparing cumulative incidence functions of non mortality events in the presence of informative coarsening and the competing risk of death we extend frequentist based hypothesis tests previously developed for non informative coarsening and propose a novel bayesian method based on comparing a posterior parameter transformation with its expected distribution under the null hypothesis of equal cumulative incidence functions both methods use estimates derived by extending previously published estimation procedures to accommodate censoring by death the data structure and analysis goal are exemplified by the aids link to the intravenous experience alive study where researchers are interested in comparing incidence of human immunodeficiency virus seroconversion by risk behavior categories coarsening in the forms of interval and right censoring and censoring by death in alive is thought to be informative thus we perform a sensitivity analysis by incorporating elicited expert information about the relationship between seroconversion and censoring into the model

mating quadratic maps with the modular group in 1994 s bullett and c penrose introduced the one complex parameter family of 2 2 holomorphic correspondences mathcal f a begin aligned left frac aw 1 w 1 right 2 left frac aw 1 w 1 right left frac az 1 z 1 right left frac az 1 z 1 right 2 3 end aligned and proved that for every value of a in 4 7 subset mathbb r the correspondence mathcal f a is a mating between a quadratic polynomial q c z z 2 c c in mathbb r and the modular group vargamma psl 2 mathbb z they conjectured that this is the case for every member of the family mathcal f a which has a in the connectedness locus we show here that matings between the modular group and rational maps in the parabolic quadratic family per 1 1 provide a better model we prove that every member of the family mathcal f a which has a in the connectedness locus is such a mating

sensitivity of the discrete time kaplan meier estimate to nonignorable censoring application in a clinical trial untestable assumptions about association between survival and censoring times can affect the validity of estimates of the survival distribution including the kaplan meier km nonparametric mle this article explores the sensitivity of the km curve to nonignorable censoring by extending the index of local sensitivity to nonignorability isni troxel et al 2004 zhang and heitjan 2006 to the case of a nonparametric survival model the method involves first specifying a coarse data selection model to describe the association between the failure and censoring processes then evaluating the slope of the nonparametric survival mle ordinate with respect to a nonignorability parameter in the neighborhood of the ignorable model we define the nonparametric mle of the survival curve for a fixed value of the nonignorability parameter and show in a simulation that isni analysis effectively captures local sensitivity to nonignorability the method measures sensitivity in the sense of identifying functionals of the nonparametric mle that nonignorability if present can affect substantially we demonstrate the method with an application to a trial comparing mechanical assistance to optimal medical management in the treatment of end stage heart failure

some applications of thermodynamic formalism to manifolds with constant negative curvature the purpose of this article is to present a different approach to the analysis of the spectrum of a compact surface of constant negative curvature to explain our ideas we recall that there exists a highly successful theory for analyzing zeta functions for closed geodesics originated by a selberg the zeros for this zeta function identify the eigenvalues of the laplacian for the surface the main tool in this analysis is the selberg trace formula 7 there exists an approach having its roots in ergodic theory and statistical mechanics for analyzing zeta functions for geodesic and more general flows the principle here is quite different from that in the selberg approach the zeta function is some form of determinant of a family of perron frobenius type operators parameterized by the complex domain the zeta function behaves like a determinant in that zeros correspond to parameters for which the corresponding operator is not invertible 10 111 since both methods apply to surfaces of constant negative curvature this suggests that there is some mechanism involving a perron frobenius type operator characterizing the laplacian spectrum of the surface 161 oooi 8708 91 7 50

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

pattern mixture and selection models for analysing longitudinal data with monotone missing patterns summary we examine three pattern mixture models for making inference about parameters of the distribution of an outcome of interest y that is to be measured at the end of a longitudinal study when this outcome is missing in some subjects we show that these pattern mixture models also have an interpretation as selection models because these models make unverifiable assumptions we recommend that inference about the distribution of y be repeated under a range of plausible assumptions we argue that of the three models considered only one admits a parameterization that facilitates the examination of departures from the assumption of sequential ignorability the three models are nonparametric in the sense that they do not impose restrictions on the class of observed data distributions owing to the curse of dimensionality the assumptions that are encoded in these models are sufficient for identification but not for inference we describe additional flexible and easily interpretable assumptions under which it is possible to construct estimators that are well behaved with moderate sample sizes these assumptions define semiparametric models for the distribution of the observed data we describe a class of estimators which up to asymptotic equivalence comprise all the consistent and asymptotically normal estimators of the parameters of interest under the postulated semiparametric models we illustrate our methods with the analysis of data from a randomized clinical trial of contracepting women

mixture cure survival models with dependent censoring summary the paper is motivated by cure detection among the prostate cancer patients in the national institutes of health surveillance epidemiology and end results programme wherein the main end point e g deaths from prostate cancer and the censoring causes e g deaths from heart diseases may be dependent although many researchers have studied the mixture survival model to analyse survival data with non negligible cure fractions none has studied the mixture cure model in the presence of dependent censoring to account for such dependence we propose a more general cure model that allows for dependent censoring we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time by using a class of archimedean copula models within this framework we consider the parameter estimation the cure detection and the two sample comparison of latency distributions in the presence of dependent censoring when a proportion of patients is deemed cured large sample results by using martingale theory are obtained we examine the finite sample performance of the proposed methods via simulation and apply them to analyse the surveillance epidemiology and end results prostate cancer data

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