extending the torelli map to toroidal compactifications of siegel space it has been known since the 1970s that the torelli map m g a g associating to a smooth curve its jacobian extends to a regular map from the deligne mumford compactification overline operatorname m g to the 2nd voronoi compactification overline operatorname a g mathrm vor we prove that the extended torelli map to the perfect cone 1st voronoi compactification overline operatorname a g mathrm perf is also regular and moreover overline operatorname a g mathrm vor and overline operatorname a g mathrm perf share a common zariski open neighborhood of the image of overline operatorname m g we also show that the map to the igusa monoidal transform central cone compactification is not regular for g 9 this disproves a 1973 conjecture of namikawa

omnibus tests for comparison of competing risks with adjustment for covariate effects summary this article develops omnibus tests for comparing cause specific hazard rates and cumulative incidence functions at specified covariate levels confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed the omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause specific hazard rates under cox proportional hazards models a simulation procedure is devised for sampling from the null distribution of the test process leading to graphical and numerical techniques for detecting significant differences in the risks the approach is applied to a cohort study of type specific hiv infection rates

comparing perfect and 2nd voronoi decompositions the matroidal locus we compare two rational polyhedral admissible decompositions of the cone of positive definite quadratic forms the perfect cone decomposition and the 2nd voronoi decomposition we determine which cones belong to both the decompositions thus providing a positive answer to a conjecture of alexeev and brunyate invent math doi 10 1007 s00222 011 0347 2 2011 as an application we compare the two associated toroidal compactifications of the moduli space of principal polarized abelian varieties the perfect cone compactification and the 2nd voronoi compactification

a class of k sample tests for comparing the cumulative incidence of a competing risk in this paper for right censored competing risks data a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups the tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory it is proposed that weight functions very similar to those for the g p tests from ordinary survival analysis be used simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples

the graphical evaluation of explanatory variables in proportional hazard regression models summary a graphical technique for assessing explanatory variables in cox s proportional hazards regression model is examined the method arises from consideration of the cumulative hazard transformation and the partial likelihood score function and consists of permuting the observed rank statistic to account for the effects of explanatory variables fitted to the model an example is provided

indecomposable higher chow cycles on jacobians we construct some natural indecomposable elements of ch g j c 1 with trivial regulator and in particular prove that ch g ind j c 1 mb q is uncountable for c a generic curve or a generic hyperelliptic curve of genus g geq 3

fractal just infinite nil lie superalgebra of finite width abstract the grigorchuk and gupta sidki groups play fundamental role in modern group theory they are natural examples of self similar finitely generated periodic groups as their natural analogues there are constructions of nil lie p algebras over a field of characteristic 2 40 and arbitrary positive characteristic 52 in characteristic zero similar examples of lie algebras do not exist by a result of martinez and zelmanov 32 the second author constructed analogues of the grigorchuk and gupta sidki groups in the world of lie superalgebras of arbitrary characteristic the virtue of that construction is that the lie superalgebras have clear monomial bases 41 that lie superalgebras have slow polynomial growth and are graded by multidegree in the generators in particular a self similar lie superalgebra q is z 3 graded by multidegree in 3 generators its z 3 components lie inside an elliptic paraboloid in space the components are at most one dimensional thus the z 3 grading of q is fine an analogue of the periodicity is that homogeneous elements of the grading q q 0 q 1 are ad nilpotent in particular q is a nil finely graded lie superalgebra which shows that an extension of the mentioned result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid but computations with q are rather technical in this paper we construct a similar but simpler and smaller example namely we construct a 2 generated fractal lie superalgebra r over arbitrary field we find a clear monomial basis of r and unlike many examples studied before we find also a clear monomial basis of its associative hull a the latter has a quadratic growth the algebras r and a are z 2 graded by multidegree in the generators positions of their z 2 components are bounded by pairs of logarithmic curves on plane the z 2 components of r are at most one dimensional thus the z 2 grading of r is fine as an analogue of periodicity we establish that homogeneous elements of the grading r r 0 r 1 are ad nilpotent in case of n graded algebras a close analogue to being simple is being just infinite unlike previous examples of lie superalgebras we are able to prove that r is just infinite but not hereditary just infinite our example is close to the smallest possible example because r has a linear growth with a growth function r m 3 m as m moreover r is of finite width 4 char k 2 in case char k 2 we obtain a lie algebra of width 2 that is not thin thus we have got a more handy analogue of the grigorchuk and gupta sidki groups the constructed lie superalgebra r is of linear growth of finite width 4 and just infinite it also shows that an extension of the result of martinez and zelmanov 32 to the lie superalgebras of characteristic zero is not valid

nilpotent associative algebras and coclass theory abstract we initiate the investigation of nilpotent associative algebras using the coclass as primary invariant we consider the coclass graph g f r associated with the nilpotent associative f algebras of coclass r first we describe the infinite paths of g f r via a precise structure description of the inverse limits corresponding to these infinite paths then we prove that the number of essentially different infinite paths in g f r is finite if and only if f is finite or r 1 thus the results of this paper state and prove equivalents to the coclass conjectures c and d as introduced by leedham green and newman for the coclass theory of finite p groups

on almost fixed point free automorphisms abstract ideas from the theory of p adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points in particular we prove that the derived length of a finite p group admitting an automorphism of order p k with p m fixed points is bounded in terms of p m k this extends a well known result of alperin dealing with the case k 1 some applications to soluble groups are also given

metabelian thin lie algebras abstract a graded lie algebra is thin if it is generated by two elements of degree 1 and each of its homogeneous ideals is located between two consecutive terms of the lower central series in this paper we give a complete classification of the metabelian thin lie algebras and their graded automorphism groups

smoothed nonparametric estimation for current status competing risks data we study the nonparametric estimation of the cumulative incidence function and the cause specific hazard function for current status data with competing risks via kernel smoothing a smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators using the smoothed estimators and the plug in principle we can estimate the cause specific hazard function which has not been studied previously we also propose semi smoothed estimators of the cause specific hazard as an alternative to the smoothed estimator and demonstrate that neither is uniformly more efficient than the other numerical studies show that a smoothed bootstrap method works well for selecting the bandwidths in the smoothed nonparametric estimation the use of the estimators is exemplified by an application to cumulative incidence and hazard of subtype specific hiv infection from a sero prevalence study in injecting drug users in thailand copyright 2013 oxford university press

the class of the locus of intermediate jacobians of cubic threefolds we study the locus of intermediate jacobians of cubic threefolds within the moduli space mathcal a 5 of complex principally polarized abelian fivefolds and its generalization to arbitrary genus the locus of abelian varieties with a singular odd two torsion point on the theta divisor assuming that this locus has expected codimension g which we show to be true for g 5 and conjecturally for any g we compute the class of this locus and of its closure in the perfect cone toroidal compactification mathcal a g mathrm perf in the chow homology and the tautological ring

graded lie algebras of maximal class iii we describe the isomorphism classes of infinite dimensional n graded lie algebras of maximal class generated by their first homogeneous component over fields of characteristic two this complements the analogous work by caranti and newman in the odd characteristic case

narrow lie algebras a coclass theory and a characterization of the witt algebra abstract in this paper we examine some narrowness conditions for lie algebras over a fieldfof characteristic zero in particular we show that the natural analogs of the main coclass conjectures forp groups hold in the context of n graded lie algebraslwhich are generated by their first homogeneous componentl1 while lie algebras of finite coclass need not be soluble we show that the positive part of the witt algebra der f x is the only non soluble n graded lie algebralof coclass 1 which is generated byl1andl2

stability of the homology of the mapping class groups of orientable surfaces the mapping class group of f fgs r is f rgs wo a where a is the topological group of orientation preserving diffeomorphisms of f which are the identity on df and fix the s punctures when r 0 and 2g s 3 an important feature of f is that it acts properly discontinuously on the teichmiller space us the quotient is the moduli space f of isometry classes of complete hyperbolic metrics of finite area on f since us is homeomorphic to euclidean space and f is virtually torsion free we have

semiparametric models for cumulative incidence functions in analyses of time to failure data with competing risks cumulative incidence functions may be used to estimate the time dependent cumulative probability of failure due to specific causes these functions are commonly estimated using nonparametric methods but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution in such cases it may be possible to model the cause specific hazard of primary interest parametrically while accounting for the other modes of failure using nonparametric estimators the cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function more surprisingly they are often nearly as efficient as fully parametric estimators we illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer

arithmetically free group gradings of lie algebras ii abstract we study lie algebras l that are graded by an arbitrary group g and have finite support x we show that l is nilpotent of x bounded class if x is arithmetically free conversely if a finite subset y of g is not arithmetically free then y supports the grading of a non nilpotent lie algebra

ideally constrained lie algebras abstract in this paper we deal with graded lie algebras l such that there exists a positive integer r such that for every positive integer i and for every homogeneous ideal i l i the inclusion i l i r 1 holds the solvable case and the r 1 case receive a special attention

quasi filiform lie algebras of maximum length revisited abstract we revisit the problem of classification of quasi filiform lie algebras of maximum length the lists found in the literature are either incomplete or non explicit en route we touch upon the classification of graded filiform lie algebras generated by two elements of degree one and three respectively and as a byproduct obtain a classification of n graded infinite dimensional lie algebras with one dimensional homogeneous components of coclass two

cohomology of graded lie algebras of maximal class abstract it was shown by a fialowski that an arbitrary infinite dimensional n graded filiform type lie algebra g i 1 g i with one dimensional homogeneous components g i such that g 1 g i g i 1 i 2 over a field of zero characteristic is isomorphic to one and only one lie algebra from three given ones m 0 m 2 l 1 where the lie algebras m 0 and m 2 are defined by their structure relations m 0 e 1 e i e i 1 i 2 and m 2 e 1 e i e i 1 i 2 e 2 e j e j 2 j 3 and l 1 is the positive part of the witt algebra in the present article we compute the cohomology h m 0 and h m 2 with trivial coefficients give explicit formulas for their representative cocycles and describe the multiplicative structure in the cohomology also we discuss the relations with combinatorics and representation theory the cohomology h l 1 was calculated by l goncharova in 1973

a lie algebra attached to a projective variety each choice of a kahler class on a compact complex manifold defines an action of the lie algebra sl 2 on its total complex cohomology if a nonempty set of such kahler classes is given then we prove that the corresponding sl 2 copies generate a semisimple lie algebra we investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori hyperkahler manifolds and flag varieties we pay special attention to the cases where this leads to a jordan algebra structure or a graded frobenius algebra

classifying 2 groups by coclass now that the conjectures of leedham green and newrnan have been proved we probe deeper into the classification of p groups using coclass we determine the pro 2 groups of coclass at most 3 and use these to classify the 2 groups of coclass at most 3 into families using extensive computational evidence we make some detailed conjectures about the structure of these families we also conjecture that the 2 groups of arbitrary fixed coclass exhibit similar behaviour

cohomology and deformations of the infinite dimensional filiform lie algebra m 2 abstract denote m 2 the infinite dimensional n graded lie algebra defined by the basis e i for i 1 and by relations e 1 e i e i 1 for all i 2 e 2 e j e j 2 for all j 3 we compute in this article the bracket structure on h 1 m 2 m 2 h 2 m 2 m 2 and in relation to this we establish that there are only finitely many true deformations of m 2 in each weight by constructing them explicitly it turns out that in weight 0 one gets as non trivial deformation only one formal non converging deformation

complex filiform lie algebras of dimension 11 in this paper we give the explicit classification of complex filiform lie algebras of dimension 11 to do this we use a method previously obtained by us in an earlier paper which is based on the concept of isomorphism between lie algebras at present this explicit classification is not known although gomez jimenez and khakimdjanov gave a list of these algebras in a non explicit way but in terms of cocycles we find that there exist 188 families of complex filiform lie algebras of dimension 11

modelling age specific survival in nesting studies using a general approach for doubly censored and truncated data in typical nest survival studies the observed sample of nests is usually biased by left truncation i e only active nests enter the study additionally the failure data may be doubly censored because the exact dates of nest initiation and failure are uncertain we present a general bivariate contingency table approach for analyzing such data we use weakly structured step spline hazard models which avoid estimability problems encountered in a strictly nonparametric approach yet still permit flexibility our method eliminates a potential source of bias noted by heisey and nordheim 1990 biometrics 46 855 862 in the nest survival method of pollock and cornelius 1988 biometrics 44 397 404 we compare our approach to related techniques developed for estimating the incubation distribution of aids

perfect forms k theory and the cohomology of modular groups abstract for n 5 6 and 7 using the classification of perfect quadratic forms we compute the homology of the voronoi cell complexes attached to the modular groups sl n z and g l n z from this we deduce the rational cohomology of those groups and some information about k m z when m 5 6 and 7

a characterization of nilpotent nonassociative algebras by invertible leibniz derivations abstract moens proved that a finite dimensional lie algebra over a field of characteristic zero is nilpotent if and only if it has an invertible leibniz derivation in this article we prove the analogous results for finite dimensional malcev jordan 1 1 right alternative zinbiel and malcev admissible noncommutative jordan algebras over a field of characteristic zero also we describe all leibniz derivations of semisimple jordan right alternative and malcev algebras

action of correspondences on filtrations on cohomology and 0 cycles of abelian varieties we prove that given a symmetrically distinguished correspondence of a suitable complex abelian variety which includes any abelian variety of dimension at most 5 powers of complex elliptic curves etc that vanishes as a morphism on a certain quotient of its middle singular cohomology then it vanishes as a morphism on the deepest part of a particular filtration on the chow group of 0 cycles of the abelian variety as a consequence we prove that an automorphism of such an abelian variety that acts as the identity on a certain quotient of its middle singular cohomology acts as the identity on the deepest part of this filtration on the chow group of 0 cycles of the abelian variety as an application we prove that for the generalized kummer variety associated to a complex abelian surface and the automorphism induced from a symplectic automorphism of the complex abelian surface the automorphism of the generalized kummer variety acts as the identity on a certain subgroup of its chow group of 0 cycles

lie algebras with almost constant free derivations abstract let l be a finite dimensional lie algebra of characteristic 0 admitting a nilpotent lie algebra of derivations d by a classical result of jacobson if d is constant free that is without non zero constants x 0 for all d only if x 0 then l is nilpotent we prove that if d is almost constant free then l is almost nilpotent in the following precise sense if m is the dimension of the fitting null component with respect to d then l contains a nilpotent subalgebra n of codimension bounded by a function of m and n and the nilpotency class of n is bounded in terms of n only this includes strengthening jacobson s theorem by giving in the case m 0 a bound for the nilpotency class of l in terms of the number of weights of d the main result can also be stated as a theorem about a locally finite lie algebra over an algebraically closed field of characteristic 0 containing a nilpotent subalgebra with finitely many weights such that its fitting null component is of finite dimension then the algebra contains a nilpotent subalgebra of finite codimension with similar bounds for the codimension and the nilpotency class the results on derivations are based on results on z p z graded lie algebras where p is a prime with zero component of dimension m these results in turn generalize the higman kreknin kostrikin theorem on the nilpotency of lie algebras with a regular automorphism of prime order

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

the intersection cohomology of the satake compactification of mathcal a _g for g le 4 we completely determine the intersection cohomology of the satake compactifications mathcal a 2 mathrm sat mathcal a 3 mathrm sat and mathcal a 4 mathrm sat except for ih 10 mathcal a 4 mathrm sat we also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the satake compactification in these genera as a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved

graded lie algebras of maximal class ii abstract we describe the isomorphism classes of infinite dimensional n graded lie algebras of maximal class over fields of odd characteristic generated by their first homogeneous component

covariate analysis of competing risks data with log linear models a general system of log linear modeling is proposed for analysis of competing risks data with discrete covariates the instantaneous cause specific failure rates approximated by step functions are analyzed by techniques for multidimensional contingency tables censored observations are accommodated counts of failures of each type and the amount of follow up are summarized in two arrays in which each cell denotes a distinct combination of failure type time interval and covariate value maximum likelihood estimators for the parameters of the model are derived by iterative proportional fitting the resulting estimates of the number of failures in each cell are used for goodness of fit tests the principal advantages of this approach are its simple display of data its computational ease for the fitting and comparison of models and its provision of explicit goodness of fit tests interpretation of the models is facilitated by reference to several alternative models for survivorship and competing risks the basic model is extended to incorporate stochastic covariates whose values change during follow up and to accommodate quantitative covariates

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

graded lie algebras of maximal class we study graded lie algebras of maximal class over a field mathbf f of positive characteristic p a shalev has constructed infinitely many pairwise non isomorphic insoluble algebras of this kind thus showing that these algebras are more complicated than might be suggested by considering only associated lie algebras of p groups of maximal class here we construct mathbf f aleph 0 pairwise non isomorphic such algebras and max mathbf f aleph 0 soluble ones both numbers are shown to be best possible we also exhibit classes of examples with a non periodic structure as in the case of groups two step centralizers play an important role

joint inference for competing risks survival data abstractthis article develops joint inferential methods for the cause specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the time to the type of failure of interest in the presence of competing risks joint inference for the two functions are needed in practice because i they describe different characteristics of a given type of failure ii they do not uniquely determine each other and iii the effects of a variable on the two functions can be different and one often does not know which effects are to be expected we study both the group comparison problem and the regression problem we also discuss joint inference for other related functions our simulation shows that our joint tests can be considerably more powerful than the bonferroni method which has important practical implications to the analysis and design of clinical studies with competing risks data we illustrate our method using a hodgkin disease data and a