algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

on the comparison of two constructions of witt vectors of non commutative rings abstract let a be any associative ring possibly non commutative and let p be a prime number let e a be the ring of p typical witt vectors as constructed by cuntz and deninger in 1 and w a be that constructed by hesselholt in 3 the goal of this paper is to answer the following question by hesselholt is h h 0 e a w a we show that in the case p 2 there is no such isomorphism possible if one insists that it be compatible with the verschiebung operator and the teichmuller map

an extended direct branching algorithm for checking equivalence of deterministic pushdown automata abstract this paper extends the direct branching algorithm of 25 for checking equivalence of deterministic pushdown automata it does so by providing a technique called halting for dealing with nodes with unbounded degree in the comparison tree this may occur when a skipping step may be applied infinitely many times to a certain node as a result of infinite sequences of e moves this extension allows the algorithm to check equivalence of two deterministic pushdown automata when none of them is real time but in a certain condition that properly contains a case where one of them is real time strict

hochschild witt complex abstract in a previous paper we have defined polynomial witt vectors functor from vector spaces over a perfect field k of positive characteristic p to abelian groups in this paper we use polynomial witt vectors to construct a functorial hochschild witt complex w c h a for any associative unital k algebra a with homology groups w h h a we prove that the group w h h 0 a coincides with the group of non commutative witt vectors defined by hesselholt while if a is commutative finitely generated and smooth the groups w h h i a are naturally identified with the terms w a i of the de rham witt complex of the spectrum of a

modelling complex survey data with population level information an empirical likelihood approach survey data are often collected with unequal probabilities from a stratified population in many modelling situations the parameter of interest is a subset of a set of parameters with the others treated as nuisance parameters we show that in this situation the empirical likelihood ratio statistic follows a chi squared distribution asymptotically under stratified single and multi stage unequal probability sampling with negligible sampling fractions simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation linearization or resampling

degeneration of l adic weight spectral sequences the degeneracy of the l adic weight spectral sequence over any trait with no assumptions on its residue field is proved by the method of log geometry in the sense of fontaine illusie

a direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata a new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata dpda s after korenjak and hopcroft s branching algorithm it is not only powerful enough to be applicable to two dpda s accepting by empty stack one of which is real time but also simple even for dpda s in lower subclasses this is the first time the branching algorithm has been used to give such a general decision procedure without ever mixing the two languages in question in other words it deals with only the equivalence equation whose left hand side consists of a pure reachable configuration of one dpda and whose right hand side that of the other

a direct branching algorithm for checking equivalence of strict deterministic vs ll k grammars abstract we present here an equivalence checking algorithm which operates directly on a pair of strict deterministic vs ll k grammars it is also straightforwardly applicable to a pair of ll k grammars though an ll k grammar is not necessarily strict deterministic the basic idea is from korenjak and hopcroft s branching algorithm for simple deterministic grammars but ours is so distinguished that it is throughout free from mixing the nonterminals of the respective grammars in question and then very simple

overconvergent witt vectors let a be a finitely generated algebra over a field k of characteristic p 0 we introduce a subring w a w a which we call the ring of overconvergent witt vectors and prove its basic properties in a subsequent paper we use the results to define an overconvergent de rham witt complex for smooth varieties over k whose hypercohomology is the rigid cohomology

the big de rham witt complex this paper gives a new and direct construction of the multi prime big de rham witt complex which is defined for every commutative and unital ring the original construction by madsen and myself relied on the adjoint functor theorem and accordingly was very indirect the construction given here also corrects the 2 torsion which was not quite correct in the original version the new construction is based on the theory of modules and derivations over a ring which is developed first the main result in this first part of the paper is that the universal derivation of a ring is given by the universal derivation of the underlying ring together with an additional structure depending directly on the ring structure in question in the case of the ring of big witt vectors this additional structure gives rise to divided frobenius operators on the module of kahler differentials it is the existence of these divided frobenius operators that makes the new construction of the big de rham witt complex possible it is further shown that the big de rham witt complex behaves well with respect to etale maps and finally the big de rham witt complex of the ring of integers is explicitly evaluated

witt vector rings and the relative de rham witt complex in this paper we develop a novel approach to witt vector rings and to the relative de rham witt complex we do this in the generality of arbitrary commutative algebras and arbitrary truncation sets in our construction of witt vector rings the ring structure is obvious and there is no need for universal polynomials moreover a natural generalization of the construction easily leads to the relative de rham witt complex our approach is based on the use of free or at least torsion free presentations of a given commutative ring r and it is an important fact that the resulting objects are independent of all choices the approach via presentations also sheds new light on our previous description of the ring of p typical witt vectors of a perfect fp algebra as a completion of a semigroup algebra we develop this description in different directions for example we show that the semigroup algebra can be replaced by any free presentation of r equipped with a linear lift of the frobenius automorphism using the result in appendix a by umberto zannier we also extend the description of the witt vector ring as a completion to all f p algebras with injective frobenius map

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

robust estimation through estimating equations summary utilizing the theory of estimating equations godambe 1960 godambe thompson 1978 this paper develops concepts of parameter defining function and effective parameter the paper provides theory and techniques for choosing from a given set of robust parameters one that is most effective or one that can most efficiently be estimated the word parameter is used in statistics in two rather distinct contexts in the data analytic context a parameter characterizes some interesting aspect of the distribution such as its mean its median or some percentile in the context of modern statistical theory founded by k pearson r a fisher and others the parameter is related to and derives its meaning from a specific probabilistic model in this second context the model is of central importance and one seeks to complete it or perfect it by estimating its unknown parameter in the first context there is considerable flexibility and a parameter can typically be defined in many ways the choice of a parameter definition involves the following considerations a how much does it tell about the interesting or practically important part of the distribution b how insensitive or robust it is with respect to the uninteresting part of the distribution c how best can it be estimated the two contexts described above may of course overlap in the present paper we develop a theory which emphasizes the data analytic meaning of the parameter the approach on the other hand is more in line with the modern statistical theory mentioned above than that of most other works on robust estimation in particular asymptotic minimaxity plays no role the theory is designed to incorporate questions a b and c raised above it is based on the theory of estimating equations godambe 1960 godambe thompson 1978 the new concepts employed are those of parameter defining function and effectiveness of a parameter these are defined in 2 1 within

fitting cox s proportional hazards models from survey data summary the proportional hazards model makes a number of assumptions which may not always be completely satisfied however fitting such models can have both descriptive and analytical value we discuss the implications of the survey design for large scale studies we propose a weighted estimator and derive a design based estimator for the variance of the estimated parameters the derivation requires using methods not previously used in the context of analysis of survey data we conduct a small simulation study comparing the proposed method with others in the literature

cohomology of exact categories and non additive sheaves abstract we use non additive sheaves to introduce an absolute notion of hochschild cohomology for exact categories as ext s in a suitable bisheaf category we compare our approach to various definitions present in the literature

zeroth hochschild homology of preprojective algebras over the integers we determine the z module structure of the preprojective algebra and its zeroth hochschild homology for any non dynkin quiver and hence the structure working over any base commutative ring of any characteristic this answers and generalizes a conjecture of hesselholt and rains producing new p torsion classes in degrees 2pl l 1 we relate these classes by p th power maps and interpret them in terms of the kernel of verschiebung maps from noncommutative witt theory an important tool is a generalization of the diamond lemma to modules over commutative rings which we give in the appendix

isocrystals associated to arithmetic jet spaces of abelian schemes abstract using buium s theory of arithmetic differential characters we construct a filtered f isocrystal h a k associated to an abelian scheme a over a p adically complete discrete valuation ring with perfect residue field as a filtered vector space h a k admits a natural map to the usual de rham cohomology of a but the frobenius operator comes from arithmetic differential theory and is not the same as the usual crystalline one when a is an elliptic curve we show that h a k has a natural integral model h a which implies an integral refinement of a result of buium s on arithmetic differential characters the weak admissibility of h a k depends on the invertibility of an arithmetic differential modular parameter thus the fontaine functor associates to suitably generic a a local galois representation of an apparently new kind

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

quantile estimation with a complex survey design estimation of the finite population distribution function and related statistics such as the median and interquartile range is considered large sample properties of estimators constructed from stratified cluster samples and properties of large sample confidence intervals are established the results are obtained within the context of a sequence of finite populations generated from a superpopulation

higher chow groups with modulus and relative milnor theory let x be a smooth variety over a field k and d an effective divisor whose support has simple normal crossings we construct an explicit cycle map from z r x d nis the nisnevich motivic complex of the pair x d to km r x d nis r a shift of the relative milnor k sheaf of x d we show that this map induces an isomorphism h m nis x d z r h xnis k r x d nis for all i dimx this generalizes the well known isomorphism in the case d 0 we use this to prove a certain zariski descent property for the motivic cohomology of the pair ak m 1 0

bokstein homomorphism as a universal object abstract we give a simple construction of the correspondence between square zero extensions r of a ring r by an r bimodule m and second maclane cohomology classes of r with coefficients in m the simplest non trivial case of the construction is r m z p r z p 2 thus the bokstein homomorphism of the title following jibladze and pirashvili we treat maclane cohomology as cohomology of non additive endofunctors of the category of projective r modules we explain how to describe liftings of r modules and complexes of r modules to r in terms of data purely over r we show that if r is commutative then commutative square zero extensions r correspond to multiplicative extensions of endofunctors we then explore in detail one particular multiplicative non additive endofunctor constructed from cyclic powers of a module v over a commutative ring r annihilated by a prime p in this case r is the second witt vectors ring w 2 r considered as a square zero extension of r by the frobenius twist r 1

orthogonality of estimating functions and nuisance parameters summary cox reid 1987 proposed the technique of orthogonalizing parameters to deal with the general problem of nuisance parameters within fully parametric models they obtained a large sample approximation to the conditional likelihood along the same lines davison 1988 studied generalized linear models in the present paper we deal with the problem of nuisance parameters within a semiparametric setup which includes the class of distributions associated with generalized linear models the technique used is that of optimum orthogonal estimating functions godambe thompson 1989 the results are related to those of cox reid 1987

on the k theory of truncated polynomial algebras revisited abstract we revisit the computation due to hesselholt and madsen of the k theory of truncated polynomial algebras for perfect fields of positive characteristic the resulting k groups are expressed in terms of big witt vectors of the field the original proof relied on an understanding of cyclic polytopes in order to determine the genuine equivariant homotopy type of the cyclic bar construction for a suitable monoid using the nikolaus scholze framework for topological cyclic homology we achieve the same result using only the homology of said cyclic bar construction as well as the action of connes operator

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

balanced repeated replication for stratified multistage survey data under imputation abstract balanced repeated replication brr is a popular method for variance estimation in surveys the standard brr method works by first creating a set of balanced pseudoreplicated datasets from the original dataset for a survey estimator the brr variance estimator is the average of squared deviations r where r is the same as but based on the data in the rth pseudoreplicated dataset only but when there are a large number of imputed missing values nonrespondents treating the imputed values as observed data and applying the standard brr variance estimation formula does not produce valid variance estimators intuitively the variation due to imputation can be captured by the brr method if every pseudoreplicated dataset is imputed in exactly the same way as the original dataset is imputed assuming that the dataset contains flags for nonrespondents but when a random imputation method such as random hot deck imputation random ratio imputation or random regression imputation is u

almost purity and overconvergent witt vectors abstract in a previous paper we stated a general almost purity theorem in the style of faltings if r is a ring for which the frobenius maps on finite p typical witt vectors over r are surjective then the integral closure of r in a finite etale extension of r p 1 is almost finite etale over r here we use almost purity to lift the finite etale extension of r p 1 to a finite etale extension of rings of overconvergent witt vectors the point is that no hypothesis of p adic completeness is needed this result thus points towards potential global analogues of p adic hodge theory as an illustration we construct modules associated with artin motives over q the modules we construct are defined over a base ring which seems well suited to generalization to a more global setting we plan to pursue such generalizations in later work

on the k theory of local fields in this paper we establish a connection between the quillen k theory of certain local fields and the de rham witt complex of their rings of integers with logarithmic poles at the maximal ideal the fieldsk we consider are complete discrete valuation fields of characteristic zero with perfect residue field k of characteristic p 2 when k contains the pth roots of unity the relationship between the k theory with z p coefficients and the de rham witt complex can be described by a sequence

cyclic homology and equivariant homology the purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of connes 9 11 see also loday and quillen 20 and if equivariant homology and cohomology theories here ii is the circle group the most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precise statements will be postponed until w 3 in this introduction we explain some of the formal similarities between the cyclic theory and the equivariant theory and give two examples where the general results apply let a be an associative algebra over a commutative ring k then one can form the cyclic homology hc a and cohomology hc a of a these groups have periodicity operators

use of estimating functions for estimation from complex surveys abstract we describe a method for point and interval estimation of population parameters from complex surveys using estimating functions the theory was originally developed for infinite populations and has recently been applied to finite populations with estimating functions a unifying framework can be given for point and interval estimation of both finite and infinite population parameters we discuss test inversion methods to derive confidence intervals for one dimensional parameters and propose a method for eliminating nuisance parameters in the multidimensional setting we show that special cases of our proposal result in conditional and orthogonal methods proposed in the literature we describe a simulation study using real data to compare the coverage probabilities of confidence intervals obtained under various approaches

the witt vectors for green functors abstract we define twisted hochschild homology for green functors this construction is the algebraic analogue of the relative topological hochschild homology thh c n and under flatness conditions it describes the e 2 term of the kunneth spectral sequence for relative thh applied to ordinary rings we obtain new algebraic invariants extending hesselholt s construction of the witt vectors of noncommutative rings we interpret our construction as providing witt vectors for green functors

on relative and overconvergent de rham witt cohomology for log schemes we construct the relative log de rham witt complex this is a generalization of the relative de rham witt complex of langer zink to log schemes we prove the comparison theorem between the hypercohomology of the log de rham witt complex and the relative log crystalline cohomology in certain cases we construct the p adic weight spectral sequence for relative proper strict semistable log schemes when the base log scheme is a log point we show it degenerates at e 2 after tensoring with the fraction field of the witt ring we also extend the definition of the overconvergent de rham witt complex of davis langer zink to log schemes x d associated with smooth schemes with simple normal crossing divisor over a perfect field finally we compare its hypercohomology with the rigid cohomology of x setminus d