voevodsky s mixed motives versus kontsevich s noncommutative mixed motives abstract we prove that the quotient of voevodsky s category of geometric mixed motives dm gm by the endofunctor q 1 2 embeds fully faithfully into kontsevich s category of noncommutative mixed motives kmm we show moreover that this embedding is compatible with the one between chow motives and noncommutative chow motives along the way we relate kmm with morel voevodsky s stable a 1 homotopy category recover the twisted algebraic k theory of kahn levine from kmm and extend elmendorf mandell s foundational work on multicategories to a broader setting

on the conservativity of the functor assigning to a motivic spectrum its motive given a 0 connective motivic spectrum e is an element of sh k over a perfect field k we determine h under bar 0 of the associated motive me is an element of dm k in terms of pi under bar 0 e using this we show that if k has finite 2 etale cohomological dimension then the functor m w sh k dm k is conservative when restricted to the subcategory of compact spectra and induces an injection on picard groups we extend the conservativity result to fields of finite virtual 2 etale cohomological dimension by considering what we call real motives

nonparametric association analysis of bivariate competing risks data although nonparametric analyses of bivariate failure times under independent censoring have been widely studied nonparametric analyses of bivariate competing risks data have not yet been investigated such analyses are important in familial association studies where multiple interacting failure types may violate the independent censoring assumption we develop nonparametric estimators for the bivariate cause specific hazards function and the bivariate cumulative incidence function that are natural analogs of their univariate counterparts and make no assumptions about the dependence of the risks the estimators are shown to be uniformly consistent and to converge weakly to gaussian processes they provide the basis for novel time dependent association measures with the associated inferences yielding tests of cause specific independence in pairs the methodology performs well in simulations with realistic sample sizes its practical utility is illustrated in an analysis of dementia in the cache county st

dynamical scaling in branching models for seismicity we propose a branching process based on a dynamical scaling hypothesis relating time and mass in the context of earthquake occurrence we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis we present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events the numerical data reproduce the hierarchical organization in time and magnitude of experimental interevent time distribution

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

triangulated categories of relative 1 motives abstract the category da 1 s of relative cohomological 1 motives is the localizing subcategory of the triangulated category da s da e t s q of relative voevodsky motives with rational coefficients over a scheme s which is generated by cohomological motives of curves over s we construct and study a candidate for the standard motivic t structure on da 1 s for s noetherian finite dimensional and excellent we show this t structure is non degenerate and relate its heart mm 1 s with deligne 1 motives over s in particular when s is regular the category of deligne 1 motives embeds in mm 1 s fully faithfully we also study the inclusion of da 1 s into the larger category da coh s of relative cohomological motives on s and prove that its right adjoint 1 preserves compact objects

effective motives with and without transfers in characteristic p abstract we prove the equivalence between the category rigdm et eff k q of effective motives of rigid analytic varieties over a perfect complete non archimedean field k and the category rigda frobet eff k q which is obtained by localizing the category of motives without transfers rigda et eff k q over purely inseparable maps in particular we obtain an equivalence between rigdm et eff k q and rigda et eff k q in the characteristic 0 case and an equivalence between dm et eff k q and da frobet eff k q of motives of algebraic varieties over a perfect field k we also show a relative and a stable version of the main statement

l algebre de hopf et le groupe de galois motiviques d un corps de caracteristique nulle ii this is the second article of a series of two aiming at constructing and studying motivic galois groups in the context of triangulated motives these motivic galois groups were constructed in the first article and their algebras of regular functions were described concretely in terms of differential forms or algebraic cycles in the present article we gather important complements to the first one in the first part of this article we describe the link between the motivic galois group and the usual galois group of a subfield of in the second part we develop the basis of a theory of ramification for the motivic galois groups by constructing motivic versions of the decomposition and inertia groups associated to a geometric valuation we also introduce the relative motivic galois group of an extension k k which measures the difference between the motivic galois groups of k and k the latter is more accessible than its absolute counterpart in effect we show that it is a quotient of the pro algebraic completion of the topological fundamental pro group of a the pro variety homk k at least when the extension k k is of finite type

motivic periods and grothendieck arithmetic invariants abstract we construct a period regulator for motivic cohomology of an algebraic scheme over a subfield of the complex numbers for the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective showing that a suitable betti de rham realization of 1 motives is fully faithful we can verify this period conjecture in several cases the divisibility properties of motivic cohomology imply that our conjecture is a neat generalization of the classical grothendieck period conjecture for algebraic cycles on smooth and proper schemes these divisibility properties are treated in an appendix by b kahn extending previous work of bloch and colliot thelene raskind

replacing model categories with simplicial ones in this paper we show that model categories of a very broad class can be replaced up to quillen equivalence by simplicial model categories

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

from algebraic cobordism to motivic cohomology let s be an essentially smooth scheme over a eld of characteristic exponent c we prove that there is a canonical equivalence of motivic spectra over s mgl a1 a2 1 c hz 1 c where hz is the motivic cohomology spectrum mgl is the algebraic cobordism spectrum and the elements an are generators of the lazard ring we discuss several applications including the computation of the slices of z 1 c local landweber exact motivic spectra and the convergence of the associated slice spectral sequences

une version relative de la conjecture des periodes de kontsevich zagier we start with a series f p r1 fr r with indeterminate and where the coecients fr fr z1 zn are holomorphic functions dened on an open neighborhood of the closed polydisc d n f z1 zn jzij 1g integrating the coecients of this series on the n dimensional real cube 0 1 n yields a laurent series r 0 1 n f when f is algebraic we say that r 0 1 n f is a series of periods in this article our goal is to determine the algebraic series f such that r 0 1 n f is zero in principle this gives informations on the transcendence properties of series of periods our main result is reminiscent to the kontsevich zagier conjecture on periods in a modied form

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

model category structures on chain complexes of sheaves in this paper we try to determine when the derived category of an abelian category is the homotopy category of a model structure on the category of chain complexes we prove that this is always the case when the abelian category is a grothendieck category as has also been done by morel but this model structure is not very useful for dening derived tensor products we therefore consider another method for constructing a model structure and apply it to the category of sheaves on a well behaved ringed space the resulting flat model structure is compatible with the tensor product and all homomorphisms of ringed spaces

the gysin triangle via localization and a 1 homotopy invariance the first author was partially supported by the nsf career award 1350472 and by the portuguese foundation for science and technology grant pest oe mat ui0297 2014

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

a note on fractional linear pure birth and pure death processes in epidemic models abstract in this note we highlight the role of fractional linear birth and linear death processes recently studied in orsingher et al 2010 5 and orsingher and polito 2010 6 in relation to epidemic models with empirical power law distribution of the events taking inspiration from a formal analogy between the equation for self consistency of the epidemic type aftershock sequences etas model and the fractional differential equation describing the mean value of fractional linear growth processes we show some interesting applications of fractional modelling in studying ab initio epidemic processes without the assumption of any empirical distribution we also show that in the framework of fractional modelling subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes moreover we discuss a simple toy model in order to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth

kaplan meier estimate on the plane estimation of the bivariate survival function from censored data is considered the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data a bivariate analogue of the kaplan meier estimate is introduced and its almost sure consistency is studied extensions to the general multivariate case are sketched

modules over motivic cohomology abstract for fields of characteristic zero we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to voevodsky s big category of motives the proof makes use of some highly structured models for motivic stable homotopy theory motivic spanier whitehead duality the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper working with rational coefficients we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory

self similar branching of aftershock sequences abstract in this paper we propose a branching aftershock sequence bass model for seismicity we suggest that the bass model is a preferred alternative to the widely studied epidemic type aftershock sequence etas model in the bass model an initial or seed earthquake is specified the subsequent earthquakes are obtained from the statistical distributions of magnitude time and location the magnitude scaling is based on a combination of the gutenberg richter scaling relation and the modified bath s law for the scaling relation of aftershocks relative to the magnitude of the seed earthquake omori s law specifies the distribution of earthquake times and a modified form of omori s law specifies the distribution of earthquake locations since the bass model is specified by the four scaling relations it is fully self similar this is not the case for etas we also give a deterministic version of bass and show that it satisfies tokunaga side branching statistics in a similar way to diffusion limited aggregation dla

vere jones self similar branching model motivated by its potential application to earthquake statistics as well as for its intrinsic interest in the theory of branching processes we study the exactly self similar branching process introduced recently by vere jones this model extends the etas class of conditional self excited branching point processes of triggered seismicity by removing the problematic need for a minimum as well as maximum earthquake size to make the theory convergent without the need for the usual ultraviolet and infrared cutoffs the distribution of magnitudes m sup of daughters of first generation of a mother of magnitude m has two branches m sup m with exponent beta d where beta and d are two positive parameters we investigate the condition and nature of the subcritical critical and supercritical regime in this and in an extended version interpolating smoothly between several models we predict that the distribution of magnitudes of events triggered by a mother of magnitude m over all generations has also two branches m sup m with exponent beta h with h d radical 1 s where s is the fraction of triggered events this corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations ofmore triggered events for a significant part of the parameter space the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources immigrants reproduces the distribution of the spontaneous sources with a single branch and is blind to the exponents beta d of the distribution of triggered events since the distribution of earthquake magnitudes is usually obtained with catalogs including many sequences we conclude that the two branches of the distribution of aftershocks are not directly observable and the model is compatible with real seismic catalogs in summary the exactly self similar vere jones model provides an attractive new approach to model triggered seismicity which alleviates delicate questions on the role of magnitude cutoffs in other non self similar models the new prediction concerning two branches in the distribution of magnitudes of aftershocks could be tested with recently introduced stochastic reconstruction methods tailored to disentangle the different triggered sequences less

cumulative incidence association models for bivariate competing risks data association models like frailty and copula models are frequently used to analyze clustered survival data and evaluate within cluster associations the assumption of noninformative censoring is commonly applied to these models though it may not be true in many situations in this paper we consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function cif a nonparametrically identifiable quantity copula models are proposed which relate the bivariate cif to its corresponding univariate cifs similarly to independently right censored data and accommodate frailty models for the bivariate cif two estimating equations are developed to estimate the association parameter permitting the univariate cifs to be estimated either parametrically or nonparametrically goodness of fit tests are presented for formally evaluating the parametric models both estimators perform well with moderate sample sizes in simulation studies the practical use of the methodology is illustrated in an analysis of dementia associations

nonparametric association analysis of exchangeable clustered competing risks data summary the work is motivated by the cache county study of aging a population based study in utah in which sibship associations in dementia onset are of interest complications arise because only a fraction of the population ever develops dementia with the majority dying without dementia the application of standard dependence analyses for independently right censored data may not be appropriate with such multivariate competing risks data where death may violate the independent censoring assumption nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data as needed with the large sibships in the cache county study time dependent association measures are evaluated using these estimators large sample inferences are studied rigorously using empirical process techniques the practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the cache county study where dementia onset clustering among siblings varies strongly by age

rigidity in motivic homotopy theory we show that extensions of algebraically closed fields induce full and faithful functors between the respective motivic stable homotopy categories with finite coefficients

mixed weil cohomologies abstract we define for a regular scheme s and a given field of characteristic zero k the notion of k linear mixed weil cohomology on smooth s schemes by a simple set of properties mainly nisnevich descent homotopy invariance stability which means that the cohomology of g m behaves correctly and kunneth formula we prove that any mixed weil cohomology defined on smooth s schemes induces a symmetric monoidal realization of some suitable triangulated category of motives over s to the derived category of the field k this implies a finiteness theorem and a poincare duality theorem for such a cohomology with respect to smooth and projective s schemes which can be extended to smooth s schemes when s is the spectrum of a perfect field this formalism also provides a convenient tool to understand the comparison of such cohomology theories

modelling multivariate failure time associations in the presence of a competing risk there has been much research on analysing multivariate failure times but little that has accommodated failures that arise in the presence of a competing failure process this paper studies the problem of describing associations among times to such failures it proposes a modified conditional hazard ratio measure of association that is tailored to competing risks data develops frailty models and a nonparametric method for describing the proposed measure and contrasts estimation by proposed methods with the standard of treating competing risks as independently censoring failure times due to targeted causes the methods are investigated on simulated and real data

motives of deligne mumford stacks abstract for every smooth and separated deligne mumford stack f we associate a motive m f in voevodsky s category of mixed motives with rational coefficients dm eff k q when f is proper over a field of characteristic 0 we compare m f with the chow motive associated to f by toen 2000 31 without the properness condition we show that m f is a direct summand of the motive of a smooth quasi projective variety

algebraic elliptic cohomology theory and flops i we define the algebraic elliptic cohomology theory coming from krichever s elliptic genus as an oriented cohomology theory on smooth varieties over an arbitrary perfect field we show that in the algebraic cobordism ring with rational coefficients the ideal generated by differences of classical flops coincides with the kernel of krichever s elliptic genus this generalizes a theorem of b totaro in the complex analytic setting

the unstable slice filtration the main goal of this paper is to construct an analogue of vo evodsky s slice filtration in the motivic unstable homotopy category the construction is done via birational invariants this is motivated by the exis tence of an equivalence of categories between the orthogonal components for voevodsky s slice filtration and the birational motivic stable homotopy cat egories constructed in 9 another advantage of this approach is that the slices appear naturally as homotopy fibres and not as in the stable setting where they are defined as homotopy cofibres which behave much better in the unstable setting

efficient estimation in the bivariate censoring model and repairing npmle the npmle in the bivariate censoring model is not consistent the problem is caused by the singly censored observations in this paper we prove that the npmle based on interval censoring the singly censored observations is ecient for this reduced data and moreover if we let the width of the interval converge to zero slowly enough then the npmle is also ecient for the original data we are able to determine a lower bound for the rate at which the bandwidth should converge to zero the eciency proof uses the general identity which holds for npmle of a linear parameter in convex models as proved in van der laan 1993a

an isomorphism of motivic galois groups abstract in characteristic 0 there are essentially two approaches to the conjectural theory of mixed motives one due to nori and the other one due to independently hanamura levine and voevodsky although these approaches are a priori quite different it is expected that ultimately they can be reduced to one another in this article we provide some evidence for this belief by proving that their associated motivic galois groups are canonically isomorphic

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations

some remarks concerning the grothendieck period conjecture we discuss various results and questions around the grothendieck period conjecture which is a counterpart concerning the de rham betti realization of algebraic vari eties over number fields of the classical conjectures of hodge and tate these results give new evidence towards the conjectures of grothendieck and kontsevich zagier concerning transcen dence properties of the torsors of periods of varieties over number fields let q be the algebraic closure of q in c let x be a smooth projective variety over q and let x an c denote the compact complex analytic manifold that it defines the grothendieck period conjecture in codimension k on x denoted gpc k x asserts that any class in the