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 negative k theory of schemes in finite characteristic abstract we show that if x is a d dimensional scheme of finite type over an infinite perfect field k of characteristic p 0 then k i x 0 and x is k i regular for i d 2 whenever the resolution of singularities holds over k this proves the k dimension conjecture of weibel c weibel k theory and analytic isomorphisms invent math 61 1980 177 197 2 9 except for d 1 i d 2 in all characteristics assuming the resolution of singularities

ladders and simplicity of derived module categories abstract recollements of derived module categories are investigated using a new technique ladders of recollements which are maximal mutation sequences the position in the ladder is shown to control whether a recollement restricts from unbounded to another level of derived category ladders also turn out to control derived simplicity on all levels an algebra is derived simple if its derived category cannot be deconstructed that is if it is not the middle term of a non trivial recollement whose outer terms are again derived categories of algebras derived simplicity on each level is characterised in terms of heights of ladders these results are complemented by providing new classes of examples of derived simple rings in particular indecomposable commutative rings as well as by a finite dimensional counterexample to the jordan holder problem for derived module categories moreover recollements are used to compute homological and k theoretic invariants

a note on k theory and triangulated categories we provide an example of two closed model categories having equivalent homotopy categories but different waldhausen k theories we also show that there cannot exist a functor from small triangulated categories to spaces which recovers quillen s k theory for exact categories and which satisfies localization

on the cohen macaulay and buchsbaum property for unions of planes in affine space the coordinate ring a of a union of planes in affine space is studied and it is asked when a is a cohen macaulay or buchsbaum ring these properties are related to the position of the planes via the notion of seminormality it is shown that a is cohen macaulay iff a is connected in codimension 2 and seminormal in an appropriate sense consideration of the cohen macaulification then yields a simple criterion for a to be buchsbaum methods with several examples are illustrated

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

stable homotopy as a triangulated functor let j i be the homotopy category of all finite spectra the homotopy category of all spectra and y 89 be the homotopy category of all prime to 2 spectra let h y abelian groups be a homological functor i e a generalized homology theory a natural question is whether h can be lifted to a triangulated functor is there a functor t y d abelian groups so that composed with the usual homology functor on d abelian groups is h here d abelian groups d z is the derived category of z modules if h is ordinary homology the answer is clearly yes after all the ordinary homology of a space is given by the singular chain complex almost by definition one has a lifting by the brown representability theorem the general statement follows from the special case h h the stable homotopy functor let us be a little more precise

intersection products for tensor triangular chow groups abstract we show that under favorable circumstances one can construct an intersection product on the chow groups of a tensor triangulated category t as defined in 5 which generalizes the usual intersection product on a non singular algebraic variety our construction depends on the choice of an algebraic model for t a tensor frobenius pair which has to satisfy a k theoretic regularity condition analogous to the gersten conjecture from algebraic geometry in this situation we are able to prove an analogue of the bloch formula and use it to define an intersection product similar to grayson s construction from 14 we then recover the usual intersection product on a non singular algebraic variety assuming a k theoretic compatibility condition

additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives abstract i panin proved in the nineties that the algebraic k theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras later merkurjev and panin described the algebraic k theory of toric varieties as a direct summand of the algebraic k theory of separable algebras in this article making use of the recent theory of noncommutative motives we extend panin and merkurjev panin s computations from algebraic k theory to every additive invariant as a first application we fully compute the cyclic homology and all its variants of twisted projective homogeneous varieties as a second application we show that the noncommutative motive of a twisted projective homogeneous variety is trivial if and only if the brauer classes of the associated central simple algebras are trivial along the way we construct a fully faithful functor from merkurjev panin s motivic category to kontsevich s category of noncommutative chow motives which is of independent interest

the derived category of complex periodic k theory localized at an odd prime abstract we prove that for an odd prime p the derived category d k u p of the p local complex periodic k theory spectrum k u p is triangulated equivalent to the derived category of its homotopy ring k u p this implies that if p is an odd prime the triangulated category d k u p is algebraic

formal completions and idempotent completions of triangulated categories of singularities abstract the main goal of this paper is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic we also discuss thomason s theorem on dense subcategories and a relation to the negative k theory

a note on k theory and triangulated derivators abstract in this paper we show an example of two differential graded algebras that have the same derivator k theory but non isomorphic waldhausen k theory we also prove that maltsiniotis s comparison and localization conjectures for derivator k theory cannot be simultaneously true

jordan holder theorems for derived categories of derived discrete algebras abstract for any positive integer n n derived simple derived discrete algebras are classified up to derived equivalence furthermore the jordan holder theorems for all kinds of derived categories of derived discrete algebras are obtained

euler class group of a laurent polynomial ring local case abstract let r be a noetherian commutative ring of dimension n 2 and let a r t t 1 assume that the height of the jacobson radical of r is at least 2 let p be a projective a module of rank n dim a 1 with trivial determinant we define an abelian group called the euler class group of a denoted by e a let be an isomorphism from a to det p to the pair p we associate an element of e a called the euler class of p denoted by e p then we prove that a necessary and sufficient condition for p to have a unimodular element is the vanishing of e p in e a earlier bhatwadekar and raja sridharan have defined the euler class group of r denoted by e r and have proved similar results for projective r module of rank n later m k das defined the euler class group of the polynomial ring r t denoted by e r t and proved similar results for projective r t modules of rank n with trivial determinant

derived azumaya algebras and generators for twisted derived categories we introduce a notion of derived azumaya algebras over ring and schemes generalizing the notion of azumaya algebras of grothendieck le groupe de brauer i algebres d azumaya et interpretations diverses dix exposes sur la cohomologie des schemas pp 46 66 north holland amsterdam 1968 we prove that any such algebra b on a scheme x provides a class b in h 1 et x mathbb z times h 2 et x mathbb g m we prove that for x a quasi compact and quasi separated scheme defines a bijective correspondence and in particular that any class in h 2 et x mathbb g m torsion or not can be represented by a derived azumaya algebra on x our result is a consequence of a more general theorem about the existence of compact generators in twisted derived categories with coefficients in any local system of reasonable dg categories generalizing the well known existence of compact generators in derived categories of quasi coherent sheaves of bondal and van den bergh mosc math j 3 1 1 36 2003 a huge part of this paper concerns the treatment of twisted derived categories as well as the proof that the existence of compact generator locally for the fppf topology implies the existence of a global compact generator we present explicit examples of derived azumaya algebras that are not represented by classical azumaya algebras as well as applications of our main result to the localization for twisted algebraic k theory and to the stability of saturated dg categories by direct push forwards along smooth and proper maps

cyclic homology cdh cohomology and negative k theory we prove a blow up formula for cyclic homology which we use to show that infinitesimal k theory satisfies cdh descent combining that result with some computations of the cdh cohomology of the sheaf of regular functions we verify a conjecture of weibel predicting the vanishing of algebraic k theory of a scheme in degrees less than minus the dimension of the scheme for schemes essentially of finite type over a field of characteristic zero

a bayesian view of doubly robust causal inference in causal inference the effect of confounding may be controlled using regression adjustment in an outcome model propensity score adjustment inverse probability of treatment weighting or a combination of these approaches based on modelling the treatment assignment mechanism along with their doubly robust extensions have been difficult to motivate using formal likelihood based or bayesian arguments as the treatment assignment model plays no part in inferences concerning the expected outcomes on the other hand forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness in this paper we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood based arguments as an alternative to bayesian propensity score analysis we propose a bayesian posterior predictive method for constructing doubly robust estimation procedures by incorporating the inverse treatment assignment probabilities as importance sampling weights in monte carlo integration

the derived category of an exact category there is some confusion in the literature regarding the derived category of an exact category 8 thomason gives a satisfactory treatment of the bounded derived category in ct 1 11 6 see also appendix a the result is that provided all weakly split epimorphisms in 8 are admissible the bounded derived category may be defined as usual although thomason does not say it the categories d 6 d d may also be defined in the same way the definition of the unbounded derived category is more difficult and is very poorly treated in the literature for instance in bbd this derived category is only defined provided every morphism in 6 admits a kernel see bbd 1 1 41 this is very unsatisfactory since very few exact categories satisfy the condition in this article we will show that d b may be defined whenever 6 is saturated karoubian in thomason s terminology an exact category is saturated if every idempotent splits i e 6 contains all direct summands of its objects for the purpose of comparing with thomason s result the bounded derived category is defined for more 8 s all that is required to define db is that whenever an idempotent e a a factors as a f ba a with fog lb then e is split thomason calls such idempotents weakly split and we will honor his notation we will show here that these constructions are in some sense best possible remark 1 8 for d 6 remarks 1 9 and 1 10 for d d d b db 6 there are two reasons why i wrote this note one is to correct the misconceptions in the literature but more importantly the proof of the key result lemma 1 2 depends on an important characterization of tpaisse subcategories due to rickard and this article is intended to highlight rickard s criterion a full triangulated subcategory y of a triangulated

the homotopy fixed point theorem and the quillen lichtenbaum conjecture in hermitian k theory abstract we settle two conjectures for computing higher grothendieck witt groups also known as hermitian k groups of noetherian schemes x under some mild conditions it is shown that the comparison map from the hermitian k theory of x to the homotopy fixed points of k theory under the natural z 2 action is a 2 adic equivalence we also prove that the mod 2 comparison map between the hermitian k theory of x and its etale version is an isomorphism on homotopy groups in the same range as for the quillen lichtenbaum conjecture in k theory applications compute higher grothendieck witt groups of complex algebraic varieties and rings of 2 integers in number fields and hence values of dedekind zeta functions

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

systems of diagram categories and k theory ii the additivity theorem for derivateurs associated to complicial biwaldhausen categories is proved also to any exact category in the sense of quillen a k theory space is associated this k theory is shown to satisfy the additivity approximation and resolution theorems

the brauer group of an affine rational surface with a non rational singularity abstract the object of study is the family of normal affine algebraic surfaces defined by equations of the form z n y a 1 x y a n x x 1 each surface x in this family is rational and contains a non rational singularity using an explicit resolution of the singularity many computations involving weil divisors and azumaya algebras on x are completely carried out the picard group and brauer group are shown to depend in subtle ways on the values a 1 a n for an odd prime n and for a general choice of x the picard group and the brauer group are computed

negative k theory of derived categories we define negative k groups for exact categories and for derived categories in the framework of frobenius pairs generalizing definitions of bass karoubi carter pedersen weibel and thomason we prove localization and vanishing theorems for these groups devissage for noetherian abelian categories additivity and resolution hold we show that the first negative k group of an abelian category vanishes and that in general negative k groups of a noetherian abelian category vanish our methods yield an explicit non connective delooping of the k theory of exact categories and chain complexes generalizing constructions of wagoner and pedersen weibel extending a theorem of auslander and sherman we discuss the k theory homotopy fiber of e e and its implications for negative k groups in the appendix we replace waldhausen s cylinder functor by a slightly weaker form of non functorial factorization which is still sufficient to prove his approximation and fibration theorems

murthy s conjecture on 0 cycles we show that the levine weibel chow group of 0 cycles mathrm ch d a of a reduced affine algebra a of dimension d ge 2 over an algebraically closed field is torsion free among several applications it implies an affirmative solution to an old conjecture of murthy in classical k theory

the mayer vietoris principle for grothendieck witt groups of schemes we prove localization and zariski mayer vietoris for higher gro thendieck witt groups alias hermitian k groups of schemes admitting an ample family of line bundles no assumption on the characteristic is needed and our schemes can be singular along the way we prove additivity fibration and approximation theorems for the hermitian k theory of exact categories with weak equivalences and duality

totally acyclic complexes over noetherian schemes abstract we define a notion of total acyclicity for complexes of flat quasi coherent sheaves on a semi separated noetherian scheme and study these complexes using the pure derived category of flat quasi coherent sheaves we prove that a scheme is gorenstein if and only if every acyclic complex of flat quasi coherent sheaves is totally acyclic our formalism also removes the need for a dualising complex in several known results for rings including jorgensen s proof of the existence of gorenstein projective precovers

rigidity and exotic models for v1 local g equivariant stable homotopy we prove that the v 1 local g equivariant stable homotopy category for g a finite group has a unique g equivariant model at p 2 this means that at the prime 2 the homotopy theory of g spectra up to fixed point equivalences on k theory is uniquely determined by its triangulated homotopy category and basic mackey structure the result combines the rigidity result for k local spectra of the second author with the equivariant rigidity result for g spectra of the first author further when the prime p is at least 5 and does not divide the order of g we provide an algebraic exotic model as well as a g equivariant exotic model for the v 1 local g equivariant stable homotopy category showing that for primes p ge 5 equivariant rigidity fails in general

on bayesian estimation of marginal structural models summary the purpose of inverse probability of treatment ipt weighting in estimation of marginal treatment effects is to construct a pseudo population without imbalances in measured covariates thus removing the effects of confounding and informative censoring when performing inference in this article we formalize the notion of such a pseudo population as a data generating mechanism with particular characteristics and show that this leads to a natural bayesian interpretation of ipt weighted estimation using this interpretation we are able to propose the first fully bayesian procedure for estimating parameters of marginal structural models using an ipt weighting our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in bayesian inference of marginal treatment effects the proposed approach is compared to existing methods in simulated data and applied to an analysis of the canadian co infection cohort

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

colocalizations of noncommutative spectra and bootstrap categories we construct a compactly generated and closed symmetric monoidal stable category nsp and show that hnsp op contains the suspension stable homotopy category of separable c algebras hoc constructed by cuntz meyer rosenberg as a fully faithful triangulated subcategory then we construct two colocalizations of nsp namely nsp k 1 and nsp z 1 both of which are shown to be compactly generated and closed symmetric monoidal we prove that kasparov kk category of separable c algebras sits inside the homotopy category of kk nsp k 1 op as a fully faithful triangulated subcategory hence kk should be viewed as the stable categorical incarnation of kasparov kk category for arbitrary pointed noncommutative spaces including nonseparable c algebras as an application we find that the bootstrap category in hnsp k 1 admits a completely algebraic description we also construct a k theoretic bootstrap category in hkk that extends the construction of the uct class by rosenberg schochet motivated by the algebraization problem we finally analyze a couple of equivalence relations on separable c algebras that are introduced via the bootstrap categories in various colocalizations of nsp

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

on integrality of p adic iterated integrals abstract the purpose of this paper is to prove integrality for certain p adic iterated coleman integrals as underlying geometry we will take the complement of a divisor d x with good reduction where x is the projective line or an elliptic curve over the witt vectors of a perfect characteristic p field as a corollary we prove a lower bound for the valuations of p adic multiple zeta values

algebraic k theory and abstract homotopy theory abstract we decompose the k theory space of a waldhausen category in terms of its dwyer kan simplicial localization this leads to a criterion for functors to induce equivalences of k theory spectra that generalizes and explains many of the criteria appearing in the literature we show that under mild hypotheses a weakly exact functor that induces an equivalence of homotopy categories induces an equivalence of k theory spectra

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

pic is a contracted functor we show that there is a natural decomposition pic a t t 1 cong pic a oplus npic a oplus npic a oplus h 1 a for any commutative ringa where pic a is the picard group of invertiblea modules andh1 a is the etale cohomology grouph1 spec a a similar decomposition of pic x t t 1 holds for any schemex this makes pic a contracted functor in the sense of bass h1 a is always a torsionfree group and is zero ifa is normal for pseudo geometric rings h1 a is an effectively computable finitely generated free abelian group we also show thath1 a t t 1 h1 a i e nh1 lh1 0 this yields the formula for group rings pic a t 1 t 1 1 t m t m 1 cong pic a oplus coprod limits i 1 m h 1 a oplus coprod limits k 1 m coprod limits i 1 2 k left k m right n k pic a

toric varieties monoid schemes and cdh descent we give conditions for the mayer vietoris property to hold for the algebraic k theory of blow up squares of toric varieties and schemes using the theory of monoid schemes these conditions are used to relate algebraic k theory to topological cyclic homology in characteristic p to achieve our goals we develop many notions for monoid schemes based on classical algebraic geometry such as separated and proper maps and resolution of singularities

voice activity detection method and apparatus using the same free field to eardrum transfer functions fetf s are developed by comparing auditory data for points in three dimensional space for a model ear and auditory data collected for the same listening location with a microphone each fetf is represented as a weighted sum of frequency dependent functions obtained from an expansion of the measured fetf s covariance matrix spatial transformation characteristic functions stcf s are applied to transform the weighted frequency dependent factors to functions of spatial variables for azimuth and elevation a generalized spline model is fit to each stcf to filter out noise and permit interpolation of the stcf between measured points sound is reproduced for a selected direction by synthesizing the weighted frequency dependent factors with the smoothed and interpolated stcf s

homological mirror symmetry for punctured spheres we prove that the wrapped fukaya category of a punctured sphere s with an arbitrary number of points removed is equivalent to the triangulated category of singularities of a mirror landau ginzburg model proving one side of the homological mirror symmetry conjecture in this case by investigating fractional gradings on these categories we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the landau ginzburg model

topological equivalences for differential graded algebras we investigate the relationship between differential graded algebras dgas and topological ring spectra every dga c gives rise to an eilenberg mac lane ring spectrum denoted hc if hc and hd are weakly equivalent then we say c and d are topologically equivalent quasi isomorphic dgas are topologically equivalent but we produce explicit counterexamples of the converse we also develop an associated notion of topological morita equivalence using a homotopical version of tilting

bass nk groups and cdh fibrant hochschild homology the k theory of a polynomial ring r t contains the k theory of r as a summand for r commutative and containing q we describe k r t k r in terms of hochschild homology and the cohomology of kahler differentials for the cdh topology we use this to address bass question whether kn r kn r t implies kn r kn r t1 t 2 the answer to this question is affirmative when r is essentially of finite type over the complex numbers but negative in general

a two step bayesian approach for propensity score analysis simulations and case study a two step bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous bayesian propensity score approaches the corresponding variance estimators are also provided the two step bayesian propensity score is provided for three methods of implementation propensity score stratification weighting and optimal full matching three simulation studies and one case study are presented to elaborate the proposed two step bayesian propensity score approach results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist based treatment effect a slight advantage is shown for the bayesian approach in small samples results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results however greater precision around the correct treatment effect parameter yields quite good results with slight improvement seen with greater precision in the propensity score equation a comparison of coverage rates for the conventional frequentist approach and proposed bayesian approach is also provided the case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non informative

k theoretic obstructions to bounded t structures schlichting conjectured that the negative k groups of small abelian categories vanish and proved this for noetherian abelian categories and for all abelian categories in degree 1 the main results of this paper are that mathrm k 1 e vanishes when e is a small stable infty category with a bounded t structure and that mathrm k n e vanishes for all n geqslant 1 when additionally the heart of e is noetherian it follows that barwick s theorem of the heart holds for nonconnective k theory spectra when the heart is noetherian we give several applications to non existence results for bounded t structures and stability conditions to possible k theoretic obstructions to the existence of the motivic t structure and to vanishing results for the negative k groups of a large class of dg algebras and ring spectra

algebraic k theory and descent for blow ups we prove that algebraic k theory satisfies pro descent for abstract blow up squares of noetherian schemes as an application we derive weibel s conjecture on the vanishing of negative k groups

recollements and stratifying ideals abstract surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories these stratifying recollements are derived from recollements of module categories can every recollement be put in this form up to equivalence a negative answer will be given after providing a characterisation of recollements equivalent to stratifying ones moreover criteria for a ring epimorphism to be stratifying will be presented as well as constructions of such epimorphisms

small sample adjustments for wald type tests using sandwich estimators the sandwich estimator of variance may be used to create robust wald type tests from estimating equations that are sums of k independent or approximately independent terms for example for repeated measures data on k individuals each term relates to a different individual these tests applied to a parameter may have greater than nominal size if k is small or more generally if the parameter to be tested is essentially estimated from a small number of terms in the estimating equation we offer some practical modifications to these robust wald type tests which asymptotically approach the usual robust wald type tests we show that one of these modifications provides exact coverage for a simple case and examine by simulation the modifications applied to the generalized estimating equations of liang and zeger 1986 conditional logistic regression and the cox proportional hazard model

method and apparatus for identifying speech in telephone signals method and apparatus for identifying telephone signals which are produced by a human voice the method includes determining a measure of the energy of predetermined frequency bins of the frequency spectrum of the signal for a frame comprised of a predetermined number of consecutive samples of the signal if the signal is an analog signal averaging the measure of the energy of the predetermined frequency bins over a predetermined number of frames to provide a frame group average energy measure determining the sum of the absolute value of the difference between the frame group average energy measure for all pairs of frame groups which are consecutive in time and comparing the sum with a predetermined amount to identify the signal as having been produced by a human voice if the sum exceeds the predetermined amount

k theory and the bridge from motives to noncommutative motives abstract in this work we present a new approach to the theory of noncommutative motives and use it to explain the different flavors of algebraic k theory of schemes and dg categories the work is divided into three main parts in the first part we use the techniques of higher algebra developed in 63 to provide a universal characterization for the symmetric monoidal 1 category underlying the motivic stable a 1 homotopy theory of morel voevodsky 107 67 more precisely given a symmetric monoidal model category v together with an object x v we characterize the underlying symmetric monoidal 1 category of the symmetric monoidal model category sp v x introduced by hovey in 43 by means of a universal property amongst symmetric monoidal 1 categories this characterization trivializes the problem of finding motivic monoidal realizations in the second part we introduce a new approach to the theory of noncommutative motives by constructing a stable motivic homotopy theory for the noncommutative spaces of kontsevich 56 55 54 the key ingredient is a notion of nisnevich topology in the noncommutative setting compatible with the classical notion this compatibility together with the universal property proved in the first part ensures the existence of a canonical monoidal map from the stable motivic theory of morel voevodsky towards these new noncommutative motives that allow us to compare the two theories in the last part of this paper we explain how this bridge can be used to explain the various flavors of algebraic k theory of dg categories more precisely we prove that the non connective k theory of dg categories introduced by schlichting 82 is the non commutative nisnevich sheafification of connective algebraic k theory then we prove that its further non commutative a 1 localization is a tensor unit in our noncommutative motives as a corollary we obtain a precise proof for an original conjecture of kontsevich claiming that k theory gives the correct mapping spaces in noncommutative motives our major application is the discovery of a canonical factorization of our motivic bridge through the 1 category of modules over the commutative algebra object representing homotopy invariant algebraic k theory of schemes the results in 77 imply that this bridge is fully faithful over a field k with resolutions of singularities so that at the motivic level no information below k theory is lost by passing to the noncommutative world

k theory and derived equivalences we show that if two rings have equivalent derived categories then they have the same algebraic k theory similar results are given for g theory and for a large class of abelian categories

k regularity cdh fibrant hochschild homology and a conjecture of vorst it is a well known fact that algebraic if theory is homotopy invariant as a functor on regular schemes if x is a regular scheme then the natural map kn x kn x x 1 is an isomorphism for all n ez this is false in general for nonregular schemes and rings to express this failure bass introduced the terminology that for any contravari ant functor v defined on schemes a scheme x is called v regular if the pullback maps v x v x x ar are isomorphisms for all r 0 if x spec i we also say that r is p regular thus regular schemes are ifn regular for every n in contrast it was observed as long ago as in 2 that a nonreduced affine scheme can never be k regular in particular if a is an artinian ring that is a o dimensional noetherian ring then a is regular that is reduced if and only if a is ifi regular in 17 vorst conjectured that for an affine scheme x of finite type over a field f and of dimension d regularity and k i regularity are equivalent vorst proved this conjecture for d 1 by proving that regularity implies normality in this paper we prove vorst s conjecture in all dimensions provided the char acteristic of the ground field f is zero in fact we prove a stronger statement we say that x is regular in codimension n in x note that for all n z if a ring r is ifn regular then it is kn i regular this is proved in 17 for n 1 and in 6 4 4 for n kh x where k x is the algebraic if theory spectrum of x and kh x is the homotopy if theory of x defined in 19 we write fk r for fk spec r theorem 0 1 let r be a commutative ring which is essentially of finite type over a field f of characteristic 0 then the following hold a if tk r is n connected then r is regular in codimension khi x is an isomorphism for i n and a surjection for i n 1 so that fk x

the relative singularity category of a non commutative resolution of singularities abstract in this article we study a triangulated category associated with a non commutative resolution of singularities in particular we give a complete description of this category in the case of a curve with nodal singularities classifying its indecomposable objects and computing its auslander reiten quiver and k group

voice activity detector for half duplex audio communication system a method 501 502 of detecting voice in an audio signal comprises the steps of determining an average peak value 703 ap representing an envelope of the audio signal determining a running instance of audio signal standard deviation 702 which corresponds to one of a number of overlapping time intervals and updating a power density function pdf by adding instances of noise to the pdf if the average peak of the audio signal exceeds the current level of the audio signal by a certain amount and if the current standard deviation value falls below a threshold for a predetermined time interval a noise floor nf is located based on the mean value of the pdf 501 and if the audio signal sustains a power level exceeding the noise floor voice activity is determined to be present in the audio signal 502 the pdf is updated by a low confidence factor 1206 if all of the standard deviation values calculated during a certain period of time are below the threshold value and by a high confidence factor 1204 if all standard deviation values within a certain longer period of time period are below the threshold value