the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

bi relative algebraic k theory and topological cyclic homology it is well known that algebraic k theory preserves products of rings however in general algebraic k theory does not preserve fiber products of rings and one defines bi relative algebraic k theory so as to measure the deviation it was proved recently by cortinas 6 that rationally bi relative algebraic k theory and bi relative negative cyclic homology agree in this paper we show that with finite coefficients bi relative algebraic k theory and bi relative topological cyclic homology agree as an application we show that for a possibly singular curve over a perfect field k of positive characteristic p the cyclotomic trace map induces an isomorphism of the p adic algebraic k groups and the p adic topological cyclic homology groups in non negative degrees as a further application we show that the difference between the p adic k groups of the integral group ring of a finite group and the p adic k groups of a maximal z order in the rational group algebra can be expressed entirely in terms of topological cyclic homology let f be a functor that to a unital associative ring a associates a symmetric spectrum f a if i a is a two sided ideal the relative term f a i is defined to be the homotopy fiber of the map f a f a i induced from the canonical projection if further f a b is a ring homomorphism such that f i f i is an isomorphism onto a two sided ideal of b there is an induced map f a i f b f i and the bi relative term f a b i is defined to be the homotopy fiber of this map then there is a distinguished triangle in the stable homotopy category

fractional evolution dirac like equations some properties and a discrete von neumann type analysis a system of fractional evolution equations results from employing the tool of the fractional calculus and following the method used by dirac to obtain his well known equation from klein gordon s one it represents a possible interpolation between dirac and diffusion and wave equations in one space dimension in this paper some analytical properties typical of the general solution of this system of equations are obtained and necessary stability bounds for a numerical scheme approximating such equations are found through the classical discrete von neumann type analysis the non local property of the time fractional differential operator leads to discretizations in terms of series here the analytical methods usually employed in the study of the stability of discrete schemes when dealing with integer order differential equations have been adapted to the complexity of the real order case

normalized random measures driven by increasing additive processes this paper introduces and studies a new class of nonparametric prior distributions random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes in particular we present results for the distribution of means under both prior and posterior conditions and via the use of strategic latent variables undertake a full bayesian analysis our class of priors includes the well known and widely used mixture of a dirichlet process

comparing k theories for complex varieties the semi topological k theory of a complex variety was defined in a recent paper by the authors with the expectation that it would prove to be a theory lying part way between the algebraic k theory of the variety and the topological k theory of the associated analytic space and thus would share properties with each of these other theories in this paper we realize these expectations by proving among other results that 1 the algebraic k theory with finite coefficients and the semi topological k theory with finite coefficients coincide on all projective complex varieties 2 semi topological k theory and topological k theory agree on certain types of generalized flag varieties and 3 assuming a result asserted by cohen and lima filho the semi topological k theory of any smooth projective variety becomes isomorphic to the topological k theory of the underlying analytic space once the bott element is inverted to illustrate the utility of our results we observe that a new proof of the quillen lichtenbaum conjecture for smooth complete curves is obtained as a corollary

do we need hundreds of classifiers to solve real world classification problems we evaluate 179 classifiers arising from 17 families discriminant analysis bayesian neural networks support vector machines decision trees rule based classifiers boosting bagging stacking random forests and other ensembles generalized linear models nearest neighbors partial least squares and principal component regression logistic and multinomial regression multiple adaptive regression splines and other methods implemented in weka r with and without the caret package c and matlab including all the relevant classifiers available today we use 121 data sets which represent the whole uci data base excluding the large scale problems and other own real problems in order to achieve significant conclusions about the classifier behavior not dependent on the data set collection the classifiers most likely to be the bests are the random forest rf versions the best of which implemented in r and accessed via caret achieves 94 1 of the maximum accuracy overcoming 90 in the 84 3 of the data sets however the difference is not statistically significant with the second best the svm with gaussian kernel implemented in c using libsvm which achieves 92 3 of the maximum accuracy a few models are clearly better than the remaining ones random forest svm with gaussian and polynomial kernels extreme learning machine with gaussian kernel c5 0 and avnnet a committee of multi layer perceptrons implemented in r with the caret package the random forest is clearly the best family of classifiers 3 out of 5 bests classifiers are rf followed by svm 4 classifiers in the top 10 neural networks and boosting ensembles 5 and 3 members in the top 20 respectively

the obstruction to excision in k theory and in cyclic homology let f a b be a ring homomorphism of not necessarily unital rings and i triangleleft a an ideal which is mapped by f isomorphically to an ideal of b the obstruction to excision in k theory is the failure of the map between relative k groups k a i k b f i to be an isomorphism it is measured by the birelative groups k a b i similarly the groups hn a b i measure the obstruction to excision in negative cyclic homology we show that the rational jones goodwillie chern character induces an isomorphism ch k a b i otimes mathbb q overset sim to hn a otimes mathbb q b otimes mathbb q i otimes mathbb q

algebraic k theory of stable c algebras abstract let a be a unital c algebra and let l denote the calkin algebra the bounded operators on a separable hilbert space modulo the compact operators k we prove the following conjecture of m karoubi the algebraic and topological k theory groups of the tensor product c algebra a l are equal the algebra a l may be regarded as a suspension of the more elementary c algebra a k thus karoubi s conjecture asserts roughly speaking that the algebraic and topological k theories of stable c algebras agree

central stability for the homology of congruence subgroups and the second homology of torelli groups abstract we prove a representation stability result for the second homology groups of torelli subgroups of mapping class groups and automorphism groups of free groups this strengthens the results of boldsen hauge dollerup and day putman we also prove a new representation stability result for the homology of certain congruence subgroups partially improving upon the work of putman sam these results follow from a general theorem on syzygies of certain modules with finite polynomial degree

techniques computations and conjectures for semi topological k theory we establish the existence of an atiyah hirzebruch like spectral sequence relating the morphic cohomology groups of a smooth quasi projective complex variety to its semi topological k groups this spectral sequence is compatible with and indeed is built from the motivic spectral sequence that relates the motivic cohomology and algebraic k theory of varieties and it is also compatible with the classical atiyah hirzebruch spectral sequence in algebraic topology in the second part of this paper we use this spectral sequence in conjunction with another computational tool that we introduce namely a variation on the integral weight filtration of the borel moore singular homology of complex varieties introduced by h gillet and c soule to compute the semi topological k theory of a large class of varieties in particular we prove that for curves surfaces toric varieties projective rational three folds and related varieties the semi topological k groups and topological k groups are isomorphic in all degrees permitted by cohomological considerations we also formulate integral conjectures relating semi topological k theory to topological k theory analogous to more familiar conjectures namely the quillen lichtenbaum and beilinson lichtenbaum conjectures concerning mod n algebraic k theory and motivic cohomology in particular we prove a local vanishing result for morphic cohomology which enables us to formulate precisely a conjectural identification of morphic cohomology by a suslin our computations verify that these conjectures hold for the list of varieties above

a fractional dirac equation and its solution this paper presents a fractional dirac equation and its solution the fractional dirac equation may be obtained using a fractional variational principle and a fractional klein gordon equation both methods are considered here we extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of caputo derivatives by applying the variational principle to a fractional action s we obtain the fractional euler lagrange equations of motion we present a lagrangian and a hamiltonian for the fractional dirac equation of order we also use a fractional klein gordon equation to obtain the fractional dirac equation which is the same as that obtained using the fractional variational principle eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard dirac equation we also provide expressions for the path integral quantization for the fractional dirac field which in the limit 1 approaches to the path integral for the regular dirac field it is hoped that the fractional dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics

updating schemes correlation structure blocking and parameterization for the gibbs sampler in this paper many convergence issues concerning the implementation of the gibbs sampler are investigated exact computable rates of convergence for gaussian target distributions are obtained different random and non random updating strategies and blocking combinations are compared using the rates the effect of dimensionality and correlation structure on the convergence rates are studied some examples are considered to demonstrate the results for a gaussian image analysis problem several updating strategies are described and compared for problems in bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice

valid post selection inference it is common practice in statistical data analysis to perform data driven variable selection and derive statistical inference from the resulting model such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori we propose to produce valid post selection inference by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals simultaneity is required for all linear functions that arise as coefficient estimates in all submodels by purchasing simultaneity insurance for all possible submodels the resulting post selection inference is rendered universally valid under all possible model selection procedures this inference is therefore generally conservative for particular selection procedures but it is always less conservative than full scheffe protection importantly it does not depend on the truth of the selected submodel and hence it produces valid inference even in wrong models we describe the structure of the simultaneous inference problem and give some asymptotic results

algebraic geometry of topological spaces i we use techniques from both real and complex algebraic geometry to study k theoretic and related invariants of the algebra c x of continuous complex valued functions on a compact hausdorff topological space x for example we prove a parameterized version of a theorem by joseph gubeladze we show that if m is a countable abelian cancellative torsion free semi normal monoid and x is contractible then every finitely generated projective module over c x m is free the particular case m mathbb n 0 n gives a parameterized version of the celebrated theorem proved independently by daniel quillen and andrei suslin that finitely generated projective modules over a polynomial ring over a field are free the conjecture of jonathan rosenberg which predicts the homotopy invariance of the negative algebraic k theory of c x follows from the particular case m mathbb z n we also give algebraic conditions for a functor from commutative algebras to abelian groups to be homotopy invariant on c algebras and for a homology theory of commutative algebras to vanish on c algebras these criteria have numerous applications for example the vanishing criterion applied to nil k theory implies that commutative c algebras are k regular as another application we show that the familiar formulas of hochschild kostant rosenberg and loday quillen for the algebraic hochschild and cyclic homology of the coordinate ring of a smooth algebraic variety remain valid for the algebraic hochschild and cyclic homology of c x applications to the conjectures of be linson soule and farrell jones are also given

an interpolation between the wave and diffusion equations through the fractional evolution equations dirac like through fractional calculus and following the method used by dirac to obtain his well known equation from the klein gordon equation we analyze a possible interpolation between the dirac and the diffusion equations in one space dimension we study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the d alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations dirac like such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator for this system of fractional evolution equations we also find an associated conserved quantity analogous to the hamiltonian for the classical dirac case

bayesian regression trees for high dimensional prediction and variable selection abstractdecision tree ensembles are an extremely popular tool for obtaining high quality predictions in nonparametric regression problems unmodified however many commonly used decision tree ensemble methods do not adapt to sparsity in the regime in which the number of predictors is larger than the number of observations a recent stream of research concerns the construction of decision tree ensembles that are motivated by a generative probabilistic model the most influential method being the bayesian additive regression trees bart framework in this article we take a bayesian point of view on this problem and show how to construct priors on decision tree ensembles that are capable of adapting to sparsity in the predictors by placing a sparsity inducing dirichlet hyperprior on the splitting proportions of the regression tree prior we characterize the asymptotic distribution of the number of predictors included in the model and show how this prior can be easily incorporated into existing markov chai

asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory in regular statistical models the leave one out cross validation is asymptotically equivalent to the akaike information criterion however since many learning machines are singular statistical models the asymptotic behavior of the cross validation remains unknown in previous studies we established the singular learning theory and proposed a widely applicable information criterion the expectation value of which is asymptotically equal to the average bayes generalization loss in the present paper we theoretically compare the bayes cross validation loss and the widely applicable information criterion and prove two theorems first the bayes cross validation loss is asymptotically equivalent to the widely applicable information criterion as a random variable therefore model selection and hyperparameter optimization using these two values are asymptotically equivalent second the sum of the bayes generalization error and the bayes cross validation error is asymptotically equal to 2 n where is the real log canonical threshold and n is the number of training samples therefore the relation between the cross validation error and the generalization error is determined by the algebraic geometrical structure of a learning machine we also clarify that the deviance information criteria are different from the bayes cross validation and the widely applicable information criterion

bayesian inference for logistic models using polya gamma latent variables we propose a new data augmentation strategy for fully bayesian inference in models with binomial likelihoods the approach appeals to a new class of polya gamma distributions which are constructed in detail a variety of examples are presented to show the versatility of the method including logistic regression negative binomial regression nonlinear mixed effect models and spatial models for count data in each case our data augmentation strategy leads to simple effective methods for posterior inference that 1 circumvent the need for analytic approximations numerical integration or metropolis hastings and 2 outperform other known data augmentation strategies both in ease of use and in computational efficiency all methods including an efficient sampler for the polya gamma distribution are implemented in the r package bayeslogit supplementary materials for this article are available online

bayesian regression tree ensembles that adapt to smoothness and sparsity ensembles of decision trees are a useful tool for obtaining flexible estimates of regression functions examples of these methods include gradient boosted decision trees random forests and bayesian classification and regression trees two potential shortcomings of tree ensembles are their lack of smoothness and their vulnerability to the curse of dimensionality we show that these issues can be overcome by instead considering sparsity inducing soft decision trees in which the decisions are treated as probabilistic we implement this in the context of the bayesian additive regression trees framework and illustrate its promising performance through testing on benchmark data sets we provide strong theoretical support for our methodology by showing that the posterior distribution concentrates at the minimax rate up to a logarithmic factor for sparse functions and functions with additive structures in the high dimensional regime where the dimensionality of the covariate space is allowed to grow nearly exponentially in the sample size our method also adapts to the unknown smoothness and sparsity levels and can be implemented by making minimal modifications to existing bayesian additive regression tree algorithms

the nilpotence conjecture in k theory of toric varieties it is shown that all nontrivial elements in higher k groups of toric varieties are annihilated by iterations of the natural frobenius type endomorphisms this is a higher analog of the triviality of vector bundles on affine toric varieties

fractionally coupled solutions of the diffusion equation we analyze a family of solutions of the diffusion equation which also satisfy an additional fractional equation in 1 1 and 3 1 dimensions the solutions may be interpreted either as coupled solutions of the diffusion equation or as a diffusion process with internal degrees of freedom

excision in algebraic k theory introduction 1 excision and the homology of affine groups 2 volodin s spaces 3 excision for rings with the triple factorization property 4 lie analogue of volodin s construction 5 the homology of nilpotent groups and nilpotent lie algebras 6 a proof of the main theorems 7 the tensor product of h unital algebras 8 the matrix ring of a small category 9 the acyclicity of triangular complexes 10 a proof of karoubi s conjecture

vanishing theorems for real algebraic cycles we establish the analogue of the friedlander mazur conjecture for teh s reduced lawson homology groups of real varieties which says that the reduced lawson homology of a real quasi projective variety x vanishes in homological degrees larger than the dimension of x in all weights as an application we obtain a vanishing of homotopy groups of the mod 2 topological groups of averaged cycles and a characterization in a range of indices of dos santos real lawson homology as the homotopy groups of the topological group of averaged cycles we also establish an equivariant poincare duality between equivariant friedlander walker real morphic cohomology and dos santos real lawson homology we use this together with an equivariant extension of the mod 2 beilinson lichtenbaum conjecture to compute some real lawson homology groups in terms of bredon cohomology

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

pro unitality and pro excision in algebraic k theory and cyclic homology the purpose of this paper is to study pro excision in algebraic k theory and cyclic homology after suslin wodzicki cuntz quillen cortinas and geisser hesselholt as well as continuity properties of andre quillen and hochschild homology a key tool is first to establish the equivalence of various pro tor vanishing conditions which appear in the literature this allows us to prove that all ideals of commutative noetherian rings are pro unital in a suitable sense we show moreover that such pro unital ideals satisfy pro excision in derived hochschild and cyclic homology it follows hence and from the suslin wodzicki criterion that ideals of commutative noetherian rings satisfy pro excision in derived hochschild and cyclic homology and in algebraic k theory in addition our techniques yield a strong form of the pro hochschild kostant rosenberg theorem an extension to general base rings of the cuntz quillen excision theorem in periodic cyclic homology a generalisation of the f igin tsygan theorem a short proof of pro excision in topological hochschild and cyclic homology and new artin rees and continuity statements in andre quillen and hochschild homology msc 19d55 primary 16e40 13d03 secondary

a widely applicable bayesian information criterion a statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one to one and if its fisher information matrix is always positive definite if otherwise it is called singular in regular statistical models the bayes free energy which is defined by the minus logarithm of bayes marginal likelihood can be asymptotically approximated by the schwarz bayes information criterion bic whereas in singular models such approximation does not hold recently it was proved that the bayes free energy of a singular model is asymptotically given by a generalized formula using a birational invariant the real log canonical threshold rlct instead of half the number of parameters in bic theoretical values of rlcts in several statistical models are now being discovered based on algebraic geometrical methodology however it has been difficult to estimate the bayes free energy using only training samples because an rlct depends on an unknown true distribution in the present paper we define a widely applicable bayesian information criterion wbic by the average log likelihood function over the posterior distribution with the inverse temperature 1 log n where n is the number of training samples we mathematically prove that wbic has the same asymptotic expansion as the bayes free energy even if a statistical model is singular for or unrealizable by a statistical model since wbic can be numerically calculated without any information about a true distribution it is a generalized version of bic onto singular statistical models

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

bayesian cart model search abstract in this article we put forward a bayesian approach for finding classification and regression tree cart models the two basic components of this approach consist of prior specification and stochastic search the basic idea is to have the prior induce a posterior distribution that will guide the stochastic search toward more promising cart models as the search proceeds such models can then be selected with a variety of criteria such as posterior probability marginal likelihood residual sum of squares or misclassification rates examples are used to illustrate the potential superiority of this approach over alternative methods

a bayesian cart algorithm a stochastic search form of classification and regression tree cart analysis breiman et al 1984 is proposed motivated by a bayesian model an approximation to a probability distribution over the space of possible trees is explored using reversible jump markov chain monte carlo methods green 1995

log linear bayesian additive regression trees for multinomial logistic and count regression models we introduce bayesian additive regression trees bart for log linear models including multinomial logistic regression and count regression with zero inflation and overdispersion bart has been app

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

the steinberg group of a monoid ring nilpotence and algorithms for a regular ring r and an affine monoid m the homotheties of m act nilpotently on the milnor unstable groups of r m this strengthens the k2 part of the main result of j gubeladze the nilpotence conjecture in k theory of toric varieties invent math 160 2005 173 216 in two ways the coefficient field of characteristic 0 is extended to any regular ring and the stable k2 group is substituted by the unstable ones the proof is based on a polyhedral combinatorial technique computations in steinberg groups and a substantially corrected version of an old result on elementary matrices by mushkudiani z mushkudiani k2 groups of monoid algebras over regular rings proc a razmadze math inst 113 1995 120 137 a similar stronger nilpotence result for k1 and algorithmic consequences for factorization of high frobenius powers of invertible matrices are also derived

greedy function approximation a gradient boosting machine function estimation approximation is viewed from the perspective of numerical optimization in function space rather than parameter space a connection is made between stagewise additive expansions and steepest descent minimization a general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion specific algorithms are presented for least squares least absolute deviation and huber m loss functions for regression and multiclass logistic likelihood for classification special enhancements are derived for the particular case where the individual additive components are regression trees and tools for interpreting such treeboost models are presented gradient boosting of regression trees produces competitive highly robust interpretable procedures for both regression and classification especially appropriate for mining less than clean data connections between this approach and the boosting methods of freund and shapire and friedman hastie and tibshirani are discussed

excision in algebraic k theory and karoubi s conjecture abstract we prove that the property of excision in algebraic k theory is for a q algebra a equivalent to the h unitality of the latter our excision theorem in particular implies karoubi s conjecture on the equality of algebraic and topological k theory groups of stable c algebras it also allows us to identify the algebraic k theory of the symbol map in the theory of pseudodifferential operators

sur la simplicite essentielle du groupe des inversibles et du groupe unitaire dans une c algebre simple let a be a simple approximately finite dimensional c algebra with unit let gl1 a be the group of invertible elements and let u1 a be that of unitaries in a in a previous work the abelianized groups gl1 a dgl1 a and u1 a du1 a have been described with grothendieck s group k0 a viewed as a dimension group for a here it is shown that the groups dgl1 a and du1 a are simple up to their centres the case of a stable c algebra and that of a c algebra with unit which is simple infinite are also studied in the last two cases moreover it is shown that there exists a natural homomorphism from milnor s group k2mil a onto k0 a

infinitesimal cohomology and the chern character to negative cyclic homology there is a chern character from k theory to negative cyclic homology we show that it preserves the decomposition coming from adams operations at least in characteristic zero

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

rational isomorphisms between k theories and cohomology theories the well known isomorphism relating the rational algebraic k theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map the segre map of infinite loop spaces moreover the associated chern character map on rational homotopy groups is shown to be a ring isomorphism a technique is introduced that establishes a useful general criterion for a natural transformation of functors on quasi projective complex varieties to induce a homotopy equivalence of semi topological singular complexes since semi topological k theory and morphic cohomology can be formulated as the semi topological singular complexes associated to algebraic k theory and motivic cohomology this criterion provides a rational isomorphism between the semi topological k theory groups and the morphic cohomology groups of a smooth complex variety consequences include a riemann roch theorem for the chern character on semi topological k theory and an interpretation of the topological filtration on singular cohomology groups in k theoretic terms

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

on the solution of fractional evolution equations this paper is devoted to the solution of the bi fractional differential equation for real 0 0 and 0 with the initial conditions here cd tu t x is the partial derivative coinciding with the caputo fractional derivative for 0 0 the laplace and fourier transforms are applied to solve the above problem in closed form the fundamental solution of these problems is established and its moments are calculated the special case 1 2 and 1 is presented and its application is given to obtain the dirac type decomposition for the ordinary diffusion equation

bayesian generalized additive models for location scale and shape for zero inflated and overdispersed count data frequent problems in applied research preventing the application of the classical poisson log linear model for analyzing count data include overdispersion an excess of zeros compared to the poisson distribution correlated responses as well as complex predictor structures comprising nonlinear effects of continuous covariates interactions or spatial effects we propose a general class of bayesian generalized additive models for zero inflated and overdispersed count data within the framework of generalized additive models for location scale and shape where semiparametric predictors can be specified for several parameters of a count data distribution as standard options for applied work we consider the zero inflated poisson the negative binomial and the zero inflated negative binomial distribution the additive predictor specifications rely on basis function approximations for the different types of effects in combination with gaussian smoothness priors we develop bayesian inference based on markov c

comparison between algebraic and topological k theory of locally convex algebras abstract this paper is concerned with the algebraic k theory of locally convex c algebras stabilized by operator ideals and its comparison with topological k theory we show that if l is locally convex and j a frechet operator ideal then all the different variants of topological k theory agree on the completed projective tensor product l j and that the obstruction for the comparison map k l j k top l j to be an isomorphism is absolute algebraic cyclic homology we prove the existence of an exact sequence theorem 6 2 1 we show that cyclic homology vanishes in the case when j is the ideal of compact operators and l is a frechet algebra whose topology is generated by a countable family of sub multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family theorem 8 3 3 this proves the generalized version of karoubi s conjecture due to mariusz wodzicki and announced in his paper m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 we also consider stabilization with respect to a wider class of operator ideals called sub harmonic every frechet ideal is sub harmonic but not conversely for example the schatten ideal l p is sub harmonic for all p 0 but is frechet only if p 1 we prove a variant of the exact sequence above which essentially says that if a is a c algebra and j is sub harmonic then the obstruction for the periodicity of k a c j is again cyclic homology theorem 7 1 1 this generalizes to all algebras a result of wodzicki for h unital algebras announced in m wodzicki algebraic k theory and functional analysis in first european congress of mathematics vol ii paris 1992 in progr math vol 120 birkhauser basel 1994 pp 485 496 the main technical tools we use are the diffeotopy invariance theorem of cuntz and the second author which we generalize in theorem 6 1 6 and the excision theorem for infinitesimal k theory due to the first author

generalized abel jacobi map on lawson homology we construct an abel jacobi type map on the homologically trivial part of lawson homology groups it generalizes the abel jacobi map constructed by griffiths by using a result of h clemens we answer affirmatively the question whether there exists a smooth projective complex variety with infinitely generated lawson homology groups l ph 2p k x bbb q when k0 as a corollary we find for any nonnegative integer j a smooth complex projective variety x carrying infinitely generated semi topological k groups k sst j x bbb q